THE PURCHASING POWER OF MONEY
 
 THE MACMILLAN COMPANY 
 
 NEW YORK • BOSTON • CHICAGO 
 SAN FRANCISCO 
 
 MACMILLAN & CO., Limited 
 
 LONDON • BOMBAY • CALCUTTA 
 MELBOURNE 
 
 THE MACMILLAN CO. OF CANADA, LTD. 
 
 TORONTO
 
 THE PURCHASING POWER 
 OF MONEY 
 
 ITS DETERMINATION 
 
 AND RELATION TO CREDIT 
 
 INTEREST AND CRISES 
 
 BY 
 mVING FISHER 
 
 morassoR of political economt in tale UNIVKBSITT 
 
 ASSISTED BY 
 
 HARRY G. BROWN 
 
 nrSTKUCTOB IN POLITICAL ECONOMY IN TALB UNIVERSITT 
 
 HEW AMU JIFVI3II' EOiTION 
 
 466 66 
 
 Nein gork 
 THE MACMILLAN COMPANY 
 
 1920 
 
 AU rights reserved
 
 CiOPTSraHT, Iffll, 
 By the MACMILLAN COMPAlTr. 
 
 Set up and electrotyped. Published March, igit. 
 
 Nodvaoli 9rni« 
 
 J. S. Gashing Co. — Berwick dc Smith 0*. 
 
 Norwood, Mass., U.S.A.
 
 2-2-3 
 
 ^S5p 
 
 
 dc-p ■ > 
 
 Co 
 
 THE MEMORY OF 
 
 SIMON NEWCOMB 
 
 6BEAT SCIENTIST, INSPIRING FRIEND, 
 
 PIONEER IN THE STUDY 
 
 OF 
 
 ** SOCIETARY circulation"
 
 PREFACE TO THE FIRST EDITION 
 
 The purpose of this book is to set forth the principles 
 determining the purchasing power of money and to 
 apply those principles to the study of historical changes 
 in that purchasing power, including in particular the 
 recent change in " the cost of living," which has aroused 
 world-wide discussion. 
 
 If the principles here advocated are correct, the pur- 
 chasing power of money — or its reciprocal, the level of 
 prices — depends exclusively on five definite factors : 
 (1) the volume of money in circulation ; (2) its velocity 
 of circulation ; (3) the volume of bank deposits subject 
 to check ; (4) its velocity ; and (5) the volume of trade. 
 Each of these five magnitudes is extremely definite, and 
 their relation to the purchasing power of money is defi- 
 nitely expressed by an "equation of exchange." In my 
 opinion, the branch of economics which treats of these 
 five regulators of purchasing power ought to be recog- 
 nized and ultimately will be recognized as an exact 
 science, capable of precise formulation, demonstration, 
 I and statistical verification. 
 
 The main contentions of this book are at bottom simply 
 a restatement and amplification of the old "quantity 
 theory " of money. With certain corrections in the usual 
 statements of that theory, it may still be called funda- 
 mentally sound. What has long been needed is a candid 
 reexamination and revision of that venerable theory rather 
 than its repudiation. 
 
 Yet in the voluminous literature on money, there seems 
 to be very little that approaches accurate formulation and
 
 VIU PREFACE TO THE FIRST EDITION 
 
 rigorous demonstration, — whether theoretical or statis- 
 tical. 
 
 In making this attempt at reconstruction, I have the 
 satisfaction of finding myself for once a conservative 
 rather than a radical in economic theory. It has seemed 
 to me a scandal that academic economists have, through 
 outside clamor, been led into disagreements over the 
 fundamental propositions concerning money. This is due 
 to the confusion in which the subject has been thrown 
 by reason of the political controversies with which it has 
 become entangled. 
 
 As some one has said, it would seem that even the 
 theorems of Euclid would be challenged and doubted 
 if they should be appealed to by one political party as 
 against another. At any rate, since the "quantity 
 theory " has become the subject of political dispute, it 
 has lost prestige and has even come to be regarded by 
 many as an exploded fallacy. The attempts by pro- 
 moters of unsound money to make an improper use of the 
 quantity theory — as in the first Bryan campaign — led 
 many sound money men to the utter repudiation of the 
 quantity theory. The consequence has been that, espe- 
 cially in America, the quantity theory needs to be rein- 
 ' troduced into general knowledge. 
 
 Besides aiming to set forth the principles affecting the 
 purchasing power of money, this book aims to illustrate 
 and verify those principles by historical facts and statis- 
 tics. In particular, the recent rise in prices is examined 
 in detail and traced to its several causes. 
 
 The study of the principles and facts concerning the 
 purchasing power of money is of far more than academic 
 interest. Such questions affect the welfare of every in- 
 habitant of the civilized world. At each turn of the tide 
 of prices, millions of persons are benefited and other 
 millions are injured.
 
 PREFACE TO THE FIRST EDITION IX 
 
 For a hundred years the world has been suffering from 
 periodic changes in the level of prices, producing alter- 
 nate crises and depressions of trade. Only by knowledge, 
 both of the principles and of the facts involved, can such 
 fluctuations in future be prevented or mitigated, and only 
 by such knowledge can the losses which they entail be 
 avoided or reduced. It is not too much to say that the 
 evils of a variable monetary standard are among the most 
 serious economic evils with which civilization has to deal ; 
 and the practical problem of finding a solution of the dif- 
 ficulty is of international extent and importance. I have 
 proposed, very tentatively, a remedy for the evils of mon- 
 etary instability. But the time is not yet ripe for the 
 acceptance of any working plan. What is at present most 
 needed is a clear and general public understanding of 
 principles and facts. 
 
 Toward such an end this book aims to contribute : — 
 
 1. A reconstruction of the quantity theory. 
 
 2. A discussion of the best form of index number. 
 
 3. Some mechanical methods of representing visually 
 the determination of the level of prices. 
 
 4. A practical method of estimating the velocity of 
 circulation of money. 
 
 5. The ascertainment statistically of the bank deposits 
 in the United States which are subject to check, as distinct 
 from " individual deposits," as usually published. 
 
 6. An improved statistical evaluation of the volume 
 of trade, as well as of the remaining elements in the 
 equation of exchange. 
 
 7. A thorough statistical verification of the (recon- 
 structed) quantity theory of money. 
 
 As it is quite impossible to do justice to some of these 
 subjects without the use of mathematics, these have been 
 freely introduced, but have been relegated, so far as
 
 X PREFACE TO THE FIRST EDITION 
 
 possible, to Appendices. This plan, which is in accord- 
 ance with that previously adopted in The Nature of Cap- 
 ital and Income and The Rate of Interest, leaves the text 
 almost wholly nonmathematical. 
 
 Most of the statistical results review and confirm the 
 conclusions of Professor Kemmerer in his valuable Money 
 and Credit Instruments in their Relation to General Prices, 
 which appeared while the present book was in course 
 of construction. I am greatly indebted to Professor 
 Kemmerer for reading the entire manuscript and for 
 much valuable criticism throughout. 
 
 My thanks are due to Professor F. Y. Edgeworth of 
 All Souls' College, Oxford, and to Professor A. W. Flux 
 of Manchester for kindly looking through the manuscript 
 of the Appendix on index numbers and for suggestions 
 and criticisms. 
 
 To Dr. A. Piatt Andrew, now Assistant Secretary of 
 the Treasury, my thanks are due for his kindness, as 
 Special Assistant to the National Monetary Commission, 
 in putting the resources of that Commission at my dis- 
 posal, and in working out, from the records of the office 
 of the Comptroller of the Currency, the volume of deposits 
 subject to check at various dates in the past. For cooper- 
 ation in carrying out these same calculations, I am like- 
 wise indebted to Mr. Lawrence O. Murray, Comptroller 
 of the Currency. These valuable figures are the first of 
 their kind. 
 
 To Mr. Gilpin of the New York Clearing House, my 
 thanks are due for his kindness in furnishing various 
 figures asked for and cited specifically in the text. 
 
 To Mr. Richard M. Hurd, President of the Lawyers 
 Mortgage Co., I am indebted for reading parts of the 
 manuscript and for valuable criticism. 
 
 To Mr. John O. Perrin, President of the American 
 National Bank of Indianapolis, I am i^idebted for statistics
 
 PREFACE TO THE FIRST EDITION XI 
 
 of the "activity" of bank accounts in liis bank, and for 
 similar figures I am indebted to the officers of the National 
 New Haven Bank and the City Bank of New Haven. 
 
 My thanks are due to the Economic Journal for permis- 
 sion to use unaltered some parts of my article on "The 
 Mechanics of Bimetallism," which first appeared in that 
 journal in 1894. 
 
 My thanks are due to the Journal of the Royal Statistical 
 Society for similar permission with reference to my article 
 on "A Practical Method for estimating the Velocity of 
 Circulation of Money," which appeared in December, 
 1909. 
 
 A number of my students have rendered valuable 
 service in gathering and coordinating statistics. I would 
 especially mention Mr. Seimin Inaoka, Mr. Morgan Porter, 
 Mr. N. S. Fineberg, Mr. W. E. Lagerquist, now in- 
 structor at Cornell Universit}'-, Messrs. G. S. and L. A. 
 Dole, Dr. John Bauer, now assistant professor at Cornell 
 University, Dr. John Kerr Towles, now instructor at the 
 University of Illinois, Dr. A. S. Field, now instructor at 
 Dartmouth College, Mr. A. G. Boesel, Mr. W. F. Hicker- 
 nell, Mr. Yasuyiro Hayakawa, Mr. Chester A. Phillips, 
 and Mr. R. N. Griswold. Mr. Griswold performed the 
 lengthy calculations involved in ascertaining an index 
 of the volume of trade. 
 
 There are two persons to whom I am more indebted 
 than to any others. These are my brother, Mr. Her- 
 bert W. Fisher, and my colleague. Dr. Harry G. Brown. 
 
 To my brother my thanks are due for a most searching 
 criticism of the whole book from the standpoint of peda- 
 gogical exposition, and to Mr. Brown for general criticism 
 and suggestions as well as for detailed work throughout. 
 In recognition of Mr. Brown's assistance, I have placed 
 
 his name on the title-page. 
 
 IRVING FISHER. 
 Yale University, February, 1911.
 
 PREFACE TO THE SECOND EDITION 
 
 The second edition is a reprint of the first with the fol- 
 lowing changes : — 
 
 1. Correction of occasional misprints. 
 
 2. Addition of data for 1910, 1911, and 1912, in the 
 tables on pages 301, 317, and the diagram between pages 
 306 and 307. 
 
 3. A change in Figure 1 (page 13) to make it conform 
 to the facts for 1912. 
 
 4. Changes in the table on page 147 with accompany- 
 ing text to make the data correspond to the facts for 1912. 
 
 5. The insertion of an addendum on pages 492-493, 
 giving the revised figures for deposits subject to check as 
 calculated by Professor Wesley Clair Mitchell. 
 
 6. An appendix to the second edition (page 494 ff.) on 
 "standardizing the dollar." 
 
 For corrections of misprints and various helpful criti- 
 cisms of the first edition I am under great obligations to a 
 number of friends and correspondents and particularly to 
 Major W. E. McKechnie, of the Indian Medical Service, 
 Etawah, United Provinces, India ; Professor Warren M. 
 Persons, Colorado College, Colorado Springs, Colo. ; Mr. 
 J. M. Keynes, Editor, Economic Journal, Kings College, 
 Cambridge ; Carl Snyder, author, New York City ; James 
 Bonar, Deputy Master of the Royal Mint, Ottawa, Canada ; 
 Professor Allyn A. Young, Washington University, St. 
 Louis, Mo.; Professor Stephen Bauer, Director, Interna- 
 tional Office of Labor Legislation, Basle, Switzerland ; 
 Professor Wesley Clair Mitchell, New York City ; Pro- 
 fessor O. M. W. Sprague, Harvard University.
 
 PREFACE TO THE SECOND EDITION XUl 
 
 I have endeavored to avoid disturbing the plates of the 
 first edition more than was absolutely necessary. Other- 
 wise I should have been glad to incorporate some changes 
 to make use of some valuable but general criticisms. In 
 particular I should have liked to modify somewhat the 
 statement of the theory of crises in Chapter IV and in 
 Chapter XI to make use of the helpful criticism of Miss 
 Minnie Throop England, of the University of Nebraska, 
 in The Quarterly Journal of Economics^ November, 1912 ; 
 also to meet a criticism of Mr. Keynes' to the effect 
 that, while my book shows that the changes in the quantity 
 of money do affect the price level, it does not show how 
 they do so. To those who feel the need of a more defi- 
 nite picture of how the price level is affected by a change 
 in the quantity of money I refer the reader to my Ele- 
 mentary Principles of Economics^ pages 242-247, and to 
 other writers on this subject, particularly Cairns. 
 
 IRVING FISHER.
 
 SUGGESTIONS TO READERS 
 
 1. The general reader will be chiefly interested in 
 Chapters I-VIII. 
 
 2. The cursory reader will find the gist of the book in 
 Chapter II. 
 
 3. Objectors to the quantity theory will find their theo- 
 retical and statistical objections discussed in Chapters 
 VIII and XII respectively. 
 
 4. Studeyits of financial history should read Chapter XII. 
 
 5. Currency reformers should read Chapter XIII. 
 
 6. The appendices are addressed mainly (though not 
 exclusively) to mathematical economists^ for whom the chief 
 interest will probably lie with the Appendix to Chapter 
 X, on Index Numbers, (which should be read as a whole,) 
 and § 6 of the Appendix to Chapter XII, on the Method 
 of Determining Velocity of Circulation. 
 
 7. The remainder of the Appendix to Chapter XII is 
 supplied chiefly in order that statistical critics may be en- 
 abled to verify the processes described in the text. 
 
 8. Chapter X and its Appendix are of chief interest to 
 students of index numbers^ a subject as fascinating to some 
 as it is dr}'- to others. 
 
 9. The analytical table of contents, the index, and the 
 running page headings have been constructed with espe- 
 cial reference to the varying needs of different classes of 
 readers. 
 
 The book is, however, designed to constitute a complete 
 whole, and it is hoped that as many as possible of those 
 who approach it from special viewpoints may, in the end, 
 read it aU.
 
 SUMMARY OF CONTENTS 
 
 OHAPTBB PAGB 
 
 I. Primary Definitions 1 » 
 
 II. Purchasing Power of Monet as belated to the "Equa- 
 tion OF Exchange " 8 ^ 
 
 in. Influence of Deposit Currenct on the Equation and 
 
 therefore on Purchasing Power 33 ~. 
 
 IV. Disturbance of Equation and of Purchasing Power 
 
 DURING Transition Periods 55 -«. 
 
 v. Indirect Influences on Purchasing Power . . .74" 
 
 VI. Indirect Influences (Continued) 90 
 
 Vn. Influence of Monetary Systems on Purchasing Power 112 
 VIII. Influence of Quantity of Money and Other Factors 
 
 ON Purchasing Power and on Each Other . . 149 
 IX. The Dispersion of Prices makes necessary an Index 
 
 OF Purchasing Power 184 
 
 X. The Best Index Numbers of Purchasing Power . . 198 
 
 XL Statistical Verification. General Historical Review 234 - 
 
 Xll. Statistical Verification. Recent Years . , . 276 '' 
 
 Xlll. The Problem of making Purchasing Power more Stable 319 y 
 
 Appendix to Chapter II 349 
 
 Appendix to Chapter III . . ...... 367 
 
 Appendix to Chapter V ........ 370 
 
 Appendix to Chapter VI. .••••.. 372 
 
 Appendix to Chapter VII .••.•.«. 376 
 
 Appendix to Chapter VIII . ..•••.. 379 
 
 Appendix to Chapter X .••••••. 885 
 
 Appendix to Chapter XII ..••■••. 430 
 
 XV
 
 ANALYTICAL TABLE OF CONTENTS 
 
 CHAPTER I 
 
 FrIMART DEFmiTIOMS 
 
 PAOK 
 
 § 1. Wealth and exchange • . 1 
 
 § 2. Exchangeable goods 4 
 
 § 3. Circulation of money against goods 6 
 
 CHAPTER II 
 
 Pdrchasing Power of Monet as related to thb Equation 
 OF Exchange 
 
 § 1. The various circulating media .... 
 
 § 2. The equation of exchange arithmetically expressed 
 
 § 3. The equation of exchange mechanically expressed 
 
 § 4. The equation of exchange algebraically expressed 
 
 § 5. Couclusiou and illustrations .... 
 
 8 
 
 14 
 21 
 
 24 
 28 
 
 CHAPTER m 
 Influence of Deposit Currency on the Equation 
 
 AND therefore ON PURCHASING POWEB 
 
 § 1. The mystery of circulating credit 33 
 
 § 2. The basis of circulating credit 40 
 
 §3. Banking limitations . . . . . . . , .42 
 
 § 4, The revised equation of exchange . . . ... 47 
 
 § 5. Deposit currency normally proportioned to money ... 49 
 
 § 6. Summary 63 
 
 CHAPTER IV 
 
 Disturbance of Equation and of Purchasing Power during 
 Transition Periods 
 
 § 1. Tardiness of interest adjustment to price movements . . 55 
 
 § 2. How a rise of prices generates a further rise . . . . 58 
 
 § 3. Extent of disturbances in equation . . .... 61 
 
 § 4. How a rise of prices culminates in a crisis .... 64
 
 XVIU ANALYTICAL TABLE OP CONTENTS 
 
 PAOB 
 
 § 5. Completion of the credit cycle 67 
 
 § 6. Summary 72 
 
 CHAPTER V 
 
 Indirect Influences on Purchasing Power 
 
 § 1. Influence of conditions of production and consumption on 
 
 trade and therefore on prices . . ... 74 
 
 § 2. Influence of conditions connecting producers and consumers 
 
 on trade and therefore on prices 77 
 
 § 3. Influence of individual habits on velocities of circulation and 
 
 therefore on prices 79 
 
 § 4. Influence of systems of payment on velocities of circulation 
 
 and therefore on prices . . . .... 83 
 
 § 5. Influence of general causes on velocities of circulation and 
 
 therefore on prices ........ 87 
 
 § 6. Influences on the volume of deposits subject to check and 
 
 therefore on prices 88 
 
 CHAPTER VI 
 Indirect Influences (Continued) 
 
 § 1. Influence of foreign trade on the quantity of money and there- 
 fore on prices 90 
 
 § 2. Influence of melting and minting on the quantity of money 
 
 and therefore on prices 96 
 
 § 3. Influence of the production and consumption of money metals 
 
 on the quantity of money and therefore on prices . . 99 
 
 § 4. Mechanical illustration of these influences .... 104 
 
 CHAPTER Vn 
 Influence of Monetary Systems on Purchasing Powbb 
 
 § 1. Gresham's Law 112 
 
 § 2. Cases when bimetallism fails immediately .... 116 
 § 3. Cases when bimetallism fails after production overtakes con- 
 sumption 121 
 
 § 4. The limping standard ; the gold-exchange standard . . 127 
 
 § 5. Bimetallism in France 132
 
 ANALYTICAL TABLE OF CONTENTS XIX 
 
 PAGE 
 
 § 6. Lessons of French experiment 135 
 
 § 7. The limping standard in India 138 
 
 § 8. The limping standard in the United States .... 140 
 
 § 9. General description of system in the United States . . . 143 
 
 CHAPTER VIII 
 
 IwPLtTENCE OF Quantity of Money and Other Factors on 
 Purchasing Power and on Each Other 
 
 § 1. The equation of exchange implies no causal sequence . . 149 
 § 2, Effects of a change in money (M). Quantity theory in causal 
 
 sense 151 
 
 § 3. Quantity theory not strictly true during transition periods . 159 
 
 § 4. Effects of a change in deposits (M') relatively to money (M) 162 
 
 § 5. Effects of changes in velocities of circulation ( V and F') . 164 
 
 § 6. Effects of changes in volume of trade (the §'s) . . . 165 
 
 § 7. Can the price level be regarded as cause as well as effect ? . 169 
 § 8. Distinction between causation of individual prices and the 
 
 price level 174 
 
 § 9. Summary 181 
 
 CHAPTEE IX 
 
 The Dispersion of Prices makes necessary an Index OP 
 Purchasing Power 
 
 § 1. Some prices cannot respond readily to price movements . . 184 
 
 § 2. Consequently other prices must over-respond .... 190 
 § 3. Transformation of the right side of the equation of exchange 
 
 iTom'EpQ to PT 194 
 
 § 4. Summary 196 
 
 CHAPTER X 
 
 The Best Index Numbers op Purchasino Power 
 
 § 1. Forms of index numbers 198 
 
 § 2. Various purposes of index numbers 204 
 
 § 3. An index number as a standard of deferred payments . . 208 
 
 § 4. Deferred payments based on total exchanges .... 217 
 
 § 5. Practical restrictions 225 
 
 § 6. Summary 231
 
 XX 
 
 ANALYTICAL TABLE OF CONTENTS 
 
 CHAPTER XI 
 Statistical Verification. General Histobicai. Review 
 
 §1- 
 §2. 
 §3. 
 §4. 
 §5. 
 §6. 
 §7. 
 §8. 
 §9. 
 §10. 
 
 §11. 
 § 12. 
 § 13. 
 § 14. 
 §15. 
 §16. 
 §17. 
 §18. 
 
 §1- 
 §2. 
 §3. 
 
 §4. 
 
 §5. 
 
 §6. 
 
 §7. 
 
 §8. 
 
 §9. 
 §10, 
 §11. 
 
 The last thousand years . 
 The last four centuries 
 The nineteenth century . 
 Its five price movements . 
 Retrospect . . . , 
 
 Outlook 
 
 Paper money . . . . 
 Paper money in France . 
 Paper money in England'. 
 Paper money in Austria . 
 Early American paper money . 
 The " greenbacks " . 
 Confidence in the greenback . 
 Confederate paper money 
 Deposit currency and crises 
 Particular crises 
 Velocity of deposits and crises 
 Summary 
 
 CHAPTER Xn 
 Statistical Verification. Recent Yeaes 
 
 Professor Kemmerer's statistics, 1879-1908 
 
 New estimates for M and M', 1890-1909 
 
 New estimates for M'V and T"', 1896-1909 
 
 New estimates for 3IV and T^ 1896-1909 
 
 Estimates for T and P, 1896-1909 , 
 
 P directly and indirectly calculated 
 
 Correcting discrepancies .... 
 
 The final results ..... 
 
 The comparative importance of price-raising causes 
 
 Influence of antecedent causes such as tariffs, etc. 
 
 Results and by-products of Chapter XII . 
 
 PAQX 
 
 234 
 
 237 
 
 238 
 240 
 246 
 248 
 250 
 252 
 253 
 255 
 256 
 258 
 261 
 263 
 265 
 267 
 270 
 274 
 
 276 
 280 
 282 
 285 
 290 
 292 
 298 
 304 
 307 
 311 
 315 
 
 CHAPTER XIII 
 The Problem of making Purchasing Power more Stable 
 
 § 1. The problem of monetary reform 319 
 
 § 2. Bimetallism as a solution 323 
 
 § 3. Other proposed solutions 328 
 
 § 4. The tabular standard 332 
 
 § 5. The writer's proposal ........ 337 
 
 § 6. Summary and conclusion 348
 
 APPENDICES 
 
 Appendix to Chapter II 
 
 FAec 
 § 1 (to Ch. II, § 3). The concept of an average .... 349 
 § 2 (to Ch. 11, § 6). The concept of velocity of circulation . . 362 
 § 3 (to Ch. II, § 6). "Arrays" ofp's, Q's, a,ndpQ's . . .355 
 § 4 (to Ch. II, § 5). " Arrays " of e's, m's, and F's . . .358 
 § 5 (to Ch. II, § 5). The coin-transfer concept of velocity and the 
 
 concept of time of turnovei 362 
 
 § 6 (to Ch. II, § 6). Algebraic demonstration of equation of ex- 
 change 364 
 
 § 7 (to Ch. II, § 6). P must be a specific form of average in order 
 
 to vary directly as M and V and inversely as the §'s, . . 364 
 
 Appendix to Chapter III 
 
 § 1 (to Ch. in, § 2). " Arrays " of A;'s and r's . . . .367 
 § 2 (to Ch. in, § 4). Algebraic demonstration of equation of ex- 
 change including deposit currency 368 
 
 Appendix to Chapter V 
 § 1 (to Ch. V, § 5). Effect of time credit on equation of exchange 370 
 
 Appendix to Chapter VI 
 
 § 1 (to Ch. VI, § 1) . Modification of equation of exchange required 
 
 by international trade 372 
 
 Appendix to Chapter Vn 
 
 § 1 (to Ch. VII, § 2) . Money substitutes unlike other substitutes . 376 
 § 2 (to Ch. VII, § 2). Limits for ratios within which bimetallism 
 
 is possible 378 
 
 Appendix to Chapter VHI 
 
 § 1 (to Ch. VIII, § 6). Statistics of turnover at Yale University . 379 
 § 2 (to Ch. VIII, § 8). Four types of commodities contrasted . 382 
 
 xxi
 
 XXll APPENDICES 
 
 Appendix to Chapter X 
 
 § 1. Each form of index number for prices implies a correlative 
 
 index number for quantities 385 
 
 § 2. Index numbers for prices occur in arithmetical pairs as also 
 do index numbers for quantities .... 
 
 § 3. General meanings of p's and §'s 
 
 § 4. Review of 44 formulae, heading table columns 
 
 § 5. Review of 8 tests, heading table rows 
 
 § 6. The interior of the table ; column 11 in particular 
 
 § 7. The 44 formulae compared .... 
 
 § 8. Reasons for preferring the median practically 
 
 § 9. Summary 
 
 390 
 392 
 393 
 400 
 408 
 418 
 425 
 428 
 
 Appendix to Chapter XII 
 
 § 1 (to Ch. Xn, § 1). Professor Kemmerer's calculations . . 430 
 § 2 (to Ch. XII, § 2) . Method of calculating M . . . .432 
 § 3 (to Ch. XII, § 2). Method of calculating J/' . . . .434 
 § 4 (to Ch. XII, § 3). Method of calculating M'V for 1896 and 
 
 1909 441 
 
 § 5 (to Ch. XII, § 3). Method of calculating MV for 1897-1908 446 
 § 6 (to Ch. XII, § 4). General practical formula for calculating V 448 
 § 7 (to Ch. XII, § 4). Application of formula to calculations of 
 
 F for 1896 and 1909 460 
 
 § 8 (to Ch. XII, § 4). Interpolating Values of Ffor 1897-1908 . 477 
 § 9 (to Ch. XII, § 5). Method of calculating T . . . .478 
 § 10 (to Ch. xn, § 5). Method of calculating P . . . .486 
 § 11 (to Ch. XII, § 7). Mutual adjustments of calculated values 
 
 oi M, M, V, W, P, T 488 
 
 § 12 (to Ch. XII, § 8). Credit and cash transactions. Comparison 
 
 with Kinley's estimates 491 
 
 § 13 (to whole Ch.). Addendum to second edition . . . 492 
 Appendix on " Standardizing the Dollar." 494
 
 ADDENDUM 
 
 (In this revised edition figures for 1910-1912 are given on pages 304, 317. 
 See also page 492.) 
 
 Data have just become available by which to bring down 
 through 1910 the statistics of Chapter XII. The results 
 are as follows : 
 
 Magnitudes in the Equation of Exchange for 1910* 
 
 
 
 M 
 
 M' 
 
 V 
 
 V 
 
 P 
 
 T 
 
 MV+M'V 
 
 PT 
 
 As first calculated 
 
 1.64 
 
 7.24 
 
 21 
 
 52.8 
 
 103.7 
 
 397 
 
 416 
 
 412 
 
 As finally adjusted 
 
 1.64 
 
 7.23 
 
 21 
 
 52.7 
 
 104.0 
 
 399 
 
 415 
 
 415 
 
 
 The table shows that the figures, as first calculated, 
 conform admirably to the equation of exchange. The 
 adjustment needed, to produce perfect conformity, in only 
 one case reaches the half of one per cent ! 
 
 From the adjusted figures we may calculate the per- 
 centages of cash and check transactions (^MV-i- MV ■\- M' V 
 and M'V -i-MV^M'V'~). These are 8% and 92%, 
 which may be added to the table on page 317. The 
 ratio of deposits to money (^M'/M^ is 4.4, which shows 
 
 * The above figures may be inserted by the reader in the tables on 
 pages 280, 281, 284, 285, 290, 292, 293, 304. The methods of deriving 
 the figures are in general the same as those explained in the Appendix to 
 Chapter XII. The antecedent figures on which the above table depends 
 may be inserted by the reader as foUovys : 
 
 M. On page 432 add (to the bottom of columns 1-8 incl. ) in the table 
 the following : 1910, 3.42, 3.42, .32, 1.41, 3.3%, 1.46, 1.G4. 
 
 M'. It is not necessary to complete the table on page 435, as the 
 Comptroller's Report for 1910 (p. 64) gives for the first time deposits 
 subject to check (7.82 billions). To this 7.82, however, three corrections 
 are needed : (1) subtract .29 for " savings accounts " improperly included 
 (estimated for me by the Comptroller's Office at half of the figure in note 
 a, lower table, p. 64, Comptr. Rpt.) ; (2) subtract .54 as "exchanges 
 for clearing house" (= f times those for national banks) ; (3) add .25 
 
 xxiii
 
 XXIV ADDENDUM 
 
 a great increase over 1909. The disproportionate growth 
 of deposits relatively to money and the excessive velocity 
 of circulation (52.7) of deposits, substantially equal to the 
 unprecedented figure for 1909, are disquieting symptoms 
 and serve only to confirm the forebodings in the text. 
 
 For aid in working out the figures in this addendum I 
 am indebted to three of my students, Mr. H. A. W. 
 Duckert, Mr. J. M. Shortliffe, and Mr. M. G. Hastings. 
 
 as the Comptroller's Office estimate, for me, of unreported deposits sub- 
 ject to check. By applying these corrections we obtain 7.24. 
 
 V. I have simply taken 21 as a safe approximate estimate on the basis 
 of the previous statistics of V (p. 478) and its assumed relation to V'. 
 
 M' V and V. Add to columns 1-7 of table on page 448 the following : 
 1910, 97.3, 66.4, 429.3, .89 (by extrapolation, an unsafe guide), 382, 52.8. 
 
 P. This is obtained (on the principles of the table on page 487) from 
 the index number 131.6 of wholesale prices for 1910 (kindly supplied in 
 advance of publication by the Bureau of Labor) and the average price 
 96.2 of stocks as given by the Commercial and Financial Chronicle, both 
 being compared with the respective figures for 1909, viz. 126.5 and 97.5. 
 They are combined by " weighting " the wholesale prices 10 and the stock 
 prices 1 and reducing the results so that the average for 1909 shall be 100. 
 
 T. This is obtained : (a) by continuing columns 1-5 of the table on 
 page 479 by inserting : 1910, 160, 113, 162, 154 ; (the extension of column 
 2 for 1910 is made by means of somewhat more complete data than 
 those enumerated on pages 480-482) ; (ft) by combining the result, 154, 
 obtained for column 5 with the figures for railway cars handled. These 
 were 19.8 millions for 1909 and 22.3 for 1910. Column 5 being weighted 
 10 and the car figures 1, we get as indices of trade : for 1909, 1718, and 
 for 1910, 1763, showing an increase of 2.6%, which, applied to the 
 (corrected) estimate of the absolute trade of 1909, viz. 387 billions, gives 
 397 as the absolute trade in 1910. 
 
 (The opportunity is here taken to correct an inadvertence on pp. 480 ff. 
 It should have been there stated that, of the 44 categories mentioned, 
 some are alternative and not independent items, viz. those having the 
 same names and differing only in the number of cities ; also that the dates 
 given do not imply that the items opposite are in all cases used for all 
 the intervening time, but only for such periods as the items were actually 
 available.) 
 
 It is noticeable that the changes in business in 1910 as compared with 
 1909 are somewhat irregular ; the sales of stocks have declined ; exports 
 and imports (both of them) have declined about 10 %.
 
 THE PURCHASING POWER OF MONEY
 
 THE PUECHASING POWER OF MONEY 
 
 CHAPTER II 
 
 PRIMARY DEFINITIONS 
 
 In order to make clear the relation which the topic 
 treated in this book bears to the general subject of 
 economics, some primary definitions are necessary. 
 
 In the first place, economics itself may be defined as 
 the science of wealth, and wealth may be defined as 
 material objects owned by human beings. Of wealth, 
 therefore, there are two essential attributes : material- 
 ity and appropriation. For it is not all material things 
 that are included under wealth, but only such as have 
 been appropriated. Wealth does not include the sun, 
 moon, and other heavenly bodies, nor even all parts 
 of the surface of this planet, but only such parts as 
 have been appropriated to the use of mankind. It 
 is, then, appropriated parts of the earth's surface and 
 the appropriated objects upon it which constitute 
 wealth. 
 
 For convenience, wealth may be classified under 
 three heads : real estate, commodities, and human 
 beings. Real estate includes the surface of the earth 
 and the other wealth attached thereto — improvements 
 such as buildings, fences, drains, railways, street im- 
 
 ' This chapter is mainly a condensation of Chapters I and II of 
 the author's Nature of Capital and Income, New York (Macmillan), 
 1906. 
 
 B 1
 
 2 THE PURCHASING POWER OF MONEY [Chap. I 
 
 provements, and so on. Commodities include all mova- 
 ble wealth (except man himself), whether raw materials 
 or finished products. There is one particular variety 
 of commodity — a certain finished product — ■ which 
 is of especial importance in the subject of which this 
 book treats ; namely, money. Any commodity to be 
 called " money " must be generally acceptable in exchange, 
 and any commodity generally acceptable in exchange 
 should be called money. The best example of a money 
 commodity is found to-day in gold coins. 
 
 Of all wealth, man himself is a species. Like his 
 horses or his cattle, he is himself a material object, and 
 like them, he is owned ; for if slave, he is owned by 
 another, and if free, by himself.^ 
 
 But though human beings may be considered as 
 wealth, human qualities, such as skill, intelligence, and 
 inventiveness, are not wealth. Just as the hardness 
 of steel is not wealth, but merely a quality of one par- 
 ticular kind of wealth, — hard steel, — so the skill of a 
 workman is not wealth, but merely a quality of another 
 particular kind of wealth — skilled workman. Similarly, 
 intelligence is not wealth, but an intelhgent man is 
 wealth. 
 
 Since materiality is one of the two essential attributes 
 of wealth, any article of wealth may be measured in 
 physical units. Land is measured in acres ; coal, in 
 tons ; milk, in quarts ; and wheat, in bushels. There- 
 fore, for estimating the quantities of different articles 
 of wealth, all the various physical units of measurement 
 
 * If we wish to include only slaves as wealth and not free men, 
 we shall have to amend our definition of wealth so as to read : 
 Wealth consists of material objects owned by human beings and 
 external to the owner. For the purpose of this book it makes no 
 practical difference whether this narrower meaning or the broader 
 one be employed.
 
 Sec. 1] PRIMARY DEFINITIONS 3 
 
 may be employed : linear measure, square measure, 
 cubic measure, and measure by weight. 
 
 Whenever any species of wealth is measured in its 
 physical units, a first step is taken toward the measure- 
 ment of that mysterious magnitude called ''value." 
 Sometimes value is looked upon as a psychical and some- 
 times as a physical phenomenon. But, although the 
 determination of value always involves a psychical 
 process — judgment — yet the terms in which the re- 
 sults are expressed and measured are physical. 
 
 It is desirable, for the sake of clearness, to lead up 
 to the concept of value by means of three preliminary 
 concepts ; namely, transfer, exchange, and price. 
 
 A transfer of wealth is a change in its ownership. 
 An exchange consists of two mutual and voluntary 
 transfers, each in consideration of the other. 
 
 When a certain quantity of one kind of wealth is 
 exchanged for a certain quantity of another kind, we 
 may divide one of the two quantities by the other, 
 and obtain the price of the latter. For instance, if 
 two dollars of gold are exchanged for three bushels of 
 wheat, the price of the wheat in gold is two thirds of a 
 dollar per bushel ; and the price of the gold in wheat 
 is one and a half bushels per dollar. It is to be noticed 
 that these are ratios of two physical quantities, the units 
 for measuring which are quite different from each other. 
 One commodity is measured in bushels, or units of 
 volume of wheat, the other in dollars, or units of weight 
 of gold. In general, a price of any species of wealth is 
 merely the ratio of two physical quantities, in whatever 
 way each may originally be measured. 
 
 This brings us, at last, to the concept of value. The 
 value of any item of wealth is its price multiplied by its 
 quantity. Thus, if half a dollar per bushel is the price
 
 4 THE PURCHASING POWER OF MONEY [Chap. 1 
 
 of wheat, the value of a hundred bushels of wheat is 
 fifty dollars. 
 
 §2 
 
 Hitherto we have confined our discussion to some 
 of the consequences of the first prerequisite of wealth — 
 that it must be material. We turn now to the second 
 prerequisite, namely, that it must be owned. To own 
 wealth is simply to have the right to benefit by it 
 that is, the right to enjoy its services or benefits. Thus 
 the owner of a loaf of bread has the right to benefit bj 
 it by eating it, by selling it, or by otherwise disposing 
 of it. The man who owns a house has the right to 
 benefit by enjoying its shelter, by selling it, or by rent- 
 ing it. This right, the right to or in the benefits of 
 wealth — or more briefly, the right to or in the wealth it- 
 self — • is called a " property right " or simply "property." 
 
 If things were always owned in fee simple, i.e. if there 
 were no division of ownership, — no partnership rights, 
 no shares, and no stock companies, — there would be 
 little practical need to distinguish property from wealth ; 
 and as a matter of fact, in the rough popular usage, any 
 article of wealth, and especially real estate, is often 
 inaccurately called a "piece of property." But the 
 ownership of wealth is frequently divided; and this 
 fact necessitates a careful distinction between the thing 
 owned and the rights of the owners. Thus, a railroad 
 is wealth. Its shares and bonded debt are rights to 
 this wealth. Each owner of shares or bonds has the 
 right to a fractional part of the benefits from the railway. 
 The total of these rights comprises the complete owner- 
 ship of, or property in, the railway. 
 
 Like wealth, property rights also may be meas- 
 ured ; but in units of a different character. The units
 
 Sec. 2] PRIMARY DEFINITIONS 5 
 
 of property are not physical, but consist of abstract 
 rights to the benefits of wealth. If a man has twenty- 
 five shares in a certain railway company, the measure- 
 ment of his property is twenty-five units just as truly 
 as though he had twenty-five bushels of wheat. What 
 he has is twenty-five rights of a specific sort. 
 
 There exist various units of property for measuring 
 property, as there are various units of wealth for meas- 
 uring wealth ; and to property may be applied pre- 
 cisely the same concepts of transfer, exchange, price, 
 and value which are applied to wealth. 
 
 Besides the distinction between wealth and property 
 rights, another distinction should here be noted. This is 
 the distinction between property rights and certificates 
 of those rights. The former are the rights to use wealth, 
 the latter are merely the written evidence of those rights. 
 Thus, the right to receive dividends from a railroad 
 is property, but the writjten paper evidencing that 
 right is a stock certificate. TT!&^%jh.t to a railway 
 trip is a property right, the ticket evidencing that 
 right is a certificate of property. The promise of 
 a bank is a property right ; the bank note on 
 which that promise is engraved is a certificate of 
 property. 
 
 Any property right which is generally acceptable in 
 exchange may be called "money." Its printed evi- 
 dence is also called money. Hence there arise three 
 meanings of the term money, viz. its meaning in the 
 sense of wealth ; its meaning in the sense of property ; ^ 
 and its meaning in the sense of written evidence. 
 From the standpoint of economic analysis the prop- 
 erty sense is the most important. 
 
 ^ Cf. Menger, Handworterbuch der Siaatswissenschaften, Jena 
 (Fischer), Vol. IV, 1900, Article, "Geld," pp. 69-71.
 
 6 THE PURCHASING POWER OP MONEY [Chap. I 
 
 What we have been speaking of as property is the right 
 to the services, uses, or benefits of wealth. By benefits 
 of wealth is meant the desirable events which occur by 
 means of wealth. Like wealth and property, benefits 
 also may be measured, but in units of a still different 
 character. Benefits are reckoned either ' ' by time, " — as 
 the services of a gardener or of a dwelling house; or 
 "by the piece," — as the use of a plow or a telephone. 
 And just as the concepts of transfer, exchange, price, 
 and value apply to wealth and property, so do they 
 apply to benefits. 
 
 The uses (benefits) of wealth, with which we have been 
 
 \4ealing, should be distinguished from the utility of 
 
 wealth. The one means desirable events, the other, 
 
 the desirability of those events. The one is usually 
 
 outside of the mind, the other always inside. 
 
 Whenever we speak of rights to benefits, the benefits 
 referred to are future benefits. The owner of a house 
 owns the right to use it from the present instant on- 
 ward. Its past use has perished and is no longer sub- 
 ject to ownership. 
 
 The term "goods" will be used in this book simply as 
 a convenient collective term to include wealth, property, 
 and benefits. The transfer, exchange, price, and value of 
 goods take on innumerable forms. Under price alone, 
 as thus fully applied to goods, fall rent, wages, rates 
 of interest, prices in terms of money, and prices in 
 terms of other goqds. But we shall be chiefly con- 
 cerned in this book with prices of goods in terms of 
 money. 
 
 §3 
 
 Little has yet been said as to the relation of wealth, 
 property and benefits to time. A certain quantity 
 of goods may be either a quantity existing at a partic-
 
 Sec. 3] PRIMARY DEFINITIONS 7 
 
 ular instant of time or a quantity produced, consumed, 
 transported, or exchanged during a period of time. 
 The first quantity is a stock, or fund, of goods ; the 
 second is a flow, or stream, of goods. The amount of 
 wheat in a flour mill on any definite date is a stock of 
 wheat, while the monthly or weekly amounts which 
 come in or go out constitute a flow of wheat. The 
 amount of mined coal existing in the United States at 
 any given moment is a stock of mined coal ; the weekly 
 amount mined is a flow of coal. 
 
 There are many applications of this distinction ; for 
 instance, to capital and income. A stock of goods, 
 whether wealth or property, existing at an instant of 
 time is called capital. A flow of benefits from such 
 capital during a period of time is called " income." In- 
 come, therefore, is one important kind of economic flow. 
 Besides income, economic flows are of three chief classes, 
 representing respectively changes of condition (such 
 as production or consumption), changes of position (such 
 as transportation, exportation, and importation), and 
 changes of ownership, which we have already called 
 " transfers." Trade is a flow of transfers. Whether for- 
 eign or domestic, it is simply the exchange of a stream of 
 transferred rights in goods for an equivalent stream 
 of transferred money or money substitutes. The second 
 of these two streams is called the "circulation" of money. 
 The equation between the two is called the "equation 
 of exchange " ; and it is this equation that constitutes 
 the subject matter of the present book.
 
 CHAPTER II 
 
 PURCHASING POWER OF MONEY AS RELATED TO THE 
 EQUATION OF EXCHANGE 
 
 § 1 
 
 We define money as what is generally acceptable in 
 exchange for goods. ^ The facility with which it may 
 thus be exchanged, or its general acceptability, is its 
 distinguishing characteristic. The general acceptability 
 may be reenforced by law, the money thus becoming 
 what is known as "legal tender"; but such reenforce- 
 ment is not essential. All that is necessary in order that 
 any good may be money is that general acceptability 
 attach to it. On the frontier, without any legal sanc- 
 tion, money is sometimes gold dust or gold nuggets. 
 In the Colony of Virginia it was tobacco. Among the 
 Indians in New England it was wampum. "In German 
 New Guinea the bent tusks of a boar are used as money. 
 In Cahfornia red birds' heads have been used in the 
 same way." ^ Stone money and shell money are so used 
 in Melanesia.^ "In Burmah Chinese gambling counters 
 are used as money. Guttapercha tokens issued by 
 
 1 For discussions on the definition of money, see A. Piatt An- 
 drew, "What ought to be called Money" in Quarterly Journal of 
 Economics, Vol. XIII ; Jevons, Money and the Mechanism of Ex- 
 change, London (Kegan Paul) and New York (Appleton), 1896; 
 Palgrave, Dictionary of Political Economy; Walker, Money, and 
 other treatises and textbooks. 
 
 2 Sumner, Folkways, Boston (Ginn), 1907, p. 147. 
 
 3 Ibid., p. 150. 
 
 8
 
 Sec. 1] THE EQUATION OF EXCHANGE 9 
 
 street car companies in South America are said to be 
 used in the same way." ^ Not many years ago in a 
 town in New York state, similar tokens got into local 
 circulation until their issue was forbidden by the United 
 States government. In Mexico large cacao beans 
 of relatively poor quahty were used as money, and on 
 the west coast of Africa little mats were used.^ The 
 list could be extended indefinitely. But whatever the 
 substance of such a commodity, it is general exchange- 
 ability which makes it money. 
 
 On the other hand, even what is made legal tender 
 may, by general usage, be deprived of its practical char- 
 acter as money. During the Civil War the govern- 
 ment attempted to circulate fifty-dollar notes, bearing 
 interest at 7.3 per cent, so that the interest amounted 
 to the very easily computed amount of a cent a day. 
 The notes, however, failed to circulate. In spite of the 
 attempt to make their exchange easy, people preferred 
 to keep them for the sake of the interest.^ Money 
 never bears interest except in the sense of creating con- 
 venience in the process of exchange. This convenience 
 is the special service of money and offsets the apparent 
 loss of interest involved in keeping it in one's pocket 
 instead of investing. 
 
 There are various degrees of exchangeability which 
 must be transcended before we arrive at real money. 
 Of all kinds of goods, perhaps the least exchangeable 
 is real estate. Only in case some person happens to be 
 found who wants it, can a piece of real estate be traded. 
 A mortgage on real estate is one degree more exchange- 
 able. Yet even a mortgage is less exchangeable than a 
 well-known and safe corporation security ; and a cor- 
 
 1 Sumner, Folkways, p. 148. '^ Ibid. 
 
 ' See Jevons, Money and the Mechanism of Exchange, p. 245.
 
 10 THE PURCHASING POWER OF MONEY [Chap. II 
 
 poration security is less exchangeable than a government 
 bond. In fact persons not infrequently buy govern- 
 ment bonds as merely temporary investments, intending 
 to sell them again as soon as permanent investments 
 yielding better interest are obtainable. One degree 
 more exchangeable than a government bond is a bill 
 of exchange ; one degree more exchangeable than a bill 
 of exchange is a sight draft ; while a check is almost 
 as exchangeable as money itself. Yet no one of these 
 is really money for none of them is ^^ generally accept- 
 able." 
 
 If we confine our attention to present and normal 
 conditions, and to those means of exchange which either 
 are money or most nearly approximate it, we shall 
 find that money itself belongs to a general class of 
 property rights which we may call " currency " or 
 '^ circulating media." Currency includes any type of 
 property right which, whether generally acceptable or 
 not, does actually, for its chief purpose and use, serve 
 as a means of exchange. 
 
 Circulating media are of two chief classes : (1) money ; 
 (2) bank deposits, which will be treated fully in the next 
 chapter. By means of checks, bank deposits serve as 
 a means of payment in exchange for other goods. A 
 check is the "certificate" or evidence of the transfer 
 of bank deposits. It is acceptable to the payee only 
 by his consent. It would not be generally accepted by 
 strangers. Yet by checks, bank deposits even more 
 than money do actually serve as a medium of exchange. 
 Practically speaking, money and bank deposits subject 
 to check are the only circulating media. If post-office 
 orders and telegraphic transfer are to be included, they 
 may be regarded as certificates of transfer of special 
 deposits, the post oflfice or telegraph company serving
 
 Sec. 1] THE EQUATION OF EXCHANGE 11 
 
 the purpose, for these special transactions, of a bank of 
 deposit. 
 
 But while a bank deposit transferable by check is 
 included as circulating media, it is not money. A 
 bank note, on the other hand, is both circulating 
 medium and money. Between these two lies the final 
 line of distinction between what is money and what 
 is not. True, the line is delicately drawn, especially 
 when we come to such checks as cashier's checks or 
 certified checks, for the latter are almost identical with 
 bank notes. Each is a demand liability on a bank, 
 and each confers on the holder the right to draw money. 
 Yet while a note is generally acceptable in exchange, a 
 check is specially acceptable only, i.e. only by the con- 
 sent of the payee. Real money rights are what a payee 
 accepts without question, because he is induced to do 
 so either by ''legal tender" laws or by a well-established 
 custom.^ 
 
 Of real money there are two kinds : primary and 
 fiduciary. Money is called " primary" if it is a commod- 
 ity which has just as much value in some use other than 
 money as it has in monetary use. Primary money has 
 its full value independently of any other wealth. Fidu- 
 ciary money, on the other hand, is money the value 
 of which depends partly or wholly on the confidence 
 that the owner can exchange it for other goods, e.g. for 
 primary money at a bank or government office, or at any 
 rate for discharge of debts or purchase of goods of mer- 
 chants. The chief example of primary money is gold 
 coin ; the chief example of fiduciary money is bank 
 notes. The qualities of primary money which make for 
 exchangeability are numerous. The most important 
 
 * See Francis Walker, Money, Trade, and Industry, New York 
 (Holt), 1879, Chapter I.
 
 12 THE PURCHASING POWER OF MONEY [Chap. II 
 
 are portability, durability, and divisibility.^ The chief 
 quality of fiduciary money which makes it exchangeable 
 is its redeemability in primary money, or else its im- 
 posed character of legal tender. 
 
 Bank notes and all other fiduciary money, as well as 
 bank deposits, circulate by certificates often called 
 ''tokens." ''Token coins" are included in this de- 
 scription. The value of these tokens, apart from the 
 rights they convey, is small. Thus the value of a silver 
 dollar, as wealth, is only about forty cents ; that is all 
 that the actual silver in it is worth. Its value as prop- 
 erty, however, is one hundred cents ; for its holder has 
 a legal right to use it in paying a debt to that amount, 
 and a customary right to so use it in payment for 
 goods. Likewise, the property value of a fifty-cent 
 piece, a quarter, a ten-cent piece, a five-cent piece, or 
 a one-cent piece is considerably greater than its value 
 as wealth. The value of a paper dollar as wealth — for 
 instance, a silver certificate — is almost nothing. It is 
 worth just its value as paper, and no more. But its 
 value as property is a hundred cents, that is, the equiva- 
 lent of one gold dollar. It represents to that extent a 
 claim of the holder on the wealth of the community. 
 
 Figure 1 indicates the classification of all circulating 
 media in the United States. It shows that the total 
 amount of circulating media is about 8| billions, of 
 which about 7 billions are bank deposits subject to 
 check, and 1^ billions, money ; and that of this 1^ 
 billions of money, 1 billion is fiduciary money and only 
 about I a billion, primary money. 
 
 In the present chapter we shall exclude the consider- 
 ation of bank deposits or check circulation and confine 
 our attention to the circulation of money, primary 
 
 1 See Jevons, Money and the Mechanism of Exchange, Chapter V.
 
 Sec. 1] 
 
 THE EQUATION OF EXCHANGE 
 
 13 
 
 and fiduciary. In the United States, the only primary 
 money is gold coin. The fiduciary money includes 
 (1) token coins, viz. silver dollars, fractional silver, 
 and minor coins ("nickels" and cents); (2) paper 
 money, viz. (a) certifi- 
 
 Deposits subject 
 
 TO CHECK 
 
 Fiduciary 
 
 MONE Y 
 
 MOWEY 
 BlLUION 
 
 Billions 
 
 Fig. 1. 
 
 cates for gold and sil- 
 ver, and (6) promissory 
 notes, whether of the 
 United States govern- 
 ment ("greenbacks"), 
 or of the National 
 banks. 
 
 Checks aside, we 
 may classify exchanges 
 into three groups : the 
 
 /'exchange of goods 
 against goods, or bar- 
 ter; the exchange of 
 
 . money against money, or changing money; and the 
 \5' exchange of money against goods, or purchase and sale. 
 Only the last-named species of exchange makes up what 
 we call the "circulation" of money. The circulation 
 of money signifies, therefore, the aggregate amount of 
 its transfers against goods. All money held for circula- 
 tion, i.e. all money, except what is in the banks and 
 United States government's vaults, is called "money in 
 circulation." 
 
 The chief object of this book is to explain the causes 
 determining the purchasing power of money. The 
 purchasing power of money is indicated by the quan- 
 tities of other goods which a given quantity of money 
 will buy. The lower we find the prices of goods, the 
 larger the quantities that can be bought by a given 
 amount of money, and therefore the higher the purchas-
 
 14 THE PURCHASING POWER OF MONEY [Chap. II 
 
 ing power of money. The higher we find the prices 
 of goods, the smaller the quantities that can be bought 
 by a given amount of money, and therefore the lower 
 the purchasing power of money. In short, the purchas- 
 ing power of money is the reciprocal of the level of 
 prices ; so that the study of the purchasing power of 
 money is identical with the study of price levels. 
 
 §2 
 
 Overlooking the influence of deposit currency, or 
 checks, the price level may be said to depend on only 
 three sets of causes : (1) the quantity of money in circu- 
 lation ; (2) its "efficiency" or velocity of circulation (or 
 the average number of times a year money is exchanged 
 for goods) ; and (3) the volume of trade (or amount of 
 goods bought by money). The so-called "quantity 
 theory," ^ i.e. that prices vary proportionately to money, 
 has often been incorrectly formulated, but (overlooking 
 checks) the theory is correct in the sense that the level 
 of prices varies directly with the quantity of money in 
 circulation, provided the velocity of circulation of that 
 money and the volume of trade which it is obliged to 
 perform are not changed. 
 
 The quantity theory has been one of the most bitterly 
 contested theories in economics, largely because the 
 recognition of its truth or falsity affected powerful 
 
 ^ This theory, though often crudely formulated, has been accepted 
 by Locke, Hume, Adam Smith, Ricardo, Mill, Walker, IMarshall, 
 Hadley, Fetter, Kemmerer and most writers on the subject. The 
 Roman Julius Paulus, about 200 a.d., stated his belief that the 
 value of money depends on its quantity. See Zuckerkandl, Theorie 
 des Preises; Kemmerer, Money and Credit Instruments in their 
 Relation to General Prices, New York (Holt), 1909. It is true 
 that many writers still oppose the quantity theory. See especially, 
 Laughlin, Principles of Money, New York (Scribner), 1903.
 
 Sec. 2] THE EQUATION OF EXCHANGE 15 
 
 interests in commerce and politics. It has been main- 
 tained — and the assertion is scarcely an exaggeration 
 — that the theorems of Euclid would be bitterly con- 
 troverted if financial or political interests were in- 
 volved. 
 
 The quantity theory has, unfortunately, been made 
 the basis of arguments for unsound currency schemes. 
 It has been invoked in behalf of irredeemable paper 
 money and of national free coinage of silver at the ratio 
 of 16 to 1. As a consequence, not a few ''sound money 
 men," believing that a theory used to support such 
 vagaries must be wrong, and fearing the political effects 
 of its propagation, have drifted into the position of 
 opposing, not only the unsound propaganda, but also 
 the sound principles by which its advocates sought 
 to bolster it up.^ These attacks upon the quantity 
 theory have been rendered easy by the imperfect com- 
 prehension of it on the part of those who have thus 
 invoked it in a bad cause. 
 
 Personally, I believe that few mental attitudes are 
 more pernicious, and in the end more disastrous, than 
 those which would uphold sound practice by denying 
 sound principles because some thinkers make unsound 
 application of those principles. At any rate, in scien- 
 tific study there is no choice but to find and state the 
 liji varnished truth. 
 
 The quantity theory will be made more clear by the 
 equation of exchange, which is now to be explained. 
 
 The equation of exchange is a statement, in math- 
 
 * See Scott, "It has been a most fruitful source of false doctrines 
 regarding monetary matters, and is constantly and successfully 
 employed in defense of harmful legislation and as a means of pre- 
 venting needed monetary reforms." Money and Banking, New 
 York, 1903, p. 68.
 
 16 THE PURCHASING POWER OF MONEY [Chap. II 
 
 ematical form, of the total transactions effected in a 
 certain period in a given community. It is obtained 
 simply by adding together the equations of exchange for 
 all individual transactions. Suppose, for instance, that 
 a person buys 10 pounds of sugar at 7 cents per pound. 
 This is an exchange transaction, in which 10 pounds of 
 sugar have been regarded as equal to 70 cents, and this 
 fact may be expressed thus : 70 cents = 10 pounds of 
 sugar multiplied by 7 cents a pound. Every other sale 
 and purchase may be expressed similarly, and by adding 
 them all together we get the equation of exchange for 
 a certain -period in a given community. During this 
 same period, however, the same money may serve, 
 and usually does serve, for several transactions. For 
 that reason the money side of the equation is of 
 course greater than the total amount of money in cir- 
 culation. 
 
 The equation of exchange relates to all the purchases 
 made by money in a certain community during a cer- 
 tain time. We shall continue to ignore checks or any 
 circulating medium not money. We shall also ignore 
 foreign trade and thus restrict ourselves to trade within 
 a hypothetical community. Later we shall reinclude 
 these factors, proceeding by a series of approximations 
 through successive hypothetical conditions to the actual 
 conditions which prevail to-day. We must, of course, 
 not forget that the conclusions expressed in each suc- 
 cessive approximation are true solely on the particular 
 hypothesis assumed. 
 
 The equation of exchange is simply the sum of the 
 equations involved in all individual exchanges in a year. 
 In each sale and purchase, the money and goods ex- 
 changed are ipso facto equivalent ; for instance, the 
 money paid for sugar is equivalent to the sugar bought.
 
 Sec. 2] THE EQUATION OF EXCHANGE 17 
 
 And in the grand total of all exchanges for a year, the 
 total money paid is equal in value to the total value 
 of the goods bought. The equation thus has a money 
 side and a goods side. The money side is the total 
 money paid, and may be considered as the product of y 
 the quantity of money multiplied by its rapidity of 
 circulation. The goods side is made up of the products 
 of quantities of goods exchanged multiplied by their 
 respective prices. 
 
 The important magnitude, called the velocity of cir- 
 culation, or rapidity of turnover, is simply the quotient y^ 
 obtained by dividing the total money payments for • 
 goods in the course of a year by the average amount 
 of money in circulation by which those payments are 
 effected. This velocity of circulation for an entire com- 
 munity is a sort of average of the rates of turnover of 
 money for different persons. Each person has his own 
 rate of turnover which he can readily calculate by di- 
 viding the amount of money he expends per year by 
 the average amount he carries. 
 
 • Let us begin with the money side. If the number of 
 dollars in a country is 5,000,000, and their velocity of 
 circulation is twenty times per year, then the total 
 amount of money changing hands (for goods) per year 
 is 5,000,000 times twenty, or $100,000,000. This is the 
 money side of the equation of exchange. 
 
 Since the money side of the equation is $100,000,000, 
 the goods side must be the same. For if $100,000,000 
 has been spent for goods in the course of the year, then 
 $100,000,000 worth of goods must have been sold in 
 that year. In order to avoid the necessity of writing 
 out the quantities and prices of the innumerable va- 
 rieties of goods which are actually exchanged, let us 
 assume for the present that there are only three kinds
 
 18 THE PURCHASING POWER OF MONEY [Chap. U 
 
 of goods, — bread, coal, and cloth ; and that the sales 
 
 are: — 
 
 200,000,000 loaves of bread at $ .10 a loaf, 
 10,000,000 tons of coal at 5.00 a ton, and 
 
 30,000,000 yards of cloth at 1 .00 a yard. 
 
 The value of these transactions is evidently $100,000,- 
 000, i.e. $20,000,000 worth of bread plus $50,000,000 
 worth of coal plus $30,000,000 worth of cloth. The 
 equation of exchange therefore (remember that the 
 money side consisted of $5,000,000 exchanged 20 times) 
 is as follows : — 
 
 S5,000,000 X 20 times a year 
 
 = 200,000,000 loaves X $ .10 a loaf 
 + 10,000,000 tons X 5.00 a ton 
 + 30,000,000 yards X 1.00 a yard. 
 
 This equation contains on the money side two magni- 
 tudes, viz. (1) the quantity of money and (2) its 
 velocity of circulation ; and on the goods side two 
 groups of magnitudes in two columns, viz. (1) the 
 quantities of goods exchanged (loaves, tons, yards), 
 and (2) the prices of these goods. The equation shows 
 that these four sets of magnitudes are mutually related. 
 Because this equation must be fulfilled, the prices must 
 bear a relation to the three other sets of magnitudes, — 
 quantity of money, rapidity of circulation, and quan- 
 tities of goods exchanged. Consequently, these prices 
 must, as a whole, vary proportionally with the quantity 
 of money and with its velocity of circulation, and in- 
 versely with the quantities of goods exchanged. 
 
 Suppose, for instance, that the quantity of money 
 were doubled, while its velocity of circulation and the 
 quantities of goods exchanged remained the same. 
 Then it would be quite impossible for prices to 
 remain unchanged. The money side would now be
 
 Sec. 2] THE EQUATION OF EXCHANGE 19 
 
 $10,000,000 X 20 times a year or $200,000,000 ; whereas, 
 if prices should not change, the goods would remain 
 $100,000,000, and the equation would be violated. 
 Since exchanges, individually and collectively, always 
 involve an equivalent quid pro quo, the two sides must 
 be equal. Not only must purchases and sales be equal 
 in amount — since every article bought by one person 
 is necessarily sold by another — but the total value of 
 goods sold must equal the total amount of money 
 exchanged. Therefore, under the given conditions, 
 prices must change in such a way as to raise the goods 
 side from $100,000,000 to $200,000,000. This doubling 
 may be accomplished by an even or uneven rise in 
 prices, but some sort of a rise of prices there must he. 
 If the prices rise evenly, they will evidently all be exactly 
 doubled, so that the equation will read : — 
 
 $10,000,000 X 20 times a year 
 
 = 200,000,000 loaves X $ .20 per loaf 
 + 10,000,000 tons X 10.00 per ton 
 + 30,000,000 yards X 2.00 per yard. 
 
 If the prices rise unevenly, the doubling must evidently 
 be brought about by compensation ; if some prices rise 
 by less than double, others must rise by enough more 
 than double to exactly compensate. 
 
 But whether all prices increase uniformly, each being 
 exactly doubled, or some prices increase more and some 
 less (so as still to double the total money value of the 
 goods purchased), the prices are doubled on the average} 
 This proposition is usually expressed by saying that the 
 "general level of prices" is raised twofold. From the 
 mere fact, therefore, that the money spent for goods 
 
 1 This does not mean, of course, that their simple arithmetical 
 average is exactly doubled. For definition of an average or "mean" 
 in general, see § 1 of Appendix to (this) Chapter II.
 
 20 THE PURCHASING POWER OF MONEY [Chap. II 
 
 must equal the quantities of those goods multipHed by 
 their prices, it follows that the level of prices must rise 
 or fall according to changes in the quantity of money, 
 unless there are changes in its velocity of circulation or 
 in the quantities of goods exchanged. 
 
 If changes in the quantity of money affect prices, so 
 will changes in the other factors — quantities of goods 
 and velocity of circulation — affect prices, and in a 
 very similar manner. Thus a doubling in the velocity 
 of circulation of money will double the lev«l of prices, 
 provided the quantity of money in circulation and the 
 quantities of goods exchanged for money remain as be- 
 fore. The equation will become : — 
 
 $5,000,000 X 40 times a year 
 
 = 200,000,000 loaves X $ .20 a loaf 
 + 10,000,000 tons X 10.00 a ton 
 + 30,000,000 yards X 2.00 a yard, 
 
 or else the equation will assume a form in which some 
 of the prices will more than double, and others less than 
 double by enough to preserve the same total value of 
 the sales. 
 
 Again, a doubling in the quantities of goods exchanged 
 will not double, but halve, the height of the price level, 
 provided the quantity of money and its velocity of 
 circulation remain the same. jJnder these circum- 
 stances the equation will become : — 
 
 ),000,000 X 20 times a year 
 
 = 400,000,000 loaves X S .05 a loaf 
 + 20,000,000 tons X 2.50 a ton 
 + 60,000,000 yards X .50 a yard, 
 
 or else it will assume a form in which some of the prices 
 are more than halved, and others less than halved, 
 BO as to preserve the equation.
 
 Sec. 3] 
 
 THE EQUATION OF EXCHANGE 
 
 21 
 
 Finally, if there is a simultaneous change in two or 
 all of the three influences, i.e. quantity of money, 
 velocity of circulation, and quantities of goods ex- 
 changed, the price level will be a compound or resultant 
 of these various influences. If, for example, the quan- 
 tity of money is doubled, and its velocity of circulation 
 is halved, while the quantity of goods exchanged remains 
 constant, the price level will be undisturbed. Like- 
 wise, it will be undisturbed if the quantity of money is 
 doubled an^ the quantity of goods is doubled, while 
 the velocity of circulation remains the same. To double 
 the quantity of money, therefore, is not always to double 
 prices. We must distinctly recognize that the quantity 
 of money is only one of three factors, all equally impor- 
 tant in determining the price level. 
 
 §3 
 
 The equation of exchange has now been expressed by 
 an arithmetical illustration. It may be also represented 
 visually, by a mechanical illustration. Such a repre- 
 sentation is embodied in Figure 2. This represents a 
 
 Fig. 2. 
 
 mechanical balance in equilibrium, the two sides of which 
 symbolize respectively the money side and the goods 
 side of the equation of exchange. The weight at the 
 left, symbolized by a purse, represents the money in 
 circulation; the ''arm" or distance from the fulcrum 
 at which this weight (purse) is hung represents the
 
 22 THE PURCHASING POWER OF MONEY [Chap. II 
 
 efficiency of this money, or its velocity of circulation. 
 On the right side are three weights, — bread, coal, and 
 cloth, symbolized respectively by a loaf, a coal scuttle, 
 and a roll of cloth. The arm, or distance of each from 
 the fulcrum, represents its price. In order that the lever 
 arms at the right may not be inordinately long, we have 
 found it convenient to reduce the unit of measure of 
 coal from tons to hundredweights, and that of cloth 
 from yards to feet, and consequently to enlarge corre- 
 spondingly the numbers of units (the measure of coal 
 changing from 10,000,000 tons to 200,000,000 hundred- 
 weights, and that of the cloth from 30,000,000 yards to 
 90,000,000 feet). The price of coal in the new unit per 
 hundredweight becomes 25 cents per hundredweight, 
 and that of cloth in feet becomes SS-g- cents per foot. 
 
 We all know that, when a balance is in equilibrium, 
 the tendency to turn in one direction equals the tend- 
 ency to turn in the other. Each weight produces on 
 its side a tendency to turn, measured by the product of 
 the weight by its arm. The weight on the left produces, 
 on that side, a tendency measured by 5,000,000 x 20; 
 while the weights on the right make a combined opposite 
 tendency measured by 200,000,000 x .10 + 200,000,000 x 
 .25-^90,000,000 X ..33i The equality of these opposite 
 tendencies represents the equation of exchange. 
 
 An increase in the weights or arms on one side re- 
 quires, in order to preserve equilibrium, a proportional 
 increase in the weights or arms on the other side. This 
 simple and familiar principle, applied to the symbolism 
 here adopted, means that if, for instance, the velocity 
 of circulation (left arm) remains the same, and if the 
 trade (weights at the right) remains the same, then any 
 increase of the purse at the left will require a lengthen- 
 ing of one or more of the arms at the right, represent-
 
 Sec. 3] 
 
 THE EQUATION OF EXCHANGE 
 
 23 
 
 ing prices. If these prices increase uniformly, they will 
 increase in the same ratio as the increase in money ; if 
 they do not increase uniformly, some will increase more 
 and some less than this ratio, maintaining an average. 
 
 Likewise it is evident that if the arm at the left 
 lengthens, and if the purse and the various weights on 
 the right remain the same, there must be an increase in 
 the arms at the right. 
 
 Again, if there is an increase in weights at the right, 
 and if the left arm and the purse remain the same, there 
 must be a shortening of right arms. 
 
 In general, a change in one of the four sets of mag- 
 nitudes must be accompanied by such a change or 
 changes in one or more of the other three as shall main- 
 tain equilibrium. 
 
 As we are interested in the average change in prices 
 rather than in the prices individually, we may simplify 
 this mechanical representation by hanging all the right- 
 hand weights at one average point, so that the arm shall 
 represent the average prices. This arm is a ''weighted 
 average" of the three original arms, the weights being 
 literally the weights hanging at the right. 
 
 This averaging of prices is represented in Figure 3, 
 which visualizes the fact that the average price of goods 
 
 X__Mi 
 
 Pro 
 
 (right arm) varies directly with the quantity of money 
 (left weight), and directly with its velocity of circulation
 
 24 THE PURCHASING POWER OF MONEY [Chap. II 
 
 (left arm), and inversely with the volume of trade (right 
 weight). 
 
 §4 
 
 We now come to the strict algebraic statement of 
 the equation of exchange. An algebraic statement is 
 usually a good safeguard against loose reasoning ; 
 and loose reasoning is chiefly responsible for the sus- 
 picion under which economic theories have frequently 
 fallen. If it is worth while in geometry to demonstrate 
 carefully, at the start, propositions which are almost 
 self-evident, it is a hundredfold more worth while to 
 demonstrate with care the propositions relating to 
 price levels, which are less self-evident ; which, indeed, 
 while confidently assumed by many, are contemptuously 
 rejected by others. 
 
 Let us denote the total circulation of money, i.e. the 
 amount of money expended for goods in a given com- 
 munity during a given year, by E (expenditure) ; and 
 the average amount of money in circulation in the com- 
 munity during the year by M (money). M will be 
 the simple arithmetical average of the amounts of money 
 existing at successive instants separated from each 
 other by equal intervals of time indefinitely small. 
 If we divide the year's expenditures, E, by the average 
 amount of money, M, we shall obtain what is called 
 the average rate of turnover of money in its exchange 
 
 E 
 
 for goods, — , that is, the velocity of circulation of 
 
 money. ^ This velocity may be denoted by V, so that 
 
 E 
 
 / ijj = ^J then E may be expressed as MV. In 
 
 words : the total circulation of money in the sense of 
 
 ^ For discussion of the concept of velocity of circulation, see 
 §§ 2, 4, 5 of Appendix to (this) Chapter II.
 
 Sec. 4] THE EQUATION OF EXCHANGE 25 
 
 money expended is equal to the total money in circu- 
 lation multiplied by its velocity of circulation or turn- 
 over. E ovMV, therefore, expresses the money side of 
 the equation of exchange. Turning to the goods side 
 of the equation, we have to deal with the prices of 
 goods exchanged and quantities of goods exchanged. 
 The average^ price of sale of any particular good, 
 such as bread, purchased in the given community 
 during the given year, may be represented by p 
 (price) ; and the total quantity of it purchased, by Q 
 (quantity) ; hkewise the average price of another 
 good (say coal) may be represented by p' and the 
 total quantity of it exchanged, by Q' ; the average 
 price and the total quantity of a third good (say cloth) 
 may be represented by p" and Q" respectively ; and so 
 on, for all other goods exchanged, however numerous. 
 The equation of exchange may evidently be expressed 
 as follows : ^ — 
 
 MV = pQ 
 
 + v'Q' 
 
 + P"Q" 
 
 + etc. 
 
 ^ This is an average weighted according to the quantities pur- 
 chased on various occasions throughout the period and country 
 considered. See § 3 of Appendix to (this) Chapter II. 
 
 2 An algebraic statement of the equation of exchange was made 
 by Simon Newcomb in his able but little appreciated Principles 
 of Political Economy, New York (Harper), 1885, p. 346. It is also 
 expressed by Edgeworth, " Report on Monetary Standard." Report 
 of the British Association for the Advancement of Science, 1887, p. 
 293, and by President Hadley, Economics, New York (Putnam), 
 1896, p. 197. See also Irving Fisher, "The Role of Capital in Eco- 
 nomic Theory," Economic Journal, December, 1899, pp. 515-521, 
 and E. W. Kemmerer, Money and Credit Instruments in their Rela- 
 tion to General Prices, New York (Holt), 1907, p. 13. While thus 
 only recently given mathematical expression, the quantity theory 
 has long been understood as a relationship among the several fac-
 
 26 THE PURCHASING POWER OF MONEY [Chap. II 
 
 The right-hand side of this equation is the sum of 
 
 terms of the form pQ — a price multipHed by a quantity 
 
 bought. It is customary in mathematics to abbreviate 
 
 such a sum of terms (all of which are of the same form) 
 
 by using ''2 " as a symbol of summation. This symbol 
 
 does not signify a magnitude as do the symbols Af , V, 
 
 p, Q, etc. It signifies merely the operation of addition 
 
 and should be read ''the sum of terms of the following 
 
 type." The equation of exchange may therefore be 
 
 written : — 
 
 MV = SpQ. 
 
 That is, the magnitudes E, M, V, the p's and the Q's 
 relate to the entire community and an entire year ; but 
 they are based on and related to corresponding magni- 
 tudes for the individual persons of which the community 
 is composed and for the individual moments of time 
 of which the year is composed.^ 
 
 The algebraic derivation of this equation is, of course, 
 essentially the same as the arithmetical derivation 
 previously given. It consists simply in adding together 
 the equations for all individual purchases within the 
 community during the year.- 
 
 By means of this equation, MV = ^pQ, the three 
 theorems set forth earlier in this chapter may be now 
 expressed as follows : — 
 
 (1) If V and the Q's remain invariable while M varies 
 in any ratio, the money side of the equation will vary 
 
 tors : amount of money, rapidity of circulation, and amount of trade. 
 See Mill, Principles of Political Economy, Book III, Chapter VIII, 
 § 3. Ricardo probably deserves chief credit for launching the theory. 
 
 " For the relations subsisting between these magnitudes (as 
 relating to the whole community and the whole year), and the 
 corresponding elementary magnitudes relating to each individual 
 and each moment, see § 4 of the Appendix to (this) Chapter II. 
 
 ^ See § 6 of Appendix to (this) Chapter II.
 
 Sec. 4] THE EQUATION OF EXCHANGE 27 
 
 in the same ratio and therefore its equal, the goods side, 
 must vary in that same ratio also ; consequently, either 
 the p's will all vary in that ratio or else some p's will 
 vary more than in that ratio and others enough less to 
 compensate and maintain the same average.^ 
 
 (2) If M and the Q's remain invariable while V varies 
 in any ratio, the money side of the equation will vary 
 in the same ratio, and therefore its equal, the goods 
 side, must vary in that ratio also; consequently, the 
 p's will all vary in the same ratio or else some will vary 
 more and others enough less to compensate. 
 
 (3) If Af and V remain invariable, the money side 
 and the goods side will remain invariable ; consequently, 
 if the Q's all vary in a given ratio, either the p's must 
 all vary in the inverse ratio or else some of them will 
 vary more and others enough less to compensate. 
 
 We may, if we wish, further simplify the right side 
 by writing it in the form PT where P is a weighted 
 average of all the p's, and T is the sum of all the Q's. 
 P then represents in one magnitude the level of prices, 
 and T represents in one magnitude the volume of trade. 
 This simplification is the algebraic interpretation of 
 the mechanical illustration given in Figure 3, where all 
 the goods, instead of being hung separately, as in 
 Figure 2, were combined and hung at an average point 
 representing their average price. 
 
 We have derived the equation of exchange, MV = 
 ^vQ, by adding together, for the right side, the sums 
 expended by different persons. But the same reasoning 
 would have derived an equation of exchange by taking 
 the sums received by different persons. The results of 
 
 ' For the nature of the average here involved and for the aver- 
 ages involved in the other two following cases, see § 7 of Appendix 
 to (this) Chapter II.
 
 1/ 
 
 28 THE PURCHASING POWER OF MONEY [Chap. II 
 
 the two methods will harmonize if the community has 
 no foreign trade ; for, apart from foreign trade, what is 
 expended by one person in the community is necessarily 
 received by some other person in that community. 
 
 If we wish to extend the reasoning so as to apply 
 to foreign trade, we shall have two equations of ex- 
 change, one based on money expended and the other 
 on money received or accepted by members of the com- 
 munity. These will always be approximately equal and 
 may or may not be exactly equal within a country ac- 
 cording to the "balance of trade" between that coun- 
 try and others. The right side of the equation based 
 on expenditures will include, in addition to the domes- 
 tic quantities already represented there, the quantities 
 of goods imporlsd and their prices, but not those ex- 
 ported ; whilo the reverse will be true of the equation 
 based on receipts. 
 
 §5 
 
 This completes our statement of the equation of 
 exchange, except for the element of check payments, 
 which is reserved for the next chapter. We have seen 
 that the equation of exchange has as its ultimate basis 
 the elementary equations of exchange pertaining to given 
 persons and given moments, in other words, the equa- 
 tions pertaining to individual transactions. Such ele- 
 mentary equations mean that the money paid in any 
 transaction is the equivalent of the goods bought at 
 the price of sale. From this secure and obvious premise 
 is derived the equation of exchange MV = '^pQ, each 
 element in which is a sum or an average of the like 
 elementary elements for different individuals and differ- 
 ent moments, thus comprising all the purchases in the 
 community during the year. Finally, from this equa-
 
 Sec. 5] THE EQUATIOJS OF EXCHANGE 29 
 
 tion we see that prices vary directly as M and F, and 
 inversely as the Q's, provided in each case only one of 
 these three sets of magnitudes varies, and the other two 
 remain unchanged. Whether to change one of the 
 three necessarily disturbs the others is a question re- 
 served for a later chapter. Those who object to the 
 equation of exchange as a mere truism are asked to 
 defer judgment until they have read Chapter VIII. 
 
 To recapitulate, we find then that, under the con- 
 ditions assumed, the price level varies (1) directly as the 
 quantity of money in circulation (M), (2) directly as 
 the velocity; of its circulation (F), (3) inversely as the 
 volume of trade done by it (T). The first of these 
 three relations is worth emphasis. It constitutes the 
 " quantity theory of money." 
 
 So important is this principle, and so bitterly con- 
 tested has it been, that we shall illustrate it further. 
 As already indicated, by "the quantity of money" is 
 meant the number of dollars (or other given monetary 
 units) in circulation. This number may be changed 
 in several ways, of which the following three are most 
 important. Their statement will serve to bring home 
 to us the conclusions we have reached and to reveal the 
 fundamental peculiarity of money on which they rest. 
 
 As a first illustration, let us suppose the government 
 to double the denominations of all money ; that is, let 
 us suppose that what has been hitherto a half dollar is 
 henceforth called a dollar, and that what has hitherto 
 been a dollar is henceforth called two dollars. Evi- 
 dently the number of "dollars" in circulation will then 
 be doubled ; and the price level, measured in terms 
 of the new "dollars," will be double what it would 
 otherwise be. Every one will pay out the same coins 
 as though no such law were passed. But he will, in
 
 30 THE PURCHASING POWER OF MONEY [Chap. II 
 
 each case, be paying twice as many ''dollars." Fol 
 example, if $3 formerly had to be paid for a pair of 
 shoes, the price of this same pair of shoes will now 
 become $6. Thus we see how the nominal quantity of 
 money affects price levels. 
 
 A second illustration is found in a debased currency. 
 Suppose a government cuts each dollar in two, coining 
 the halves into new ''dollars" ; and, recalling all paper 
 notes, replaces them with double the original number — • 
 two new notes for each old one of the same denomination. 
 In short, suppose money not only to be renamed, as in 
 the first illustration, but also reissued ; prices in the de- 
 based coinage will again be doubled just as in the first 
 illustration. The subdivision and recoinage is an im- 
 material circumstance, unless it be carried so far as 
 to make counting difficult and thus to interfere with 
 the convenience of money. Wherever a dollar had 
 been paid before debasement, two dollars — i.e. two 
 of the old halves coined into two of the new dollars — 
 will now be paid instead. 
 
 In the first illustration, the increase in quantity was 
 simply nominal, being brought about by renaming 
 coins. In the second illustration, besides renaming, the 
 further fact of recoining is introduced. In the first 
 case the number of actual pieces of money of each kind 
 was unchanged, but their denominations were doubled. 
 In the second case, the number of pieces is also doubled 
 by splitting each coin and reminting it into two coins, 
 each of the same nominal denomination as the original 
 whole of which it is the half, and by similarly redoubUng 
 the paper money. 
 
 For a third illustration, suppose that, instead of 
 doubhng the number of dollars by splitting them in 
 two and recoining the halves, the government duplicates
 
 Sec. 5J THE EQUATION OF EXCHANGE 31 
 
 each piece of money in existence and presents the du- 
 phcate to the possessor of the original.^ (We must in 
 this case suppose, further, that there is some effectual 
 bar to prevent the melting or exporting of money. 
 Otherwise the quantity of money in circulation will 
 not be doubled : much of the increase will escape.) If 
 the quantity of money is thus doubled, prices will also 
 be doubled just as truly as in the second illustration, in 
 which there were exactly the same denominations. The 
 only difference between the second and the third 
 illustrations will be in the size and weight of the coins. 
 The weights of the individual coins, instead of being 
 reduced, will remain unchanged ; but their number 
 will be doubled. This doubling of coins must have the 
 same effect as the 50 per cent debasement, i.e. it must 
 have the effect of doubling prices. 
 
 The force of the third illustration becomes even more 
 evident if, in accordance with Ricardo's presentation,^ 
 we pass back by means of a seigniorage from the third 
 illustration to the second. That is, after duplicating 
 all money, let the government abstract half of each coin, 
 thereby reducing the weight to that of the debased 
 coinage in the second illustration, and removing the 
 only point of distinction between the two. This 
 ''seigniorage" abstracted will not affect the value of the 
 coins, so long as their number remains unchanged. 
 
 In short, the quantity theory asserts that (provided 
 velocity of circulation and volume of trade are un- 
 changed) if we increase the number of dollars, whether 
 
 ^ Cf. J. S. Mill, Principles of Political Economy, Book III, Chap- 
 ter VIII, § 2. Ricardo in his reply to Bosanquet uses an illus- 
 tration similar in principle though slightly different in form. See 
 Works, 2d ed., London (Murray), 1852, p. 346. 
 
 » Works, 2d ed., London (Murray), 1852, pp. 346 and 347 
 (reply to Bosanquet, Chapter VI) ; see also pp. 213 and 214.
 
 32 THE PURCHASING POWER OF MONEY [Chap. II 
 
 by renaming coins, or by debasing coins, or by increasing 
 coinage, or by any other means, prices will be increased 
 in the same proportion. It is the number, and not 
 the weight, that is essential. This fact needs great 
 emphasis. It is a fact which differentiates money 
 from all other goods and explains the peculiar manner in 
 which its purchasing power is related to other goods. 
 Sugar, for instance, has a specific desirability dependent 
 on its quantity in pounds. Money has no such quality. 
 The value of sugar depends on its actual quantity. If 
 the quantity of sugar is changed from 1,000,000 pounds 
 to 1,000,000 hundredweight, it does not follow that a 
 hundredweight will have the value previously possessed 
 by a pound. But if money in circulation is changed 
 from 1,000,000 units of one weight to 1,000,000 units 
 of another weight, the value of each unit will remain 
 unchanged. 
 
 The quantity theory of money thus rests, ultimately, 
 upon the fundamental pecuUarity which money alone of 
 all goods possesses, — the fact that it has no power to 
 satisfy human wants except a power to purchase things 
 which do have such power. ^ 
 
 1 Cf . G. F. Knapp, Staatliche Theorie des Geldes, Leipzig, 1905 ; 
 L. von Bortkiewiez, " Die geldtheoretischen und die wahrungspoli- 
 tisehen Consequenzen des ' Nominalismus,' " Jahrbuch fiir Gesetz- 
 gebung, Verwaltung und Volkswirtschaft, October, 1906 ; Bertrand 
 Nogaro, " L'experience bimetalliste du XIX siecle et la theorie 
 generale de la monnaie," Revue d'Economie politique, 1908.
 
 CHAPTER III 
 
 INFLUENCE OF DEPOSIT CURKENCY ON THE EQUATION 
 AND THEREFORE ON PURCHASING POWER 
 
 § 1 
 
 We are now ready to explain the nature of bank 
 deposit currency, or circulating credit. Credit, in 
 general, is the claim of a creditor against a debtor. 
 Bank deposits subject to check are the claims of the 
 creditors of a bank against the bank, by virtue of which 
 they may, on demand, draw by check specified sums 
 of money from the bank. Since no other kind of bank 
 deposits will be considered by us, we shall usually 
 refer to "bank deposits subject to check" simply as 
 ''bank deposits." They are also called "circulating 
 credit." Bank checks, as we have seen, are merely 
 certificates of rights to draw, i.e. to transfer bank de- 
 posits. The checks themselves are not the currency; 
 the bank deposits which they represent are the currency. 
 
 It is in the connection with the transfer of bank 
 deposits that there arises that so-called "mystery of 
 banking" called "circulating credit." Many persons, 
 including some economists, have supposed that credit 
 is a special form of wealth which may be created 
 out of whole cloth, as it were, by a bank. Others have 
 maintained that credit has no foundation in actual 
 wealth at all, but is a kind of unreal and inflated bubble 
 with a precarious, if not wholly illegitimate, existence. 
 As a matter of fact, bank deposits are as easy to under- 
 stand as bank notes, and what is said in this chapter 
 D 33
 
 34 THE PURCHASING POWER OF MONEY [Chap. Ill 
 
 of bank deposits may in substance be taken as true 
 also of bank notes. The chief difference is a formal one, 
 the notes circulating from hand to hand, while the 
 deposit currency circulates only by means of special 
 orders called "checks." 
 
 To understand the real nature of bank deposits, let 
 us imagine a hypothetical institution, — a kind of 
 primitive bank existing mainly for the sake of deposits 
 and the safe keeping of actual money. The original 
 bank of Amsterdam was somewhat like the bank we 
 are now imagining. In such a bank a number of people 
 deposit $100,000 in gold, each accepting a receipt for the 
 amount of his deposit. If this bank should issue a 
 ''capital account," or statement, it would show $100,000 
 in its vaults and $100,000 owed to depositors, as fol- 
 lows : — 
 
 Assets Liabilities 
 
 Gold $100,000 I Due depositors . . $100,000 
 
 The right-hand side of the statement is, of course, 
 made up of smaller amounts owed to individual de- 
 positors. Assuming that there is owed to A, $10,000, 
 to B, $10,000, and to all others $80,000, we may write 
 the bank statement as follows : — 
 
 Assets Liabilities 
 
 Gold $100,000 
 
 $100,000 
 
 Due depositor A . . $10,000 
 Due depositor B . . 10,000 
 Due other depositors 80,000 
 
 $100,000 
 
 Now assume that A wishes to pay B $1000. A could 
 go to the bank with B, present certificates or checks 
 for $1000, obtain the gold, and hand it over to B, who 
 might then redeposit it in the same bank, merely hand-
 
 Sec. 1] DEPOSIT CURRENCY 35 
 
 ing it back through the cashier's window and taking a 
 new certificate in his own name. Instead, however, 
 of both A and B visiting the bank and handhng the 
 money, A might simply give B a check for $1000. The 
 transfer in either case would mean that A's holding in 
 the bank was reduced from S 10,000 to $9000, and that 
 B's was increased from $10,000 to $11,000. The state- 
 ment would then read : — 
 
 Assets Liabilities 
 
 Gold $100,000 
 
 $100,000 
 
 Due depositor A . . $ 9,000 
 Due depositor B . . 11,000 
 Due other depositors 80,000 
 
 $100,000 
 
 Thus the certificates, or checks, would circulate in 
 place of cash among the various depositors in the bank. 
 What really changes ownership, or ''circulates," in 
 such cases is the rigM to draw money. The check is 
 merely the evidence of this right and of the transfer of 
 ohis right from one person to another. 
 
 In the case under consideration, the bank would be con- 
 ducted at a loss. It would be giving the time and labor 
 of its clerical force for the accommodation of its deposi- 
 tors, without getting anything in return. But such a 
 hypothetical bank would soon find — much as did the 
 bank of Amsterdam^ — that it could ''make money" by 
 lending at interest some of the gold on deposit. This 
 could not offend the depositors; for they do not expect 
 or desire to get back the identical gold they de- 
 posited. What they want is simply to be able at any 
 time to obtain the same amount of gold. Since, then, 
 
 1 See Dunbar's Theory and History of Banking, 2d ed., edited 
 by O. M. W. Sprague, New York and London (G. P. Putnam's 
 Sons), 1901, pp. 113-116.
 
 36 
 
 THE PURCHASING POWER OF MONEY [Chap. Ill 
 
 their arrangement with the bank calls for the payment^ 
 not of any particular gold, but merely of a definite 
 amount, and that but occasionally, the bank finds it- 
 self free to lend out part of the gold that otherwise 
 would lie idle in its vaults. To keep it idle would be 
 a great and needless waste of opportunity. 
 
 Let us suppose, then, that the bank decides to loan 
 out half its cash. This is usually done in exchange for 
 promissory notes of the borrowers. Now a loan is 
 really an exchange of money for a promissory note 
 which the lender — in this case the bank — receives 
 in place of the gold. Let us suppose that so-called 
 borrowers actually draw out S50,000 of gold. The 
 bank thereby exchanges money for promises, and its 
 books will then read : — 
 
 Assets 
 
 Gold reserve . . . 
 Promissory notes . 
 
 $50,000 
 50,000 
 
 $100,000 
 
 Liabilities 
 
 Due depositor A . , 
 Due depositor B . , 
 Due other depositors 
 
 $ 9,000 
 11,000 
 80,000 
 
 $100,000 
 
 It will be noted that now the gold in the bank is 
 only $50,000, while the total deposits are still 
 S100,000. In other words, the depositors now have 
 more "'money on deposit" than the bank has in its 
 vaults ! But, as will be shown, this form of expression 
 involves a popular fallacy in the word ''money." 
 Something good is behind each loan, but not necessarily 
 money. 
 
 Next, suppose that the borrowers become, in a sense, 
 depositors also, by redepositing the $50,000 of cash 
 which they borrowed, in return for the right to draw out 
 the same sum on demand. In other words, suppose
 
 Sec. 1] 
 
 DEPOSIT CURRENCY 
 
 37 
 
 that after borrowing $50,000 from the bank, they lend 
 it back to the bank. The bank's assets will thus be 
 enlarged by $50,000, and its obligations (or credit 
 extended) will be equally enlarged; and the balance 
 sheet will become : — 
 
 Assets 
 
 Gold reserve . . 
 Promissory notes . 
 
 iX 
 
 Ct^ 
 
 $100,000 
 50,000 
 
 $150,000 
 
 Liabilities 
 
 Due depositor A . . 
 Due depositor B . . 
 Due old depositors . 
 Due new depositors, 
 i.e. the borrowers . 
 
 5 9,000 
 11,000 
 80,000 
 
 50,000 
 $150,000 
 
 What happened in this case was the following : Gold 
 was borrowed in exchange for a promissory note and 
 then handed back in exchange for a right to draw. 
 Thus the gold really did not budge; but the bank 
 received a promissory note and the depositor a right to 
 draw. Evidently, therefore, the same result would have 
 followed if each borrower had merely handed in his prom- 
 issory note and received, in exchange, a right to draw. 
 As this operation most frequently puzzles the beginner 
 in the study of banking, we repeat the tables repre- 
 senting the conditions before and after these ''loans," 
 i.e. these exchanges of promissory notes for present 
 rights to draw.^ 
 
 1 In the ultimate analysis, and outside of its function of insuring 
 credit, a bank is really an intermediary between borrowers and 
 lenders. It is by virtue of bringing borrowers and ultimate lenders 
 together and providing the former with a supply of loans which 
 would not otherwise exist, that a bank simultaneously tends to 
 lower the rate of interest and increase the supply of credit cur- 
 rency. See paper by Harry G. Brown, in the Quarterly Journal of 
 Economics, August, 1910, on "Commercial Banking and the Rate of 
 Interest." 4 p f* I* r*
 
 38 THE PURCHASING POWER OF MONEY [Chap. Ill 
 
 
 Before the Loans 
 
 
 Assets 
 
 Liabilities 
 
 
 Gold reserve . . 
 
 . $100,000 1 Due depositors . . 
 After the Loans 
 
 $100,000 
 
 Gold reserve . . . 
 Promissory notes . 
 
 . $100,000 
 50,000 
 
 Due depositors . . 
 
 $150,000 
 
 Clearly, therefore, the intermediation of the money in 
 this case is a needless complication, though it may help 
 to a theoretical miderstanding of the resultant shifting 
 of rights and liabilities. Thus the bank may receive 
 deposits of gold or deposits of promises. In exchange 
 for the promises it may give, or lend, either a right 
 to draw, or gold, — the same that was deposited by 
 another customer. Even when the borrower has 
 only a promise, by fiction he is still held to have de- 
 posited money ; and like the original cash depositors, he 
 is given the right to make out checks. The total value 
 of rights to draw, in whichever way arising, is termed 
 ''deposits." Banks more often lend rights to draw (or 
 deposit rights) than actual cash, partly because of the 
 greater convenience to borrowers, and partly because 
 the banks wish to keep their cash reserves large, in order 
 to meet large or unexpected demands. It is true that 
 if a bank loans money, part of the money so loaned will 
 be redeposited by the persons to whom the borrowers 
 pay it in* the course of business ; but it will not neces- 
 sarily be redeposited in the same bank. Hence the 
 average banker prefers that the borrower should not 
 withdraw actual cash. 
 
 Besides lending deposit rights, banks may also lend 
 their own no^es, called ''bank notes." And the 
 principle governing bank notes is the same as the prin-
 
 Sec. 1] 
 
 DEPOSIT CURRENCY 
 
 39 
 
 ciple governing deposit rights. The holder simply gets 
 a pocketful of bank notes instead of a bank account. 
 In either case the bank must be always ready to pay 
 the holder — to ''redeem its notes" — as well as pay 
 its depositors, on demand, and in either case the bank 
 exchanges a promise for a promise. In the case of the 
 note, the bank has exchanged its bank note for a cus- 
 tomer's promissory note. The bank note carries no 
 interest, but is payable on demand. The customer's 
 note bears interest, but is payable only at a definite 
 date. 
 
 Assuming that the bank issues $50,000 of notes, the 
 balance sheet will now become : — ., 'L, 
 
 Assets 
 
 Gold reserve . . . . $100,000 
 Loans 100,000 
 
 Liabilities 
 
 $200,000 
 
 Due depositors , 
 Due note holders 
 
 % 
 
 $150,000 
 50,000 
 
 $200,000 
 
 We repeat that by means of credit the deposits (and 
 notes) of a bank may exceed its cash. There would 
 be nothing mysterious or obscure about this fact, nor 
 about credit in general, if people could be induced not 
 to think of banking operations as money operations. 
 To so represent them is metaphorical and misleading. 
 They are no more money operations than they are 
 real estate transactions. A bank depositor, A, has not 
 ordinarily ''deposited money"; and whether he has 
 or not, he certainly cannot properly say that he "has 
 money in the bank." What he does have is the bank's 
 promise to pay money on demand. The bank owes him 
 money. When a private person owes money, the 
 creditor never thinks of saying that he has it on deposit 
 in the debtor's pocket.
 
 40 THE PURCHASING POWER OF MONEY [Chap. Ill 
 
 §2 
 
 It cannot be too strongly emphasized that, in any 
 balance sheet, the value of the liabilities rests on that 
 of the assets. The deposits of a bank are no excep- 
 tion. We must not be misled by the fact that the 
 cash assets may be less than the deposits. When 
 the uninitiated first learn that the number of dol- 
 lars which note holders and depositors have the right 
 to draw out of a bank exceeds the number of dollars 
 in the bank, they are apt to jump to the conclusion 
 that there is nothing behind the notes or deposit liabil- 
 ities. Yet behind all these obligations there is always, 
 in the case of a solvent bank, full value ; if not actual 
 dollars, at any rate dollars' worth of property. By no 
 jugglery can the liabilities exceed the assets except in 
 insolvency, and even in that case only nominally, 
 for the true value of the liabiUties (''bad debts") will 
 only equal the true value of the assets behind them. 
 
 These assets, as already indicated, are largely the 
 notes of merchants, although, so far as the theory of 
 banking is concerned, they might be any property 
 whatever. If they consisted in the ownership of real 
 estate or other wealth in ''fee simple," so that the 
 tangible wealth which property always represents 
 were clearly evident, all mystery would disappear. 
 But the effect would not be different. Instead of 
 taking grain, machines, or steel ingots on deposit, in 
 exchange for the sums lent, banks prefer to take interest- 
 bearing notes of corporations and individuals who own, 
 directly or indirectly, grain, machines, and steel ingots : 
 and by the banking laws the banks are even compelled 
 to take the notes instead of the ingots. The bank 
 finds itself with liabilities which exceed its cash assets ;
 
 Sec. 2] DEPOSIT CURRENCY 41 
 
 but in either case the excess of habilities is balanced by 
 the possession of other assets than cash. These other 
 assets of the bank are usually liabilities of business 
 men. These liabilities are in turn supported by the 
 assets of the business men. If we continue to follow 
 up the ultimate basis of the bank's liabilities we shall 
 find it in the visible tangible wealth of the world. 
 
 This ultimate basis of the entire credit structure is 
 kept out of sight, but the basis exists. Indeed, we may 
 say that banking, in a sense, causes this visible, tangible 
 wealth to circulate. If the acres of a landowner or 
 the iron stoves of a stove dealer cannot circulate in [y 
 literally the same way that gold dollars circulate, yet 
 the landowner or stove dealer may give to the bank a 
 note on which the banker may base bank notes or de- 
 posits ; and these bank notes and deposits will circulate 
 like gold dollars. Through banking, he who possesses 
 wealth difficult to exchange can create a circulating 
 medium. He has only to give to a bank his note — for 
 which, of course, his property is liable — get in return the 
 right to draw, and lo ! his comparatively unexchange- 
 able wealth becomes liquid currency. To put it crudely, 
 banking is a device for coining into dollars land, stoves, 
 and other wealth not otherwise generally exchangeable. 
 
 It is interesting to observe that the formation of 
 the great modern ''trusts" has given a considerable 
 impetus to deposit currency ; for the securities of large 
 corporations are more easily used as ''collateral se- 
 curity" for bank loans than the stocks and bonds of 
 small corporations or than partnership rights. 
 
 We began by regarding a bank as substantially a 
 cooperative enterprise, run for the convenience and at 
 the expense of its depositors. But, as soon as it reaches 
 the point of lending money to X, Y , and Z, on time,
 
 42 THE PURCHASING POWER OF MONEY [Chap. Ill 
 
 while itself owing money on demand, it assumes 
 toward X, Y, and Z and its cash depositors risks which 
 the depositors would be unwilling to assume. To 
 meet this situation, the responsibility and expense of 
 running the bank are taken by a third class of people — 
 stockholders — who are willing to assume the aug- 
 mented risk for the sake of the chance of profit. Stock- 
 holders, in order to guarantee the depositors against loss, 
 put in some cash of their own. Their contract is, in 
 effect, to make good any loss to depositors. Let us sup- 
 pose that the stockholders put in $50,000, viz. S40,000 
 in cash and $10,000 in the purchase of a bank building. 
 The accounts now stand : — 
 
 Assets Liabilities 
 
 Cash $140,000 
 
 Loans 100,000 
 
 Building 10,000 
 
 $250,000 
 
 Due depositors . . $150,000 
 Due note holders . . 50,000 
 Due stockholders . 50,000 
 
 $250,000 
 
 The accounts as they now stand include the chief fea- 
 tures of an ordinary modern bank, — a so-called "bank 
 of deposit, issue, and discount." 
 
 We have seen that the assets must be adequate to meet 
 the liabilities. We now wish to point out that the form 
 of the assets must be such as will insure meeting the lia- 
 bilities promptly. Since the business of a bank is to fur- 
 nish quickly available property (cash or credit) in place 
 of the "slower" property of its depositors, it fails of its 
 purpose when it is caught with insufficient cash. Yet 
 it "makes money " partly by tying up its quick property, 
 i.e. lending it out where it is less accessible. Its prob-
 
 Sec. 3] DEPOSIT CURRENCY 43 
 
 lem in policy is to tie up enough to increase its prop- 
 erty, but not to tie up so much as to get tied up itself. 
 So far as anything has yet been said to the contrary, 
 a bank might increase indefinitely its loans in relation 
 to its cash or in relation to its capital. If this were 
 so, deposit currency could be indefinitely inflated. 
 
 There are limits, however, imposed by prudence and 
 sound economic policy, on both these processes. In- 
 solvency and insufficiency of cash must both be avoided. 
 Insolvency is that condition which threatens when loans 
 are extended with insufficient capital. Insufficiency 
 of cash is that condition which threatens when loans 
 are extended unduly relatively to cash. Insolvency 
 is reached when assets no longer cover liabilities (to 
 others than stockholders), so that the bank is unable 
 to pay its debts. Insufficienc}'^ of cash is reached when, 
 although the bank's total assets are fully equal to its 
 liabilities, the actual cash on hand is insufficient to 
 meet the needs of the instant, and the bank is unable 
 to pay its debts on demand. 
 
 The less the ratio of the value of the stockholders' 
 interests to the value of liabilities to others, the greater 
 is the risk of insolvency; the risk of insufficiency of 
 cash is the greater, the less the ratio of the cash to the 
 demand liabilities. In other words, the leading safe- 
 guard against insolvency lies in a large capital and sur- 
 plus, but the leading safeguard against insufficiency of 
 cash lies in a large cash reserve. Insolvency proper 
 may befall any business enterprise ; insufficiency of 
 cash relates especially to banks in their function of 
 redeeming notes and deposits. 
 
 Let us illustrate insufficiency of cash. In our bank's 
 accounts as we left them, there was a reserve of $140,000 
 of cash, and $200,000 of demand liabilities (deposits
 
 44 THE PURCHASING POWER OF MONEY [Chap. Ill 
 
 and notes). The managers of the bank may think 
 this reserve of $140,000 unnecessarily large or the loans 
 unnecessarily small. They may then extend their loans 
 (extended to customers in the form of cash, notes or 
 deposit accounts) until the cash reserve is reduced, 
 say to $40,000, and the liabihties due depositors and note 
 holders increased to $300,000. If, under these cir- 
 cumstances, some depositor or note holder demands 
 $50,000 cash, immediate payment will be impossible. 
 It is true that the assets still equal the liabilities. There 
 is full value behind the $50,000 demanded ; but the 
 understanding was that depositors and note holders 
 should be paid in money and on demand. Were this 
 not a stipulation of the deposit contract, the bank 
 might pay the claims thus made upon it by transfer- 
 ring to its creditors the promissory notes due it from 
 its debtors ; or it might ask the customers to wait until 
 it could turn these securities into cash.f. 
 
 Since a bank cannot follow either of these plans, it 
 tries, where insufficiency of cash impends, to forestall this 
 condition by "calling in" some of its loans, or if none 
 can be called in, by selling some of its securities or other 
 property for cash. But it happens unfortunately that 
 there is a limit to the amount of cash which a bank 
 can suddenly realize. No bank could escape failure if 
 a large percentage of its note holders and depositors 
 should simultaneously demand cash payment.- The 
 paradox of a panic is well expressed by the case of 
 the man who inquired of his bank whether it had cash 
 available for paying the amount of his deposit, saying, 
 "If you can pay me, I don't want it ; but if you can't, 
 
 ^ See Irving Fisher, The Nature of Capital and' Income, Chapter V. 
 2Cf. Ricardo, Works, 2d ed., London (Murray), 1852, p. 217 
 {Principles of Political Economy and Taxation, Chapter XXVII).
 
 Sec. 3] DEPOSIT CURRENCY 45 
 
 I do." Such was the situation in 1907 in Wall Street. 
 All the depositors at one time wanted to be sure their 
 money ' ' was there. ' ' Yet it never is there all at one time. 
 
 Since, then, insufficiency of cash is so troublesome 
 a condition, — so difficult to escape when it has arrived, 
 and so difficult to forestall when it begins to ap- 
 proach, — a bank must so regulate its loans and note 
 issues as to keep on hand a sufficient cash reserve, and 
 thus prevent insufficiency of cash from even threaten- 
 ing. It can regulate the reserve by alternately selling 
 securities for cash and loaning cash on securities. The 
 more the loans in proportion to the cash on hand, 
 the greater the profits, but the greater the danger also. 
 In the long run a bank maintains its necessary reserve 
 by means of adjusting the interest rate charged for 
 loans. If it has few loans and a reserve large enough to 
 support loans of much greater volume, it will endeavor 
 to extend its loans by lowering the rate of interest. 
 If its loans are large and it fears too great demands 
 on the reserve, it will restrict the loans by a high interest 
 charge. Thus, by alternately raising and lowering in- 
 terest, a bank keeps its loans within the sum which the 
 reserve can support, but endeavors to keep them (for 
 the sake of profit) as high as the reserve will support. 
 
 If the sums owed to individual depositors are large, 
 relatively to the total liabilities, the reserve should be 
 proportionately large, since the action of a small num- 
 ber of depositors can deplete it rapidly.^ Similarly, the 
 reserves should be larger against fluctuating deposits 
 (as of stock brokers) or those known to be temporary.^ 
 
 ' Victor Morawetz, The Banking and Currency Problem in the 
 United States, New York (The North American Review Publish- 
 ing Co.), 1909, pp. 36 and 37. Also Kem merer, Money and Prices, 
 1909, p. 80. 2 Ibid.
 
 46 THE PURCHASING POWER OF MONEY [Chap. Ill 
 
 The reserve in a large city of great bank activity needs 
 to be greater in proportion to its demand liabilities than 
 in a small town with infrequent banking transactions. 
 
 Experience dictates differently the average size of 
 deposit accounts for different banks according to the 
 general character and amount of their business. For 
 every bank there is a normal ratio, and hence for a 
 whole community there is also a normal ratio — an 
 average of the ratios for the different banks. No 
 absolute numerical rule can be given. Arbitrary rules 
 are often imposed by law. National banks in the 
 United States, for instance, are required to keep a re- 
 serve for their deposits, varying according as they are 
 or are not situated in certain cities designated by law 
 as ''reserve" cities, i.e. cities where national banks 
 hold deposits of banks elsewhere. These reserves are 
 all in defense of deposits. In defense of notes, on 
 the other hand, no cash reserve is required, — that is, 
 of national banks. True, the same economic princi- 
 ples apply to both bank notes and deposits, but the law 
 treats them differently. The government itself chooses 
 to undertake to redeem the national bank notes on 
 demand. 
 
 The state banks are subject to varying restrictions.^ 
 Thus the requirement as to the ratio of reserve to de- 
 posits varies from 12| per cent to 22^ per cent, being 
 usually between 15 per cent and 20 per cent. Of the 
 reserve, the part which must be cash varies from 10 per 
 cent (of the reserve) to 50 per cent, being usually 40 
 per cent. 
 
 Such legal regulation of banking reserves, however, 
 
 * "Digest of State Banking Statutes," in Reports of the National 
 Monetary Commission, 61st Congress, 2d Session Senate Document, 
 No. 353.
 
 Sec. 4] DEPOSIT CURRENCY 47 
 
 is not a necessary development of banking. In Can- 
 ada, the law makes the notes practically coordinate 
 with the deposits. Indeed, banking may exist with- 
 out government regulations at all. ''George Smith's 
 money " furnishes an illustration. George Smith, Alex- 
 ander Mitchell and others established in 1839 an 
 Insurance Company which, though forbidden to exer- 
 cise "banking privileges," issued certificates of deposit 
 payable to bearer, and these certificates were actually 
 circulated like bank notes. ^ 
 
 §4 
 
 The study of banking operations, then, discloses two 
 species of currency : one, bank notes, belonging to 
 the category of money; and the other, deposits, be- 
 longing outside of that category, but constituting an 
 excellent substitute. Referring these to the larger 
 category of goods, we have a threefold classification 
 of goods : first, money ; second, deposit currency, or 
 simply deposits ; and third, all other goods. And by 
 the use of these, there are six possible types of ex- 
 change : — 
 
 (1) Money against money, 
 
 (2) Deposits against deposits, 
 
 (3) Goods against goods, 
 
 (4) Money against deposits, 
 
 (5) Money against goods, 
 
 (6) Deposits against goods. 
 
 For our purpose, only the last two types of exchange 
 are important, for these constitute the circulation of 
 currency. As regards the other four, the first and third 
 have been previously explained as "money changing" 
 and "barter" respectively. The second and fourth 
 
 * See Horace White, Money and Banking
 
 48 THE PURCHASING POWER OF MONEY [Chap. Ill 
 
 are banking transactions : the second being such as 
 the selling of drafts for checks, or the mutual cancel- 
 lation of bank clearings; and the fourth being such 
 operations as the depositing or the withdrawing of 
 money, by depositing cash or cashing checks. 
 
 The analysis of the balance sheets of banks has pre- 
 pared us for the inclusion of bank deposits or circulating 
 credit in the equation of exchange. We shall still use 
 M to express the quantity of actual money, and V to 
 express the velocity of its circulation. Similarly, we 
 shall now use M' to express the total deposits subject 
 to transfer by check ; and 7' to express the average 
 velocity of circulation. The total value of purchases 
 in a year is therefore no longer to be measured by MV, 
 but by MV + M'V. The equation of exchange, there- 
 fore, becomes : — 
 
 MV + M'V = 2pQ = PT} 
 
 Let us again represent the equation of exchange by 
 means of a mechanical picture. In Figure 4, trade, 
 
 ^Tr^H.M.^„.,|,„,j,.,n_„in,..,j_.„,|,„,||i,.jiii,jii,ij.|.,j,M,j^ 
 
 Fig. 4. 
 
 as before, is represented on the right by the weight of 
 a miscellaneous assortment of goods ; and their average 
 price by the distance to the right from the fulcrum, or 
 
 1 The equation of exchange is also stated by Kemmerer, Money 
 and Credit Instruments in their Relation to General Prices, so as to 
 inelude bank credit, although in a somewhat different way. That 
 credit acts on prices in the same manner as money is by no means 
 a newly established principle. See, for example, MiU, Principles oj 
 Political Economy, Book III, Chapter XII, §§ 1, 2.
 
 Sec. 5] DEPOSIT CURRENCY 49 
 
 the length of the arm on which this weight hangs. 
 Again at the left, money (ikf ) is represented by a weight 
 in the form of a purse, and its velocity of circulation ( V) 
 by its arm ; but now we have a new weight at the left, 
 in the form of a bank book, to represent the bank de- 
 posits {M'). The velocity of circulation (V) of these 
 bank deposits is represented by its distance from the 
 fulcrum or the arm at which the book hangs. 
 
 This mechanism makes clear the fact that the average 
 price (right arm) increases with the increase of money or 
 bank deposits and with the velocities of their circulation, 
 and decreases with the increase in the volume of trade. 
 
 Recurring to the left side of the equation of exchange, 
 OT MV + M'V, we see that in a community without 
 bank deposits the left side of the equation reduces 
 simply to MV, the formula used in Chapter II ; for 
 in such a community the term " M'V " vanishes. The 
 introduction of M' tends to raise prices. That is, the 
 hanging of the bank book on the left requires a lengthen- 
 ing of the arm at the right. 
 
 Just as E was used to denote the total circulation 
 of money, MV, so we may now use E' to denote the 
 total circulation of deposits, M'V. 
 
 Like E, M, and V, so also E', M', and V are sums 
 and averages of corresponding magnitudes pertaining 
 to different parts of the year, or different persons.^ 
 
 §5 
 
 With the extension of the equation of monetary 
 circulation to include deposit cii'culation, the influence 
 
 1 The mathematical analysis of E', M', and V in terms of 
 "arrays" of e"s, m"s, and t;"s, etc., is precisely parallel to that of 
 E, M, and V, given in the Appendix to Chapter II. See also §§1 
 and 2 of Appendix to (this) Chapter III.
 
 50 THE PURCHASING POWER OF MONEY [Chap. IH 
 
 exerted by the quantity of money on general prices 
 becomes less direct ; and the process of tracing this 
 influence becomes more difficult and complicated. It 
 has even been argued that this interposition of circulating 
 credit breaks whatever connection there may be be- 
 tween prices and the quantity of money. ^ This would 
 be true if circulating credit were independent of money. 
 But the fact is that the quantity of circulating credit, M' , 
 tends to hold a definite relation to M, the quantity of 
 money in circulation; that is, deposits are normally 
 a more or less definite multiple of money. 
 
 Two facts normally give deposits a more or less 
 definite ratio to money. The first has been already 
 explained, viz. that bank reserves are kept in a more 
 or less definite ratio to bank deposits. The second 
 is that individuals, firms, and corporations preserve 
 more or less definite ratios between their cash trans- 
 actions and their check transactions, and also between 
 their money and deposit balances.^ These ratios are 
 determined by motives of individual convenience and 
 habit. In general, business firms use money for wage 
 payments, and for small miscellaneous transactions 
 included under the term ''petty cash"; while for 
 settlements with each other they usually prefer 
 checks. These preferences are so strong that we 
 could not imagine them overridden except tempora- 
 
 1 An almost opposite view is that of Laughlin that normal credit 
 cannot affect prices because it is not an offer of standard money and 
 cannot affect the value of the standard which alone determines general 
 prices. See the Principles of Money, New York (Seribner), 1903, p. 97. 
 Both views are inconsistent with that upheld in this book. 
 
 2 This fact is apparently overlooked by Laughlin when he argues 
 that there is not "any reason for limiting the amount of the deposit 
 currency, or the assumption of an absolute scarcity of specie re- 
 serves." See Principles of Money, p. 127.
 
 Sec. 5] DEPOSIT CURRENCY 51 
 
 rily and to a small degree. A business firm would 
 hardly pay car fares with checks and liquidate its 
 large liabilities with cash. Each person strikes an 
 equilibrium between his use of the two methods of 
 payment, and does not greatly disturb it except for 
 short periods of time. He keeps his stock of money 
 or his bank balance in constant adjustment to the 
 payments he makes in money or by check. Whenever 
 his stock of money becomes relatively small and his 
 bank balance relatively large, he cashes a check. In 
 the opposite event, he deposits cash. In this way 
 he is constantly converting one of the two media of 
 exchange into the other. A private individual usually 
 feeds his purse from his bank account ; a retail com- 
 mercial firm usually feeds its bank account from its 
 till. The bank acts as intermediary for both. 
 
 In a given community the quantitative relation of 
 deposit currency^ to money is determined by several 
 considerations of convenience. In the first place, the 
 more highly developed the business of a community, 
 the more prevalent the use of checks. Where business 
 is conducted on a large scale, merchants habitually 
 transact their larger operations with each other by 
 means of checks, and their smaller ones by means of 
 cash. Again, the more concentrated the population, 
 the more prevalent the use of checks. In cities it is 
 more convenient both for the payer and the payee to 
 make large payments by check ; whereas, in the coun- 
 try, trips to a bank are too expensive in time and effort 
 to be convenient, and therefore more money is used 
 in proportion to the amount of business done.^ Again, 
 
 1 The convenient expression "deposit currency" is used by 
 Laughlin, The Principles of Money, p. 118. 
 
 * See Kinley's "Credit Instruments," Report of the National
 
 52 THE PURCHASING POWER OF MONEY [Chap. Ill 
 
 the wealthier the members of the community, the more 
 largely will they use checks. Laborers seldom use 
 them; but capitalists, professional and salaried men 
 use them habitually, for personal as well as business 
 transactions. 
 
 There is, then, a relation of convenience and custom 
 between check and cash circulation, and a more or less 
 stable ratio between the deposit balance of the average 
 man or corporation and the stock of money kept in 
 pocket or till. This fact, as applied to the country 
 as a whole, means that by convenience a rough ratio 
 is fixed between M and M'. If that ratio is disturbed 
 temporarily, there will come into play a tendency to 
 restore it. Individuals will deposit surplus cash, or 
 they will cash surplus deposits. 
 
 Hence, both money in circulation (as shown 
 above) and money in reserve (as shown previously) 
 tend to keep in a fixed ratio to deposits. It follows 
 that the two must be in a fixed ratio to each 
 other. 
 
 It further follows that any change in M, the quantity 
 of money in circulation, requiring as it normally does 
 a proportional change in M', the volume of bank de- 
 posits subject to check, will result in an exactly pro- 
 portional change in the general level of prices except, 
 of course, so far as this effect be interfered with by 
 concomitant changes in the F's or the Q's. The 
 truth of this proposition is evident from the equation 
 MV + M'V =^pQ; for if, say, M and M' are 
 doubled, while V and F' remain the same, the left 
 side of the equation is doubled and therefore the right 
 side must be doubled also. But if the Q's remain 
 
 Monetary Commission, Senate Document, 399, 61st Congress, 2d 
 Session, 1910, p. 188.
 
 Sec. 6] DEPOSIT CURRENCY 53 
 
 unchanged, then evidently all the p's must be doubled, 
 or else if some are less than doubled, others must be 
 enough more than doubled to compensate. 
 
 §6 
 
 The contents of this chapter may be formulated in 
 a few simple propositions : — 
 
 (1) Banks supply two kinds of currency, viz. bank 
 notes — which are money ; and bank deposits (or 
 rights to draw) — which are not money. 
 
 (2) A bank check is merely a certificate of a right 
 to draw. 
 
 (3) Behind the claims of depositors and note holders 
 stand, not simply the cash reserve, but all the assets of 
 the bank. 
 
 (4) Deposit banking is a device by which wealth, 
 incapable of direct circulation, may be made the basis 
 of the circulation of rights to draw. 
 
 (5) The basis of such circulating rights to draw or 
 deposits must consist in part of actual money, and it 
 should consist in part also of quick assets readily ex- 
 changeable for money. 
 
 (6) Six sorts of exchange exist among the three classes 
 of goods, money, deposits, and other goods. Of these 
 six sorts of exchange, the most important for our pres- 
 ent purposes are the exchanges of money and deposits 
 against goods. 
 
 (7) The equation of money circulation extended so 
 as to include bank deposits reads thus : — 
 
 MV + M'V = ^pQ or PT. 
 
 (8) There tends to be a normal ratio of bank deposits 
 (ilf' ) to the quantity of money {M) ; because business 
 
 C^
 
 54 THE PURCHASING POWER OF MONEY [Chap. Ill 
 
 convenience dictates that the available currency shall 
 be apportioned between deposits and money in a cer- 
 tain more or less definite, even though elastic, ratio. 
 
 (9) The inclusion of deposit currency does not nor- 
 mally disturb the quantitative relation between money 
 and prices.
 
 CHAPTER IV 
 
 DISTURBANCE OF EQUATION AND OF PURCHASING POWER 
 DURING TRANSITION PERIODS 
 
 In the last chapter it was shown that the quantity 
 of bank deposits normally maintains a definite ratio 
 to the quantity of money in circulation and to the 
 amount of bank reserves. As long as this normal 
 relation holds, the existence of bank deposits merely 
 magnifies the effect on the level of prices produced by 
 the quantity of money in circulation and does not in 
 the least distort that effect. Moreover, changes in 
 velocity or trade will have the same effect on prices, 
 whether bank deposits are included or not. 
 
 But during periods of transition this relation between 
 money (M) and deposits (M') is by no means rigid. 
 
 We are now ready to study these periods of transition. 
 The change which constitutes a transition may be 
 a change in the quantity of money, or in any other factor 
 of the equation of exchange, or in all. Usually all are 
 involved, but the chief factor which we shall select for 
 study (together with its effect on the other factors) 
 is quantity of money. If the quantity of money 
 were suddenly doubled, the effect of the change would 
 not be the same at first as later. The ultimate effect 
 is, as we have seen, to double prices ; but before this 
 happens, the prices oscillate up and down. In this 
 chapter we shall consider the temporary effects during 
 
 55
 
 56 THE PURCHASING POWER OF MONEY [Chap. IV 
 
 the period of transition separately from the permanent 
 or ultimate effects which were considered in the last 
 chapter. These permanent or ultimate effects follow 
 after a new equilibrium is established, — if, indeed, 
 such a condition as equilibrium may be said ever to 
 be established. What we are concerned with in this 
 chapter is the temporary effects, i.e. those in the tran- 
 sition period. 
 
 The transition periods may be characterized either by 
 rising prices or by falling prices. Rising prices must 
 be clearly distinguished from high prices, Suiid falling from 
 low. With stationary levels, high or low, we have in 
 this chapter nothing to do. Our concern is with ris- 
 ing or falling prices. Rising prices mark the transition 
 between a low and a high level of prices, just as a hill 
 marks the transition between flat lowlands and flat 
 highlands. 
 
 Since the study of these acclivities and declivities 
 is bound up with that of the adjustment of interest 
 rates, our first task is to present a brief statement 
 regarding the effects of rising and falling prices^ on 
 the rate of interest. Indeed, the chief object of this 
 chapter is to show that the peculiar behavior of the 
 rate of interest during transition periods is largely 
 responsible for the crises and depressions in which price 
 movements end. 
 
 It must be borne in mind that although business loans 
 are made in the form of money, yet whenever a man 
 borrows money, he does not do this in order to hoard 
 the money, but to purchase goods with it. To all 
 intents and purposes, therefore, when A borrows one 
 hundred dollars from B in order to purchase, say, one 
 
 ' For a fuller statement, see Irving Fisher, The Rate of Interest, 
 New York (Macmillan), 1907, Chapters V, XIV.
 
 Sec. 1] TRANSITION PERIODS 57 
 
 hundred units of a given commodity at one dollar per 
 unit, it may be said that B is virtually lending A one 
 hundred units of that commodity. And if at the end 
 of a year A returns one hundred dollars to B, but the 
 price of the commodity has meanwhile advanced, then B 
 has lost a fraction of the purchasing power originally 
 loaned to A. For even though A should happen to 
 return to B the identical coins in which the loan was 
 made, these coins represent somewhat less than the 
 original quantity of purchasable commodities. Bear- 
 ing this in mind in our investigation of interest rates, 
 let us suppose that prices are rising at the rate of 3 per 
 cent each year. It is plain that the man who lends $100 
 at the beginning of the year must, in order to get 5 per 
 cent interest in purchasing power, receive back both 
 $103 (then the equivalent of the $100 lent) plus 5 per 
 cent of this, or a total of $108.15. That is, in order to 
 get 5 per cent interest in actual purchasing power, he 
 must receive a little more than 8 per cent interest in 
 money. The 3 per cent rise of prices thus ought to add 
 approximately 3 per cent to the rate of interest. Rising 
 prices, therefore, in order that the relations between 
 creditor and debtor shall be the same during the rise 
 as before and after, require higher money interest than 
 stationary prices require. 
 
 Not only will lenders require, but borrowers can afford 
 to pay higher interest in terms of money ; and to some 
 extent competition will gradually force them to do so.' 
 Yet we are so accustomed in our business dealings to 
 consider money as the one thing stable, — to think of 
 a "dollar as a dollar" regardless of the passage of time, 
 that we reluctantly yield to this process of readjustment, 
 thus rendering it very slow and imperfect. When prices 
 
 ^ Rate o/ Interest, Chapter XIV.
 
 58 THE PURCHASING POWER OF MONEY [Chap. IV 
 
 are rising at the rate of 3 per cent a year, and the nor- 
 mal rate of interest — i.e. the rate which would exist were 
 prices stationary — is 5 per cent, the actual rate, though 
 it ought (in order to make up for the rising prices) to 
 be 8.15 per cent, will not ordinarily reach that figure; 
 but it may reach, say, 6 per cent, and later, 7 per cent. 
 This inadequacy and tardiness of adjustment are fostered, 
 moreover, by law and custom, which arbitrarily tend to 
 keep down the rate of interest. 
 
 A similar inadequacy of adjustment is observed when 
 prices are falling. Suppose that, by the end of a year, 
 $97 will buy as much as $100 at the beginning. In that 
 case the lender, in order to get back a purchasing power 
 equivalent to his principal and 5 per cent interest, 
 should get, not $105, but only $97 + 5 per cent of $97 
 or $101.85. Thus the rate of interest in money should 
 in this case be 1.85 per cent, or less than 2 per cent, 
 instead of the original 5 per cent. In other words, the 
 3 per cent fall of prices should reduce the rate of interest 
 by approximately 3 per cent. But as a matter of fact, 
 such a perfect adjustment is seldom reached, and money 
 interest keeps far above 2 per cent for a considerable 
 time.^ 
 
 §2 
 
 We are now ready to study temporary or transitional 
 changes in the factors of our equation of exchange. Let 
 us begin by assuming a slight initial disturbance, such 
 as would be produced, for instance, by an increase in the 
 quantity of gold. This, through the equation of ex- 
 change, will cause a rise in prices. As prices rise, 
 profits of business men, measured in money, will rise 
 also, even if the costs of business were to rise in the same 
 
 * Rate of Interest, loc. cit.
 
 Sec. 2] TRANSITION PERIODS 59 
 
 proportion. Thus, if a man who sold $10,000 of goods 
 at a cost of $6000, thus clearing $4000, could get double 
 prices at double cost, his profit would be double also, 
 being $20,000 - $12,000, which is $8000. Of course 
 such a rise of prices would be purely nominal, as it 
 would merely keep pace with the rise in price level. 
 The business man would gain no advantage, for his 
 larger money profits would buy no more than his former 
 smaller money profits bought before. But, as a matter 
 of fact, the business man's profits will rise more than this 
 because the rate of interest he has to pay will not ad- 
 just itself immediately. Among his costs is interest, 
 and this cost will not, at first, rise. Thus the profits will 
 rise faster than prices. Consequently, he will find him- 
 self making greater profits than usual, and be en- 
 couraged to expand his business by increasing his bor- 
 rowings. These borrowings are mostly in the form of 
 short-time loans from banks; and, as we have seen, 
 short-time loans engender deposits. As is well known, 
 the correspondence between loans and deposits is re- 
 markably exact. ^ Therefore, deposit currency (M') will 
 increase, but this extension of deposit currency tends 
 further to raise the general level of prices, just as the in- 
 crease of gold raised it in the first place.^ Hence prices, 
 which were already outstripping the rate of interest, 
 tend to outstrip it still further, enabling borrowers, 
 
 ^ See J. Pease Norton, Statistical Studies in the New York Money 
 Market (Macmillan), 1902, chart at end. 
 
 * See article by Knut Wicksell in the Jahrbucher fur National- 
 ohoiomie, 1897 (Band 68), pp. 228-243, entitled "Der Bankzins als 
 Rej^ulator der Warenpreise." This article, while not dealing di- 
 rectly with credit cycles as related to panics, points out the con- 
 nection between the rate of interest on bank loans and changes 
 ii Ithe level of prices due to the resulting expansion and contraction 
 of^uch loans.
 
 60 THE PURCHASING POWER OF MONEY [Chap. IV 
 
 who were already increasing their profits, to increase 
 them still further. More loans are demanded, and 
 although nominal interest may be forced up some- 
 what, still it keeps lagging below the normal level. 
 Yet nominally the rate of interest has increased; 
 and hence the lenders, too, including banks, are led to 
 become more enterprising. Beguiled by the higher 
 nominal rates into the belief that fairly high interest 
 is being realized, they extend their loans, and with the 
 resulting expansion of bank loans, deposit currency 
 (M'), already expanded, expands still more. Also, if 
 prices are rising, the money value of collateral may be 
 greater, making it easier for borrowers to get large 
 credit.^ Hence prices rise still further.^ This sequence 
 of events may be briefly stated as follows : — 
 
 1. Prices rise (whatever the first cause may be; but 
 we have chosen for illustration an increase in the amount 
 of gold). 
 
 2. The rate of interest rises, but not sufficiently. 
 
 3. Enterprisers (to use Professor Fetter's term), en- 
 couraged by large profits, expand their loans. 
 
 4. Deposit currency (M') expands relatively to 
 money (M). 
 
 5. Prices continue to rise, that is, phenomenoin No. 1 
 is repeated. Then No. 2 is repeated, and so on. 
 
 In other words, a slight initial rise of prices sets in 
 motion a train of events which tends to repeat itself. 
 Rise of prices generates rise of prices, and continues 
 to do so as long as the interest rate lags behind its normal 
 figure. 
 
 1 See Kinley, Money, New York (Maomillan), 1904, p. 223. 
 * See Wicksell, op. cit. 
 
 I 
 'i
 
 Sec. 3J TRANSITION PERIODS 61 
 
 §3 
 
 The expansion of deposit currency indicated in this 
 cumulative movement abnormally increases the ratio of 
 M' to M. This is evident if the rise of prices begins in 
 a change in some element or elements in the equation 
 other than the quantity of money ; for if M remains 
 constant and M' increases, the ratio M' to M must in- 
 crease also. If M increases in any ratio, M' will increase 
 in a greater ratio. If it increased only in the same ratio, 
 prices would increase in that ratio (assuming velocities 
 and quantities unchanged); and if prices increased in 
 that ratio, loans (which being made to buy goods must 
 be adjusted to the prices of goods) would have to be 
 increased in that ratio in order to secure merely the 
 same goods as before. But enterprisers, wishing to 
 profit by the lag in interest, would extend the loans 
 beyond this old or original point. Therefore, deposits 
 based on loans would increase in a greater ratio. That 
 is, the ratio M' to M would increase. In other words, 
 during the period while M is increasing, M' increases 
 still faster, thus disturbing the normal ratio between 
 these two forms of currency. 
 
 This, however, is not the only disturbance caused by 
 the increase in M. There are disturbances in the Q's (or 
 in other words T) in V, and in V. These will be taken 
 up in order. Trade (the Q's) will be stimulated by the 
 easy terms for loans. This effect is always observed 
 during rising prices, and people note approvingl}^ that 
 ''business is good" and "times are booming." Such 
 statements represent the point of view of the ordinary 
 business man who is an "enterpriser-borrower." They 
 do not represent the sentiments of the creditor, the 
 salaried man, or the laborer, most of whom are silent but
 
 62 THE PURCHASING POWER OF MONEY [Chap. IV 
 
 long-suffering, — paying higher prices, but not getting 
 proportionally higher incomes. 
 
 , The first cause of the unhealthy increase in trade lies 
 / K in the fact that prices, like interest, lag behind their 
 
 ' full adjustment and have to be pushed up, so to speak, 
 by increased purchases. This is especially true in cases 
 where the original impetus came from an increase in 
 money. The surplus money is first expended at nearly 
 the old price level, but its continued expenditure grad- 
 ually raises prices. In the meantime the volume of 
 purchases will be somewhat greater than it would have 
 been had prices risen more promptly. In fact, from the 
 point of view of those who are selling goods, it is the 
 possibility of a greater volume of sales at the old prices 
 which gives encouragement to an increase of prices. 
 Seeing that they can find purchasers for more goods 
 than before at the previously prevailing prices, or for as 
 many goods as before at higher prices, they will charge 
 these higher prices. 
 
 But the amount of trade is dependent, almost en- 
 tirely, on other things than the quantity of currency, 
 so that an increase of currency cannot, even temporarily, 
 very greatly increase trade. In ordinarily good times 
 practically the whole community is engaged in labor, pro- 
 ducing, transporting, and exchanging goods. The in- 
 crease of currency of a "boom" period cannot, of itself, 
 increase the population, extend invention, or increase 
 the efficiency of labor. These factors pretty definitely 
 limit the amount of trade which can be reasonably 
 carried on. So, although the gains of the enterpriser- 
 borrower may exert a psychological stimulus on trade, 
 though a few unemployed may be employed, and some 
 others in a few lines induced to work overtime, and al- 
 though there may be some additional buying and selling
 
 Sec. 3] TEANSITION PERIODS 63 
 
 which is speculative, yet almost the entire effect of an 
 increase of deposits must be seen in a change of 
 prices. Normally the entire effect would so express 
 itself, but transitionally there will be also some increase 
 in the Q's. 
 
 We next observe that the rise in prices — fall in 
 the purchasing power of money — will accelerate the y^ 
 circulation of money. We all hasten to get rid of any 
 commodity which, like ripe fruit, is spoiling on our 
 hands. ^ Money is no exception; when it is depreciat- 
 ing, holders will get rid of it as fast as possible. As 
 they view it, their motive is to buy goods which appre- 
 ciate in terms of money in order to profit by the rise in 
 their value. The inevitable result is that these goods «x 
 rise in price still further. The series of changes, then, 
 initiated by rising prices, expressed more fully than 
 before, is as follows : — "^ 
 
 1. Prices rise. 
 
 2. Velocities of circulation (F and V) increase; 
 the rate of interest rises, but not sufficiently. 
 
 3. Profits increase, loans expand, and the Q's in- 
 crease. 
 
 4. Deposit currency {M') expands relatively to 
 money (M). 
 
 5. Prices continue to rise; that is, phenomenon 
 No. 1 is repeated. Then No. 2 is repeated, and so on. ^ 
 
 It will be noticed that these changes now involve all 
 
 * For statistical proof, see Pierre des Essars, Journal de la SociitS 
 de Statistique de Paris, April, 1895, p. 143. The figures relate only 
 to velocity of bank deposits. No corresponding figures for velocity 
 of circulation of money exist. Pierre des Essars has shown that 
 in European banks V reaches a maximum in crisis years almost 
 without fail. The same I find true in this country as shown by 
 the ratio of clearings to deposits in New York, Boston, and Phila- 
 delphia.
 
 64 THE PURCHASING POWER OF MONEY [Chap. IV 
 
 the magnitudes in the equation of exchange. They are 
 temporary changes, pertaining only to the transition 
 period. They are Hke temporary increases in power and 
 readjustments in an automobile climbing a hill. 
 
 § 4 
 Evidently the expansion coming from this cycle of 
 / causes cannot proceed forever. It must ultimately 
 spend itself. The check upon its continued operation 
 lies in the rate of interest. It was the tardiness of the 
 rise in interest that was responsible for the abnormal 
 condition. But the rise in interest, though belated, is 
 progressive, and, as soon as it overtakes the rate of 
 rise in prices, the whole situation is changed. If prices 
 are rising at the rate of 2 per cent per annum, the boom 
 will continue only until interest becomes 2 per cent 
 higher. It then offsets the rate of rise in prices. The 
 banks are forced in self-defense to raise interest be- 
 cause they cannot stand so abnormal an expansion 
 of loans relatively to reserves. As soon as the interest 
 rate becomes adjusted, borrowers can no longer hope 
 to make great profits, and the demand for loans ceases 
 to expand. 
 
 There are also other forces placing a limitation on 
 i\ further expansion of deposit currency and introducing 
 a tendency to contraction. Not only is the amount 
 of deposit currency limited both by law and by prudence 
 to a certain maximum multiple of the amount of bank 
 reserves ; but bank reserves are themselves limited by 
 the amount of money available for use as reserves. 
 Further, with the rise of interest, the value of certain 
 collateral securities, such as bonds, on the basis of 
 which loans are made, begins to fall. Such securities, 
 being worth the discounted value ofj fixed sums, fall
 
 Sec. 4] TRANSITION PERIODS 65 
 
 as interest rises ; and therefore they cannot be used as 
 collateral for loans as large as before. This check to 
 loans is, as previously explained, a check to deposits 
 also. 
 
 With the rise of interest, those who have counted 
 on renewing their loans at the former rates and for the 
 former amounts are unable to do so. It follows that 
 some of them are destined to fail. The failure (or 
 prospect of failure) of firms that have borrowed heavily 
 from banks induces fear on the part of many depositors 
 that the banks will not be able to realize on these loans. 
 Hence the banks themselves fall under suspicion, and for 
 this reason depositors demand cash. Then occur ''runs 
 on the banks," which deplete the bank reserves at the 
 very moment they are most needed.^ Being short of 
 reserves, the banks have to curtail their loans. It is 
 then that the rate of interest rises to a panic figure. 
 Those enterprisers who are caught must have currency ^ 
 to liquidate their obligations, and to get it are willing 
 to pay high interest. Some of them are destined to 
 become bankrupt, and, with their failure, the demand 
 for loans is correspondingly reduced. This culmination 
 of an upward price movement is what is called a crisis,^ — ' 
 a condition characterized by bankruptcies, and the bank- 
 
 * A part of the theory of crises here presented is similarly ex- 
 plained in a paper by Harry G. Brown, Yale Review, August, 1910, 
 entitled "Typical Commeroial Crises versus a Money Panic." 
 
 2 Irving Fisher, Rate of Interest, pp. 325, 326. 
 
 ^ This is the definition of a crisis given by Juglar and the his- 
 tory of crises which he gives in detail corresponds to the descrip- 
 tion. See Juglar, Des Crises Commerciales et de leur retour 
 periodique en France en Angleterre et aux Etats-Unis. 2d ed., 
 Paris (Guillaumin), 1889, pp. 4 and 5. See also translation of part 
 dealing with the United States, by De Courcey W. Thom, A Brie} 
 History of Panics in the United States, New York (Putnam), 1893, 
 pp. 7-10. 
 
 ¥
 
 66 THE PURCHASING POWER OF MONEY [Chap. IV 
 
 ruptcies being due to a lack of cash when it is most 
 needed. 
 
 It is generally recognized that the collapse of bank 
 credit brought about by loss of confidence is the essential 
 fact of every crisis, be the cause of the loss of confidence 
 what it may. What is not generally recognized, and 
 what it is desired in this chapter to emphasize, is that 
 this loss of confidence (in the typical commercial crisis 
 here described) is a consequence of a belated adjustment 
 in the interest rate. 
 
 It is not our purpose here to discuss nonmonetary 
 causes of crises, further than to say that the monetary 
 / causes are the most important when taken in connection 
 with the maladjustments in the rate of interest. The 
 other factors often emphasized are merely effects of 
 this maladjustment. " Overconsumption " and ''over- 
 investment ' ' are cases in point . The reason many people 
 spend more than they can afford is that they are relying 
 on the dollar as a stable unit when as a matter of fact 
 its purchasing power is rapidly falling. The bond- 
 holder, for instance, is beguiled into trenching on his 
 capital. He never dreams that he ought to lay by a 
 sinking fund because the decrease in purchasing power 
 of money is reducing the real value of his principal. 
 Again, the stockholder and enterpriser generally are 
 beguiled by a vain reliance on the stability of the rate 
 of interest, and so they overinvest. It is true that for 
 a time they are gaining what the bondholder is losing 
 and are therefore justified in both spending and in- 
 vesting more than if prices were not rising ; and at 
 first they prosper. But sooner or later the rate of 
 interest rises above what they had reckoned on, and they 
 awake to the fact that they have embarked on enterprises 
 which cannot pay these high rates.
 
 3ec. 5] TRANSITION PERIODS 67 
 
 Then a curious thing happens : borrowers, unable 
 to get easy loans, blame the high rate of interest for 
 conditions which were really due to the fact that the 
 previous rate of interest was not high enough. Had 
 the previous rate been high enough, the borrowers 
 never would have overinvested. 
 
 §5 
 
 The contraction of loans and deposits is accompanied 
 by a decrease in velocities, and these conspire to pre- 
 vent a further rise of prices and tend toward a fall. 
 The crest of the wave is reached and a reaction sets in. 
 Since prices have stopped rising, the rate of interest, 
 which has risen to compensate the rise of prices, should 
 fall again. But just as at first it was slow to rise, so 
 now it is slow to fall. In fact, it tends for a time to 
 rise still further. 
 
 The mistakes of the past of overborrowing compel 
 the unfortunate victims of these mistakes to borrow 
 still further to protect their solvency. It is this special 
 abnormality which marks the period as a ''crisis." 
 Loans are wanted to continue old debts or to pay these 
 debts by creating new ones. They are not wanted 
 because of new investments but because of obligations 
 connected with old (and ill-fated) investments. The 
 problem is how to get extricated from the meshes of 
 past commitments. It is the problem of liquidation. 
 Even when interest begins to fall, it falls slowly, and 
 failures continue to occur. Borrowers now find that 
 interest, though nominally low, is still hard to meet. 
 Especially do they find this true in the case of contracts 
 made just before prices ceased rising or just before they 
 began to fall. The rate of interest in these cases is 
 agreed upon before the change in conditions takes place.
 
 68 THE PURCHASING POWER OF MONEY [Chap. IV 
 
 There will, in consequence, be little if any adjustment 
 in lowering nominal interest. Because interest is hard 
 to pay, failures continue to occur. There comes to be 
 a greater hesitation in lending on any but the best 
 security, and a hesitation to borrow save when the 
 prospects of success are the greatest. Bank loans tend 
 to be low, and consequently deposits {M') are reduced. 
 The contraction of deposit currency makes prices fall 
 still more. Those who have borrowed for the purpose 
 of buying stocks of goods now find they cannot sell 
 them for enough even to pay back what they have 
 borrowed. Owing to this tardiness of the interest rate 
 in falling to a lower and a normal level, the sequence 
 of events is now the opposite of what it was before : — 
 
 1. Prices fall. 
 
 2. The rate of interest falls, but not sufficiently. 
 
 3 . Enterpriser-borrowers, discouraged by small profits, 
 contract their borrowings. 
 
 4. Deposit currency {M') contracts relatively to 
 money (M). 
 
 5. Prices continue to fall; that is, phenomenon 
 No. 1 is repeated. Then No. 2 is repeated, and so on. 
 
 Thus a fall of prices generates a further fall of prices. 
 The cycle evidently repeats itself as long as the rate 
 of interest lags behind. The man who loses most is 
 the business man in debt. He is the typical business 
 man, and he now complains that ''business is bad." 
 There is a "depression of trade." 
 
 During this depression, velocities (V and V) are 
 abnormally low. People are less hasty to spend money 
 or checks when the dollars they represent are rising 
 in purchasing power. The Q's (or quantities in trade) 
 decline because (1) the initiators of trade — the enter- 
 priser-borrowers — are discouraged ; (2) the inertia of
 
 Sec. 5] TRANSITION PERIODS 69 
 
 high prices can be overcome only by a falling off of 
 expenditures ; (3) trade against money which alone the 
 Q's represent gives way somewhat to barter. For a 
 time there is not enough money to do the business 
 which has to be done at existing prices, for these prices 
 are still high and will not immediately adjust them- 
 selves to the sudden contraction. When such a ' ' money 
 famine" exists, there is no way of doing all the business 
 except by eking out money transactions with barter. 
 But while recourse to barter eases the first fall of prices, 
 the inconvenience of barter immediately begins to 
 operate as an additional force tending to reduce prices 
 by inducing sellers to sell at a sacrifice if only money 
 can be secured and barter avoided ; although this ef- 
 fect is partly neutralized for a time by a decrease in 
 the amount of business which people will attempt 
 under such adverse conditions. A statement includ- 
 ing these factors is : — 
 
 1. Prices fall. 
 
 2. Velocities of circulation (F and V) fall; the rate 
 of interest falls, but not sufficiently. 
 
 3. Profits decrease; loans and the Q's decrease. 
 
 4. Deposit currency (M') contracts relatively to 
 money (M). 
 
 Prices continue to fall ; that is, phenomenon No. 1 
 is repeated. Then No. 2 is repeated, and so on. 
 
 The contraction brought about by this cycle of causes 
 becomes self-Hmiting as soon as the rate of interest 
 overtakes the rate of fall in prices. After a time, 
 normal conditions begin to return. The weakest 
 producers have been forced out, or have at least been 
 prevented from expanding their business by increased 
 loans. The strongest firms are left to build up a new 
 credit structure. The continuous fall of prices has
 
 70 THE PURCHASING POWER OP .VIONEY [Chap. IV 
 
 made it impossible for most borrowers to pay the old 
 high rates of interest ; the demand for loans diminishes, 
 and interest falls to a point such that borrowers can 
 at last pay it. Borrowers again become willing to take 
 ventures ; failures decrease in number ; bank loans 
 cease to decrease; prices cease to fall; borrowing 
 and carrying on business become profitable ; loans are 
 again demanded ; prices again begin to rise, and there 
 occurs a repetition of the upward movement already 
 described. 
 
 We have considered the rise, culmination, fall, and 
 recovery of prices. These changes are abnormal 
 oscillations, due to some initial disturbance. The up- 
 ward and downward movements taken together con- 
 stitute a complete credit cycle, which resembles the 
 forward and backward movements of a pendulum.^ 
 In most cases the time occupied by the swing of the 
 commercial pendulum to and fro is about ten years. 
 While the pendulum is continually seeking a stable 
 position, practically there is almost always some oc- 
 currence to prevent perfect equilibrium. Oscillations 
 are set up which, though tending to be self-corrective, 
 are continually perpetuated by fresh disturbances. 
 \ Any cause which disturbs equilibrium will suffice to 
 I set up oscillations. One of the most common of such 
 causes is an increase in the quantity of money. ^ An- 
 other is a shock to business confidence (affecting enter- 
 prise, loans, and deposits). A third is short crops, 
 affecting the Q's. A fourth is invention. 
 
 The factors in the equation of exchange are there- 
 
 ' For a mathematical treatment of this analogy, see Pareto, 
 Cours d'Sconomie politique, Lausanne, 1897, pp. 282-284. 
 
 * Such would seem to be the explanation of the panic of 1907. 
 Cf. Irving Fisher, Rate of Interest, p. 336.
 
 Sec. 5] TRANSITION PERIODS 71 
 
 fore continually seeking normal adjustment. A ship 
 in a calm sea will ''pitch" only a few times before 
 coming to rest, but in a high sea the pitching never 
 ceases. While continually seeking equiUbrium, the 
 ship continually encounters causes which accentuate 
 the oscillation. The factors seeking mutual adjustment 
 are money in circulation, deposits, their velocities, the 
 Q's and the p's. These magnitudes must always be 
 linked together by the equation MV + M'V = 2pQ. 
 This represents the mechanism of exchange. But in 
 order to conform to such a relation the displacement 
 of any one part of the mechanism spreads its effects 
 during the transition period over all parts. Since 
 periods of transition are the rule and those of equi- 
 librium the exception, the mechanism of exchange is 
 almost always in a dynamic rather than a static con- 
 dition. 
 
 It must not be assumed that every credit cycle is so 
 marked as to produce artificially excessive business ac- 
 tivity at one time and "hard times" at another. The 
 rhythm may be more or less extreme in the width of its 
 fluctuations. If banks are conservative in making loans 
 during the periods of rising prices, and the expansion of 
 credit currency is therefore limited, the rise of prices is 
 likewise limited, and the succeeding fall is apt to be less 
 and to take place more gradually. If there were a bet- 
 ter appreciation of the meaning of changes in the price 
 level and an endeavor to balance these changes by ad- 
 justment in the rate of interest, the oscillations might 
 be very greatly mitigated. It is the lagging behind 
 of the rate of interest which allows the oscillations to 
 reach so great proportions. On this point Marshall 
 well says : " The cause of alternating periods of in- 
 flation and depression of commercial activity ... is
 
 72 THE PURCHASING POWER OF MONEY [Chap. IV 
 
 intimately connected with those variations in the real 
 rate of interest which are caused by changes in the 
 purchasing power of money. For when prices are 
 likely to rise, people rush to borrow money and buy 
 goods, and thus help prices to rise ; business is inflated, 
 and is managed recklessly and wastefully ; those working 
 on borrowed capital pay back less real value than they 
 borrowed, and enrich themselves at the expense of 
 the community. When afterwards credit is shaken 
 and prices begin to fall, every one wants to get rid of 
 commodities which are falling in value and to get hold 
 of money which is rapidly rising; this makes prices 
 fall all the faster, and the further fall makes credit 
 shrink even more, and thus for a long time prices fall 
 because prices have fallen." ^ 
 
 A somewhat different sort of cycle is the seasonal 
 fluctuation which occurs annually. Such fluctuations, 
 for the most part, are due, not to the departure from a 
 state of equilibrium, but rather to a continuous adjust- 
 ment to conditions, which, though changing, are normal 
 and expected. As the autumn periods of harvesting and 
 crop moving approach, there is a tendency toward a 
 lower level of prices, followed after the passing of this 
 period and the approach of winter by a rise of prices. 
 
 § 6 
 
 In the present chapter we have analyzed the phe- 
 nomena characteristic of periods of transition. We 
 have found that one such "boom" period leads to a 
 reaction, and that the action and reaction complete a 
 cycle of "prosperity" and "depression." 
 
 It has been seen that rising prices tend towards a 
 
 ^ Marshall, Principles of Economics, Sth ed., London (Macmillan), 
 1907, Vol. I, p. 594.
 
 Sec. 6] TRANSITION PERIODS 73 
 
 higher nominal interest, and f alUng prices tend towards a 
 lower, but that in general the adjustment is incomplete. 
 With any initial rise of prices comes an expansion of loans, 
 owing to the fact that interest does not at once adjust 
 itself. This produces profits for the enterpriser-bor- 
 rower, and his demand for loans further extends de- 
 posit currency. This extension still further raises 
 prices, a result accentuated by a rise in velocities though 
 somewhat mitigated by an increase in trade. When 
 interest has become adjusted to rising prices, and loans 
 and deposits have reached the limit set for them by the 
 bank reserves and other conditions, the fact that prices 
 no longer are rising necessitates a new adjustment. 
 Those whose business has been unduly extended now 
 find the high rates of interest oppressive. Failures 
 result, constituting a commercial crisis. A reaction sets 
 in ; a reverse movement is initiated. A fall of prices, 
 once begun, tends to be accelerated for reasons exactly 
 corresponding to those which operate in the opposite 
 situation.
 
 CHAPTER V 
 
 INDIRECT INFLUENCES ON PURCHASING POWER 
 § 1 
 
 Thus far we have considered the level of prices as 
 affected by the volume of trade, by the velocities of 
 circulation of money and of deposits, and by the quan- 
 tities of money and of deposits. These are the only 
 influences which can directly affect the level of prices. 
 Any other influences on prices must act through these 
 five. There are myriads of such influences (outside of 
 the equation of exchange) that affect prices through 
 these five. It is our purpose in this chapter to note 
 the chief among them, excepting those that affect the 
 volume of money {M) ; the latter will be examined in 
 the two following chapters. 
 
 We shall first consider the outside influences that 
 affect the volume of trade and, through it, the price 
 level. The conditions which determine the extent of 
 trade are numerous and technical. The most important 
 may be classified as follows : — 
 
 1. Conditions affecting producers. 
 
 (a) Geographical differences in natural resources. 
 (6) The division of labor. 
 
 (c) Knowledge of the technique of production. 
 
 (d) The accumulation of capital. 
 
 2. Conditions affecting consumers. 
 
 (a) The extent and variety of human wants. 
 
 74
 
 Sec. 1] INDIRECT INFLUENCES 75 
 
 3. Conditions connecting producers and consumers. 
 
 (a) Facilities for transportation. 
 
 (b) Relative freedom of trade. 
 
 (c) Character of monetary and banking systems. 
 
 (d) Business confidence. 
 
 1 (a). It is evident that if all localities were exactly 
 alike in their natural resources and in their compara- 
 tive costs of production little or no trade would be set 
 up between them. It is equally true that the greater 
 the difference in the costs of production of different arti- 
 cles in different localities, the more likely is there to be 
 trade between them and the greater the amount of that 
 trade. Primitive trade had its raison d'etre in the fact 
 that the regions of this earth are unlike in their prod- 
 ucts. The traders were travelers between distant coun- 
 tries. Changes in commercial geography still produce 
 changes in the distribution and volume of trade. The 
 exhaustion of gold and silver mines in Nevada and of 
 lumber in Michigan have tended to reduce the volume 
 of trade of these regions, both external and internal. 
 Contrariwise, cattle raising in Texas, the production of 
 coal in Pennsylvania, of oranges in Florida, and of ap- 
 ples in Oregon have increased the volume of trade for 
 these communities respectively. 
 
 1 (6). Equally obvious is the influence of the division 
 of labor. Division of labor is based in part on differences 
 in comparative costs or efforts as between men, — cor- 
 responding to geographic differences as between coun- 
 tries. These two, combined, lead to local differentia- 
 tion of labor, making, for example, the town of Sheffield 
 famous for cutlery, Dresden for china, Venice for glass, 
 Paterson for silks, and Pittsburg for steel. 
 
 1 (c). Besides local and personal differentiation, the 
 state of knowledge of production will affect trade.
 
 76 THE PURCHASING POWER OF MONEY [Chap. V 
 
 The mines of Africa and Australia were left unworked 
 for centuries by ignorant natives but were opened by 
 white men possessing a knowledge of metallurgy. Vast 
 coal fields in China await development, largely for lack 
 of knowledge of how to extract and market the coal. 
 Egypt awaits the advent of scientific agriculture, to 
 usher in trade expansion. Nowadays, trade schools 
 in Germany, England, and the United States are in- 
 creasing and diffusing knowledge of productive tech- 
 nique. 
 
 1 (d). But knowledge, to be of use, must be applied ; 
 and its application usually requires the aid of capital. 
 The greater and the more productive the stock or capital 
 in any community, the more goods it can put into the 
 currents of trade. A mill will make a town a center 
 of trade. Docks, elevators, warehouses and railway 
 terminals help to transform a harbor into a port of 
 commerce. 
 
 Since increase in trade tends to decrease the general 
 level of prices, anything which tends to increase trade 
 likewise tends to decrease the general level of prices. 
 We conclude, therefore, that among the causes tending 
 to decrease prices are increasing geographical or personal 
 specialization, improved productive technique, and the 
 accumulation of capital. The history of commerce 
 shows that all these causes have been increasingly 
 operative during a long period including the last century. 
 Consequently, there has been a constant tendency, from 
 these sources at least, for prices to fall. 
 
 2 (a). Turning to the consumers' side, it is evident 
 that their wants change from time to time. This is 
 true even of so-called natural wants, but more con- 
 spicuously true of acquired or artificial wants. 
 
 Wants are, as it were, the mainsprings of economic
 
 Sec. 2] INDIRECT INFLUENCES 77 
 
 activity which in the last analysis keep the economic 
 world in motion. The desire to have clothes as fine as 
 the clothes of others, or finer, or different, leads to the 
 multiplicity of silks, satins, laces, etc. ; and the same 
 principle apphes to furniture, amusements, books, works 
 of art, and every other means of gratification. 
 
 The increase of wants, by leading to an increase in 
 trade, tends to lower the price level. Historically, 
 during recent times through invention, education, and 
 the emulation coming from increased contact in centers 
 of population, there has been a great intensification and 
 diversification of human wants and therefore increased 
 trade. Consequently, there has been from these causes 
 a tendency of prices to fall. 
 
 §2 
 
 3 (a). Anything which facilitates intercourse tends 
 to increase trade. Anything that interferes with inter- 
 course tends to decrease trade. First of all, there are 
 the mechanical facilities for transport. As Macaulay 
 said, with the exception of the alphabet and the printing 
 press, no set of inventions has tended to alter civilization 
 so much as those which abridge distance, — such as 
 the railway, the steamship, the telephone, the tele- 
 graph, and that conveyer of information and advertise- 
 ments, the newspaper. These all tend, therefore, to 
 decrease prices. 
 
 3 (b). Trade barriers are not only physical but legal. 
 A tariff between countries has the same influence in 
 decreasing trade as a chain of mountains. The freer 
 the trade, the more of it there will be. In France, 
 many communities have a local tariff (octroi) which 
 tends to interfere with local trade. In the United States 
 trade is free within the country itself, but between the
 
 78 THE PURCHASING POWER OF MONEY [Chap. V 
 
 United States and other countries there is a high pro- 
 tective tariff. The very fact of increasing faciUties 
 for transportation, lowering or removing physical 
 barriers, has stimulated nations and communities to 
 erect legal barriers in their place. Tariffs not only 
 tend to decrease the frequency of exchanges, but to the 
 extent that they prevent international or interlocal 
 division of labor and make countries more alike as well 
 as less productive, they also tend to decrease the 
 amounts of goods which can be exchanged. The ulti- 
 mate effect is thus to raise prices. 
 
 3 (c). The development of efficient monetary and 
 banldng systems tends to increase trade. There have 
 been times in the history of the world when money was 
 in so uncertain a state that people hesitated to make 
 many trade contracts because of the lack of knowledge 
 of what would be required of them when the contract 
 should be fulfilled. In the same way, when people 
 cannot depend on the good faith or stability of banks, 
 they will hesitate to use deposits and checks. 
 
 3 (d). Confidence, not only in banks in particular, 
 but in business in general, is truly said to be "the 
 soul of trade." Without this confidence there can- 
 not be a great volume of contracts. Anything that 
 tends to increase this confidence tends to increase 
 trade. In South America there are many places wait- 
 ing to be developed simply because capitalists do not 
 feel any security in contracts there. They are fearful 
 that by hook or by crook the fruit of any investments 
 they may make will be taken from them. 
 
 We see, then, that prices will tend to fall through 
 increase in trade, which may in turn be brought about 
 by improved transportation, by increased freedom of 
 trade, by improved monetary and banking systems,
 
 Sec. 3] INDIRECT INFLUENCES 79 
 
 and by business confidence. Historically, during recent 
 years, all of these causes have tended to grow in power, 
 except freedom of trade. Tariff barriers, however, have 
 only partly offset the removal of physical barriers. The 
 net effect has been a progressive lowering of trade re- 
 strictions, and therefore the tendency, so far as this 
 group of causes goes, has been for prices to fall. 
 
 §3 
 
 Having examined those causes outside the equation 
 which affect the volume of trade, our next task is to 
 consider the outside causes that affect the velocities 
 of circulation of money and of deposits. For the most 
 part, the causes affecting one of these velocities affect 
 the other also. These causes may be classified as 
 follows : — 
 
 1. Habits of the individual. 
 
 (a) As to thrift and hoarding. 
 
 (6) As to book credit. 
 
 (c) As to the use of checks. 
 
 2. Systems of payments in the community. 
 
 (a) As to frequency of receipts and of disburse- 
 ments. 
 
 (6) As to regularity of receipts and disbursements. 
 
 (c) As to correspondence between times and 
 amounts of receipts and disbursements. 
 
 3. General Causes. 
 
 (a) Density of population. 
 
 (6) Rapidity of transportation. 
 1 (a). Taking these up in order, we may first con- 
 sider what influence thrift has on the velocity of cir- 
 culation. Velocity of circulation of money is the same 
 thing as its rate of turnover It is found by dividing 
 the total payments effected by money in a year by the
 
 80 THE PURCHASING POWER OF MONEY [Chap. V 
 
 amount of money in circulation in that year. It de- 
 pends upon the rates of turnover of the individuals 
 who compose the society. This velocity of circula- 
 tion or rapidity of turnover of money is the greater 
 for each individual the more he spends, with a given 
 average amount of cash on hand; or the less average 
 cash he keeps, with a given yearly expenditure. 
 
 The velocity of circulation of a spendthrift may be 
 presumed to be greater than the average.^ He is al- 
 ways apt to be ''short" of funds, — to have a small 
 average balance on hand. But his thrifty neighbor 
 takes care to provide himself with cash enough to meet 
 all contingencies. The latter tends to hoard and lay 
 by his money, and will, therefore, have a slower velocity 
 of circulation. When, as used to be the custom in 
 France, people put money away in stockings and kept 
 it there for months, the velocity of circulation must 
 have been extremely slow. The same principle applies 
 to deposits. In a certain university town the banks 
 often refuse to take deposits from students of spend- 
 ing habits because the average balances of the latter 
 are so low ; or insist on a special stipulation that the 
 balance shall never fall below $100. 
 
 Hoarded money is sometimes said to be withdrawn 
 from circulation. But this is only another way of say- 
 ing that hoarding tends to decrease the velocity of 
 circulation. 
 
 A man who is thrifty is usually, to some extent, a 
 hoarder either of money ^ or of bank deposits. Laborers 
 who save usually keep their savings in the form of 
 
 ^ Cf . Jevons, Money and the Mechanism of Exchange, New York 
 (Appleton), 1896, p. 336. 
 
 ^ Cf. Harrison H. Brace, Gold Production and Future Prices, 
 New York (Bankers' Publishing Co.), 1910, p. 122.
 
 Sec. 3] INDIRECT INFLUENCES 81 
 
 money until enough is accumulated to be deposited 
 in a savings bank. Those who have bank accounts 
 will likewise accumulate considerable deposits when 
 preparing to make an investment. Banks whose de- 
 positors are "rapidly making money" and periodi- 
 cally investing the same, have, it is said, less active 
 accounts than banks whose depositors ''live up to their 
 incomes." 
 
 1 (6). The habit of "charging," i.e. using book 
 credit, tends to increase the velocity of circulation of 
 money, because the man who gets things "charged" 
 does not need to keep on hand as much money as he 
 would if he made all payments in cash. A man who 
 pays cash daily needs to keep cash for daily contin- 
 gencies. The system of cash payments, unlike the 
 system of book credit, requires that money shall be 
 kept on hand in advance of purchases. Evidently, if 
 money must be provided in advance, it must be pro- 
 vided in larger quantities than when merely required 
 to liquidate past debts. This is true for two reasons : 
 First, in advance of purchases, there is always uncer- 
 tainty as to when money will be needed and how much, 
 while after bills are incurred, the exact sum needed 
 is known. Secondly, and as a consequence of the first 
 circumstance, money held in advance must be held 
 a longer time than money received after a use for it 
 has been contracted for. In short, to keep money in 
 advance requires (a) a larger margin for unforeseen 
 contingencies and (6) a longer period before being dis- 
 bursed during which the money is idle. In the system 
 of cash payments, a man must keep money idle in 
 advance lest he be caught in the embarrassing position 
 of lacking it when he most needs it. With book credit, 
 he knows that even if he should be caught without a
 
 82 THE PURCHASING POWER OP MONEY [Chap. V 
 
 cent in his pocket, he can still get supplies on credit. 
 These he can pay for when money comes to hand. 
 Moreover, this money need not lie long in his pocket. 
 Immediately it is received, there is a use awaiting it to 
 pay debts accumulated. Now, to shorten the period 
 of waiting evidently decreases the average balance 
 carried, even if in the end the same sums are received 
 and disbursed. For instance, a laborer receiving and 
 spending $7 a week, if he cannot ''charge," must make 
 his week's wages last through the week. If he spends 
 $1 a day, his weekly cycle must show on successive 
 days at least as much as $7, $6, $5, $4, $3, $2, and 
 $1, at which time another $7 comes in. This makes 
 an average of at least $4. But if he can charge every- 
 thing and then wait until pay day to meet the resulting 
 obligations, he need keep nothing through the week, 
 paying out his $7 when it comes in. His weekly cycle 
 need show no higher balances than $7, $0, $0, $0, $0, 
 $0, $0, the average of which is only SI. 
 
 Through book credit, therefore, the average amount 
 of money or bank deposits which each person must keep 
 at hand to meet a given expenditure is made less. This 
 means that the rate of turnover is increased ; for if 
 people spend the same amounts as before, but keep 
 smaller amounts on hand, the quotient of the amount 
 spent divided by the amount on hand must increase. 
 
 But we have seen that to increase the rate of turn- 
 over will tend to increase the price level. Therefore, 
 book credit tends to increase the price ^ level. More- 
 over, a community can to some extent cover the relative 
 scarcity of money of a period when business is large 
 
 ' This indirect effect on the price level must not be confused with 
 the direct effect sometimes claimed. See § 1 of Appendix to (this) 
 Chapter V.
 
 Sec. 4] INDIRECT INFLUENCES 83 
 
 with the relative surplus of a period when fewer de- 
 mands are made on its supply of money. Otherwise, 
 to maintain the same general level of prices, there would 
 have to be considerably more money when business 
 was large ; and this money, unless it were some form 
 of elastic bank currency which could be canceled and 
 retired, would lie idle during those seasons when busi- 
 ness was slack. 
 
 In short, book credit economizes money (M) even 
 though it may not economize money payments {E) 
 and therefore increases the velocity of circulation 
 of money {E/M). 
 
 1 (c). The habit of using checks rather than money 
 will also affect the velocity of circulation; because a 
 depositor's surplus money will immediately be put 
 into the bank in return for a right to draw by check. 
 
 Banks thus offer an outlet for any surplus pocket 
 money or surplus till money, and tend to prevent 
 the existence of idle hoards. In like manner surplus 
 deposits may be converted into cash — that is, ex- 
 changed for cash — as desired. In short, those who 
 make use both of cash and deposits have the opportunity, 
 by adjusting the two, to prevent either from being idle. 
 
 We see, then, that three habits — spendthrift habits, 
 the habit of charging, and the habit of using checks — • 
 all tend to raise the level of prices through their effects 
 on the velocity of circulation of money, or of deposits. 
 It is believed that these habits (except probably the 
 first) have been increasing rapidly during modern times. 
 
 §4 
 
 2 (a). The more frequently money or checks are 
 received and disbursed, the shorter is the average in- 
 terval between the receipt and the expenditure of money
 
 84 THE PURCHASING POWER OF MONEY [Chap. V 
 
 or checks and the more rapid is the velocity of circula- 
 tion. 
 
 This may best be seen from an example. A change 
 from monthly to weekly wage payments tends to 
 increase the velocity of circulation of money. If a 
 laborer is paid weekly $7 and reduces this evenly each 
 day, ending each week empty-handed, his average cash, 
 as we have seen, would be a little over half of $7 or 
 about $4. This makes his turnover nearly twice a 
 week. Under monthly payments the laborer who 
 receives and spends an average of $1 a day will have 
 to spread the $30 more or less evenly over the follow- 
 ing 30 days. If, at the next pay day, he comes out 
 empty-handed, his average money during the month 
 has been about $15. This makes his turnover about 
 twice a month. Thus the rate of turnover is more 
 rapid under weekly than under monthly payments. 
 
 The same result would hold if we assumed that, 
 instead of ending the cycle empty-handed, he ended 
 it with a given fraction — say half — of his wages 
 unspent. Under weekly payments, he would begin 
 with $10.50, and end with $3.50, averaging about $7. 
 Under monthly payments he would thus begin with an 
 average of $45, and end with $15, averaging about $30. 
 In the former case his average velocity of circulation 
 would be once a week and in the latter once a month. 
 The turnover will thus still be about four times as 
 rapid under weekly as under monthly payment. 
 Thus if the distribution of expenditure over the two 
 cycles should have exactly the same ''time shape "^ 
 (distribution in time), weekly payments would ac- 
 
 ^ Compare Adolphe Landry, "La Rapidite de la Circulation 
 Monetaire," Extrait de La Revue d' Economie 'politique, Fevrier, 
 1905.
 
 Sec. 4] INDIRECT INFLUENCES 85 
 
 celerate the velocity of circulation in the same ratio 
 which a month bears to a week. As a matter of his- 
 tory, however, it is not likely that the substitution 
 of weekly payments for monthly payments has in- 
 creased the rapidity of circulation of money among 
 workingmen fourfold, because the change in another 
 element, book credit, would be likely to cause a some- 
 what compensatory decrease. Book credit is less 
 likely to be used under weekly than under monthly 
 payments. Where this book-credit habit or habit 
 of '^ charging" is prevalent, the great bulk of money 
 is spent on pay day. It is probable that the substitu- 
 tion of weekly for monthly payments, when it has 
 taken place, has enabled many workingmen, who 
 formerly found it necessary to trade on credit, to make 
 their own payments in cash, thus tendmg to decrease 
 the velocity of turnover of money. 
 
 Frequency of disbursements evidently has an effect 
 similar to the effect of frequency of receipts ; i.e. it 
 tends to accelerate the velocity of turnover, or cir- 
 culation. 
 
 2 (6). Regularity oi payment also facilitates the turn- 
 over. "When the workingman can be fairly certain 
 of both his receipts and expenditures, he can, by close 
 calculation, adjust them so precisely as safely to end 
 each payment cycle with an empty pocket. This 
 habit is extremely common among certain classes of 
 city laborers. On the other hand, if the receipts and 
 expenditures are irregular, either in amount or in time, 
 prudence requires the worker to keep a larger sum on 
 hand, to insure against mishaps.^ Even when fore- 
 known with certainty, irregular receipts require a 
 larger average sum to be kept on hand. This state- 
 
 * Compare Landry, ibid.
 
 86 THE PURCHASING POWER OF MONEY [Chap. V 
 
 merit holds, at least, if we assume that the frequency 
 of payments per year is the same as in the case of 
 regular payments, and that the "tune shape" of ex- 
 penditures between receipts is also the same. Thus, 
 suppose that a workman spends at the rate of $1 a 
 day and receives at the average rate of $1 a day. The 
 average amount that he will require to keep on hand 
 will be less if his receipts occur once every fortnight 
 than if they occur at intervals of three weeks and one 
 week respectively in alternation. For, supposing he 
 tries to come out empty-handed just before each pay- 
 ment, in the former case he will evidently need an aver- 
 age sum each fortnight of $7 ; but in the latter case, he 
 will need for the first period of three weeks, or twenty- 
 one days, $10.50, and in the second period $3.50, 
 the average of which — remembering that the $10.50 
 applies for three weeks and the $3.50 for one week — 
 will be $8.75. We may, therefore, conclude that reg- 
 ularity, both of receipts and of payments, tends to 
 increase velocity of circulation. 
 
 2 (c). Next, consider the synchronizing of receipts 
 and disbursements, i.e. making payments at the same 
 intervals as obtaining receipts. Where payments such 
 as rent, interest, insurance and taxes occur at periods 
 irrespective of the times of receipts of money, it is 
 often necessary to accumulate money or deposits in 
 advance, thus increasing the average on hand, with- 
 drawing money from use for a time, and decreasing 
 the velocity of circulation. This result may, however, 
 be obviated if the individual is willing and able to 
 borrow in order to meet his tax or other special ex- 
 pense, repaying the loan later at his convenience. 
 This is one of the ways in which banking, as already 
 explained, through loans and deposits, serves the con-
 
 Sec. 5] INDIRECT INFLUENCES 87 
 
 venience of the public and increases the velocity of 
 circulation of money and deposits. Similarly book 
 credit may obviate the inconveniences arising from 
 the disharmony between the times of receipt and dis- 
 bursement; for we have already seen that it is a great 
 convenience to the spender of money or of deposits, 
 if dealers to whom he is in debt will allow him to 
 postpone payment until he has received his money 
 or his bank deposit. This arrangement obviates the 
 necessity of keeping much money or deposits on hand, 
 and therefore increases their velocity of circulation. 
 We conclude, then, that synchronizing and regu- 
 larity of payment, no less than frequency of pa3nnent, 
 have tended to increase prices by increasing velocity 
 of circulation. 
 
 §5 
 
 3 (a). The more densely populated a locality, the 
 more rapid will be the velocity of circulation. ^ 
 
 There is definite evidence that this is true of bank 
 deposits. The following figures ^ give the velocities of 
 circulation of deposits in ten cities, arranged in order 
 of size: — 
 
 Paris 116 Lisbon 29 
 
 Berlin 161 Indianapolis 30 
 
 Brussels 123 New Haven 16 
 
 Madrid 14 Athens 4 
 
 Rome 43 Santa Barbara 1 
 
 Madrid is the only city seriously out of its order in 
 respect to velocity of circulation. 
 
 1 This is pointed out by Kinley, Money, New York (Macmillan), 
 1904, p. 156. 
 
 ^ These figures are the medians of those of Pierre des Essars for 
 European banks (Journal de la Societe de Statistique de Paris, April, 
 1895) supplemented by data secured by me from a few American 
 banks.
 
 88 THE PURCHASING POWER OF MONEY [Chap. V 
 
 3 (b). Again, the more extensive and the speedier the 
 transportation in general, the more rapid the circulation 
 of money.* Anything which makes it easier to pass 
 money from one person to another will tend to increase 
 the velocity of circulation. Railways have this effect. 
 The telegraph has increased the velocity of circulation of 
 deposits, since these can now be transferred thousands of 
 miles in a few minutes. Mail and express, by facilitat- 
 ing the transmission of bank deposits and money, have 
 likewise tended to increase their velocity of circulation. 
 
 We conclude, then, that density of population and 
 rapidity of transportation have tended to increase 
 prices by increasing velocities. Historically this con- 
 centration of population in cities has been an im- 
 portant factor in raising prices in the United States. 
 
 Ordinarily, the velocity of circulation of money and 
 the velocity of circulation of deposits will be similarly 
 influenced by similar causes. In time of panics, 
 however, if the confidence of depositors is shaken, 
 the tendency is for deposits to be withdrawn while 
 money is hoarded. Hence, for a time, the two velocities 
 may change in opposite directions, although there are 
 no good statistics for verifying this supposition. 
 
 §6 
 
 Lastly, the chief specific outside influences on the 
 volume of deposits subject to check are: — 
 
 (1) The system of banking and the habits of the 
 people in utilizing that system. 
 
 (2) The habit of charging. 
 
 1. It goes without saying that a banking system must 
 
 1 Cf. Jevons, Money and the Mechanism of Exchange, New York 
 (Appleton), 1896, p. 336; also Kinley, Money, New York (Mao- 
 miUan), 1904, pp. 156 i nd 157.
 
 Sec. 6] INDIRECT INFLUENCES 89 
 
 be devised and developed before it can be used. The 
 invention of banking has made deposit currency pos- 
 sible, and its adoption has undoubtedly led to a great 
 increase in deposits and consequent rise of prices. 
 Even in the last decade the extension in the United 
 States of deposit banking has been an exceedingly 
 powerful influence in that direction. In Europe de- 
 posit banking is still in its infancy. 
 
 2. ''Charging" is often a preliminary to payment 
 by check, rather than by cash. If a customer did not 
 have his obligations ''charged," he would pay in money 
 and not by check. ^ The ultimate effect of this practice, 
 therefore, is to increase the ratio of check payments to 
 cash payments {E' to E) and the ratio of deposits to 
 money carried {M' to M), and therefore to increase 
 the amount of credit currency which a given quantity 
 of money can sustain. 
 
 This effect, the substitution of checks for cash pay- 
 ments, is probably by far the most important effect 
 of "charging," and exerts a powerful influence toward 
 raising prices. 
 
 ^ Andrew, " Credit and the Value of Money." Reprint from Papen 
 and Proceedings of the Seventeenth Annual Meeting American Economic 
 Association, December, 1904, p. 10.
 
 CHAPTER VI 
 
 INDIRECT INFLUENCES (continued) 
 
 We have now considered those influences outside the 
 equation of exchange which affect the volume of trade 
 (the Q's), the velocities of circulation of money and 
 deposits (V and V), and the amount of deposits (M'). 
 We have reserved for separate treatment in this chapter 
 and the following the outside influences that affect the 
 quantity of money (M). 
 
 The chief of these may be classified as follows : — 
 
 1. Influences operating through the exportation and 
 importation of money. 
 
 2. Influences operating through the melting or mint- 
 ing of money. 
 
 3. Influences operating through the production and 
 consumption of money metals. 
 
 4. Influences of monetary and banking systems, to be 
 treated in the next chapter. 
 
 The first to be considered is the influence of foreign 
 trade. Hitherto we have confined our studies of price 
 levels to an isolated community, having no trade re- 
 lation with other communities. In the modern world, 
 however, no such community exists, and it is important 
 to observe that international trade gives present-day 
 problems of money and of the price level an interna- 
 tional character. If all countries had their irredeem- 
 able paper money, and had no money acceptable 
 elsewhere, there could be no international adjustment 
 
 90
 
 Sec. 1] INDIRECT INFLUENCES CONTINUED 91 
 
 of monetary matters. Price levels in different countries 
 would have no intimate connection. Indeed, to some 
 extent the connection is actually broken between exist- 
 ing countries which have different metallic standards, 
 — for example, between a gold-basis and a silver-basis 
 country, — although through their nonmonetary uses 
 the two metals are still somewhat bound together. 
 But where two or more nations trading with each 
 other use the same standard, there is a tendency for the 
 price levels of each to influence profoundly the price 
 levels of the other. 
 
 The price level in a small country like Switzerland 
 depends largely upon the price level in other countries. 
 Gold, which is the primary or full weight money in 
 most civihzed nations, is constantly travelling from one 
 country or community to another. When a single 
 small country is under consideration, it is therefore 
 preferable to say that the quantity of money in that 
 country is determined by the universal price level, 
 rather than to say that its level of prices is determined 
 by the quantity of money within its borders. An 
 individual country bears the same relation to the world 
 that a lagoon bears to the ocean. The level of the 
 ocean depends, of course, upon the quantity of water 
 in it. But when we speak of the lagoon, we reverse the 
 statement, and say that the quantity of water in it 
 depends upon the level of the ocean. As the tide in 
 the outside ocean rises and falls, the quantity of water 
 in the lagoon will adjust itself accordingly. 
 
 To simplify the problem of the distribution of money 
 among different communities, we shall, for the time 
 being, ignore the fact that money consists ordinarily 
 of a material capable of nonmonetary uses and may 
 be melted or minted.
 
 92 THE PURCHASING POWER OF MONEY [Chap. VI 
 
 Let US, then, consider the causes that determine the 
 quantity of money in a state hke Connecticut. If the 
 level of prices in Connecticut temporarily falls below 
 that of the surrounding states, Rhode Island, Massa- 
 chusetts, and New York, the effect is to cause an export 
 of money from these states to Connecticut, because 
 people will buy goods wherever they are cheapest and 
 sell them wherever they are dearest. With its low 
 prices, Connecticut becomes a good place to buy from, 
 but a poor place to sell in. But if outsiders buy of 
 Connecticut, they will have to bring money to buy 
 with. There will, therefore, be a tendency for money 
 to flow to Connecticut until the level of prices there 
 rises to a level which will arrest the influx. If, on the 
 other hand, prices in Connecticut are higher than in 
 surrounding states, it becomes a good place to sell to and 
 a poor place to buy from. But if outsiders sell to Con- 
 necticut, they will receive money in exchange. There 
 is then a tendency for money to flow out of Connecticut 
 until the level of prices in Connecticut is lower. 
 
 But it must not be inferred that the prices of various 
 articles or even the general level of prices will become 
 precisely the same in different countries. Distance, 
 ignorance as to where the best markets are to be found, 
 tariffs, and costs of transportation help to maintain 
 price differences. The native products of each region 
 tend to be cheaper in that region. They are exported 
 as long as the excess of prices abroad is enough to more 
 than cover the cost of transportation. Practically, a 
 commodity will not be exported at a price which would 
 not at least be equal to the price in the country of origin, 
 plus the freight. Many commodities are shipped only 
 one way. Thus, wheat is shipped from the United 
 States to England, but not from England to the United
 
 Sec. 1] INDIRECi" INFLUENCES CONTINUED 93 
 
 States. It tends to be cheaper in the United States. 
 Large exportations raise its price in America toward the 
 price in England, but it will usually keep below that 
 price by the cost of transportation. Other commodities 
 that are cheap to transport will be sent in either direc- 
 tion, according to market conditions. 
 
 But, although international and interlocal trade will 
 never bring about exact uniformity of price levels, it 
 will, to the extent that it exists, produce an adjustment 
 of these levels toward uniformity by regulating in the 
 manner already described the distribution of money. 
 If one commodity enters into international trade, it 
 alone will suffice, though slowly, to act as a regulator 
 of money distribution ; for in return for that com- 
 modity, money may flow and, as the price level rises 
 or falls, the quantity of that commodity sold may 
 be correspondingly adjusted. In ordinary intercourse 
 between nations, even when a deliberate attempt is 
 made to interfere with it by protective tariffs, there 
 will always be a large number of commodities thus 
 acting as outlets and inlets. And since the quantity 
 of money itself affects prices for all sorts of commodi- 
 ties, the regulative effect of international trade applies, 
 not simply to the commodities which enter into that 
 trade, but to all others as well. It follows that now- 
 adays international and interlocal trade is constantly 
 regulating price levels throughout the world. 
 
 We must not leave this subject without emphasizing 
 the effects of a tariff on the purchasing power of money. 
 When a country adopts a tariff, the tendency is for the 
 level of prices to rise. A tariff obviously raises the 
 prices of the ''protected" goods. But it does more 
 than that, — it tends also to raise the prices of goods 
 in general. Thus, the tariff first causes a decrease
 
 94 THE PURCHASING POWER OF MONEY [Chap. VI 
 
 in imports. Though in the long run this decrease in 
 imports will lead to a corresponding decrease in exports, 
 yet at first there will be no such adjustment. The 
 foreigner will, for a time, continue to buy from the pro- 
 tected country almost as much as before. This will 
 result temporarily in an excess of that country's exports 
 over its imports, or a so-called ''favorable" balance of 
 trade, and a consequent inflow of money. This inflow 
 will eventually raise the prices, not alone of protected 
 goods, but of other goods as well. The rise will con- 
 tinue till it reaches a point high enough to put a stop 
 to the ''favorable" balance of trade. 
 
 Although the "favorable balance" of trade created 
 by a tariff is temporary, it leaves behind a permanent 
 increase of money and of prices. The tariff wall is a 
 sort of dam, causing an elevation in the prices of the 
 goods impounded behind it. 
 
 This fact is sometimes overlooked in the theory of 
 international trade as commonly set forth. Emphasis 
 is laid instead on the fact that in the last analysis the 
 trade is of goods for goods, not of money for goods, and 
 that a tariff on imports reduces, not only imports, but 
 exports also, — that it merely interrupts temporarily the 
 virtual barter between nations. The effect of a tax on 
 imports is likened to that of a tax on exports. But in 
 respect to effects on price levels a tax on imports and a 
 tax on exports are diametrically opposed. If we place 
 our tax on exports, we first interfere with exports. The 
 imports are not checked until money has flowed out 
 and has reduced the general price level enough to de- 
 stroy the "unfavorable" balance of trade first created. 
 We conclude that the general purchasing power of 
 money is reduced by a tariff and that it would be in- 
 creased by a tax on exports.
 
 Sec. 1] INDIRECT INFLUENCES CONTINUED 95 
 
 This is, perhaps, the chief reason why a protective 
 tariff seems to many a cause of prosperity. It furnishes 
 a temporary stimulus, not only to protected industries, 
 but to trade in general, which is really simply the stimu- 
 lus of money inflation. 
 
 Our present interest in international trade, however, 
 is mainly directed to its effects on international price 
 levels. Except for the export or import of money to 
 adjust the price levels, international trade is at bottom 
 merely an interchange of goods. Where the price level 
 is not concerned, the money value of the goods sold by a 
 country will exactly equal the value of those bought. 
 Only when there is a difference in these values, or a 
 "balance of trade," will there be any flow of money 
 and consequently any tendency to modify the price 
 level.^ 
 
 We have shown how the international and interlocal 
 equilibrium of prices may be disturbed by differential 
 changes in the quantity of money alone. It may also 
 be disturbed by differential changes in the volume 
 of bank deposits ; or in the velocity of circulation of 
 money ; or in the velocity of circulation of bank de- 
 posits ; or in the volume of trade. But whatever may 
 be the source of the difference in price levels, equilibrium 
 will eventually be restored through an international or 
 interlocal redistribution of money and goods brought 
 about by international and interlocal trade. Other 
 elements in the equation of exchange than money and 
 commodities cannot be transported from one place to 
 another. 
 
 Except for transitional effects, then, international 
 differences of price levels produce changes only in one 
 
 1 For mathematical statement, see § 1 of Appendix to (this) 
 Chapter VI.
 
 96 THE PURCHASING POWER OF MONEY [Chap. VI 
 
 of the elements in the equation of exchange, — the 
 volume of money. Practically, of course, transition 
 periods may be incessant or chronic. It seldom happens 
 that a nation has no balance of trade. For decades Ori- 
 ental nations took silver from Occidental nations even 
 when silver was, under the bimetallic regime, at a stable 
 ratio with gold. In Europe there was a consequent 
 long-continued tendency for prices to fall, and in Asia 
 a tendency to rise, with all the other transitional effects 
 involved. 
 
 §2 
 
 We have seen how M in the equation of exchange 
 is affected by the import or export of money. Con- 
 sidered with reference to the M in any one of the coun- 
 tries concerned, the M's, in all the others are ''outside 
 influences." 
 
 Proceeding now one step farther, we must consider 
 those influences on M that are not only outside of the 
 equation of exchange for a particular country, but out- 
 side those for the whole world. Besides the monetary 
 inflow and outflow through import and export, there 
 is an inflow and outflow through minting and melting. 
 In other words, not only do the stocks of money in the 
 world connect with each other like interconnecting 
 bodies of water, but they connect in the same way with 
 the outside stock of bullion. In the modern world one 
 of the precious metals, such as gold, usually plays the 
 part of primary money, and this metal has two uses, — 
 a monetary use and a commodity use. That is to say, 
 gold is not only a money material, but a commodity as 
 well. In their character of commodities, the precious 
 metals are raw materials for jewelry, works of art, and 
 other products into which they may be wrought. It is
 
 Sec. 2] INDIRECT INFLUENCES CONTINUED 97 
 
 in this unmanufactured or raw state that they are 
 called bullion. 
 
 Gold money may be changed into gold bullion, and 
 vice versa. In fact, both changes are going on con- 
 stantly, for if the value of gold as compared with other 
 commodities is greater in the one use than in the other, 
 gold will immediately flow toward whichever use is 
 more profitable, and the market price of gold bullion 
 will determine the direction of the flow. Since 100 
 ounces of gold, y^ fine, can be transformed into $1860, 
 the market value of so much gold bullion, ^^ fine, must 
 tend to be $1860. If it costs nothing to have bullion 
 coined into money, and nothing to melt money into 
 bullion, there will be an automatic flux and reflux from 
 money to bullion and from bullion to money that will 
 prevent the price of bullion from varying greatly. On 
 the one hand, if the price of gold bullion is greater than 
 the money which could be minted from it, no matter 
 how slight the difference may be, the users of gold who 
 require bullion — notably jewelers — will save this 
 difference by melting gold coin into bullion. Con- 
 trariwise, if the price of bullion is less than the value 
 of gold coin, the owners of bullion will save the differ- 
 ence by taking bullion to the mint and having it coined 
 into gold dollars, instead of selling it in the bullion 
 market. The effect of melting coin, on the one hand, 
 is to decrease the amount of gold money and increase 
 the amount of gold bullion, thereby lowering the value 
 of gold as bullion and raising the value of gold as money; 
 thereby lowering the price level and restoring the equal- 
 ity between bullion and money. The effect of minting 
 bullion into coin is, by the opposite process, to bring the 
 value of gold as coin and the value of gold as bullion 
 again into equilibrium. In practice, the balance is
 
 98 THE PURCHASING POWER OF MONEY [Chap. VI 
 
 probably ^ maintained chiefly by turning newly mined 
 gold into the one or the other use according to the mar- 
 ket. By thus feeding the two reservoirs according to 
 their respective needs there is saved the necessity of any 
 great amount of interflow between money and the arts. 
 
 Where a charge — called " seigniorage " — is made for 
 changing bulhon into coin, or where the process in- 
 volves expense or delay, the flow of bullion into currency 
 will be to that extent impeded. But under a modern 
 system of free coinage and with modern methods of 
 metallurgy, both melting and minting may be performed 
 so inexpensively and so quickly that there is practically 
 no cost or delay involved. In fact, there are few in- 
 stances of more exact price adjustment than the ad- 
 justment between gold bullion and gold coin. It 
 follows that the quantity of money, and therefore its 
 purchasing power, is directly dependent on that of gold 
 bullion. 
 
 The stability of the price of gold bullion expressed in 
 gold coin causes confusion in the minds of many people, 
 giving them the erroneous impression that there is no 
 change in the value of money. Indeed, this stability has 
 often been cited to show that gold is a stable standard 
 of value. Dealers in objects made of gold seem to 
 misunderstand the significance of the fact that an ounce 
 of gold always costs about $18.60 in the United States 
 or £3 17s. 10-2 <i. i^i England. This means nothing 
 more than the fact that gold in one form and meas- 
 ured in one way will always bear a constant ratio to 
 gold in another form and measured in another way. 
 An ounce of gold bullion is worth a fixed number of gold 
 dollars, for the same reason that a pound sterling of 
 
 1 Cf. De Launay, The World's Gold, New York (Putnam), 1908, 
 pp. 179-183.
 
 Sec. 3] INDIRECT INFLUENCES CONTINUED 99 
 
 gold is worth a fixed number of gold dollars, or that a 
 gold eagle is worth a fixed number of gold dollars. 
 
 Except, then, for extremely slight and temporary- 
 fluctuations, gold bullion and gold money must always 
 have the same value. Therefore, in the following dis- 
 cussion respecting the more considerable fluctuations 
 affecting both, we shall speak of these values inter- 
 changeably as 'Hhe value of gold." 
 
 § 3 
 
 The stock of bullion is not the ultimate outside 
 influence on the quantity of money. As the stock of 
 bullion and the stock of money influence each other, 
 so the total stock of both is influenced by production 
 and consumption. The production of gold consists of 
 the output of the mines, which constantly tends to add 
 to the existing stocks both of bullion and coin. The 
 consumption of gold consists of the use of bullion in 
 the arts by being wrought up into jewelry, gilding, etc., 
 and of losses by abrasion, shipwreck, etc. If we con- 
 sider the amount of gold coin and bullion as contained 
 in a reservoir, production would be the inflow from 
 the mines, and consumption the outflow to the arts 
 and by destruction and loss. To the inflow from the 
 mines should be added the reinflow from forms of art 
 into which gold had previously been wrought, but 
 which have grown obsolete. This is illustrated by 
 the business of producing gold bullion by burning 
 gold picture frames. 
 
 We shall consider first the inflow or production, 
 and afterward the outflow or consumption. The reg- 
 ulator of the inflow (which practically means the 
 production of gold from the mines) is its estimated 
 ''marginal cost of production."
 
 100 THE PURCHASING POWER OF MONEY [Chap. VI 
 
 Mining is a hazardous business and estimates are 
 subject to great error. But however erroneous the 
 estimated cost, it exerts a regulatory power over pro- 
 duction. Wherever the estimated cost of producing 
 a dollar of gold is less than the existing value of a dollar 
 in gold, it will normally be produced. Wherever the 
 cost of production exceeds the existing value of a dollar, 
 gold will normally not be produced. In the former 
 case the production of gold is profitable ; in the latter 
 it is unprofitable. There will be an intermediate or 
 neutral point at which normally profitable production 
 ceases and unprofitable production begins, a point at 
 which the cost of producing $100 will be exactly $100. 
 The cost at this point is called the marginal cost of 
 production. At the richest mines, the cost of produc- 
 tion is extremely small. From this low standard the 
 cost gradually rises at other mines, until the marginal 
 mine is reached, at which the cost will normally be 
 equal to the value of the product. In fact, there 
 exists a marginal point of production, not only as 
 among different mines, but for each mine individually. 
 The fact that cost tends in general to increase with 
 increased product is due to the fact that gold is an 
 extractive industry. It is subject to the law of increas- 
 ing cost, or, as it is often expressed, ''the law of decreas- 
 ing returns." If a mine is only moderately worked, the 
 cost of production per ounce of gold will be less than 
 if it is worked at more nearly its full capacity, and 
 there will always be a rate of working such that the 
 cost per ounce of any extension in that rate of working 
 will make the extension barely profitable. It will pay 
 to extend production to the point where the additional 
 return is just equal to the consequent additional cost, 
 but no further. The mine operator may unintention-
 
 Sec. 3] INDIRECT INFLUENCES CONTINUED 101 
 
 ally or temporarily overshoot the mark or fall within 
 it, but such errors will only stimulate him to correct 
 them; and gold production will always tend toward 
 an equilibrium in which the marginal cost of produc- 
 tion will (when interest is added) be equal to the 
 value of the product. 
 
 This holds true in whatever way cost of production 
 is measured, whether in terms of gold itself, or in 
 terms of some other commodity such as wheat, or of 
 commodities in general, or of any supposed ''absolute" 
 standard of value. In gold-standard countries gold 
 miners do actually reckon the cost of producing gold 
 in terms of gold. From their standpoint it is a need- 
 less complication to translate the cost of production 
 and the value of the product into some other standard 
 than gold. They are interested in the relation between 
 the two, and this relation will not be affected by the 
 standard. 
 
 To translate the cost and value from gold money 
 into wheat, it is only necessary to divide both cost 
 and value by the price of wheat in gold money. 
 Such a change in the method of expressing both 
 cost and value will not affect their relation to each 
 other. 
 
 To illustrate how the producer of gold measures 
 everything in terms of gold, suppose that the price 
 level rises. Assuming that the rise of prices applies 
 to wages, machinery, fuel, and the other expenses of 
 producing gold, he will then have to pay more dollars 
 for wages, machinery, fuel, etc., while the prices ob- 
 tained for his product (expressed in those same dol- 
 lars) will, as always, remain unchanged. Conversely, 
 a fall in the level will lower his cost of production 
 (measured in dollars), while the price of his product
 
 102 THE PURCHASING POWER OF MONET [Chap. VI 
 
 will still remain the same.^ Thus we have a constant 
 number expressing the price of gold product and a 
 variable number expressing its cost of production. 
 
 If we express the same phenomena, not in terms of 
 gold, but in terms of wheat, or rather, let us say, in 
 terms of goods in general, we shall have the opposite 
 conditions. When prices rise, the purchasing power of 
 money falls, and this purchasing power is the value of 
 the product expressed in terms of goods in general. 
 If the mining costs change with the general price move- 
 ment, there will not occur any change in the cost of 
 producing gold relatively to goods. There will, however, 
 be a change in the value of the gold product. That 
 is, we shall then have a variable number expressing the 
 price of the gold product and a constant number ex- 
 pressing its cost of production. 
 
 Thus the comparison between price and cost of 
 production is the same, whether we use gold or other 
 commodities as our criterion. In the one view — 
 i.e. when prices are measured in gold — a rise of prices 
 means a rise in the gold miner's cost of production; 
 in the other view — i.e. when prices are measured 
 in other goods — the same rise in prices means a fall in 
 the price (purchasing power) of his product. In either 
 view he will be discouraged. He will look at his troubles 
 in the former light, i.e. as a rise in the cost of produc- 
 tion ; but we shall find it more useful to look at them 
 in the latter, i.e. as a fall in the purchasing power of 
 the product. In either case the comparison is between 
 the cost of the production of gold and the purchasing 
 power of gold. If this purchasing power is above the 
 cost of production in any particular mine, it will pay 
 
 1 Cf . Mill, Principles of Political Economy, Book III, Chapter 
 IX, § 2.
 
 Sec. 3] INDIRECT INFLUENCES CONTINUED 103 
 
 to work that mine. If the purchasing power of gold 
 is lower than the cost of production of any particular 
 mine, it will not pay to work that mine. Thus the 
 production of gold increases or decreases with an in- 
 crease or decrease in the purchasing power of gold. 
 
 So much for the inflow of gold and the conditions 
 regulating it. We turn next to outflow or consumption 
 of gold. This has two forms, viz. consumption in the 
 arts and consumption for monetary purposes. 
 
 First we consider its consumption in the arts. If 
 objects made of gold are cheap — that is, if the prices 
 of other objects are relatively high — then the relative 
 cheapness of the gold objects will lead to an increase in 
 their use and consumption. Expressing the matter in 
 terms of money prices, when prices of everything else 
 are higher and people's incomes are likewise higher, 
 while gold watches and gold ornaments generally re- 
 main at their old prices, people will use and consume 
 more gold watches and ornaments. 
 
 These are instances of the consumption of gold in the 
 form of commodities. The consumption and loss of gold 
 as coin is a matter of abrasion, of loss by shipwreck 
 and other accidents. It changes with the changes in 
 the amount of gold in use and in its rapidity of ex- 
 change. The outlets from this reservoir represent the 
 consumption of gold coins by loss. Just as production 
 is regulated by marginal cost of what is produced, so is 
 consumption regulated by marginal utility of what is 
 consumed. This is not the place to enter into a dis- 
 cussion of the essential symmetry between these two 
 marginal magnitudes, a symmetry often lost sight of 
 because cost is usually measured objectively and util- 
 ity subjectively. Both are measurable in either way. 
 The subjective method is the more fundamental, but
 
 104 THE PURCHASING POWER OF MONEY [Chap. VI 
 
 takes us farther away from our present discussion than 
 is necessary or profitable. 
 
 We see then that the consumption of gold is stimu- 
 lated by a fall in the value (purchasing power) of gold, 
 while the production of gold is decreased. The pur- 
 chasing power of money, being thus played upon by 
 the opposing forces of production and consumption, 
 is driven up or down as the case may be.^ 
 
 In any complete picture of the forces determining 
 the purchasing power of money we need to keep prom- 
 inently in view three groups of factors : (1) the 
 production or the ''inflow" of gold (i.e. from the mines) ; 
 (2) the consumption or "outflow" (into the arts and 
 by destruction and loss); and (3) the "stock" or 
 reservoir of gold (whether coin or bullion) which 
 receives the inflow and suffers the outflow. The re- 
 lations among these three sets of magnitudes can be 
 set forth by means of a mechanical illustration, given 
 in Figure 5. This represents two connected reservoirs 
 of Uquid, Gb and G,n- The contents of the first reservoir 
 represent the stock of gold bullion, and the contents 
 of the second the stock of gold money. Since purchas- 
 
 1 The theory here presented, that the value of gold bullion 
 and the cost of production of gold affect prices by way of the 
 quantity of money, is the one which economists have generally 
 held. A different view is represented by Laughlin, who says, "the 
 quantity of money used as the actual media of exchange no more 
 determines price than the entries of deeds and conveyances in 
 the county records determine the prices of the land whose sale is 
 stated in the papers recorded," and that "price is an exchange 
 relation between goods and the standard money commodity, whether 
 that money commodity be used as a medium of exchange or not." 
 See The Principles of Money, New York (Scribner), 1903, pp. 317 
 and 318.
 
 Sec. 4] 
 
 INDIRECT INFLUENCES CONTINUED 
 
 105 
 
 ing power increases with scarcity, the distance from 
 the top of the cisterns, 00, to the surface of the hquid, 
 is taken to represent the purchasing power of gold over 
 other goods. A lowering of the level of the liquid 
 indicates an increase in the purchasing power of money, 
 since we measure this purchasing power downward 
 from the line 00 to the surface of the liquid. We shall 
 not attempt to represent other forms of currency ex- 
 plicitly in the diagram. We have seen that normally 
 the quantities of other currency are proportional to 
 
 ■tf i-^"'-' '-m i ^ 
 
 Fig. 5. 
 
 the quantity of primary money, which we are supposing 
 to be gold. Therefore, the variation in the purchasing 
 power of this primary money may be taken as rep- 
 resentative of the variation of all the currency. We 
 shall now explain the shapes of these cisterns. The 
 shape of the cistern G,n must be such as will make the 
 distance of the liquid surface below 00 decrease with 
 an increase of the liquid, in exactly the same way as 
 the purchasing power of gold decreases with an increase 
 in its quantity. That is, as the quantity of liquid in 
 Gm doubles, the distance of the surface from the line
 
 106 THE PURCHASING POWER OF MONEY [Chap. VI 
 
 00 should decrease by one half. In a similar manner 
 the shape of the gold bullion cistern must be such as 
 will make the distance of the hquid surface below 00 
 decrease with an increase of the liquid in the same way 
 as the value of gold bullion decreases with an increase 
 of the stock of gold bullion. The shapes of the two 
 cisterns need not, and ordinarily will not, be the same, 
 for we can scarcely suppose that halving the purchas- 
 ing power of gold will always exactly double the amount 
 of bullion in existence. 
 
 Both reservoirs have inlets and outlets. Let us 
 consider these in connection v/ith the bulUon reservoir 
 {Gi). Here each inlet represents a particular mine 
 supplying bullion, and each outlet represents a partic- 
 ular use in the arts consuming gold bullion. Each 
 mine and each use has its own distance from 00. 
 There are, therefore, three sets of distances from 00 : 
 the inlet distances, the outlet distances, and the liquid- 
 surface distance. Each inlet distance represents the 
 cost of production for each mine, measured in goods ; 
 each outlet distance represents the value of gold in 
 some particular use, likewise measured in goods. The 
 surface distance, as we have already explained, repre- 
 sents the value of bullion, likewise measured in goods, 
 — in other words, its purchasing power. 
 
 It is evident that among these three sets of levels 
 there will be discrepancies. These discrepancies serve 
 to interpret the relative state of things as between 
 bullion and the various flows — in and out. If an 
 inlet at a given moment be above the surface level, 
 i.e. at a less distance from 00, the interpretation is 
 that the cost of production is less than the purchasing 
 power of the bullion. Hence the mine owner will turn 
 on his spigot and keep it on until, perchance, the sur-
 
 Sec. 4] INDIRECT INFLUENCES CONTINUED 107 
 
 face level rises to the level of his mine, — i.e. until 
 the surface distance from 00 is as small as the inlet 
 distance, — i.e. until the purchasing power of bullion 
 is as small as the cost of production. At this point 
 there is no longer any profit in mining. So much for 
 inlets ; now let us consider the outlets. If an outlet 
 at a given moment be below the surface level, — i.e. 
 at a greater distance from 00, — the interpretation is 
 that the value of gold in that particular use is greater 
 than the purchasing power of bullion. Hence gold 
 bullion will flow into these uses where its worth is 
 greater than as bullion. That is, it will flow out of all 
 outlets helow the surface in the reservoir. 
 
 It is evident, therefore, that at any given moment, 
 only the inlets above the surface level, and only the 
 outlets below it, will be called into operation. As the 
 surface rises, therefore, more outlets will be brought 
 into use, but fewer inlets. That is to say, the less the 
 purchasing power of gold as bullion, the more it will 
 be used in the arts, but the less profitable it will be for 
 the mines to produce it, and the smaller will be the 
 output of the mines. As the surface falls, more inlets 
 will come into use and fewer outlets. 
 
 We turn now to the money reservoir (G™) . The fact 
 that gold has the same value either as bullion or as 
 coin, because of the interflow between them, is in- 
 terpreted in the diagram by connecting the bullion 
 and coin reservoirs, in consequence of which both will 
 (like water) have the same level. The surface of the 
 liquid in both reservoirs will be the same distance be- 
 low the line 00, and this distance represents the value 
 of gold or its purchasing power. Should the inflow 
 at any time exceed the outflow, the result will neces- 
 sarily be an increase in the stock of gold in existence.
 
 108 THE PURCHASING POWER OF MONEY [Chap. VI 
 
 This will tend to decrease the purchasing power or 
 value of gold. But as soon as the surface rises, fewer 
 inlets and more outlets will operate. That is, the 
 excessive inflow or production on the one hand will 
 decrease, and the deficient outflow or consumption on 
 the other hand will increase, checking the inequality 
 between the outflow and inflow. If, on the other hand, 
 the outflow should temporarily be greater than the in- 
 flow, the reservoir will tend to subside. The purchas- 
 ing power will increase ; thus the excessive outflow 
 will be checked, and the deficient inflow stimulated, — 
 restoring equilibrium. The exact point of equilibrium 
 may seldom or never be realized, but as in the case 
 of a pendulum swinging back and forth through a posi- 
 tion of equilibrium, there will always be a tendency to 
 seek it. 
 
 It need scarcely be said that our mechanical diagram 
 is intended merely to give a picture of some of the chief 
 variables involved in the problem under discussion. 
 It does not of itself constitute an argument, or add 
 any new element ; nor should one pretend that it in- 
 cludes explicitly all the factors which need to be con- 
 sidered. But it does enable us to grasp the chief 
 factors involved in determining the purchasing power 
 of money. It enables us to observe and trace the 
 following important variations and their effects : — 
 
 First, if there be an increased production of gold — 
 due, let us suppose, to the discovery of new mines or 
 improved methods of working old ones — this may be 
 represented by an increase in the number or size of the 
 inlets into the Gb reservoir. The result will evidently 
 be an increase of ''inflow" into the bullion reservoir, 
 and from that into the currency reservoir, a consequent 
 gradual filling up of both, and therefore a decrease in
 
 Sec. 4] INDIRECT INFLUENCES CONTINUED 109 
 
 the purchasing power of money. This process will be 
 checked finally by the increase in consumption. And 
 when production and consumption become equal, an 
 equilibrium will be established. An exhaustion of gold 
 mines obviously operates in exactly the reverse manner. 
 
 Secondly, if there be an increase in the consumption 
 of gold — as through some change of fashion — it 
 may be represented by an increase in the number or 
 size of the outlets of Gt. The result will be a draining 
 out of the bullion reservoir, and consequently a de- 
 creased amount in the currency reservoir : hence an 
 increase in the purchasing power of gold, which in- 
 crease will be checked finally by an increase in the out- 
 put of the mines as well as by a decrease in consump- 
 tion. When the increased production and the decreased 
 consumption become equal, equilibrium will again be 
 reached. 
 
 If the connection between the currency reservoir 
 and the bullion reservoir is closed by a valve, that 
 is, if the mints are closed so that gold cannot flow 
 from bullion into money (although it can flow in the 
 reverse direction), then the purchasing power of the 
 gold as money may become greater than its value as 
 bullion. Any increase in the production of gold will 
 then tend only to fill the bullion reservoir and decrease 
 the distance of the surface from the line 00, i.e. lower 
 the value of gold bullion. The surface of the liquid 
 in the money reservoir will not be brought nearer 00. 
 It may even by gradual loss be lowered farther away. 
 In other words, the purchasing power of money will 
 by such a valve be made entirely independent of the 
 value of the bullion out of which it was first made. 
 
 An illustration of this principle is found in the history 
 of the silver currency in India. After long discussion the
 
 110 THE PURCHASING POWER OF MONEY [Chap. VI 
 
 mints of India were closed to silver in 1893. Previous 
 to that time the value of coined silver had followed 
 closely the value of silver bullion, but the closure 
 produced an immediate divergence between the two. 
 The rupee has remained independent of silver ever since ; 
 and during the first six years — until 1899 — it was 
 independent of gold also. Its present relation to the 
 latter metal will be discussed in the next chapter. 
 
 We have now discussed all but one of the outside in- 
 fluences upon the equation of exchange. That one is 
 the character of the monetary and banking system 
 which affects the quantity of money and deposits. 
 This we reserve for special discussion in the following 
 chapter. Meanwhile, it is also noteworthy that al- 
 most all of the influences affecting either the quantity 
 or the velocities of circulation have been and are pre- 
 dominantly in the direction of higher prices. Almost 
 the only opposing influence is the increased volume 
 of trade; but this is partly neutralized by increased 
 velocities due to the increased trade itself. We may 
 here point out that some of those influences discussed 
 in this and the preceding chapter operate in more than 
 one way. Consider, for instance, technical knowledge 
 and invention, which affect the equation of exchange 
 by increasing trade. So far as these increase trade, 
 the tendency is to decrease prices ; but so far as they 
 develop metallurgy and the other arts which increase 
 the production and easy transportation of the precious 
 metals, they tend to increase prices. So far as they 
 make the transportation and transfer of money and 
 deposits quicker, they also tend to increase prices. 
 So far as they lead to the development of the art of 
 banking, they likewise tend to increase prices, both by 
 increasing deposit currency {M') and by increasing the
 
 Sec. 4] INDIRECT INFLUENCES CONTINUED 1 1 1 
 
 velocity of circulation both of money and deposits. 
 So far as they lead to the concentration of population 
 in cities, they tend to increase prices by accelerating 
 circulation. 
 
 Finally, so far as per capita trade is increased through 
 this or any other cause, there is a tendency to decrease 
 prices. What the net effect of the development of the 
 arts may be during any given period will depend on the 
 predominant direction in which the arts are developed.
 
 CHAPTER VII 
 
 INFLUENCE OF MONETARY SYSTEMS ON PURCHASING 
 
 POWER 
 
 Thus far we have considered the influences that de- 
 termine the purchasing power of money when the money 
 in circulation is all of one kind. The illustration given 
 in the previous chapter shows how the money mecha- 
 nism operates when a single metal is used. We have 
 now to consider the monetary systems in which more 
 than one kind of money is used. 
 
 One of the first difficulties in the early history of 
 money was that of keeping two (or more) metals in 
 circulation. One of the two would become cheaper than 
 the other, and the cheaper would drive out the dearer. 
 This tendency was observed by Nicolas Oresme, 
 afterwards Count Bishop of Lisieux, in a report to 
 Charles V of France, about 1366, and by Copernicus 
 about 1526 in a report or treatise written for Sigis- 
 mund I, King of Poland.^ Macleod in his Elements 
 of Political Economy, published in 1857,^ before he had 
 become aware of the earlier formulations of Oresme 
 and Copernicus,^ gave the name ''Gresham's Law" to 
 this tendency, in honor of Sir Thomas Gresham, who 
 stated the principle in the middle of the sixteenth cen- 
 
 1 Henry Dunning Macleod, The History of Economics, New York 
 (Putnam), 1896, pp. 37 and 38. 
 
 2 P. 477. 
 
 » Macleod, The History of Economics, pp. 38 and 39. 
 
 112
 
 Sec. IJ INFLUENCE OF MONETARY SYSTEMS 113 
 
 tury. The tendency seems in fact, to have been rec- 
 ognized even among the ancient Greeks, being men- 
 tioned in the "Frogs" of Aristophanes : * — 
 
 ^'For your old and standard pieces valued and approved and tried, 
 Here among the Grecian nations and in all the world beside, 
 Recognized in every realm for trusty stamp and pure assay. 
 Are rejected and abandoned for the trash of yesterday, 
 For a vile, adulterate issue, drossy, counterfeit, and base 
 Which the traffic of the City passes current in their place." 
 
 Gresham's or Oresme's Law is ordinarily stated in 
 the form, ''Bad money drives out good money," for 
 it was usually observed that the badly worn, defaced, 
 light-weight, ''clipped," "sweated," and otherwise de- 
 teriorated money tended to drive out the full-weight, 
 freshly minted coins. This formulation, however, is 
 not accurate. It is not true that "bad" coins, e.g. 
 worn, bent, defaced, or even clipped coins, will drive 
 out other money just because of their worn, bent, de- 
 faced, or clipped condition. Accurately stated, the 
 Law is simply this : Cheap money will drive out dear 
 money. The reason the cheaper of two moneys always 
 prevails is that the choice of the use of money rests 
 chiefly with the man who gives it in exchange, not 
 with the man who receives it. When any one has 
 the choice of paying his debts in either of two moneys, 
 motives of economy will prompt him to use the 
 cheaper. If the initiative and choice lay principally 
 with the person who receives, instead of the person who 
 pays the money, the opposite would hold true. The 
 dearer or "good" money would then drive out the 
 cheaper or "bad" money. 
 
 What then becomes of the dearer money ? It may 
 
 1 893-898, Frere's translation.
 
 114 THE PURCHASING POWER OF MONEY [Chap. Vli 
 
 be hoarded, or go into the melting pot, or go abroad, — 
 hoarded and melted from motives of economy, and 
 sent abroad because, where foreign trade is involved, it 
 is the foreigner who receives the money, rather than 
 ourselves who give it, who dictates what kind of money 
 shall be accepted. He will take only the best, because 
 our legal-tender laws do not bind him. 
 
 The better money might conceivably be used in ex- 
 change at a premium, i.e. at its bullion value; but the 
 difficulties of arranging payments in it, which would 
 be satisfactory to both parties, are such that in practice 
 it is never so used in large quantities. In fact, the force 
 of Gresham's Law is so great that it will even sacrifice 
 the convenience of a whole nation. For instance, in 
 Italy fifteen years ago the overissue of paper money 
 drove not only gold across the Alps, but also silver 
 and copper. These could circulate in Southern France 
 at a par with corresponding coins there because France 
 and Italy belonged to the Latin Union. Consequently, 
 for a time there was very little small change left, below 
 the denomination of 5 lire notes. Customers at retail 
 stores often found it impossible to make their pur- 
 chases because they lacked the small denominations 
 necessary, and because the storekeeper lacked the same 
 small denominations, and could not make change. To 
 meet the difficulty, 30,000,000 of 1 lire notes were 
 issued, and these were so much in demand that dealers 
 paid a premium for them. 
 
 Gresham's Law applies not only to two rival moneys 
 of the same metal; it applies to all moneys that cir- 
 culate concurrently. Until ''milling" the edges of 
 coins was invented and a ''limit of tolerance" of the 
 mint (deviation from the standard weight) was adopted, 
 much embarrassment was felt in commerce from the
 
 Sec. 2] INFLUENCE OF MONETARY SYSTEMS 115 
 
 fact that the chpping and debasing of coin was a com- 
 mon practice. Nowadays, however, any coin which has 
 been so "sweated" or cUpped as to reduce its weight 
 appreciably ceases to be legal tender, and being com- 
 monly rejected by those to whom it is offered ceases 
 to be money. Within the customary ^ or legal limits of 
 tolerance, however — that is, as long as the cheaper 
 money retains the "money" power — it will drive 
 out the dearer. 
 
 §2 
 
 The obvious effect of Gresham's Law is to decrease \ 
 the purchasing power of money at every opportunity, j 
 The history of the world's currencies is largely a record 
 of money debasements, often at the behest of the 
 sovereign. Our chief purpose now, in considering 
 Gresham's Law, is to formulate more fully the causes 
 determining the purchasing power of money under 
 monetary systems subject to the operation of Gresham's 
 Law. The first application is to bimetallism. 
 
 In order to understand fully the influence of any 
 monetary system on the purchasing power of money, 
 we must first understand how the system works. ^ It 
 has been denied that bimetallism ever did work or can 
 be made to work, because the cheaper metal will drive 
 out the dearer. Our first task is to show, quite irrespec- 
 tive of its desirability, that bimetallism can and does 
 "work" under certain circumstances, but not under 
 others. To make clear when it will work and when it 
 will not work, we shall continue to employ the mechani- 
 
 ' Sometimes custom is less strict than law. For instance, in 
 California worn gold coin below the mint limit of tolerance con- 
 tinues to circulate. It is called "bank gold." 
 
 'Irving Fisher, "The Mechanics of Bimetallism," (British) 
 Economic Journal, September, 1894, pp. 527-536.
 
 116 THE PURCHASING POWER OF MONEY [Chap. VH 
 
 cal illustration ^ of the last chapter, in which the amount 
 of gold bullion is represented by the contents of res- 
 ervoir Gb (Figs. 6, 7). Here, as before, we represent 
 the purchasing power or value of gold by the distance 
 of the water level below the zero level, 00. In the 
 last chapter, our figure represented only one metal, 
 gold, and represented that metal in two reservoirs, — the 
 bullion reservoir and the coin reservoir. We shall now, 
 one step at a time, elaborate that figure. First, as in 
 Figure 6 a, we add a reservoir for silver bullion {St), a 
 
 reservoir of somewhat different shape and size from 
 Gi. This reservoir may be used i to show the relation 
 
 ^ In its present application it is somewhat like a symbolism 
 suggested by Jevons in his Money and the Mechanism of Exchange, 
 New York (Appleton), 1896, p. 140.
 
 Sec. 2] INFLUENCE OF MONETARY SYSTEMS 117 
 
 between the value or purchasing power of silver and 
 its quantity in the arts and as bullion. Here, then, 
 are three reservoirs. At first the silver one is entirely 
 isolated; but after a while we shall connect it with 
 the middle one. For the present, let us suppose that 
 the middle one, which contains money, is entirely filled 
 with gold money only (Fig. 6 a), no silver being yet 
 used as money. In other words, the monetary system 
 is the same as that discussed in the last chapter. The 
 only change we have introduced is to add to the pic- 
 ture another reservoir {St), entirely detached, showing 
 the quantity and value of silver bullion. 
 
 We next suppose a pipe opened at the right, connect- 
 ing Sb with the money reservoir; that is, we introduce 
 bimetallism. Under bimetallism, governments open 
 their mints to the free coinage of both metals at a fixed 
 ratio, i.e. a fixed ratio between the said metals. For 
 instance, if a silver dollar contains 16 grains of silver 
 for every grain of gold in a gold dollar, the ratio is said 
 to be 16 to 1. Under this system, the debtor has the 
 option, unless otherwise bound by his contract, of mak- 
 ing payment either in gold or in silver money. These, 
 in fact, are the two requisites of complete bimetallism, 
 viz. (1) the free and unlimited coinage of both metals at 
 a fixed ratio, and (2) the unlimited legal tender of each 
 metal at that ratio. ^ These new conditions are repre- 
 sented in Figure 6 b (and later, Fig. 7 b) , where a pipe gives 
 silver an entrance into the money or central reservoir.^ 
 
 1 The possibility of government's fixing any ratio between gold 
 and silver to which the market ratio will conform has been so bitterly 
 disputed that in addition to the positive argument contained in the 
 text, a negative criticism of what are believed to be the chief fal- 
 lacies underlying these disputes is inserted in § 1 of the Appendix 
 to (this) Chapter VII. 
 
 2 Of course a unit of water represents gold and silver at their
 
 118 THE PURCHASING POWER OF MONEY [Chap. Vlt 
 
 What we are about to represent is not the relations 
 between mines, bullion, and arts, but the relations be- 
 tween bulhon (two kinds) and coins. We may, there- 
 fore, disregard for the present all inlets and outlets 
 except the connections between the bulhon reservoirs 
 and coin reservoir. 
 
 Now in these reservoirs the surface distances below 
 00 represent, as we have said, purchasing power 
 of gold and silver. But each unit of silver (say each 
 drop of silver water, whether as money or as bulhon) 
 contains sixteen times as many grains as each unit of 
 gold (say each drop of gold water, whether as money 
 or as bullion). That is, a unit of water represents a 
 dollar of gold or a dollar of silver. All we wish to 
 represent is the relative purchasing power of corre- 
 sponding units. 
 
 The waters representing gold and silver money are 
 separated by a movable film /. In Figure 6 a this film 
 is at the extreme right ; in Figure 6 6, at the extreme 
 left; in Figure 7 a, again at the right; and in Figure 7 h, 
 midway. The a figures represent conditions before 
 the mints are opened to silver. The h figures repre- 
 sent conditions after they have been opened and Gres- 
 ham's Law has operated. If, just previous to the in- 
 troduction of bimetallism, the silver level in S^ is below 
 the gold level in Gj, the statute introducing bimetallism 
 will be inoperative, i.e. the silver bullion will not flow 
 uphill, as it were, into the money reservoir ; but if, as 
 in Figure 6 a or in 7 a, the silver level is higher, then as 
 
 coining weights. If the bimetallic ratio is 16 to 1, the cisterns 
 must be so constructed that a cubic inch of water shall represent 
 an ounce of gold or 16 ounces of silver and that the number of 
 inches separating the surfaces of liquid from 00 shall represent the 
 marginal utility of an ounce of gold and of 16 ounces of silver, 
 respectively.
 
 Sec. 2] 
 
 INFLUENCE OF MONETARY SYSTEMS 
 
 119 
 
 soon as the mints are open to silver, it will flow into 
 circulation. Being at first cheaper than gold, it will 
 push out the gold money through the left tube (i.e. by- 
 melting) into the bullion market. This expulsion of 
 gold may be complete, as shown in Figure 6 b, or only 
 partial, as shown in Figure 7 b. The expulsion will 
 
 FiQ. 7. 
 
 continue just as long as there is a premium on gold ; 
 that is, as long as the silver level in the bullion reservoir 
 is above the gold level in the money reservoir ; i.e. as 
 long as silver bullion is cheaper than gold money. 
 
 Let mm, as shown in Figure 6 a, be the mean level ; 
 that is, a level such that the volume x above it equals 
 the combined vacant volumes y and z below it. This 
 line, mm, remains the mean level, whatever may be the
 
 120 THE PURCHASING POWER OF MONEY [Chap. VII 
 
 distribution of the contents among the three reservoirs. 
 As soon as the connecting pipe is inserted, silver will 
 flow into the money reservoir and, in accordance with 
 Gresham's Law, will displace gold. 
 
 Here we have to distinguish two cases : (1) when the 
 silver x above the mean hne, mm, exceeds the total con- 
 tents of the money reservoir below this line; (2) when x 
 is less than said lower contents. In the first case, it 
 is evident that silver will sweep gold wholly out of 
 circulation, as shown in Figure 6 b, where the film has 
 moved from the extreme right to the extreme left. 
 The contents of silver in the bullion reservoir are less 
 than before, and the contents of gold in the bullion 
 reservoir greater than before. 
 
 But this redistribution is only the first effect of open- 
 ing the mints to silver. The balance between produc- 
 tion and consumption has been upset both for gold 
 and for silver. The increased value of silver (lowered 
 level in Sh) has stimulated production, bringing into 
 operation silver mines (uncovered inlets at right) ; 
 and, on the other hand, the decreased value of gold 
 (raised level in Gh) has discouraged gold production, 
 shutting off gold mines (covered inlets at left). Like 
 alterations are effected in the outflows, i.e. the con- 
 sumption, waste, and absorption of each metal. 
 
 The result is that the levels resulting from the 
 first redistribution will not necessarily be permanent. 
 They may recede toward their original respective 
 levels, and under all ordinary conditions will do so. 
 But in any case, — and this is the point to be em- 
 phasized, — they cannot return entirely to those levels. 
 Such a supposition would be untenable, as the follow- 
 ing reasoning shows. Suppose, for the moment, that 
 silver should return to its original level. Then the
 
 Sec. 3] INFLUENCE OF MONETARY SYSTEMS 121 
 
 silver inflow (production) would also return to its origi- 
 nal rate dependent on that level, but the silver outflow 
 (consumption, waste, etc.) would be greater than 
 originally. The consumption in the arts would be the 
 same; but the waste and absorption of silver money 
 constitute an additional drain. Therefore, consump- 
 tion (equal to production before) will now exceed pro- 
 duction, and the high original level cannot be main- 
 tained. The conclusion follows that, whatever the new 
 level of permanent equilibrium, it lies below the old. 
 The same argument, mutatis mutandis, proves that for 
 gold the new level of permanent equilibrium lies above 
 the old. The gap between the two original levels has 
 therefore been reduced. Even though bimetallism has 
 failed to bring about a concurrent circulation of both 
 metals and a parity of values at the given coinage 
 ratio, it has resulted in reducing the value of the dearer 
 metal (gold) and increasing that of the cheaper (silver). 
 This effect of mutual approach will be referred to in 
 discussing the second case which follows. 
 
 §3 
 
 So much for the first case, where x is larger than the 
 contents of the money reservoir below mm. In the 
 second case, x is supposed to be smaller than the con- 
 tents of the money reservoir below the line mm ; that 
 is, there is not enough silver to push all the gold out 
 of circulation. Under these circumstances, disregard- 
 ing for the moment any change in production or 
 consumption, the opening of the pipe — the opening 
 of the mints to silver — will bring the whole system 
 of liquids to the common level mm. In other words, 
 the premium on gold bullion will disappear (Fig. 7 6), 
 and its purchasing power and the purchasing power
 
 122 THE PURCHASING POWER OF MONEY [Chap. VII 
 
 of silver bullion will be a mean between their original 
 
 purchasing powers, this mean being the distance of the 
 
 I mean line, mm, below 00. In other words, bimetallism 
 
 1 in this case succeeds; that is, it will establish and 
 
 V. maintain an equality for a time between the gold and 
 
 silver dollars in the money reservoir. 
 
 But the equilibrium which we have just found is a 
 mere equalization of levels produced by a redistribution 
 of the existing stocks of gold and silver among the 
 various reservoirs. It will be disturbed as soon as 
 these stocks are disturbed. A permanent equilibrium 
 requires that the stocks shall remain the same, — re- 
 quires, in other words, an equality between production 
 and consumption for each metal. After the inrush of 
 silver from the silver bullion to the money reser- 
 voir, it is evident that the production and consump- 
 tion of gold need no longer be equal to each other, 
 nor need the production and consumption of silver 
 be equal to each other. The same stimulation of sil- 
 ver production and discouragement of gold production 
 will occur that occurred in the case considered in the 
 last section. The result may be that silver will, in 
 the end, entirely displace gold; or again it may fail to 
 do so. 
 
 There may be, then, two possibilities. One possibility 
 is obvious, namely, that gold may be completely driven 
 out, the result being the same as already represented in 
 the lower part of Figure 6. In the second possibility, 
 gold will not be pushed out. 
 
 The reality of this second possibility will be clear if 
 we attempt first to deny it. Suppose, therefore, that the 
 film / be at the extreme left, and permanent equilib- 
 rium finally established. In the illustrative mechanism 
 the gold level will be lower than before, and the silver
 
 Sec. 3] INFLUENCE OF MONETARY SYSTEMS 123 
 
 level higher. How much lower and higher depends 
 evidently on technical conditions of the production and 
 consumption corresponding to the situation. It is of 
 course not inconceivable that the gold level may be so 
 much lower and the silver level so much higher as to 
 make their relative positions reversed, i.e. to make 
 the gold level higher than the silver level. But in this 
 event it is quite impossible that the film / should be 
 at the left. Gold, now being the cheaper, would flow 
 into circulation and displace silver. Under the con- 
 ditions we are now imagining, the film cannot stay 
 at either extreme. If it is at the right, silver will be 
 cheaper than gold and will move it leftward ; if it 
 is at the left, gold will be cheaper than silver and 
 will move it rightward. Under these circumstances, 
 evidently, equilibrium must lie between these extremes, 
 as in Figure 7 b. The conditions of production and con- 
 sumption under which bimetallism can succeed are 
 therefore (1) that under silver monometallism a gold 
 dollar would in equilibrium be cheaper than a silver 
 dollar, and (2) that under gold monometallism silver 
 would be cheaper than gold. A bimetallic level, there- 
 fore, when bimetallism is feasible, must always lie 
 between the levels which the two metals would have 
 assumed under gold monometallism, gold being currency 
 and silver not, and for the same reasons it must lie 
 between the levels which the two metals would have 
 under silver monometallism, silver being currency and 
 gold not.^ In all our reasoning we have supposed a 
 given legal ratio between the two metals. But bimetal- 
 lism, impossible at one ratio, is always possible at 
 
 ^ But it does not necessarily lie between the level of the currency 
 under gold monometallism and its level under silver mono- 
 metallism.
 
 124 THE PURCHASING POWER OF MONEY [Chap. VII 
 
 another. There will always be two limiting ratios be- 
 tween which bimetalUsm is possible.^ 
 
 It is easy to show that the two limiting ratios for a 
 single nation are narrower than for a combination of 
 nations, since the currency reservoir is, for one nation, 
 smaller than for many, while the arts reservoirs are 
 virtually larger by the amount of the monometalHc 
 currencies of the remaining nations. When bimetalUsm 
 has broken down at one ratio, it can always be set in 
 operation again at another, but the transition requires 
 a depreciation of the currency. The only way of re- 
 introducing the metal which has passed out of the 
 currency reservoir is by lowering the amount of it in 
 the monetary unit, — unless the still more drastic 
 measure is adopted of raising the coinage weight of 
 money alread}' in circulation. 
 
 I It should also be pointed out that two nations can- 
 not both maintain bimetallism at two different ratios 
 unless the difference is less than the cost of shipment. 
 One of the two nations would lose the metal which it 
 undervalued and find itself on a monometallic basis. 
 
 A few additional observations may now be stated. 
 The temporary and normal equiUbriums which have 
 been considered separately are in fact quite distinctly 
 separated in time.! The time of redistributing existing 
 stocks of metal, according to a newly enacted law, 
 depends on the rapidity of transportation, melting, and 
 minting, and would be measured in months or weeks. 
 Normal equihbrium, however, depends on the slow 
 working of changes in the rates of production and 
 consumption, and would be measured in years. The 
 normal equilibrium, if once established, is permanent so 
 long as the conditions of production and consumption 
 1 See § 2 of Appendix to (this) Chapter VII.
 
 Sec. 3] INFLUENCE OF MONETARY SYSTEMS 125 
 
 do not change. Slight alterations of these conditions — 
 the exhaustion of mines, the discovery of new leads, 
 etc. — will cause slight variations in the proportions of 
 gold and silver money, that is, in the position of the 
 film /. The oscillations of this film (and not of the 
 price ratio as in the case of two unconnected com- 
 modities) reflect these changing conditions. But, in 
 all probability, this film will sooner or later reach one 
 of its limits. The probable time for such an event is, 
 however, very long. The gold currency of the world 
 is, roughly speaking, perhaps $5,000,000,000 ; the annual 
 production of silver, reckoning at its present market 
 price, is roughly about $100,000,000. Supposing a 
 system of international bimetallism at, say, 36 to 1 to 
 be initially in normal equilibrium, consider the effect 
 of an enormous increase in the silver production, say 
 a half, or $50,000,000. Then a hundred years would 
 be required to push out gold without taking into account 
 the fact that, as the pushing proceeds, the excess of 
 production over consumption steadily declines. If 
 this excess dwindles uniformly from $50,000,000 to zero, 
 the period would be double, or two hundred years. 
 When we add to these considerations the fact that, 
 while the stimulus to the production of one metal acts 
 quickly, the ensuing check to the production of the 
 other acts more slowly, owing to the fixity of the ''sunk" 
 capital, and that, therefore, the volume of the currency 
 is greater at the end than at the beginning; also the 
 fact that the currency reservoir is itself constantly 
 expanding ; and finally the fact that fluctuations of 
 production are likely to be in either direction, and for 
 either metal, we may be tolerably confident that, if 
 initially successful with the film near the middle position, 
 international bimetallism would continue successful
 
 126 THE PURCHASING POWER OF MONEY [Chap. VII 
 
 for many generations. The initial success depends, 
 as has been seen, upon the ratio enacted. 
 
 It is to be observed that bimetalUsm can never avoid 
 a slight premium. On the contrary, it is this difference 
 of level which supplies the force which compells change 
 from one point of equiUbrium to another.^ 
 
 In a series of years, the bimetallic level remains 
 intermediate between the changing levels which the 
 two metals would separately follow. Bimetallism 
 spreads the effect of any single fluctuation over the 
 combined gold and silver markets. ^ The steadying 
 power of bimetallism depends on the breadths of the res- 
 ervoirs, and not on the position of the film /. It remains 
 in full force, no matter what may be the proportions 
 
 ^ As long as the premium lasts, the cheaper metal will doubtless 
 circulate somewhat faster, and the dearer somewhat more slowly, 
 than when there is no premium. This may, if desired, be repre- 
 sented by conceiving the thickness of the currency reservoir to 
 decrease on the one side of / and increase on the other, making one 
 metal "go farther" (cover more area in the diagram) than normally, 
 and hasten the motion of / to the equilibrium point. Sluggishness 
 (increase of thickness), of which "hoarding" is the chief application, 
 is referred to below. 
 
 "■ To represent the steadying effect on a single fluctuation, we 
 observe that under bimetallism the three reservoirs act as one. 
 Therefore, compared with monometallism, the fluctuations are 
 diminished in the inverse ratio of the liquid surfaces over which 
 the fluctuations spread. Thus, if the combined breadths of the 
 two left reservoirs at water level are two thirds of the combined 
 breadths of the three, an influx of gold which, if distributed only 
 over the two reservoirs, would make a layer an inch in depth, 
 would, over the three, have a depth of two thirds of an inch. Like- 
 wise the right reservoir being one third the aggregate width, an 
 inch fluctuation of silver, when merely merchandise, would be 
 reduced to one third of an inch, when connection is maintained 
 with the money reservoir. The breadths of the reservoir, which 
 here play the important role, are the rate of increase of commodity 
 relative to decrease of marginal utility. The law of inverse breadth 
 applies with exactness only to static, or short-time readjustments.
 
 Sec. 4] INFLUENCE OF MONETARY SYSTEMS 127 
 
 of gold and silver money, and is as great when only 
 one nation is bimetallic as when the whole world adopts 
 the system. Even if only Switzerland had a system 
 of bimetallism in successful operation, it would, until 
 its breakdown, keep together and equalize the currencies 
 of the whole world, wherever either gold or silver was 
 standard. In fact, the world would have all the benefits 
 of bimetallism enjoyed by Switzerland without its evils 
 and dangers. This international function would cease 
 abruptly as soon as the system of bimetallism should 
 fail. 
 
 It should be pointed out that the equalizing effect 
 maintained is relative only. It is conceivable that one 
 metal would be steadier alone than when joined to the 
 other. In a later chapter we shall consider the extent 
 to which this equalization is an advantage. Here 
 we confine ourselves to showing merely the mechanical 
 operation of the bimetallic system.^ 
 
 §4 
 
 Bimetallism is to-day a subject of historical interest 
 only. It is no longer practiced; but its former prev- 
 alence has left behind it in many countries, including 
 France and the United States, a monetary system 
 which is sometimes called the ^^ limpin g ' ' ptan d ard . 
 Such a system comes about when, in a system of 
 bimetallism, before either metal can wholly expel the 
 other, the mint is closed to the cheaper of them, but the 
 coinage that has been accomplished up to date is not 
 recalled. Suppose silver to be the metal thus excluded, 
 as in France and the United States. Any money 
 
 ^Cf. Leonard Darwin, Bimetallism, London (Murray), 1897, 341 
 pp. ; Bertrand Nogaro, "U experience bimetalliste," Revue d' economic 
 politique, 1908.
 
 128 THE PURCHASING POWER OF MONEY [Chap. VII 
 
 already coined in that metal and in circulation is kept 
 in circulation at par with gold. This parity may con- 
 tinue even if limited additional amounts of silver be 
 coined from time to time. There will then result a 
 difference in value between silver bullion and silver coin, 
 the silver coin being overvalued. This situation is 
 represented in Figure 8. Here the pipe connection 
 between the money reservoir and the silver-bullion 
 
 Fig. 8. 
 
 reservoir has been, as it were, cut off, or, let us say, 
 stopped by a valve which refuses passage of silver from 
 the bullion reservoir to the money reservoir but not 
 the reverse (for no law ever can prevent the melting 
 down of silver coins into bullion). Newly mined silver 
 cannot now become money, and thus lower the pur- 
 chasing power of the money. 
 
 On the other hand, new supplies of gold continue to 
 affect the value of currency, as before, — the value, not 
 only of the gold, but also of the concurrently circulating 
 overvalued silver. If more gold should flow into the 
 money reservoir, it would raise the currency level. 
 Should this level ever become higher than the level 
 of the silver bullion reservoir, silver would flow from 
 the money reservoir into the bullion reservoir ; for the
 
 Sec. 4] INFLUENCE OF MONETARY SYSTEMS 129 
 
 passage in that direction (i.e. melting) is still free. 
 So long, however, as the currency level is below the 
 silver level, i.e. so long as the coined silver is worth 
 more than the uncoined, there will be no flow of silver 
 in either direction. The legal prohibition prevents 
 the flow in one direction, and the laws of relative levels 
 prevent its flow in the other. 
 
 In the case just discussed, the value of the coined 
 silver will be equal to the value of gold at the legal ratio. 
 Precisely the same principle applies in the case of any 
 money, the coined value of which is greater than the 
 value of its constituent material. Take the case, for 
 instance, of paper money. So long as it has the dis- 
 tinctive characteristic of money, — general acceptability 
 at its legal value, — and is limited in quantity, its value 
 will ordinarily be equal to that of its legal equivalent 
 in gold. If its quantity increases indefinitely, it will 
 gradually push out all the gold and entirely fill the 
 money reservoir, just as silver would do under bimetal- 
 lism if produced in sufficiently large amounts. Like- 
 wise, credit money and credit in the form of bank 
 deposits would have this effect. To the extent that 
 they are used, they lessen the demand for gold, decrease 
 its value as money, and cause more of it to go into 
 the arts or to other countries. 
 
 So long as the quantity of silver or other token 
 money, e.g. paper money, is too small to displace gold 
 completely, gold will continue in circulation. The value 
 of the other money in this case cannot fall below that 
 of gold. For if it should, it would, by Gresham's Law, 
 displace gold, which we have supposed it is not of suffi- 
 cient quantity to do. The parity between silver coin 
 and gold under the "limping" standard is, therefore, 
 not necessarily dependent on any redeemability in gold,
 
 130 THE PURCHASING POWER OF MONEY [Chap. Vll 
 
 but may result merely from limitation in the amount of 
 silver coin. Such limitation is usually sufficient to 
 maintain parity despite irredeemability. This is not 
 always true, however ; for if the people should lose con- 
 fidence in some form of irredeemable paper or token 
 money, even though it were not overissued, it would de- 
 preciate and be nearly as cheap in money form as it is in 
 the raw state. A man is willing to accept money at its 
 face value so long as he has confidence that every one 
 else is ready to do the same. But it is possible, for 
 instance, for a mere fear of overissue to destroy this 
 confidence. The payee, who, under ordinary circum- 
 stances, submits patiently to whatever money is cus- 
 tomary or legal tender, may then take a hand and 
 insist on ''contracting out" of the offending standard.^ 
 That is, he may insist on making all his future con- 
 tracts in terms of the better metal, — - gold, for instance, 
 — and thus contribute to the further downfall of the 
 depreciated paper. 
 
 Irredeemable paper money, then, like our irredeemable 
 silver dollars, may circulate at par with other money, 
 if limited in quantity and not too unpopular. If it 
 is gradually increased in amount, such irredeemable 
 
 * In the mechanical interpretation, since the law would now be 
 inoperative, the film would no longer yield to pressure from the 
 right, and an appreciable difference of level on its two sides would 
 ensue. Such a mechanism would illustrate the concurrent cir- 
 culation of two metals at independent valuations, but experience 
 shows that such a condition is too full of inconveniences to be 
 maintained long. The silver will be progressively tabooed, that is, 
 its velocity of circulation will gradually decrease. This, as we 
 have seen, may be figured by supposing the currency reservoir (on 
 the right of the film only) to be thickened, thus bringing the film 
 to the right. If the silver is completely tabooed, the film will be 
 completely to the right, and there will be gold monometallism. 
 The monetary result of such discrimination against silver is thus 
 the appreciation of gold.
 
 Sec. 4] INFLUENCE OF MONETARY SYSTEMS 131 
 
 money may expel all metallic money and be left in 
 undisputed possession of the field. 
 
 But though such a result — a condition of irredeem- 
 able paper money as the sole currency — is possible, it 
 has seldom if ever proved desirable. Unless safeguarded, 
 irredeemability is a constant temptation to abuse, and 
 this fact alone causes business distrust and discourages 
 long-time contracts and enterprises. Irredeemable 
 paper money has almost invariably proved a curse to 
 the country employing it. While, therefore, redeema- 
 bility is not absolutely essential to produce parity of 
 value with the primary money, practically it is a wise 
 precaution. The lack of redeemability of silver dollars 
 in the United States is one of the chief defects in our 
 unsatisfactory monetary system, and a continuing 
 danger. 
 
 It is possible to have various degrees of redeemability. 
 One of the most interesting systems of partial redeem- 
 ability is the system now known as the gold-exchange 
 standard, by which countries, not themselves on a strict 
 gold basis, nevertheless maintain substantial parity with 
 gold through the foreign exchanges. By this system the 
 government or its agent, while not redeeming its cur- 
 rency in gold, redeems it in orders on gold abroad. 
 That is, the government sells bills of exchange on Lon- 
 don or New York at a stated price. The currency which 
 it thus receives, and in a sense redeems, it keeps out of 
 circulation until the price of foreign exchange falls {i.e. 
 until the demand for redemption ceases). 
 
 The gold-exchange standard may be regarded as a 
 kind of limping standard with the added feature of 
 partial redemption. 
 
 This added feature, however, greatly modifies the 
 nature of the limping standard. The limping standard
 
 132 THE PURCHASING POWER OF MONEY [Chap. VII 
 
 without the gold-exchange attachment may at any time 
 break down, if the silver (or whatever else the over- 
 valued money may be) should become so redundant, 
 relatively to trade, as completely to displace gold. As 
 soon as all gold is driven abroad, parity with gold ceases. 
 But with the gold-exchange system this catastrophe is 
 avoided. In fact, with this system it is not necessary to 
 have gold in circulation at any time. The willingness of 
 the government to sell foreign exchange at a fixed price, 
 and to lock up the silver it receives thereby, takes that 
 much currency out of circulation just as effectively as 
 though the equivalent of gold had been exported. So 
 long as the government is willing and able to maintain 
 the price of bills of exchange with a gold country, it, 
 ipso facto, maintains approximate parity with gold.^ 
 
 We have now to illustrate, by historical examples, the 
 principles just explained. The first and most important 
 case is that of France. The ratio of 15^ to 1 was 
 adopted by France in 1785 and continued by the law 
 of 1803. The history of France and the Latin Union 
 during the period from 1785, and especially from 1803, 
 to 1873 is instructive. It affords a practical illustration 
 of the theory that when conditions are favorable, gold 
 and silver can be kept tied together for a considerable 
 period by means of bimetaUism. During this period 
 the public was ordinarily unconscious of any disparity 
 of value, and only observed the changes from the rela- 
 tive predominance of gold to the relative predominance 
 of silver in the currency and vice versa. In the whole- 
 sale bullion market, it is true, there were slight varia- 
 
 1 Cf. Charles A. Conant, " The Gold Exchange Standard," Eco- 
 nomic Journal, June, 1909, pp. 190-200.
 
 Sec. 5] INFLUENCE OF MONETARY SYSTEMS 133 
 
 tions from the ratio of 162 to 1. But such variations 
 simply supplied the force to restore equilibrium. 
 
 From 1803 until about 1850 the tendency was for 
 silver to displace gold. In our mechanical terms there 
 was, for the most part, an inflow on the right-hand side 
 of the money reservoir, and the film was gradually 
 pressed leftward. The statistics for the movements 
 of gold and silver are not given separately and continu- 
 ously before 1830. But from 1830 to 1847, inclusive, 
 there was a net export of gold of 73,000,000 francs, 
 although five of the years showed an import, making 
 an average export of over 4,000,000 francs a year.^ 
 From 1830 until 1851 there was a net importation of 
 silver in every year, amounting to a total for the period 
 of 2,297,000,000 francs or an average of over 104,000,000 
 francs a year.^ The statistics for silver are taken to 
 1851 because after that year the movement for silver 
 was reversed, while for gold the inward flow began 
 with 1848. Silver was displacing gold and filling up 
 the currency reservoir. Nevertheless, the reservoir 
 was expanding so fast, that is, trade was increasing, that 
 there was no increase of prices, but rather a decrease. 
 By 1850, the film had practically reached its limit. 
 Bimetallism would have broken down and resulted in 
 silver monometallism then and there, except for the 
 fact that, as though to save the day, gold had just been 
 discovered in California. The consequence of the new 
 and increased gold production was a reverse movement, 
 an inflow of gold into the French currency and an out- 
 flow of silver. From 1848 to 1870, inclusive, the net 
 importation of gold amounted to 5,153,000,000 francs 
 or over 224,000,000 francs a year, while the net exporta- 
 
 ^ W. A. Shaw, The History of the Currency, 3d ed., London 
 (Clement Wilson), 1899, p. 183. 2 j^^i^,, p. 184.
 
 134 THE PURCHASING POWER OF MONET [Chap. VII 
 
 tion of silver from 1852 to 1864, inclusive, amounted to 
 1,726,000,000 francs or nearly 133,000,000 francs a year.^ 
 Gold was displacing silver and filling the currency. It 
 seemed probable that France would be entirely 
 drained of her silver currency and come to a gold basis. 
 France formed with Belgium, Italy, and Switzerland 
 in 1865, and Greece in 1868, the Latin Monetary Union. 
 The amount of silver in the subsidiary coins was re- 
 duced, but the standard silver coins were kept at the old 
 ratio with gold. But the new gold mines were gradu- 
 ally exhausted, while silver production increased, with 
 the consequence that there was again a reversal of 
 the movement. From 1871 to 1873, inclusive, the 
 exportation of gold netted 375,000,000 francs, or an 
 average of 125,000,000 francs a year, while from 1865 
 to 1873, inclusive, the net importation of silver was 
 860,000,000 francs, or over 94,000,000 francs a year. 
 Thus, even before the gold began to flow out, in 1871, 
 silver had begun to flow in, i.e. in 1865. Silver grad- 
 ually pushed gold out of circulation and, had not France 
 and the other countries of the Latin Union successively 
 suspended the free coinage of silver in 1873-1878, they 
 would have found themselves on a silver, instead of a 
 gold, basis. It has been claimed by bimetallists that 
 this action in demonetizing silver was itself the cause of 
 the breakdown. The truth is, that the breakdown 
 was the cause of demonetization, although demonetiza- 
 tion, by keeping back silver from circulation and keeping 
 gold in circulation, did operate to widen the breach 
 already made. 
 
 The film, in other words, was close to the left limit, and 
 the currency reservoir was filled for the most part with 
 
 ^ W. A. Shaw, The History of the Currency, 3d ed., London 
 (Clement Wilson), 1899, pp. 183 and 184.
 
 Sec. 6] INFLUENCE OF MONETARY SYSTEMS 135 
 
 silver. The Latin Union might conceivably have main- 
 tained bimetalHsm longer if other countries had joined 
 with them. But it had to absorb, not only much of 
 the silver provided by the mines, but also a considerable 
 amount which had previously formed part of the mon- 
 etary stock of Germany and which, at the adoption of 
 the gold standard by that country following the Franco- 
 Prussian War, was thrown on the market. That is, 
 not only silver mines, but countries demonetizing silver, 
 dumped silver on the Latin Union. Add to this the 
 movement toward the gold standard in Scandinavia 
 and the United States, and it becomes evident that the 
 obstacles were many for a union comprising so few, and 
 mostly unimportant, states. 
 
 The parity with gold of the silver remaining in circu- 
 lation in the Latin Union is now preserved on the prin- 
 ciples explained earher in the chapter, viz. by limiting 
 its quantity, as well as by making it full legal tender 
 and receivable for public dues. 
 
 §6 
 
 It is strange that the lessons of the French and other 
 experiments do not seem to be generally understood 
 either by monometallists or bimetaUists. For instance, 
 uncompromising monometallists have pointed to the 
 variation in the value of gold and silver during the three 
 quarters of a century as disproving the possibility of 
 maintaining a legal ratio. They might as well point to 
 the ripples on a pond or the slight gradient of a river, 
 as disproving the fact that water seeks a level. These 
 ripples are really evidence of the process of seeking a 
 level and are trifling as compared with those which in 
 all probability would have taken place had there not 
 been a legal ratio. The diagram and tables used in
 
 136 THE PURCHASING POWER OF MONEY [Chap. Vii 
 
 Shaw's History of the Currency and the similar diagram 
 here given show that dm-ing the period of inflowing 
 silver, 1803 to 1850, in spite of the great increase in 
 the quantity of silver, the ratio was changed from 15 J 
 to 1 by at most only .75 points or slightly over 4.8 per 
 cent in any year, and the average departure was only 
 .29 points or 1.9 per cent. Moreover, the greater part of 
 the deviation is explainable by the seigniorage charge 
 then in force in France.^ During the succeeding period 
 from 1851 to 1870, characterized largely by an inflow of 
 gold, the maximum departure (in the opposite direction) 
 was .31 points or 2 per cent, with an average departure 
 of .14 points or .9 per cent, while during the succeeding 
 period of inflowing silver and outflowing gold, from 
 1871 to 1873, the ratio rose above 15i to 1 by a maxi- 
 mum of .42 points or 2.7 per cent and an average of 
 .21 points or 1.4 per cent. Contrast these figures with 
 those since 1873." The maximum departure from the 
 ratio of 15J to 1 since 1873 is 23.65 points, or 152.6 
 percent, and the average departure 10.4 points, or 67.1 
 per cent.^ The history of the ratio is shown in Figure 9. 
 On the other hand, bimetallists have often failed to 
 see that this experiment illustrates the limits as well 
 as the possibilities of bimetallism. In 1850 bimetallism 
 had almost broken down in France and would have been 
 succeeded by silver monometallism had not the in- 
 creased production of gold reversed the flow. In 1865, 
 
 1 Cf. J. F. Johnson, Money and Currency, Boston (Ginn) 1905, 
 p. 227. 
 
 2 Although France did not entirely suspend the coinage of the 
 silver five-franc pieces until 1876, yet limitation began with 1874. 
 See W. A. Shaw, The History of the Currency, pp. 194, 196. 
 
 ' These figures are compiled from data given in W. A. Shaw, 
 The History of the Currency, p. 159, and Reports of the Director of the 
 Mint.
 
 Sec. 6] 
 
 INFLUENCE OF MONETARY SYSTEMS 
 
 137 
 
 gold had largely driven out silver. By 1873, gold had 
 again largely disappeared, and it seems evident that it 
 would have disappeared entirely had not the suspension 
 of the free coinage of silver followed. A continuance 
 
 H in ! HMH'iWMiu,!'fr» i ' ! !H;Mi[ [ !lJ i i l ii niHli t H l H Mnupu 'i UHU<!HliHfHHimaa ay^HtiiHHli!i-a!iiti^^ 
 
 Fig. 9. 
 
 of bimetallism at a ratio of 15^ to 1 by France and the 
 Latin Union alone would doubtless have been im- 
 possible. Yet the attempt, though a failure, would have 
 kept the ratio nearer 15| to 1 than it actually has been;
 
 138 THE PURCHASING POWER OF MONEY [Chap. VII 
 
 for the Union would have furnished a large market for 
 silver. Possibly bimetallism could have been main- 
 tained longer, despite increased silver production, had 
 not several other countries adopted the gold standard 
 in these critical years. This fact helped to flood the 
 countries of the Latin Union with silver and drain them 
 of their gold. These countries were suffering all the 
 expense and trouble of maintaining the ratio between 
 gold and silver, while other countries were reaping most 
 of the benefits. Herein lies one of the weaknesses of 
 bimetallism as a practical political proposition, — each 
 country prefers that some other country or countries 
 should be the ones to adopt it. There is little prospect, 
 therefore, in the future, of any single country taking the 
 initiative, and still less of any international agreement. 
 
 § 7 
 
 The system now in use in France is also employed 
 in many other countries which, like France, have been 
 forced to adopt it or else become silver-standard coun- 
 tries. After the rupture of the bimetallic tie, which 
 until 1873 linked all gold and silver countries together, 
 the commercial world broke into two parts, gold-stand- 
 ard countries and silver-standard countries; and many 
 desiring to join the ranks of the former, but in danger of 
 being thrust among the latter, saved themselves by 
 closing their mints to silver and thereby adopting the 
 limping standard. One of these countries was British 
 India. 
 
 The case of India is interesting because it never was 
 a bimetallic country, and at the time of the adoption 
 of the present system, in which gold is the standard, 
 no gold was in circulation. The mints were closed to 
 silver in June, 1893, and the legal ratio put the rupee
 
 Sec. 7] INFLUENCE OF MONETARY SYSTEMS 139 
 
 at 16c?. At first, to the great discomfiture of those 
 who had advocated the new system, this value was 
 not maintained. But failure at first was to be ex- 
 pected because no gold was in circulation, and un- 
 suspected coined stores of silver existed to swell the 
 circulation in spite of the closure of the mints. More- 
 over, the government accepted from banks and others 
 considerable amounts of silver which had been shipped 
 to India before the closing of the mints, and coined it, 
 and a considerable amount was withdrawn from the 
 government reserve and put into circulation. The 
 value of the rupee fell by 1895 to as low as ISd. But 
 even from the first the value of the rupee kept above 
 the value of its contained silver. If it fell as compared 
 with the then appreciating gold, it rose as compared 
 with the value of silver bullion. Surely this may be 
 held to show that the value of money has some relation 
 to its quantity, apart altogether from the quantity and 
 the value of the constituent material. Furthermore, 
 the value of the rupee rose gradually, even in rela- 
 tion to the gold standard, from 13d. in 1895 to 15| in 
 1898 and to 16d., the legal par, by 1899, where it has 
 since remained. As the Indian government has, during 
 the last decade, paid out rupees for gold on demand, at 
 this rate, the value of the rupee cannot go appreciably 
 higher. Should it do so, gold would be presented for 
 rupees, more rupees would have to be issued, and this 
 would continue until their value had fallen to IQd. per 
 rupee.^ 
 
 The system of India is virtually the gold-exchange 
 standard described in § 4. The same system is now in 
 
 • For a brief history and discussion of the Indian experience, 
 see E. W. Kemmerer, Money and Credit Instruments in their Relo' 
 tion to Prices, pp. 36-39.
 
 140 THE PURCHASING POWER OF MONEY [Chap. VII 
 
 successful operation in the Philippines, in Mexico, and 
 
 in Panama.^ It withstood a severe test in India when, 
 in 1908, the trade balance was "adverse " and required 
 the sale of over £8,000,000 of bills on London be- 
 fore the Indian currency was sufficiently contracted to 
 stem the tide. 
 
 §8 
 
 Among the nations which now have the limping 
 standard is the United States. In 1792, Congress 
 adopted complete bimetallism. Full legal-tender qual- 
 ity was given to both gold and silver coins ; both were 
 to be coined freely and without limit at the ratio of 
 15 ounces of silver to 1 of gold. 
 
 This soon came to be below the market ratio as 
 affected by conditions abroad and especially in France. 
 In consequence, gold tended to leave the country. It is 
 impossible to state with exactness how soon this move- 
 ment began, but Professor Laughlin sets it as early as 
 1810 and concludes that by 1818 little gold was in cir- 
 culation.2 America, although nominally a bimetallic 
 country, became actually a silver country. 
 
 Influenced partly by the desire to bring gold back 
 into circulation, and partly also, perhaps, by the sup- 
 posed discoveries of gold in the South, Congress passed 
 acts in 1834 and 1837 estabhshing the ratio of ''16 to 
 
 ^ See Charles A. Conant, "The Gold Exchange Standard in the 
 Light of Experience," Economic Journal, June, 1909, pp. 190-200 ; 
 Hanna, Conant, and Jenks, Report on the Introduction of the Gold Ex- 
 change Standard into China, the Philippine Islands, Panama, and 
 other Silver-using Countries and on the Stability of Exchange, Wash- 
 ington (Government Printing Office), 1904; Kemraerer, "Estab- 
 lishment of the Gold Exchange Standard in the Philippines," 
 Quarterly Journal of Economics, August, 1905, pp. 600-605. 
 
 ^ The History of Biynetallism in the United States, New York 
 (D. Appleton and Company), 1901, 4th ed., p. 29.
 
 Sec. 8] INFLUENCE OF MONETARY SYSTEMS 141 
 
 1," — or, more exactly, 16.002 to 1 in 1834 and 15.998 
 to 1 in 1837. Whereas silver money had been over- 
 valued by the previous laws, by these new laws gold 
 was overvalued. That is, the commercial ratio con- 
 tinued to be near 15| to 1, while the monetary ratio 
 was slightly greater. This remained the case up to 
 1850; consequently, in accordance with Gresham's 
 Law, gold money, now the cheaper, drove out silver 
 money, and the United States became a gold-standard 
 country. In 1853, to prevent the exportation of our 
 subsidiary silver coins, their weight was reduced. 
 
 The United States continued to be a gold-using 
 country until the period of the Civil War, during which 
 ''greenbacks," or United States notes, were issued in 
 considerable excess. Again Gresham's Law came into 
 operation. Gold was in turn driven from the currency, 
 and the United States came to a paper standard.^ 
 For some years after the close of the war the country 
 remained on a paper standard, little gold being in 
 circulation except on the Pacific coast, and not much 
 silver anywhere. 
 
 In 1873 Congress passed a law (called by bimetallists 
 the ''Crime of '73") by which the standard silver dollar 
 was entirely omitted from the list of authorized coins. 
 
 Of course this could not have had any immediate 
 effect on the value of gold and silver, because the coun- 
 try was at the time on a paper basis. But when specie 
 payments (i.e. gold and silver payments) were resumed 
 in 1879, this repeal of the free coinage of silver brought 
 the country to a gold standard, not to a silver one. 
 
 1 See especially Wesley Clair Mitchell, History of the Greenbacks, 
 Chicago (The University of Chicago Press), 1903 ; also his Gold, 
 Prices, and Wages under the Greenback Standard, Berkeley, California 
 (University of California Press), 1908.
 
 142 THE PURCHASING POWER OF MONEY [Chap. VII 
 
 Had it not been for the law of 1873, the United States, 
 when it returned in 1879 to a metalHc basis, would have 
 been a silver country with a standard considerably 
 below the gold standard it actually reached. Our 
 monetary problems would then have been very different 
 from what they actually became. 
 
 But in returning to a gold basis we reintroduced 
 the silver dollar in a minor role. Although the free 
 coinage of silver was not resumed, the advocates of 
 silver, through the " Bland- AlUson Act" of 1878 and 
 the "Sherman Act" of 1890, which replaced it, succeeded 
 in pledging the government to the purchase of large, 
 but not unlimited, amounts of silver and the coinage 
 of a large, but not unlimited, number of silver dollars. 
 The Bland-Allison Act required the Secretary of the 
 Treasury to purchase every month from $2,000,000 to 
 $4,000,000 worth of silver and to coin it into standard 
 silver dollars. The Sherman Act required the pur- 
 chase every month of 4,500,000 ounces of silver. 
 
 Under these acts 554,000,000 silver dollars were 
 coined, although less than 20 per cent of them have 
 ever been in actual circulation. Silver certificates 
 redeemable in silver dollars on demand, and, for a time 
 treasury notes, have circulated in the place of this 
 immense mass of silver. The silver dollars (and there- 
 fore the silver certificates) maintain their value on 
 a parity with gold primarily because they are limited 
 in amount. If any question were raised as to their 
 parity with gold, the treasury would probably offer to 
 specifically redeem them in gold. No law directly 
 provides for the redemption of silver in gold, but 
 it is made the duty^ of the Secretary of the Treasury 
 to take such measures as will maintain its parity 
 with gold.
 
 Sec. 9] INFLUENCE OF MONETARY SYSTEMS 143 
 
 In 1893 the Sherman Act was repealed, and in 1900 
 a law was passed specifically declaring that the United 
 States shall be on a gold basis. 
 
 §9 
 
 The system of the limping standard, now obtaining 
 in the United States, logically forms a connecting link 
 between complete bimetallism and those "composite" 
 systems by which any number of different kinds of 
 money may be simultaneously kept in circulation. The 
 manner in which most modern civilized states have 
 solved the problem of concurrent circulation has been 
 to use gold as a standard, and to use silver, nickel, and 
 copper chiefly as subsidiary money, limited in quantity, 
 with, in most cases, limited amounts of paper money, 
 the latter being usually redeemable. The possible 
 variations of this composite system are unlimited. 
 In the United States at present we have a system 
 which is very complicated and objectionable in many 
 of its features — especially (as we shall presently see) 
 in its lack of elasticity. Gold is the standard and is 
 freely coined. A limited number of silver dollars, 
 worth, moneywise, more than double their value bullion- 
 wise, are a heritage of former bimetallic laws long 
 since rendered inoperative by the paper money of the 
 Civil War and expressly repealed in 1873. The two 
 attempts of 1878 and 1890 to return halfway to bi- 
 metallism by the purchase of silver — attempts dis- 
 continued in 1893 — have greatly swollen the volume 
 of coined silver. The attempt to force silver dollars 
 into circulation was not acceptable to the business 
 world, and Congress therefore issued instead the two 
 forms of paper mentioned. The chief form is the 
 "silver certificate." For each silver certificate a silver
 
 144 THE PURCHASING POWER OF MONEY [Chap. VII 
 
 dollar is kept in the vaults of the United States gov- 
 ernment. 
 
 The absurdity of the situation consists in the fiction 
 that somehow the silver keeps paper at par with gold. 
 The paper would keep its parity with gold just as well 
 if there were no silver. A silver dollar as silver is worth 
 less than a gold dollar just as truly as a paper dollar, 
 as paper, is worth less than a gold dollar. The fact 
 that the silver is worth more than the paper will not 
 avail in the least to make the paper worth a whole 
 dollar so long as the silver is not itself worth a whole 
 dollar. A pillar which reaches only halfway to the 
 ceiling cannot hold the ceiling up any more than a 
 pillar an inch high. 
 
 The paper representatives of silver would continue 
 to circulate as well as they do now, even if the " silver 
 behind them" were nonexistent, although the absurdity 
 of the situation would then be so apparent that they 
 would probably be retired. Whether the half billion 
 dollars of new currency, which came into circulation 
 with the Bland and Sherman Acts, are of silver, over- 
 valued to the extent of 50 per cent, or of paper, over- 
 valued to the extent of 100 per cent, does not really 
 affect the principle of the limping standard which keeps 
 silver dollars at par with gold. The idle silver in the 
 treasury vaults represents mere waste, a subsidy given 
 by the government to encourage silver mining. Its 
 only real effect to-day is to mislead the public into 
 the belief that in some way it keeps or helps to keep 
 silver certificates at par with gold;^ whereas they are 
 kept at par by the limitation on its amount. The 
 
 1 Seager, in his Introduction to Economics, 3d ed., New York (Holt), 
 1908, p. 317, urges that the government should attempt gradually 
 to dispose of this silver and substitute an equal value of gold.
 
 Sec. 9] INFLUENCE OF MONETARY SYSTEMS 145 
 
 silver and its paper representatives cannot fall below 
 par without displacing gold, and they cannot displace 
 gold because there are not enough of them. 
 
 Another and equally useless anomaly is the existing 
 volume of ''greenbacks." These are United States 
 government notes. Under the law of 1875, the green- 
 backs were by 1879 retired in sufficient numbers to 
 restore parity with gold ; but by a counterlaw of 1878, 
 347,000,000 of them were kept in circulation and are 
 in circulation now. As soon as redeemed, they must 
 be reissued ; they cannot be retired. They are a fixed 
 ingredient in our money pot pourri, neither expansive 
 nor shrinkable. They have been kept at par with gold 
 because : (1) they are limited in amount ; (2) they are 
 redeemable in gold on demand ; (3) they are receivable 
 for taxes and are legal tender. But it is absurd to 
 redeem but not retire — in fact, almost a contradiction 
 in terms. This absurdity has at times seriously embar- 
 rassed the government. 
 
 The next feature of our currency to be considered 
 is the bank note. Although the National Bank acts 
 wiped out the old, ill-assorted state bank notes, they tied 
 the new notes up with the war debt, and they have re- 
 mained so tied ever since, in spite of the fact that the 
 advantages of the connection have long been terminated 
 and the disadvantages have grown acute. National 
 bank notes cannot legally be issued in excess of the 
 government debt, however urgent the need for them; 
 nor can the government pay its debt without thereby 
 compelling national banks to cancel their notes. 
 
 One of the curious anomalies of the situation is that 
 the prices of United States bonds are so high, and 
 therefore the rate of interest returned on these bonds so 
 low that there is actually less inducement to issue bank
 
 146 THE PURCHASING POWER OF MONEY [Chap. VII 
 
 notes in regions where the rate of interest is high, as in 
 the West, than in regions where it is low, as in the East. 
 
 The result is an inelastic currency which, instead of 
 adjusting itself to the seasonal fluctuations in trade, 
 and thus mitigating the ensuing variations in the price 
 level, remains a hard and solid mass to which the other 
 elements in the equation of exchange must adapt 
 themselves.^ 
 
 The remaining features of our currency system, such 
 as fractional and minor coins, adjusted to public 
 demand, are satisfactory. The gold and currency 
 certificates of deposit are scarcely independent features, 
 as they are simply government receipts for public con- 
 venience representing the deposit of gold or greenbacks. 
 
 The status in the United States July 1, 1912, is 
 represented in the table on the opposite page taken 
 from Comptrollers' Reports and Treasurers' Reports. 
 
 We see here a currency system in which gold, the 
 basis of it all, enters as between one third and one half 
 the circulation outside of the Treasury and banks and 
 a little over half the money in banks used as reserves 
 for deposits (and for bank notes, though these are also 
 guaranteed by the government). The remaining money 
 in circulation consists almost wholly of inelastic and 
 almost constant elements. Consequently, a change in 
 the quantity of gold in circulation will not cause a pro- 
 portional change in the quantity of all money in circu- 
 lation, but only about one third as much. Since, 
 however, almost all the money can be used as bank 
 reserves, even national bank notes being so used by 
 state banks and trust companies, the proportionate 
 
 1 The Aldrich-Vreeland Act of 1908 has not changed this situa- 
 tion. However helpful it may be in mitigating the evils of crises, it 
 does not give elasticity of the currency in ordinary times.
 
 Sec. 9] 
 
 INFLUENCE OF MONETARY SYSTEMS 
 
 147 
 
 relations between money in circulation, money in re- 
 serves, and bank deposits will hold true approximately 
 as the normal condition of affairs. The legal require- 
 ments as to reserves strengthen the tendency to pre- 
 serve such a relationship. 
 
 Money in the United States (in Millions) 
 
 
 
 Gold 
 
 Silver 
 
 U.S. 
 Notes 
 
 Bank 
 
 Notes 
 
 Subsidiary 
 
 AND Minor 
 
 Coins 
 
 Total 
 
 In U.S. Treasury . 
 In banks .... 
 Outside both . . . 
 
 2641 
 8012 
 752 3 
 
 26^ 
 217 « 
 323 
 
 9 
 253 
 
 85 
 
 40 
 108 
 597 
 
 26 
 
 38 
 
 107 
 
 365 
 1417 
 1864 
 
 Total .... 
 
 1817 
 
 566 
 
 347 
 
 745 
 
 171 
 
 3646 
 
 
 In the United States, then, we have a currency sys- 
 tem in which, as has been observed, the only really 
 adjustable money is gold. As gold requires time for 
 minting or transportation, the adjustment is slow and 
 clumsy as compared with the prompt issue or retirement 
 of bank notes practiced in other countries. The seasonal 
 changes in the purchasing power of money, as well as 
 the changes connected with crises and credit cycles, are 
 
 ^ " Free " gold {i.e. exclusive of gold held in Treasury for gold 
 certificates held by the public) . 
 
 - Including 563 millions of gold certificates for which gold was 
 on deposit in the United States government vaults. 
 
 ' Including 380 millions of gold certificates for which gold was 
 on deposit in the United States government vaults. 
 
 * "Free" {i.e. exclusive of silver held in the Treasury for silver 
 certificates held by the public) . 
 
 ^ Including 194 millions of silver certificates for which silver was 
 on deposit in the United States government vaults. 
 
 * Including 275 millions of silver certificates for which silver was 
 on deposit in the United States government vaults.
 
 148 THE PURCHASING POWER OF MONEY [Chap. VII 
 
 therefore greatly and needlessly aggravated. As this 
 second edition goes to press, there seems a likelihood 
 that Congress may at last enact legislation designed to 
 remedy this condition.
 
 CHAPTER VIII 
 
 INFLUENCE OF QUANTITY OP MONEY AND OTHER FAC- 
 TORS ON PURCHASING POWER AND ON EACH OTHER 
 
 §1 
 
 The chief purpose of the foregoing chapters is 
 to set forth the causes determining the purchasing 
 power of money. This purchasing power has been 
 studied as the effect of five, and only five, groups of 
 causes. The five groups are money, deposits, their veloc- 
 ities of circulation, and the volume of trade. These 
 and their effects, prices, we saw to be connected 
 by an equation called the equation of exchange, 
 MV+ M'V = 2pQ. The five causes, in turn, we found 
 to be themselves effects of antecedent causes lying en- 
 tirely outside of the equation of exchange, as follows : 
 the volume of trade will be increased, and therefore 
 the price level correspondingly decreased by the dif- 
 ferentiation of human wants ; by diversification of in- 
 dustry; and by facilitation of transportation. The 
 velocities of circulation will be increased, and there- 
 fore also the price level increased by improvident 
 habits ; by the use of book credit; and by rapid trans- 
 portation. The quantity of money will be increased, 
 and therefore the price level increased correspondingly 
 (2 by the import and minting of money, and, anteced- 
 ently, by the mining of the money metal ; by the 
 introduction of another and initially cheaper money 
 metal through bimetallism ; and by the issue of bank 
 
 149 V
 
 150 THE PURCHASING POWER OF MONEY [Chap. VIU 
 
 notes and other paper money. The quantity of de- 
 posits will be increased, and therefore the price level- 
 increased by extension of the banking system and by' 
 the use of book credit. The reverse causes produce, of 
 course, reverse effects. 
 
 Thus, behind the five sets of causes which alone 
 affect the purchasing power of money, we find over a 
 dozen antecedent causes. If we chose to pursue the 
 inquiry to still remoter stages, the number of causes 
 would be found to increase at each stage in much the 
 same way as the number of one's ancestors increases 
 with each generation into the past. In the last analysis 
 myriads of factors play upon the purchasing power of 
 money; but it would be neither feasible nor profitable 
 to catalogue them. The value of our analysis consists 
 rather in simplifying the problem by setting forth 
 clearly the five proximate causes through which all 
 others whatsoever must operate. At the close of our 
 study, as at the beginning, stands forth the equation of 
 exchange as the great determinant of the purchasing 
 power of money. With its aid we see that normally the 
 quantity of deposit currency varies directly with the 
 quantity of money, and that therefore the introduction 
 of deposits does not disturb the relations we found to 
 hold true before. That is, it is still true that (1) prices 
 vary directly as the quantity of money, provided the 
 volume of trade and the velocities of circulation remain 
 unchanged ; (2) that prices vary directly as the veloci- 
 ties of circulation (if these velocities vary together), 
 provided the quantity of money and the volume of 
 trade remain unchanged; and (3) that prices vary 
 inversely as the volume of trade, provided the quantity 
 of money — and therefore deposits — and their ve- 
 locities remain unchanged.
 
 Sec. 2] QUANTITY THEORY 151 
 
 §2 
 
 It is proposed in this chapter to inquire how far these 
 propositions are really causal propositions. We shall 
 study in detail the influence of each of the six magni- 
 tudes on each of the other five. This study will afford 
 answers to the objections which have often been raised 
 to the quantity theory of money. 
 
 To set forth all the facts and possibilities as to causa- 
 tion we need to study the effects of varying, one at a 
 time, the various magnitudes in the equation of ex- 
 change. We shall in each case distinguish between the 
 effects during transition periods and the ultimate or 
 normal effects after the transition periods are finished. 
 For simplicity we shall in each case consider the normal 
 or ultimate effects first and afterward the abnormal or 
 transitional effects. 
 
 Since almost all of the possible effects of changes in 
 the elements of the equation of exchange have been 
 already set forth in previous chapters, our task in this 
 chapter is chiefly one of review and rearrangement. 
 
 Our first question therefore is : given (say) a doubling 
 of the quantity of money in circulation {M), what are 
 the normal or ultimate effects on the other magnitudes 
 in the equation of exchange, viz. : M\ V, V, the p's 
 and the Q's ? 
 
 We have seen, in Chapter III, that normally the effect 
 of doubling money in circulation {M) is to double 
 deposits {M') because under any given conditions of 
 industry and civilization deposits tend to hold a fixed or 
 normal ratio to money in circulation. Hence the ulti- 
 mate effect of a doubhng in M is the same as that of dou- 
 bling both M and M'. We propose next to show that this 
 doubling of M and M' does not normally change V, V or
 
 152 THE PURCHASING POWER OF MONEY [Chap. VIII 
 
 the Q's, but only the p's. The equation of exchange of 
 itself does not affirm or deny these propositions. 
 
 For aught the equation of exchange itself tells us, 
 the quantities of money and deposits might even vary 
 inversely as their respective velocities of circulation. 
 Were this true, an increase in the quantity of money 
 would exhaust all its effects in reducing the velocity of 
 circulation, and could not produce any effect on prices. 
 If the opponents of the "quantity theory" could estabhsh 
 such a relationship, they would have proven their case 
 despite the equation of exchange. But they have not 
 even attempted to prove such a proposition. As a 
 matter of fact, the velocities of circulation of money 
 and of deposits depend, as we have seen, on technical 
 conditions and bear no discoverable relation to the 
 quantity of money in circulation. Velocity of circula- 
 tion is the average rate of "turnover," and depends on 
 countless individual rates of turnover. These, as we 
 have seen, depend on individual habits. Each person 
 regulates his turnover to suit his convenience. A 
 given rate of turnover for any person implies a given 
 time of turnover — that is, an average length of time a 
 dollar remains in his hands. He adjusts this time of 
 turnover by adjusting his average quantity of pocket 
 money, or till money, to suit his expenditures. He 
 will try to avoid carrying too little lest, on occasion, 
 he be unduly embarrassed; and on the other hand 
 to avoid encumbrance, waste of interest, and risk 
 of robbery, he will avoid carrying too much. Each 
 man's adjustment is, of course, somewhat rough, and 
 dependent largely on the accident of the moment; 
 but, in the long run and for a large number of people, 
 the average rate of turnover, or what amounts to 
 the same thing, the average time money remains in
 
 Sec. 2] QUANTITY THEORY 163 
 
 the same hands, will be very closely determined. It 
 will depend on density of population, commercial cus- 
 toms, rapidity of transport, and other technical condi- 
 tions, but not on the quantity of money and deposits 
 nor on the price level. These may change without any 
 effect on velocity. If the quantities of money and de- 
 posits are doubled, there is nothing, so far as velocity of 
 circulation is concerned, to prevent the price level from 
 doubUng. On the contrary, doubling money, deposits, 
 and prices would necessarily leave velocity quite un- 
 changed. Each individual would need to spend more 
 money for the same goods, and to keep more on hand. 
 The ratio of money expended to money on hand would 
 not vary. If the number of dollars in circulation and 
 in deposit should be doubled and a dollar should come 
 to have only half its former purchasing power, the 
 change would imply merely that twice as many dollars 
 as before were expended by each person and twice as ' 
 many kept on hand. The ratio of expenditure to stock 
 on hand would be unaffected. 
 
 If it be objected that this assumes that with the 
 doubling in M and M' there would be also a doubling 
 of prices, we may meet the objection by putting the 
 argument in a slightly different form. Suppose, for a 
 moment, that a doubling in the currency in circulation 
 should not at once raise prices, but should halve the ve- 
 locities instead ; such a result would evidently upset for 
 each individual the adjustment which he had made of 
 cash on hand. Prices being unchanged, he now has 
 double the amount of money and deposits which his ^ 
 
 convenience had taught him to keep on hand. He will \ ^ 
 then try to get rid of the surplus money and deposits by V v 
 buying goods. But as somebody else must be found to l^?^^v 
 take the money off his hands, its mere transfer will not Jj
 
 154 THE PURCHASING POWER OF MONEY [Chap. VIII 
 
 diminish the amount in the community. It will sim- 
 ply increase somebody else's surplus. Everybody has 
 money on his hands beyond what experience and con- 
 venience have shown to be necessary. Everybody will 
 want to exchange this relatively useless extra money 
 for goods, and the desire so to do must surely drive up 
 the price of goods. No one can deny that the effect of 
 every one's desiring to spend more money will be to 
 raise prices. Obviously this tendency will continue 
 until there is found another adjustment of quantities 
 to expenditures, and the F's are the same as originally. 
 That is, if there is no change in the quantities sold 
 (the Q's), the only possible effect of doubling M and M' 
 will be a doubling of the p's ; for we have just seen that 
 the y's cannot be permanently reduced without causing 
 people to have surplus money and deposits, and there 
 cannot be surplus money and deposits without a desire 
 to spend it, and there cannot be a desire to spend it 
 without a rise in prices. In short, the only way to get rid 
 of a plethora of money is to raise prices to correspond. 
 
 So far as the surplus deposits are concerned, there 
 might seem to be a way of getting rid of them by can- 
 celing bank loans, but this would reduce the normal 
 ratio which M' bears to M, which we have seen tends 
 to be maintained. 
 
 We come back to the conclusion that the velocity of 
 circulation either of money or deposits is independent 
 of the quantity of money or of deposits. No reason has 
 been, or, so far as is apparent, can be assigned, to show 
 why the velocity of circulation of money, or deposits, 
 should be different, when the quantity of money, or 
 deposits, is great, from what it is when the quantity 
 is small. 
 
 There still remains one seeming way of escape from
 
 Sec. 2J QUANTITY THEORY 155 
 
 the conclusion that the sole effect of an increase in the 
 quantity of money in circulation will be to increase 
 prices. It may be claimed — in fact it has been claimed 
 — that such an increase results in an increased volume 
 of trade. We now proceed to show that (except during 
 transition periods) the volume of trade, like the velocity 
 of circulation of money, is independent of the quantity 
 of money. An inflation of the currency cannot increase 
 the product of farms and factories, nor the speed of 
 freight trains or ships. The stream of business depends 
 on natural resources and technical conditions, not on 
 the quantity of money. The whole machinery of pro- 
 duction, transportation, and sale is a matter of physical 
 capacities and technique, none of which depend on the 
 quantity of money. The only way in which the quan- 
 tities of trade appear to be affected by the quantity of 
 money is by influencing trades accessory to the creation 
 of money and to the money metal. An increase of gold 
 money will, as has been noted, bring with it an increase 
 in the trade in gold objects. It will also bring about 
 an increase in the sales of gold mining machinery, in 
 gold miners' services, in assaying apparatus and labor. 
 These changes may entail changes in associated trades. 
 Thus if more gold ornaments are sold, fewer silver orna- 
 ments and diamonds may be sold. Again the issue of 
 paper money may affect the paper and printing trades, 
 the employment of bank and government clerks, etc. 
 In fact, there is no end to the minute changes in the Q's 
 which the changes mentioned, and others, might bring 
 about. But from a practical or statistical point of view 
 they amount to nothing, for they could not add to nor 
 subtract one tenth of 1 per cent from the general aggre- 
 gate of trade. Only a very few Q's would be appre- 
 ciably affected, and those few very insignificant. Prob-
 
 156 THE PURCHASING POWER OF MONEY [Chap. VIII 
 
 ably no one will deny this, but some objectors might 
 claim that, though technique of production and trade de- 
 termine most of these things, nevertheless the Q's — the 
 actual quantities of goods exchanged for money and deposit 
 currency — might conceivably vary according as barter 
 is or is not resorted to. If barter were as convenient 
 as sale-and-purchase, this contention would have force. 
 There would then be little need of distinguishing be- 
 tween money as the generally acceptable medium of ex- 
 change and other property as not generally acceptable. 
 If all property were equally acceptable, all property 
 would be equally money ; or if there were many kinds of 
 property nearly as exchangeable as money, resort to 
 barter would be so easy that some of the goods sold for 
 money could be almost equally well bartered for some- 
 thing else. But as long as there were any preference 
 at all for the use of money, resort to barter would be 
 reluctantly made and as a temporary expedient only. 
 We have seen this when studying transition periods. 
 Under normal conditions and in the long run only a 
 negligible fraction of modern trade can be done through 
 barter. We conclude, therefore, that a change in the 
 quantity of money will not appreciably affect the quanti- 
 ties of goods sold for money. 
 
 Since, then, a doubling in the quantity of money: 
 (1) will normally double deposits subject to check in the 
 same ratio, and (2) will not appreciably affect either the 
 velocity of circulation of money or of deposits or the vol- 
 ume of trade, it follows necessarily and mathematically 
 that the level of prices must double. While, therefore, 
 the equation of exchange, of itself, asserts no causal 
 relations between quantity of money and price level, 
 any more than it asserts a causal relation between any 
 other two factors, yet, when we take into account con-
 
 Sec. 2] QUANTITY THEORY 157 
 
 ditions known quite apart from that equation, viz., 
 that a change in M produces a proportional change in 
 M', and no changes in V, V\ or the Q's, there is no pos- 
 sible escape from the conclusion that a change in the 
 quantity of money (M) must normally cause a propor- 
 tional change in the price level (the p's). 
 
 One of the objectors to the quantity theory attempts 
 to dispose of the equation of exchange as stated by 
 Newcomb, by calling it a mere truism. While the 
 equation of exchange is, if we choose, a mere "truism," 
 based on the equivalence, in all purchases, of the money 
 or checks expended, on the one hand, and what they 
 buy, on the other, yet in view of supplementary 
 knowledge as to the relation of M to M ', and the non- 
 relation of M to V, V, and the Q's, this equation is 
 the means of demonstrating the fact that normally 
 the p's vary directly as M, that is, demonstrating the 
 quantity theory. ''Truisms" should never be neg- 
 lected. The greatest generalizations of physical science, 
 such as that forces are proportional to mass and ac- 
 celeration, are truisms, but, when duly supplemented 
 by specific data, these truisms are the most fruitful 
 sources of useful mechanical knowledge. To throw 
 away contemptuously the equation of exchange because 
 it is so obviously true is to neglect the chance to formu- 
 late for economic science some of the most important 
 and exact laws of which it is capable. 
 
 We may now restate, then, in what causal sense the 
 quantity theory is true. It is true in the sense that one 
 of the normal effects of an increase in the quantity of money 
 is an exactly proportional increase in the general level of 
 prices.^ 
 
 ' Cf . Albert Aupetit, Essai sur la theorie generale de la monnaie, 
 Paris (Guillaumin), 1901. 
 
 y'
 
 158 THE PURCHASING POWER OF MONEY [Chap. VIII 
 
 To deny this conclusion requires a denial of one 
 or more of the following premises upon which it 
 rests : — 
 
 (1) The equation of exchange, MV -\- M'V = ^pQ. 
 
 (2) An increase of M normally causes a proportional 
 increase of M'. 
 
 (3) An increase of M does not normally affect V, V, 
 or the Q's. 
 
 If these three premises be granted, the conclusion 
 must be granted. If any of the premises be denied, the 
 objector must show wherein the fallacy lies. Premise 
 (1) has been justified in Chapter II and Chapter III, 
 and mathematically demonstrated in the Appendices to 
 Chapters II and III. Premise (2) has been shown to 
 be true in Chapter III and premise (3) in the present 
 chapter. 
 
 So much pains has been taken to establish these prem- 
 ises and to emphasize the results of the reasoning based 
 on them because it seems nothing less than a scandal 
 iji Economic Science that there should be any ground 
 for dispute on so fundamental a proposition. 
 
 The quantity theory as thus stated does not claim 
 that while money is increased in quantity, other causes 
 may not affect M', V, V, and the Q's, and thus aggra- 
 vate or neutralize the effect of M on the p's. But these 
 are not the effects of M on the p's. So far as M by 
 itself is concerned, its effect on the p's is strictly propor- 
 tional. 
 
 The importance and reality of this proposition are not 
 diminished in the least by the fact that these other 
 causes do not historically remain quiescent and allow 
 the effect on the p's of an increase in M to be seen alone. 
 The effects of M are blended with the effects of changes 
 in the other factors in the equation of exchange just as
 
 Sec. 3] QUANTITY THEORY 159 
 
 the effects of gravity upon a falling body are blended 
 with the effects of the resistance of the atmosphere. 
 
 Finally, it should be noted that, in accordance with 
 principles previously explained, no great increase of 
 money (M) in any one country or locality can occur 
 without spreading to other countries or localities. As 
 soon as local prices have risen enough to make it profit- 
 able to sell at the high prices in that place and buy at 
 the low prices elsewhere, money will be exported. The 
 production of gold in Colorado and Alaska first results 
 in higher prices in Colorado and Alaska, then in send- 
 ing gold to other sections of the United States, then in 
 higher prices throughout the United States, then in 
 export abroad, and finally in higher prices throughout 
 the gold-using world. 
 
 §3 
 
 We have emphasized the fact that the strictly pro- 
 portional effect on prices of an increase in M is only the 
 normal or ultimate effect after transition periods are 
 over. The proposition that prices vary with money 
 holds true only in comparing two imaginary periods for 
 each of which prices are stationary or are moving alike 
 upward or downward and at the same rate. 
 
 As to the periods of transition, we have seen that an 
 increase in M produces effects not only on the p's, but 
 on all the magnitudes in the equation of exchange. We 
 saw in Chapter IV on transition periods that it increases 
 M' not only in its normal ratio to M, but often, tem- 
 porarily, beyond that ratio. We saw that it also 
 quickened V and V temporarily. 
 
 As previously noted, while V and V usually move in 
 sympathy, they may move in opposite directions when 
 a panic decreases confidence in bank deposits. Then 
 people pay out deposits as rapidly as possible and
 
 160 THE PUECHASING POWER OF MONEY [Chap. VIII 
 
 money as slowly as possible — the last-named tendency 
 being called hoarding. 
 
 We saw also that an increase of M during a period of 
 rising prices stimulated the Q's. Finally we saw that a 
 reduction in M caused the reverse effects of those above 
 set forth, decreasing V and V, decreasing M' not abso- 
 lutely only, but in relation to M, and decreasing the Q's 
 partly because of the disinclination to sell at low money 
 prices which are believed to be but temporary, partly 
 because of a slight substitution of barter for sales; for if 
 M should be very suddenly reduced, some way would 
 have to be found to keep trade going, and barter would 
 be temporarily resorted to in spite of its inconvenience. 
 This would bring some relief, but its inconvenience 
 would lead sellers to demand money whenever possible, 
 and prospective buyers to supply themselves there- 
 with. The great pressure to secure money would en- 
 hance its value — that is, would lower the prices of 
 other things. This resultant fall of prices would make 
 the currency more adequate to do the business required, 
 and make less barter necessary. The fall would proceed 
 until the abnormal pressure, due to the inconvenience 
 of barter, had ceased. Practically, however, in the 
 world of to-day, even such temporary resort to barter is 
 trifling. The convenience of exchange by money is 
 so much greater than the convenience of barter, that 
 the price adjustment would be made almost at once. If 
 barter needs to be seriously considered as a relief from 
 money stringency, we shall be doing it full justice if 
 we picture it as a safety-valve, working against a 
 resistance so great as almost never to come into opera- 
 tion and then only for brief transition intervals. For all 
 practical purposes and all normal cases, we may assume 
 that money and checks are necessities for modern trade.
 
 Sec. 3] QUANTITY THEORY 161 
 
 The peculiar effects during transition periods are 
 analogous to the peculiar effects in starting or stopping 
 a train of cars. Normally the caboose keeps exact 
 pace with the locomotive, but when the train is starting 
 or stopping this relationship is modified by the gradual 
 transmission of effects through the intervening cars. 
 Any special shock to one car is similarly transmitted 
 to all the others and to the locomotive. 
 
 We have seen, for instance, that a sudden change in 
 the quantity of money and deposits will temporarily 
 affect their velocities of circulation and the volume of 
 trade. Reversely, seasonal changes in the volume of 
 trade will affect the velocities of circulation, and even, 
 if the currency system is elastic, the quantity of money 
 and deposits. In brisk seasons, as when ''money is 
 needed to move the crops, " the velocity of circulation 
 is evidently greater than in dull seasons. Money is 
 kept idle at one time to be used at another, and such 
 seasonal variations in velocity reduce materially the 
 variations which otherwise would be necessary in the 
 price level. In a similar way seasonal variations in the 
 price level are reduced by the alternate expansion and 
 contraction of an elastic bank currency. In this case 
 temporarily, and to an extent limited by the amount of 
 legal tender currency, money or deposits or both may 
 be said to adapt themselves to the amount of trade. 
 In these two ways, then, both the rise and fall of prices 
 are mitigated.^ Therefore the " quantity theory "will 
 not hold true strictly and absolutely during transition 
 periods. 
 
 1 Cf. Hildebrand, Theorie des Geldes, Chapter XI, who, though 
 seemingly unconscious of its bearing on the velocity of circulation, 
 calls attention to the difference between two communities having 
 the same expenditures, but one having a uniform trade and the 
 other a trade "bunched" in certain seasons — say the crop seasons.
 
 162 THE PURCHASING POWER OF MONEY [Chap. VIII 
 
 We have finished our sketch of the effects of M, and 
 now proceed to the other magnitudes. 
 
 §4 
 
 As to deposits (M'), this magnitude is always depend- 
 ent on M. Deposits are payable on demand in money. 
 They require bank reserves of money, and there must 
 be some relation between the amount of money in cir- 
 culation (M), the amount of reserves (/*), and the 
 amount of deposits (M'). Normally we have seen that 
 the three remain in given ratios to each other. But 
 what is a normal ratio at one state of industry and civi- 
 lization may not be normal at another. Changes in 
 population, commerce, habits of business men, and 
 banking facihties and laws may produce great changes 
 in this ratio. Statistically, as will be shown in Chapter 
 XII, the ratio M'/M has changed from 3.1 to 4.1 in 
 fourteen years. 
 
 Since M' is normally dependent on M, we need not 
 ask what are the effects of an increase of Af' ; for these 
 effects have been included under the effects of M. But, 
 since the ratio of M' to M may change, we do need to 
 ask what are the effects of this change. 
 
 Suppose, as has actually been the case in recent years, 
 that the ratio of M' to M increases in the United States. 
 If the magnitudes in the equations of exchange in 
 other countries with which the United States is con- 
 nected by trade are constant, the ultimate effect on M 
 is to make it less than what it would otherwise have 
 been, by increasing the exports of gold from the United 
 States or reducing the imports. In no other way can 
 the price level of the United States be prevented from 
 rising above that of other nations in which we have 
 assumed this level and the other magnitudes in the
 
 JSec. 4] QUANTITY THEORY 163 
 
 equation of exchange to be quiescent. WTiile the ulti- 
 mate effect then is to increase the volume of circulating 
 media, this increase is spread over the whole world. 
 Although the extension of banking is purely local, its 
 effects are international. In fact, not only will there 
 be a redistribution of gold money over all gold coun- 
 tries, but there will be a tendency to melt coin into 
 bullion for use in the arts. 
 
 The remaining effects are the same as those of an 
 increase in M which have already been studied. That 
 is, there will be no (ultimate) appreciable effect on V, 
 V, or the Q's, but only on the p's, and these will rise, 
 relatively to what they would otherwise have been, 
 throughout the world. In foreign countries the normal 
 effect will be proportional to the increase of money in 
 circulation which they have acquired through the dis- 
 placement of gold in the United States. In the United 
 States the effect will not be proportional to the in- 
 crease in M', since M has moved in the opposite direc- 
 tion. It will be proportional to the increase in M + M' 
 if V and V are equal, and less than in that proportion 
 if V is less than V, as is the actual fact. 
 
 In any case the effect on prices is extremely small, 
 being spread over the whole commercial world. Taking 
 the world as a whole, the ultimate effect is, as we have 
 seen, to raise world prices slightly and to melt some 
 coin. The only appreciable ultimate effect of increas- 
 ing the ratio of M' to M in one country is to expel 
 money from that country into others. All of these 
 effects are exactly the same as those of increasing the 
 issue of bank notes, so long as they continue redeem- 
 able in gold or other exportable money. An issue 
 beyond this point results in isolating the issuing coun- 
 try and therefore in rapidly raising prices there in-
 
 164 THE PURCHASING POWER OF MONEY [Chap. VIII 
 
 stead of spreading the efifect over other countries. 
 This is what happened in the United States during the 
 Civil War. 
 
 As to transitional effects, it is evident that, before 
 the expulsion of gold from the United States, there must 
 be an appreciable rise in prices there, of which traders 
 will then take advantage by selling in the United States, 
 shipping away money, and buying abroad. During the 
 period of rising prices all the other temporary effects 
 peculiar to such a period, effects which have been 
 described at length elsewhere, will be in evidence. 
 
 Exactly opposite effects of course follow a decrease of 
 M' relatively to M. 
 
 §5 
 
 /We come next to the effects of changes in velocities 
 (F and V). These effects are closely similar to those 
 just described. The ultimate effects are on prices,' 
 and not on quantity of money or volume of trade. 
 But a change in the velocity of circulation of money in 
 any country, connected by international trade with 
 other countries, will cause an opposite change in the 
 quantity of money in circulation in that country. 
 There will be a redistribution of money among the 
 countries of the world and of money metal as between 
 money and the arts. 
 
 The normal effect, then, of increasing V or F' in any 
 country is to decrease M by export, to decrease Af' 
 proportionally, and to raise prices (p's) slightly through- 
 out the world. There is no reason to believe that there 
 will, normally, be any effects on the volume of trade. 
 It is quite possible that a change in one of the two 
 velocities will cause a corresponding change in the 
 other, or, at any rate, that most of the causes which 
 increase one will increase the other. Increased density
 
 Sec. 5] QUANTITY THEORY 165 
 
 of population, for instance, in all probability quickens 
 the flow both of money and checks. Unfortunately, 
 however, we have not sufficient empirical knowledge of 
 the two sorts of velocity to assert, with confidence, any 
 relations between them 
 
 During transition periods the effects of changes in 
 velocities are doubtless the same as the effects of in- 
 creased currency. 
 
 §6 
 
 Our next question is as to the effects of a general 
 increase or decrease in the Q's, i.e. in the volume of 
 trade. 
 
 An increase of the volume of trade in any one country, 
 say the United States, ultimately increases the money 
 in circulation {M). In no other way could there be 
 avoided a depression in the price level in the United 
 States as compared with foreign countries. The in- 
 crease in M brings about a proportionate increase in 
 M'. Besides this effect, the increase in trade undoubt- 
 edly has some effect in modifying the habits of the 
 community with regard to the proportion of check and 
 cash transactions, and so tends somewhat to increase 
 M' relatively to M ; as a country grows more commercial 
 the need for the use of checks is more strongly felt.^ 
 
 As to effects on velocity of circulation, we may 
 distinguish three cases. The first is where the change 
 in volume of trade corresponds to a change in popula- 
 
 1 This is very far from asserting as Laughlin does that ' ' The 
 limit to the increase in legitimate credit operations is always ex- 
 pansible with the increase in the actual movement of goods" ; see 
 the Principles of Money, New York (Scribner), 1903, p. 82. We 
 have seen, in Chapter IV, that deposit currency is proportional to 
 the amount of money ; a change in trade may indirectly, i.e. by 
 changing the habits of the community, influence the proportion, 
 but, except for transition periods, it cannot influence it directly.
 
 166 THE PURCHASING POWER OP MONET [ChAP. VIII 
 
 tion, as when there is an increase in trade from the set- 
 tUng of new lands, without any greater concentration in 
 previously settled areas, and without any change in the 
 per capita trade or in the distribution of trade among 
 the elements of the population. Under such conditions 
 no reason has been assigned, nor apparently can be as- 
 signed, to show why the velocity of circulation of money 
 should be other for a condition in which the volume of 
 trade is large than for a condition in which it is small. 
 
 The second case is where the increase in volume of 
 trade corresponds to an increased density of population, 
 but no change in per capita trade. In this case, the closer 
 settlement may facilitate somewhat greater velocity. 
 
 The third case is where the change in the volume of 
 trade does affect the per capita trade or the distribution 
 of trade in the population. 
 
 There are then several ways in which the velocity of 
 circulation may conceivably be affected. First, any 
 change in trade, implying a change in methods of 
 transportation of goods, will imply a change in meth- 
 ods of transportation of money ; quick transportation 
 means usually more rapid circulation. 
 
 Secondly, a changed distribution of trade will alter 
 the relative expenditures of different persons. If their 
 rates of turnover are different, a change in their ex- 
 penditures will clearly alter the relative importance or 
 weighting of these rates in the general average, thus 
 changing that average without necessarily changing 
 the individual rates of turnover. For instance, an 
 increased trade in the southern states, where the veloc- 
 ity of circulation of money is presumably slow, would 
 tend to lower the average velocity in the United States, 
 simply by giving more weight to the velocity in the 
 slower portions of the country.
 
 Sec. 6] QUANTITY THEORY 167 
 
 Thirdly, a change in individual expenditures, when 
 due to a real change in the quantity of goods purchased, 
 may cause a change in individual velocities. It seems 
 to be a fact that, at a given price level, the greater a 
 man's expenditures the more rapid his turnover; that 
 is, the rich have a higher rate of turnover than the 
 poor. They spend money faster, not only absolutely 
 but relatively to the money they keep on hand. Statis- 
 tics collected at Yale University of a number of cases of 
 individual turnover show this clearly.^ In other words, 
 the man who spends much, though he needs to carry 
 more money than the man who spends little, does not 
 need to carry as much in proportion to his expenditure. 
 This is what we should expect ; since, in general, the 
 larger any operation, the more economically it can be 
 managed. Professor Edgeworth ^ has shown that the 
 same rule holds in banking. When two banks are con- 
 solidated, the reserve needed is less than the sum of the 
 two previous reserves. 
 
 We may therefore infer that, if a nation grows richer 
 per capita, the velocity of circulation of money will 
 increase. This proposition, of course, has no reference 
 to nominal increase of expenditure. As we have seen, 
 a doubling of all prices and incomes would not affect 
 anybody's rate of turnover of money. Each person 
 would need to make exactly twice the expenditure for 
 the same actual result and to keep on hand exactly 
 twice the money in order to meet the same contingencies 
 in the same way. The determinant of velocity is real 
 expenditure, not nominal. But a person's real expendi- 
 ture is only another name for his volume of trade. We 
 
 ' See § 1 of Appendix to (this) Chapter VIII. 
 * "Mathematical Theory of Banking,'! Journal of the Royal Sta- 
 iistical Society, March, 1888.
 
 168 THE PURCHASING POWER OF MONEY [Chap. VIII 
 
 conclude, therefore, that a change in the volume of 
 trade, when it affects the per capita trade, affects ve- 
 locity of circulation as well. 
 
 We find then that an increase in trade, unlike an 
 increase in currency {M and M') or velocities {V and V) 
 has other effects than simply on prices — effects, in 
 fact, of increasing magnitudes on the opposite side of 
 the equation, V and V, and (though only indirectly by 
 affecting business convenience and habit) M' relatively 
 to M. If these effects increase the left side as much as 
 the increase in trade itself (the Q's) directly increases 
 the right side, the effect on prices will be nil. If the 
 effect on the left side exceeds that on the right, prices 
 will rise. Only provided the effect on the left side is 
 less than the increase in trade will prices fall, and then 
 not proportionately to the increase in trade. 
 
 In a former chapter, it was shown that a change in 
 trade, provided currency {M and M') and velocities 
 {V and V) remained the same, produced an inverse 
 change in prices. But now we find that the proviso is 
 inconsistent with the premise ; currency and velocities 
 can remain the same only by the clumsy hypothesis 
 that the various other causes affecting them shall be 
 so changed as exactly to neutralize the increase in trade. 
 If these various other causes remain the same, then 
 currency and velocities will not remain the same. 
 
 This is the first instance in our study where we have 
 found that normally, i.e. apart from temporary or 
 transitional effects, we reach different results by assum- 
 ing causes to vary one at a time, than by assuming the 
 algebraic factors in the equation to vary one at a time. 
 The ''quantity theory" still holds true — that prices 
 (p's) vary with money {M) — when we assume that 
 other causes remain the same, as well as when we assumed
 
 Sec. 7] QUANTITY THEORY 169 
 
 merely that other algebraic factors remain the same; 
 and all the other theorems stated algebraically were 
 found to hold causationally, excepting only the theorem 
 as to variation in trade. While the main purpose of 
 this chapter is to justify the "quantity theory" as 
 expressing a causal as well as an algebraic relation, it is 
 important to point out that causal and algebraic theo- 
 rems are not always identical. 
 
 As to the transitional effects of a change in the 
 volume of trade, these depend mainly on one of the 
 two possible directions in which prices move. If 
 they move upward, the transitional effects are similar 
 to those we are already familiar with for periods of 
 rising prices ; if downward, they are similar to those 
 incident to such a movement. 
 
 We have now studied the effects of variations in 
 each of the factors in the equation of exchange (save 
 one) on the other factors. We have found that in 
 each case except in the case of trade (the Q's) the 
 ultimate effect was on prices (the p's). The only 
 group of factors which we have not yet studied as cause 
 are the prices (p's) themselves. Hitherto they have 
 been regarded solely as effects of the other factors. 
 But the objectors to the quantity theory have main- 
 tained that prices should be regarded as causes rather 
 than as effects. Our next problem, therefore, is to ex- 
 amine and criticize this proposition. 
 
 So far as I can discover, except to a limited extent 
 during transition periods, or during a passing season (e.g. 
 the fall), there is no truth whatever in the idea that the 
 price level is an independent cause of changes in any of 
 the other magnitudes M, M', V, V, or the Q's. To
 
 170 THE PURCHASING POWER OF MONEY [Chap. VIII 
 
 show the untenabiHty of such an idea let us grant for 
 the sake of argument that — in some other way than 
 as the effect of changes in M, M', V, V, and the Q's — 
 the prices in (say) the United States are changed to 
 (say) double their original level, and let us see what 
 effect this cause will produce on the other magnitudes 
 in the equation. 
 
 It is clear that the equality between the money side 
 and the goods side must be maintained somehow, and 
 that if the prices are raised the quantity of money or 
 the quantity of deposits or their velocities must be 
 raised, or else the volume of business must be reduced. 
 But examination will show that none of these solutions 
 is tenable. 
 
 The quantity of money cannot be increased. No 
 money will come from abroad, for we have seen that 
 a place with high prices drives money away. The 
 consequence of the elevation of prices in the United 
 States will be that traders will sell in the United States 
 where prices are high, and take the proceeds in money 
 and buy abroad where prices are low. It will be as 
 difficult to make money flow into a country with high 
 prices as to make water run up hill. 
 
 For similar reasons money will not come in via the 
 mint. Since bullion and gold coin originally had the 
 same value relatively to goods, after the supposed dou- 
 bling of prices, gold coin has lost half its purchasing 
 power. No one will take bullion to the mint when he 
 thereby loses half its value. On the contrary, as we saw 
 in a previous chapter, the result of high prices is to make 
 men melt coin. 
 
 Finally, the high prices will not stimulate mining, 
 but on the contrary they will discourage it, nor will 
 high prices discourage consumption of gold, but on the
 
 Sec. 7] QUANTITY THEORY 171 
 
 contrary they will stimulate it. These tendencies have 
 all been studied in detail. Every principle we have 
 found regulating the distribution of money among 
 nations (the distribution of money metal as between 
 money and the arts or the production and consumption 
 of metals) works exactly opposite to what would be 
 necessary in order to bring money to fit prices instead 
 of prices to fit money. 
 
 It is equally absurd to expect high prices to increase 
 the quantity of deposits (M'). We have seen that 
 the effect would be to diminish the quantity of money 
 in circulation (M) ; but this money is the basis of the 
 deposit currency {M'), and the shrinkage of the first 
 will entail the shrinkage of the second. The reduction 
 of M and M' will not tend to favor, but on the con- 
 trary will tend to pull down the high prices we have 
 arbitrarily assumed. 
 
 The appeal to the velocities (F and F') is no more 
 satisfactory. These have already been adjusted to 
 suit individual convenience. To double them might 
 not be a physical possibility, and would certainly be 
 a great inconvenience. 
 
 There is left the forlorn hope that the high prices will 
 diminish trade (the Q's). But if all prices including 
 the prices of services are doubled, there is no reason 
 why trade should be reduced. Since the average person 
 will not only pay, but also receive high prices, it is 
 evident that the high prices he gets will exactly make 
 him able to stand the high prices he pays without 
 having to reduce his purchases. 
 
 We conclude that the hjrpothesis of a doubled price 
 level acting as an independent cause controlling the 
 other factors in the equation of exchange and uncon- 
 trolled by them is untenable. Any attempt to maintain
 
 172 THE PURCHASING POWER OF MONEY [Chap. VIII 
 
 artificially high prices must result, as we have seen, not 
 in adjusting the other elements in the equation of ex- 
 change to suit these high prices, but on the contrary 
 in arousing their antagonism. Gold will go abroad 
 and into the melting pot, will be produced less and 
 consumed more until its scarcity as money will pull 
 down the prices. The price level is normally the one 
 absolutely passive element in the equation of exchange. 
 It is controlled solely by the other elements and the 
 causes antecedent to them, but exerts no control over 
 them. 
 
 But though it is a fallacy to think that the price level 
 in any community can, in the long run, affect the 
 money in that community, it is true that the price level 
 in one community may affect the money in another 
 community. This proposition has been repeatedly 
 made use of in our discussion, and should be clearly 
 distinguished from the fallacy above mentioned. The 
 price level in an outside community is an influence 
 outside the equation of exchange of that community, 
 and operates by affecting its money in circulation and 
 not by directly affecting its price level. The price level 
 outside of New York City, for instance, affects the 
 price level in New York City only via changes in the 
 money in New York City. Within New York City 
 it is the money which influences the price level, and not 
 the price level which influences the money. The price 
 level is effect and not cause. Moreover, although the 
 price level outside of New York is a proximate cause 
 of changes of money in New York, that price level in 
 turn is cause only in a secondary sense, being itself an 
 effect of the other factors in the equation of exchange 
 outside of New York City. For the world as a whole 
 the price level is not even a secondary cause, but solely
 
 Sec 7] QUANTITY THEORY 173 
 
 an effect — of the world's money, deposits, velocities^ 
 and trade. 
 
 We have seen that high prices in any place do not 
 cause an increase of the money supply there; for money 
 flows away from such a place. In the same way high 
 prices at any time do not cause an increase of money 
 at that time; for money, so to speak, flows away from 
 that time. Thus if the price level is high in January as 
 compared with the rest of the year, bank notes will not 
 tend to be issued in large quantities then. On the con- 
 trary, people will seek to avoid paying money at the 
 high prices and wait till prices are lower. When that 
 time comes they may need more currency; bank notes 
 and deposits may then expand to meet the excessive 
 demands for loans which may ensue. Thus currency 
 expands when prices are low and contracts when prices 
 are high, and such expansion and contraction tend to 
 lower the high prices and raise the low prices, thus work- 
 ing toward mutual equality. We see then that, so far from 
 its being true that high prices cause increased supply of 
 money, it is true that money avoids the place and time 
 of high prices and seeks the place and time of low 
 prices, thereby mitigating the inequality of price levels. 
 
 What has been said presupposes that purchasers have 
 the option to change the place and time of their pur- 
 chases. To the extent that their freedom to choose 
 their market place or time is interfered with, the cor- 
 rective adjustment of the quantity of money is pre- 
 vented. The anomalous time of a panic may even be 
 characterized by necessity to meet old contracts which 
 afford no choice of deferring the payment. There may 
 then be a "money famine" and a feverish demand for 
 emergency currency needed to liquidate outstanding 
 contracts which would never have been entered into if
 
 174 THE PURCHASING POWER OF MONEY [Chap. VIII 
 
 the situation had been foreseen. That such anomalous 
 conditions do not negative the general thesis that prices 
 are the effect and not the cause of currency (including 
 deposit currency) is shown statistically by Minnie 
 Throop England.^ 
 
 §8 
 
 Were it not for the fanatical refusal of some econo- 
 mists to admit that the price level is in ultimate anal- 
 ysis effect and not cause, we should not be at so great 
 pains to prove it beyond cavil. It is due our science 
 to demonstrate its truths. The obligation to do this 
 carries with it the obligation to explain if possible why 
 so obvious a truth has not been fully accepted. 
 
 One reason has already been cited, the fear to give 
 aid and comfort to the enemies of all sound economists, 
 — the unsound money men. Another may now 
 receive attention, viz. the fallacious idea that the 
 price level cannot be determined by other factors in 
 the equation of exchange because it is already deter- 
 mined by other causes, usually alluded to as ''supply 
 and demand," This vague phrase has covered multi- 
 tudes of sins of slothful analysts in economics. Those 
 who place such implicit reliance on the competency of 
 supply and demand to fix prices, irrespective of the 
 quantity of money, deposits, velocity, and trade, will 
 have their confidence rudely shaken if they will follow 
 the reasoning as to price causation of separate articles. 
 They will find that there are always just one too few 
 equations to determine the unknown quantities in- 
 volved.2 The equation of exchange is needed in each 
 
 ^ " Statistical inquiry into the influence of credit upon the level 
 of prices," University Studies (University of Nebraska), January, 
 1907, pp. 41-83. 
 
 * Cf. Irving Fisher, " Mathematical Investigations in the Theory
 
 Sec. 8J QUANTITY THEORY 175 
 
 case to supplement the equations of supply and 
 demand. 
 
 It would take us too far afield to insert here a com- 
 plete statement of price-determining principles. But 
 the compatibility of the equation of exchange with 
 the equations which have to deal with prices individu- 
 ally may be brought home to the reader sufficiently for 
 our present purposes by emphasizing the distinction 
 between (1) individual prices relatively to each other 
 and (2) the price level. The equation of exchange de- 
 termines the latter (the price level) only, and the latter 
 only is the subject of this book. It will not help, but 
 only hinder the reader to mix with the discussion of 
 price levels the principles determining individual prices 
 relatively to each other. It is amazing how tenaciously 
 many people cling to the mistaken idea that an indi- 
 vidual price, though expressed in money, may be deter- 
 mined wholly without reference to money. Others, 
 more open-minded but almost equally confused, see the 
 necessity of including the quantity of money among the 
 causes determining prices, but in the careless spirit of 
 eclecticism simply jumble it in with a miscellaneous 
 collection of influences affecting prices, with no regard 
 for their mutual relations. It should be clearly recog- 
 nized that price levels must be studied independently of 
 individual prices. 
 
 The legitimacy of separating the study of price levels 
 from that of prices will be clearly recognized, when it is 
 seen that individual prices cannot be fully determined 
 by supply and demand, money cost of production, etc., 
 without surreptitiously introducing the price level 
 itself. We can scarcely overemphasize the fact that 
 
 and Value of Prices," Transactions of the Connecticut Academy of 
 Arts and Sciences, Vol. IX, 1892, p. 62.
 
 176 THE PURCHASING POWER OF MONEY [Chap. VIII 
 
 the ''supply and demand" or the ''cost of production" 
 of goods in terms of money do not and cannot com- 
 pletely determine prices. Each phrase, fully expressed, 
 already implies mo7iey. There is always hidden some- 
 where the assumption of a general price level. Yet 
 writers, like David A. Wells, ^ have seriously sought 
 the explanation of a general change in price levels in the 
 individual price changes of various commodities con- 
 sidered separately. Much of their reasoning goes no 
 farther than to explain one price in terms of other 
 prices. If we attempt to explain the money price of 
 a finished product in terms of the money prices of its 
 raw materials and other money costs of prices of pro- 
 duction, it is clear that we merely shift the problem. 
 We have still to explain these antecedent prices. In 
 elementary textbooks much emphasis is laid on the 
 fact that "demand" and "supply" are incomplete 
 designations and that to give them meaning it is neces- 
 sary to add to each the phrase "at a price." But 
 emphasis also needs to be laid on the fact that "demand 
 at a price" and "supply at a price" are still incom- 
 plete designations, and that to give them meaning it 
 is necessary to add "at a price level." The demand 
 for sugar is not only relative to the price of sugar, but 
 also to the general level of other things. Not only 
 is the demand for sugar at ten cents a pound greater 
 than the demand at twenty cents a pound (at a given 
 level of prices of other things), but the demand at 
 twenty cents at a high level of prices is greater than the 
 demand at twenty cents at a low level of prices. In 
 fact if the price level is doubled, the demand at twenty 
 cents a pound will be as great as the demand was before 
 
 ' Recent Economic Changes, New York (Appleton), 1890, Chap- 
 ter IV.
 
 Sec. 8] QUANTITY THEORY 177 
 
 at ten cents a pound, assuming that the doubling apphes 
 likewise to wages and incomes generally. The signifi- 
 cance of a dollar lies in what it will buy ; and the equiv- 
 alence between sugar and dollars is at bottom an equiv- 
 alence between sugar and what dollars will buy. A 
 change in the amount of what dollars will buy is as 
 important as a change in the amount of sugar. The 
 price of sugar in dollars depends partly on sugar and 
 partly on dollars, — that is, on what dollars will buy 
 — that is, on the price level. Therefore, beneath the 
 price of sugar in particular there lies, as one of the bases 
 of that particular price, the general level of prices. We 
 have more need to study the price level preparatory 
 to a study of the price of sugar than to study the price 
 of sugar preparatory to a study of the price level. 
 We cannot explain the level of the sea by the height 
 of its individual waves; rather must we explain in 
 part the position of these waves by the general level 
 of the sea. Each ''supply curve" or "demand curve" 
 rests upon the unconscious assumption of a price level 
 already existing. Although the curves relate to a com- 
 modity, they relate to it only as compared with money. 
 A price is a ratio of exchange between the commodity 
 and money. The money side of each exchange must 
 never be forgotten nor the fact that money already 
 stands in the mind of the purchaser for a general pur- 
 chasing power. Although every buyer and seller who 
 bids or offers a price for a particular commodity tacitly 
 assumes a given purchasing power of the money bid or 
 offered, he is usually as unconscious of so doing as the 
 spectator of a picture is unconscious of the fact that he 
 is using the background of the picture against which to 
 measure the figures in the foreground. As a conse- 
 quence, if the general level changes, the supply and
 
 178 THE PURCHASING POWER OF MONEY [Chap. Vlii 
 
 demand curves for the particular commodity considered 
 will change accordingly. If the purchasing power of 
 the dollar is reduced to half its former amount, these 
 curves will be doubled in height ; for each person will 
 give or take double the former money for a given 
 quantity of the commodity. If, through special causes 
 affecting a special commodity, the supply and demand 
 curves of that commodity and their intersection are 
 raised or lowered, then the supply and demand curves 
 of some other goods must change in the reverse direc- 
 tion. That is, if one commodity rises in price (without 
 any change in the quantity of it or of other things 
 bought and sold, and without any change in the volume 
 of circulating medium or in the velocity of circulation), 
 then other commodities must fall in price. The in- 
 creased money expended for this commodity will be 
 taken from other purchases. In other words, the waves 
 in the sea of prices have troughs. This can be seen from 
 the equation of exchange. If we suppose the quantity 
 of money and its velocity of circulation to remain 
 unaltered, the left side of the equation remains the 
 same, and therefore the right side must remain unal- 
 tered also. Consequently, any increase in one of its 
 many terms, due to an increase of any individual price, 
 must occur at the expense of the remaining terms. 
 
 It is, of course, true that a decrease in the price of any 
 particular commodity will usually be accompanied 
 by an increase in the amount of it exchanged, so that 
 the product of the two may not decrease and may even 
 increase if the amount exchanged increases sufficiently. 
 In this case, since the right side of our equation re- 
 mains the same, the effect of the increase in some 
 terms will necessarily be a decrease in others ; and the 
 remaining terms of the right side must decrease to some
 
 Sec. 8] QUANTITY THEORY 179 
 
 extent. The effect may be a general or even a universal 
 lowering of prices. Even in this case the reduction in 
 the price level has no direct connection with the reduc- 
 tion in the price of the particular commodity, but is 
 due to the increase in the amount of it exchanged.^ 
 
 The reactionary effect of the price of one commodity 
 on the prices of other conunodities must never be lost 
 sight of. Much confusion will be escaped if we give 
 up any attempt to reason directly from individual 
 prices. Improvements in production will affect price 
 levels simply as they affect the volume of business 
 transacted. Any rational study of the influence of 
 improvements in methods of production upon the level 
 of prices should, therefore, fix attention, first, on the 
 resulting volume of trade, and should aim to discover 
 whether this, in turn, carries prices upwards or down- 
 wards. 
 
 One of the supposed causes of high prices to-day, 
 much under discussion at the present time, is that of 
 industrial and labor combinations. From what has 
 been said, it must be evident that, other things remain- 
 ing equal, trusts cannot affect the general level of prices 
 through manipulating special commodities except as 
 they change the amounts sold. If prices for one com- 
 modity are changed without a change in the number 
 of sales, the effect on the price level will be neutralized 
 by compensatory changes in other prices. If trade 
 unions seek to raise prices of labor while trusts raise 
 prices of commodities, the general level of everything 
 may rise or fall; but it can rise only by a general 
 decrease in the quantities of commodities, labor, etc., 
 sold, or by an increase of currency, or by an increase in 
 velocities of circulation. If there is neither an increase 
 * For further discussion, see § 2 of Appendix to (this) Chapter VIII.
 
 180 THE PURCHASING POWER OF MONEY [Chap. VIII 
 
 nor decrease in volume of business, and if the quantity 
 and velocity of circulation of money and its substitutes 
 remain unchanged, the price level cannot change. 
 Changes in some parts of the price level may occur only 
 at the expense of opposite changes in other parts. 
 
 We have seen that the price level is not determined 
 by individual prices, but that, on the contrary, any 
 individual price presupposes a price level. We have 
 seen that the complete and only explanation of a price 
 level is to be sought in factors of the equation of ex- 
 change and whatever antecedent causes affect those 
 factors. The terms ''demand" and ''supply, " used in 
 reference to particular prices, have no significance what- 
 ever in explaining a rise or fall of price levels. In con- 
 sidering the influence affecting individual prices we say 
 that an increase in supply lowers prices, but an increase 
 in demand raises them. But in considering the influ- 
 ences affecting price levels we enter upon an entirely 
 different set of concepts, and must not confuse the prop- 
 osition that an increase in the trade (the Q's) tends to 
 lower the price level, with the proposition that an in- 
 crease in supply tends to lower an individual price. 
 Trade (the Q's) is not supply — in fact is no more to 
 be associated with supply than with demand. The Q's 
 are the quantities finally sold by those who supply, and 
 bought by those who demand. 
 
 We may here state a paradox which will serve to 
 bring out clearly the distinction between the causation 
 of individual prices relatively to each other and the 
 causation of the general level of prices. The paradox 
 is that although an increased demand for any individual 
 commodity results in a greater consumption at a higher 
 price, yet an increased general demand for goods will 
 result in a greater trade (the Q's) at lower prices.
 
 Bec. 9] QUANTITY THEORY 181 
 
 We cannot, therefore, reason directly from particular 
 to general prices; we can reason only indirectly by refer- 
 ence to the effects on quantities. Sometimes the rise 
 in an individual price raises and at other times lowers 
 the general price level. ^ To draw a physical parallel 
 let us suppose that a thousand piles have been driven 
 in a quicksand and that the owner wishes to raise their 
 level a foot. He gets hoisting apparatus and planting 
 it on the piles pulls one of them up a foot. He then 
 pulls up another and continues until he has pulled up 
 each of the thousand. But if every time he has pulled 
 one up a foot he has pushed down 999 over g^g of a 
 foot, when he has finished, he will find his thousand 
 piles lower than when he began. Each time a pile has 
 risen, the average level of all has fallen. 
 
 The proposition that a general increase in demand, 
 resulting in an increase in trade, tends to decrease and 
 and not to increase the general level of prices, may be 
 regarded as a sort of pons asinorum to test one's knowl- 
 edge of the fundamental distinction between those 
 influences affecting the general price level and those 
 affecting the rise and fall of a particular price with re- 
 spect to that level. 
 
 § 9 
 
 We have seen that the various factors represented in 
 the equation of exchange do not stand on the same 
 causal footing. Prices are the passive element and their 
 general level must conform to the other factors. The 
 causal propositions we have found to be true normally, 
 i.e. after transitions are completed, are in brief as 
 follows : — 
 
 1. An increase in the quantity of money (M) tends 
 
 ' For further discussion, see § 2 of Appendix to (this) Chapter 
 VIII.
 
 182 THE PURCHASING POWER OF MONEY [Chap. VIIX 
 
 to increase deposits (M') proportionally, and the increase 
 in these two (M and M') tends to increase prices pro- 
 portionally. 
 
 2. An increase in the quantity of money in one 
 country tends to spread to others using the same money 
 metal, and to the arts, as soon as the price levels or the 
 relative value of money and bullion differ enough to 
 make export or melting of the money metal profitable 
 and to raise slightly world prices. 
 
 3. An increase in deposits (M') compared with money 
 (M) tends likewise to displace and melt coin, and to 
 raise world prices. 
 
 4. An increase in velocities tends to produce similar 
 effects. 
 
 5. An increase in the volume of trade (the Q's) tends, 
 not only to decrease prices, but also to increase velocities 
 and deposits relatively to money and through them to 
 neutralize partly or wholly the said decrease in prices. 
 
 6. The price level is the effect and cannot be the cause 
 of change in the other factors. 
 
 7. Innumerable causes outside the equation of ex- 
 change may affect M, M' , V, V , and the Q'sand through 
 them affect the p's. Among these outside causes are 
 the price levels in surrounding countries. 
 
 8. The causation of individual prices can only explain 
 prices as compared among themselves. It cannot ex- 
 plain the general level of prices as compared with money. 
 
 9. Some of the foregoing propositions are subject 
 to slight modification during transition periods. It is 
 then true, for instance, that an increase in the quantity 
 of money {M) besides having the effects above men- 
 tioned will change temporarily the ratio of M' to M and 
 disturb temporarily V, V, and the Q's, making a credit 
 cycle.
 
 Sec. 9] QUANTITY THEORY 183 
 
 In general, then, our conclusion as to causes and 
 effects is that normally the price level (the p's) is the 
 effect of all the other factors in the equation of exchange 
 (M, M', V, F', and the Q's) ; that among these other 
 factors, deposits {M') are chiefly the effect of money, 
 given the normal ratio of M' to M ; that this ratio is 
 partly the effect of trade ( the Q's) ; that V and V are 
 also partly the effects of the Q's ; and that all of the 
 magnitudes, M, M', V, V, and the Q's are the effects of 
 antecedent causes outside the equation of exchange, ad 
 infinitum. 
 
 The main conclusion is that we find nothing to inter- 
 fere with the truth of the quantity theory that variations 
 in money (M) produce normally proportional changes 
 in prices.
 
 CHAPTER IX 
 
 THE DISPERSION OF PRICES MAKES NECESSARY AN 
 INDEX OF PURCHASING POWER 
 
 § 1 
 
 We have found that the general level of prices is 
 determined by the other magnitudes in the equation, of 
 exchange. But we have not hitherto defined exactly 
 what a "general level" may mean. There was no need 
 of such a definition so long as we assumed, as we have 
 usually done hitherto, that all prices move in perfect 
 unison. But practically prices never do move in per- 
 fect unison. Their dispersion would render impossible 
 the statistical study of general price movements were 
 there no practical method of indicating the general 
 movement. A simple figure indicating the general 
 trend of thousands of prices is a great statistical con- 
 venience. It also simplifies our equation of exchange 
 by converting the right side, which now consists of 
 thousands of terms, into a single simple term. 
 
 Such an indication is called an "index number" of 
 the price level. Its reciprocal indicates, of course, the 
 purchasing power of money. 
 
 The present chapter will, then, treat of the dispersion 
 of prices, the next chapter of index numbers which this 
 dispersion renders a practical necessity, and the two 
 following chapters of the practical statistical use of index 
 numbers. 
 
 The chief conclusion of our previous study is that an 
 increase of money, other things equal, causes a pro- 
 
 184
 
 Sec. 1] DISPERSION OF PRICES 185 
 
 portional increase in the level of prices. In other words, 
 the p's in the sum SpQ tend to rise in proportion 
 to the increase in money. It was noted, however, that 
 the adjustment is not necessarily uniform, and that 
 if some p's do not rise as much as in this proportion, 
 others must rise more. In this connection, we observe 
 that some prices cannot adjust themselves at once, 
 and some not at all. This latter is true, for instance, 
 of prices fixed by contract. A price so fixed cannot 
 be affected by any change coming into operation be- 
 tween the date of the contract and that of its fulfillment. 
 Even in the absence of explicit contracts, prices may be 
 kept from adjustment by implied understandings and 
 by the mere inertia of custom. Besides these restric- 
 tions on the free movement of prices, there are often 
 legal restrictions ; as, for example, when railroads are 
 prohibited from charging over two cents per passenger 
 per mile, or when street railways are limited to five-cent 
 or three-cent fares. 
 
 Whatever the causes of nonadjustment, the result is 
 that the prices which do change will have to change in 
 a greater ratio than would be the case were there no 
 prices which do not change. Just as an obstruction 
 put across one half of a stream causes an increase in 
 current in the other half, so any deficiency in the move- 
 ment of some prices must cause an excess in the move- 
 ment of others. 
 
 In order to picture to ourselves what are the classes 
 of prices which rise or fall, we must survey the entire 
 field of prices. Prices, measured as we are accustomed 
 to measure them, in terms of money, are the ratios of 
 exchange between other goods and money. The 
 term "goods," as previously explained, is a collective 
 term comprising all wealth, property, and services,
 
 186 THE PURCHASING POWER OF MONEY [Chap. IX 
 
 these being the magnitudes designated in sales. The 
 chief subclasses under these three groups, which occur 
 in actual sales, may be indicated as follows : — 
 
 Wealth 
 
 Property 
 
 Services 
 
 j Real estate 
 [ Commodities 
 
 Stocks 
 
 Bonds 
 
 Mortgages 
 
 Private notes 
 
 Time bills of exchange 
 
 Of rented real estate 
 
 Of rented commodities 
 
 Of hired workers 
 . Of some or all these agencies combined. 
 
 The prices of these various classes of goods cannot 
 all move up and down in perfect unison. Some are far 
 more easily adjustable than others. Only by extremely 
 violent hypotheses could we imagine perfect adjust- 
 ability in all. The order of adjustability from the least 
 to the most adjustable may be roughly indicated as 
 follows : ^ — 
 
 1. Contract prices of properties and services, espe- 
 cially where the contracts are for a long time ; these in- 
 clude bonds, mortgage notes, use of real estate by leases. 
 
 2. Contract prices of properties and services, where 
 the contracts are for a shorter time ; these include 
 bills of exchange, use of rented real estate and com- 
 modities, services of workmen, etc. 
 
 1 Cf. Jevons's admirable " Classification of Incomes according as 
 they suffer from Depreciation," Investigations in Currency and 
 Finance, London (Macmillan), 1884, p. 80, and after. See also The 
 Gold Siipply and Prosperity, edited by Byron W. Holt, New York 
 (The Moody Corporation), 1907, especially the Conclusion or 
 Summary by the editor, beginning on page 193.
 
 Sec. 1] DISPERSION OF PRICES 187 
 
 3. Prices of commodities made of the money metal. 
 
 4. Prices of substitutes for said commodities. 
 
 5. Prices fixed by law, as court fees, postage, tolls, 
 use of public utilities, salaries, etc. 
 
 6. Prices fixed by custom, as medical fees, teachers' 
 salaries, etc., and to some extent wages. 
 
 7. Prices of real estate. 
 
 8. Prices of most commodities at retail. 
 
 9. Prices of most commodities at wholesale. 
 10. Prices of stocks. 
 
 Take, for instance, bonds and mortgages. In order 
 that the prices of these may be perfectly adjustable, we 
 should have to suppose, not only that there were no 
 restraint from custom or law, but that the contracts 
 were perfectly readjusted to each new price level. 
 We should have to suppose, for instance, that after 
 the price level had doubled in height, because cur- 
 rency had doubled, there would be a $2000 bond 
 wherever there had been a $1000 bond. This, obvi- 
 ously, is not the case. The holder of a $1000 bond 
 can receive at its maturity only $1000, besides in- 
 terest payments in the interim. If, meanwhile, the 
 price level doubles, he will receive no more. It is 
 true that a change of price level will, in time, change 
 the volume of new loans. A merchant, to lay in a 
 given stock of goods, will need to borrow a larger 
 sum if prices are high than if they are low. Per- 
 sonal notes and bills of exchange will be drawn for 
 double the amount which would have obtained had 
 the price level not doubled. Similarly, a corporation 
 issuing bonds for new projects may have to issue a 
 larger amount. But obligations outstanding when the 
 price levels change cannot be thus adjusted; their 
 prices can vary only slightly during the interim be-
 
 188 THE PURCHASING POWER OF MONEY (Chap. IX 
 
 tween issue and maturity. The fact that their face 
 value is expressed in money sets very definite Umits 
 to their prices.^ If, because of a doubling in the quan- 
 tity of money, the value and profits of a railroad 
 measured in money were doubled, the bondholder could 
 not, on that account, realize more money for his bond. 
 The value of the bond is not greatly affected by the 
 valuation and profits of the railroad, so long as these 
 are sufficient to guarantee the bond. The bond is an 
 agreement to pay stated sums at stated times. It repre- 
 sents a limited money value carved out of the road. 
 The only ways in which the money price of a bond or 
 salable debt can vary at all are by variations in the 
 rate of money interest and by changes in the degree of 
 certainty of payment. Only so far as these features are 
 affected by the changes in the volume of money will 
 the value of bonds be affected. We have seen, for in- 
 stance, that inflation, while it is taking place, raises 
 interest.^ It therefore lowers the price of bonds during 
 the transition period.^ Again if violent changes in the 
 price level increase or decrease the number of bank- 
 ruptcies, they thereby affect the degree of certainty of 
 payment, and consequently affect the value of bonds. 
 But these ways of affecting prices of such securities ex- 
 pressed in money are of less account than the ordinary 
 effect of inflation or contraction on price levels, and of 
 a different character. 
 
 1 See article by Walter S. Logan on the "Duty of Gold," in The 
 Gold Supply and Prosperity, edited by Byron W. Holt, New York 
 (The Moody Corporation), 1907, p. 106. See also Ricardo, "Essay 
 on the High Price of Bullion," Works, 2d ed., London (Murray), 
 1852, p. 287. 2 Supra, Chapter IV, § 1. 
 
 ' See article by Robert Goodbody, " More Gold means Higher 
 'Time' Money and Lower Bond Prices," in The Gold Supply and 
 Prosperity, edited by Byron W. Holt, New York (The Moody 
 Corporation) 1907, p. 163 and after.
 
 Sec. 1] DISPERSION OF PRICES 189 
 
 The chief pecuHarity of these forms of property hes, 
 then, in the fact that they are expressed in terms of 
 money and therefore are compelled to keep in certain 
 peculiar relations to money. Being based on contracts, 
 the money terms of which during a given period must 
 not be changed, they are not free to be influenced in 
 the same ways as other property. The existence of 
 such contracts constitutes one of the chief arguments 
 for a system of currency such that the uncertainties 
 of its purchasing power are a minimum. An uncertain 
 monetary standard disarranges contracts and discour- 
 ages their formation. 
 
 The longer the contract, the larger the nonadjusta- 
 bility. A fifty-year bond usually means a relative fixity 
 of price for half a century. Only at the end of that 
 time, if prices have risen, can bonds, issued de novo 
 for the means of purchasing goods, be correspondingly 
 more numerous or of correspondingly larger denomi- 
 nations. A 30-days' bill of exchange, on the other 
 hand, while it cannot change much in price, is can- 
 celed at the end of a month. The relative fixity of 
 price is, therefore, of shorter duration. 
 
 A special class of goods, the prices of which cannot 
 fluctuate greatly with other prices, are those special 
 commodities which consist largely of the money metal. 
 Thus, in a country employing a gold standard, the 
 prices of gold for dentistry, of gold rings and ornaments, 
 gold watches, gold-rimmed spectacles, gilded picture 
 frames, etc., instead of varying in proportion to other 
 prices, always vary in a smaller proportion. The 
 range of variation is the narrower, the more predomi- 
 nantly the price of the article depends upon the gold 
 as one of its raw materials. 
 
 From the fact that gold-made articles are thus more
 
 190 THE PURCHASING POWER OF MONEY [Chap. IX 
 
 or less securely tied in value to the gold standard, it 
 follows also that the prices of substitutes for such 
 articles will tend to vary less than prices in general. 
 These substitutes will include silver watches, ornaments 
 of silver, and various other forms of jewelry, whether 
 containing gold or not. It is a fundamental principle 
 of relative prices that the prices of substitutes will move 
 in sympathy. In the case of perfect substitutes, the 
 prices must always be equal or must bear a fixed ratio 
 to each other.^ 
 
 The remaining items in our list require little comment. 
 The imperfect adjustability of prices fixed bylaw and 
 custom and the perfect adjustability of wholesale prices 
 of commodities and prices of stocks are famihar to all. 
 
 ^ §2 
 
 The fact that wages, salaries, the price of gold in non- 
 monetary forms, etc., and especially the prices of bonded 
 securities, cannot change in proportion to monetary 
 fluctuations, means, then, that the prices of other things, 
 such as commodities in general and stocks, must change 
 much more than in proportion. This supersensitiveness 
 to the influence of the volume of currency (or its velocity 
 of circulation or the volume of business) applies in a 
 maximum degree to stocks. Were a railroad to double 
 in money value, the result would be, since the monej' 
 value of the bonds could not increase appreciably, that 
 the money value of the stock would more than double. 
 Stocks are shares in physical wealth the value of which, 
 in money, can fluctuate. Since the money price of 
 bonds is relatively inflexible, that of stocks will fluctuate 
 
 ^ See Irving Fisher, '* Mathematical Investigations in the Theory 
 of Value and Prices," Transactions of the Connecticut Academy o} 
 Arts and Sciences, 1892, p. 66 and after.
 
 Sec. 2] DISPERSION OF PRICES 191 
 
 more than the price of the physical wealth as a whole. 
 The reason is that these securities not only feel the 
 general movement which all adjustable elements feel, 
 but must also conform to a special adjustment to make 
 up for the rigid nonadjustability of the bonds associated 
 with them. 
 
 To illustrate, let us suppose the right side of the 
 equation of exchange to consist of the following ele- 
 ments : — 
 
 Miscellaneous adjustable elements such as commodi- 
 ties, having a value of $ 95,000,000 
 
 Five thousand shares of stock at $1000 per share, 
 
 making a value of 5,000,000 
 
 Five thousand bonds on the same underljdng wealth 
 
 at $1000 each, making a value of 5,000,000 
 
 Miscellaneous nonadjustable elements such as other 
 bonds, notes, government salaries, government 
 fees, dentists' gold, etc., having a value of . . . 20,000,000 
 
 $125,000,000 
 
 Let us suppose that, with no change in the velocities of 
 currency circulation or in the volume of business, there 
 is an increase of 40 per cent in the quantities of currency. 
 Then, the total value of goods exchanged will have 
 to increase from $125,000,000 to $175,000,000. Let 
 us assume that the last two items are absolutely non- 
 adjustable; then none of the increase of $50,000,000 
 can occur through any change in these items, which will 
 remain at $5,000,000 and $20,000,000, respectively, or 
 $25,000,000 in all. Consequently, the first two items 
 must rise by the whole of the $50,000,000, that is, from 
 $100,000,000 to $150,000,000 or 50 per cent. To dis- 
 tribute this increase of $50,000,000 over the first two 
 or adjustable items, let us assume that the total $10,- 
 000,000 worth of actual wealth, which consists half of
 
 192 THE PURCHASING POWER OF MONEY [Chap. IX 
 
 stocks and half of bonds, will rise in the same ratio 
 as the $95,000,000 worth of adjustable elements rise. 
 Now the whole (comprising all three items) evidently 
 rises from $105,000,000 to $155,000,000, making an in- 
 crease of 47.6 per cent. This, therefore, is the common 
 percentage which we are to assume applies equally to 
 the first item and the combination of the second and 
 third. Applied to the former it makes an increase from 
 $95,000,000 to $140,200,000. Apphed to the latter it 
 makes an increase from $10,000,000 to $14,800,000. 
 But since half of the property consists of bonds and 
 cannot increase, the whole of the increase, $4,800,000, 
 must belong to the stock alone. This will, therefore, 
 rise from $5,000,000, to $9,800,000, a rise of 96 per 
 cent. The four items then change as follows : — 
 
 First item — from $95,000,000 to $140,200,000, or 
 47.6 per cent. 
 
 Second item — from $5,000,000 to $9,800,000, or 
 96 per cent. 
 
 Third item and fourth item — no change. 
 
 All items combined — from $125,000,000 to $175,- 
 000,000, or 40 per cent. 
 
 Besides the dispersion of price changes produced by 
 the fact that some prices respond more readily than 
 others to changes in the factors determining price levels, 
 M, M', V, V, and the Q's, a further dispersion is pro- 
 duced by the fact that the special forces of supply and 
 demand are playing on each individual price, and caus- 
 ing relative variations among them. Although these 
 forces do not, as we have before emphasized, neces- 
 sarily affect the general price level, they do affect the 
 number and extent of individual divergencies above and 
 below that general level. Each individual price will 
 have a fluctuation of its own.
 
 Bcc. 2] DISPERSION OP PRICES 193 
 
 Among the special factors working through supply 
 and demand, changes in the rate of interest should be 
 particularly mentioned. Whether or not due to monetary 
 changes, a movement of interest will tend to make the 
 prices of different things vary in different directions or 
 to different extents. The prices of all goods, the bene- 
 fits of which accrue in the remote future, depend on the 
 rate of interest. The standard example is that of bonds 
 and other securities. Another good example is that of 
 real estate. In the case of farm lands yielding a con- 
 stant rental, a reduction of interest causes an increase 
 of value in the inverse ratio. If interest falls from 5 
 per cent to 4 per cent, the value will increase in the ratio 
 4 to 5. If the benefits or services are not constant each 
 year, but are massed together in the remote future, the 
 price may be still sensitive to a change in the rate of 
 interest. In the case of land used for forest growing 
 from which the trees are to be cut in half a century, 
 the value will be extremely sensitive. A fall in interest 
 from 5 per cent to 4 per cent will cause a rise of the 
 value of the land, in the ratio not of 4 to 5, but nearly 
 of 4 to 7.^ On the other hand, mining land or quarries 
 with a limited life will be less sensitive. The same 
 is true of dwellings, machinery, fixtures, and other 
 durable but not indestructible instruments, and so on 
 down the scale until we reach perishable and transient 
 commodities, such as food and clothing, which are only 
 indirectly affected by changes in the rate of interest. 
 
 It is evident, therefore, that prices must constantly 
 change relatively to each other, whatever happens to their 
 
 1 From figures showing yield of forest of white pine in New 
 Hampshire, New Hampshire Forestry Commission Report, 1905-1906, 
 p. 246. See F. R. Fairchild, "Taxation of Timberland," Report of 
 the National Conservation Commission, 60th Congress, 2d Session, 
 Senate Document 676, vol. II, p. 624. 
 o
 
 194 THE PURCHASING POWER OF MONEY [Chap. IX 
 
 general level. It would be as idle to expect a uniform 
 movement in prices as to expect a uniform movement 
 for all bees in a swarm. On the other hand, it would 
 be as idle to deny the existence of a general move- 
 ment of prices because they do not all move ahke, as 
 to deny a general movement of a swarm of bees because 
 the individual bees have different movements. 
 
 §3 
 
 Corresponding to changes in an individual price there 
 will be changes in the quantity of the given commodity 
 which is exchanged at that price. In other words, as 
 each p changes, the Q connected with it will change also ; 
 this, because usually any influence affecting the price 
 of a commodity will also affect the consumption of it. 
 Changes in supply or demand or both make changes in 
 the quantity exchanged. Otherwise expressed, the 
 point of intersection of the supply and demand curve 
 may move laterally as well as vertically. 
 
 This changing of the Q's introduces a new complica- 
 tion. We have in many of our previous discussions 
 been assuming, as was admissible theoretically, that 
 all the Q's remain unchanged while we investigate 
 the changes in the p's due to changes in the currency or 
 in velocities of circulation. But practically we can 
 never get an opportunity to study such a case. Again, 
 in order to show the effect of a change in ''the volume of 
 business" upon the price level, we supposed a case in 
 which all the Q's were uniformly changed. Such a 
 supposition is not only impossible to carry out in prac- 
 tice, but is difficult to conceive even in theory ; because, 
 as we have just seen, each Q is associated with a p. In 
 showing the effect of a change in the volume of business 
 upon the level of prices we cannot assume that all the
 
 Sec. 3J DISPERSION OF PRICES 195 
 
 Q's change uniformly in one direction and all the p's 
 uniformly in the other. If the first set change uni- 
 formly, the second cannot change uniformly. A dou- 
 bling in the quantities of all commodities sold, or (what 
 is almost the same thing), a doubling of the quantities 
 consumed, would change their relative desirabilities 
 and therefore their relative prices. To double the 
 quantity of salt might make its marginal desirability 
 zero, while to double the quantity of roses might scarcely 
 lower their marginal desirability at all.^ 
 
 We see, therefore, that it is well-nigh useless to speak 
 of uniform changes in prices (p's) or of uniform changes 
 in quantities exchanged (Q's). In place of positing 
 such uniform changes, we must now proceed to the 
 problem of developing some convenient method of 
 tracing these two groups of changes. We must formu- 
 late two magnitudes, the price level and the volume of 
 trade. This problem is especially difficult because, in 
 measuring changes in the price level, we shall need 
 to use the quantities (Q's) in some way as weights in 
 our process of averaging ; and we now find, not only 
 that the prices whose average we seek are extremely 
 variable, but that the weights by which we attempt to 
 construct the average are variable also. 
 
 It is desired, then, in the equation of exchange, to 
 convert the right side, ^pQ, into a form PT where T 
 measures the volume of trade, and P is an ''index 
 number" expressing the price level at which this trade 
 is carried on. These magnitudes — price level (P) 
 and volume of trade (T) — need now to be more pre- 
 cisely formulated. Especially does P become hence- 
 forth the focal point in our study. 
 
 ^ Cf. Jevons, Theory of Political Economy, London (Maemillan), 
 1888, pp. 155-156.
 
 196 THE PURCHASING POWER OF MONEY [Chap. IX 
 
 As explained in the next chapter, there are an in- 
 definite number of ways of conceiving and forming 
 index numbers of prices and volume of trade. We shall 
 here mention only the simplest. T may be conceived as 
 the sum of all the Q's, and P as the average of all the p's. 
 This method is practically useful only provided suitable 
 units of measure are selected. It must be remembered 
 that the various Q's are measured in different units. 
 Coal is sold by the ton, sugar by the pound, wheat by 
 the bushel, etc. If we now add together these tons, 
 pounds, bushels, etc., and call this grand total so many 
 "units" of commodity, we shall have a very arbitrary 
 summation. It will make a difference, for instance, 
 whether we measure coal by tons or hundredweights. 
 The system becomes less arbitrary if we use, as the unit 
 for measuring any goods, not the unit in which it is 
 commonly sold, but the amount which constitutes a 
 "dollar's worth" at some particular year called the base 
 year. Then every price, in the base year, is one dollar, 
 and therefore the average of all prices in that year is 
 also one dollar. For any other year the average price 
 {i.e. the average of the prices of the newly chosen units 
 which in the base year were worth a dollar) will be the 
 index number representing the price level, while the 
 number of such units will be the volume of trade. 
 
 The equation of exchange now assumes the form 
 
 MV + M'V = PT 
 
 and its right member is the product of the index number 
 (P) of prices multipUed by the volume of trade {T). 
 
 §4 
 
 In this chapter we have seen that prices do not, and 
 in fact cannot, move in perfect unison. The reasons
 
 Sec. 4] DISPERSION OP PRICES 197 
 
 for dispersion are principally three: (1) Many prices 
 are restrained by previous contract, by legal prohibition, 
 or by force of custom. (2) Some prices are intimately 
 related to the money metal. (3) Each individual price 
 is subject to special variation under the influence of its 
 particular supply and demand. There exists, however, 
 a compensation in price movements in the sense that the 
 failure of one set of prices to respond to any influence 
 on the price level will necessitate a correspondingly 
 greater change in other prices. 
 
 The quantities sold likewise vary, and their variations 
 are bound up with those of prices. 
 
 In order to express in one figure the general movement 
 of prices, an index number (P) is constructed ; and 
 in order to express in one figure the general movement of 
 trade, an index of trade (T) is constructed. The nature 
 of these indices will form the subject of the next chapter.
 
 CHAPTER X 
 
 THE BEST INDEX NUMBERS OF PURCHASING POWER 
 
 §1 
 
 In the previous chapter the necessity for an index 
 number (P) was shown and a particular form of index 
 number was suggested. This form of index number 
 had been shown in Chapter II and its appendix to meet 
 certain conditions (of proportionality of price level to 
 quantity of money, etc.) required by the equation of 
 exchange, MV+M'V' = PT, In the present chapter, 
 this index number will be compared with others and 
 the general purposes of index numbers discussed, in- 
 cluding purposes having little direct concern with the 
 equation of exchange. 
 
 Index numbers may be compared in respect to (1) 
 form, under which term are included methods of weight- 
 ing and of determining the "base" prices; (2) the 
 selection of elements to be included. In this section 
 we shall consider the question of form. 
 
 The number of possible forms of index numbers is 
 infinite. They differ enormously in complexity, in ease 
 of calculation, and in conformity to various other tests. 
 A few of the simplest may here be mentioned. Their 
 discussion will be brief and will in many cases be dog- 
 matic. Full proofs and discussions are contained in 
 the mathematical appendix.^ 
 
 If in 1900 the average price per pound of sugar was 
 6 cents, and in 1910 it was 8 cents, the ratio of the price 
 
 1 See Appendix to (this) Chapter X, §§ 1-8, where 44 types of 
 index numbers are compared. 
 
 198
 
 Sec. 1] THE BEST INDEX NUMBERS 199 
 
 in 1910 to that in 1900 must have been f or 133^ per 
 cent. If, in the same period, the average price of coal 
 per ton had changed from $4 to $6, the corresponding 
 ratio for coal must have been | or 150 per cent. If the 
 price of a given grade of cloth, on the other hand, fell 
 from 10 cents to 8 cents a yard, the ratio for cloth must 
 have been ^q or 80 per cent. P is an average of all 
 these three price ratios and other price ratios, that is, 
 an average of 133^ per cent, 150 per cent, 80 per cent, 
 etc. The simple arithmetical average of these three 
 ratios specified would be imfo + i50%+S0fo ^ or 121 
 
 per cent. The simple geometric average would be 
 -v/l33i X 150 X 80, or 117 per cent. 
 
 These are examples of simple or unweighted averages. 
 Since, however, weighted averages have many advan- 
 tages in theory and some advantages in practice, we 
 shall proceed to consider them. 
 
 There are innumerable methods of weighting ^ and of 
 averaging. None of them is perfectly satisfactory 
 from a theoretical standpoint. We must choose what 
 seems to be best from a practical standpoint. The 
 effect of changed volume of currency or changed veloc- 
 ity of circulation on the whole series of prices is complex, 
 and cannot, even in theory, be compressed into one 
 figure representing all price changes, any more than a 
 
 1 For discussions of different ways that have been proposed, 
 see Walsh, The Measurement of General Exchange Value, New York 
 and London (Maemillan), 1901 ; Edgeworth, "Report on Best 
 Methods of Ascertaining and Measuring Variations in the Value of 
 the Monetary Standard" ; Report of the British Association for the 
 Advancement of Science for 1887, pp. 247-301 ; ditto for 1888, pp. 
 181-209 ; ditto for 1889, pp. 133-164. Nitti, La misura delle varior 
 zioni di valore delta moneta, Turin, 624 pp. ; also the Appendix to 
 (this) Chapter X.
 
 200 THE PURCHASING POWER OF MONEY [Chap. X 
 
 lens can be constructed which will focus in one point 
 all the rays of light reaching it from a given point. 
 But, although in the science of optics we learn that a 
 perfect lens is theoretically impossible, nevertheless, for 
 all practical purposes lenses may be constructed so 
 nearly perfect that it is well worth while to study and 
 construct them. So, also, while it seems theoretically 
 impossible to devise an index number, P, which shall 
 satisfy all of the tests we should like to impose,^ it is, 
 nevertheless, possible to construct index numbers which 
 satisfy these tests so well for practical purposes that we 
 may profitably devote serious attention to the study 
 and construction of index numbers. 
 
 The index number mentioned in Chapter IX may be 
 constructed by the following process: Suppose that the 
 year 1910 is the period to be considered in our equation 
 of exchange MV + M'V = ^pQ = PT. We select 
 another year (say 1900) and call it the " base " year. 
 This means that the prices of 1910 are to be expressed 
 as a percentage of the prices of the equation of exchange 
 for 1900. 
 
 Next we obtain an expression for trade (or T). 
 As shown in the appendix to this chapter, every form 
 of index number, P, for prices implies a correlative 
 form of index for trade, T, and vice versa. It is con- 
 venient to select T first. We observe that trade (or T) 
 is not the value of transactions measured at the actual 
 prices of the year 1910, for this value is PT or 2pQ, 
 
 1 Cf. Mill, Political Economy, Book III, Chapter XV ; Sidgwick, 
 Principles of Political Economy, Book I, Chapter II ; "Report of 
 Committee on Value of Monetary Standard," Report of the British 
 Association for the Advancement of Science, 1887 ; Wesley C. Mitchell, 
 Gold, Prices, and Wages under the Greenback Standard, Berkeley, 1908 
 (University of California Press), p. 19; and Appendix to (this) 
 Chapter X.
 
 Sec. 1] THE BEST INDEX NUMBERS 201 
 
 that is, the entire right side of the equation. Trade 
 (T) by itself must be divorced from the price level (P) ; 
 it may be conceived as the value which the total trans- 
 actions would have had if the actual quantities sold had 
 been sold at the base prices. It is thus the sum of a 
 number of terms, each term being the product of the 
 quantity, or Q, pertaining to 1910 and the price, or p, 
 pertaining to the base year 1900. Algebraically it is 
 Pi>Q + p'oQ' + p'\Q" + etc., or, more briefly, ^PoQ, where 
 the prices of 1910 are expressed simply as p, p', p", 
 etc., and those of the base year, 1900, are expressed 
 
 as Po^ V\j P"o, etc. 
 
 Having defined this ideal value (T), we now define 
 P as the ratio of the real value of transactions in 1910 
 (2pQ) to that ideal (2poQ). More fully expressed, P is 
 the ratio of a real value (the value of the trade of 
 1910 at the prices of 1910) to an ideal value (the value 
 of the trade of 1910 at the prices of 1900). This ratio 
 is really a weighted arithmetical average of price ratios.^ 
 The foregoing method is simple both in conception and 
 in mathematical expression, ^ and appears to furnish, 
 theoretically at least, the best form of P, or index num- 
 ber of prices. The particular form of P (viz. 2pQ -h 
 2poQ) which we have just described is, then, associated 
 with and dependent on a particular form of T (viz. 
 2poQ). T msbj be called an index number of trade, and 
 we may say that the particular form of T (viz. 2p„Q) 
 is the best form of index or barometer of trade. 
 
 Another method of conceiving the same form of 
 index number of prices is that mentioned at the close of 
 
 * See Appendix to (this) Chapter X for a table and discussion 
 of forty-four sample types of index numbers. 
 
 ■^ It is formula 11 of the large table in the Appendix to (this) 
 Chapter X.
 
 202 THE PURCHASING POWER OF MONEY [Chap. X 
 
 the preceding chapter, as follows: Conceive each kind 
 of goods to be measured in a new physical unit — viz. 
 the amount which was worth one dollar in the base 
 year (1900) — and let us use this unit for each other year 
 (as 1910). Thus instead of a pound as the unit for 
 sugar we take as the unit whatever amount of sugar was 
 a dollar's worth in 1900. Hence the price of sugar in 
 the base year, 1900, was $1, as of course was the price 
 of everything else. If, now, the price of sugar in any 
 other year (as 1910) is $1.25 in terms of the new unit 
 (viz. the amount which was a dollar's worth in 1900), 
 we know that the price has risen 25 per cent. In this 
 way P may be defined simply as an average price instead 
 of as an average price ratio and T as the total number 
 of the new units of goods sold of all kinds. The right 
 side of the equation is now simply the product of the 
 total number of units sold, multiplied by their average 
 price. 
 
 The two definitions of P which have been given (viz. 
 the ratio of real to ideal values, and the average price in 
 1910 of all goods when measured in dollar's worth of 
 1900) are interchangeable ; and both definitions of T 
 (ideal values of transactions in 1910 at prices of 1900, and 
 total number of units sold in 1910, the units being 
 each a dollar's worth in 1900) are interchangeable. 
 There are other ways of defining P and T without chang- 
 ing their meanings. Thus ''P is the weighted arith- 
 metical average of the ratios of prices of goods in 1910 
 to those of 1900, when these ratios are weighted accord- 
 ing to the values of the goods exchanged in 1910 reck- 
 oned at the prices of 1900." Whichever of these defi- 
 nitions we prefer, the system of index numbers is the 
 same and has advantages over most other systems. 
 Above all, it enables us to say without qualification that
 
 Sec. 1] THE BEST INDEX NUMBERS 203 
 
 if the quantities sold remain unchanged, so that T will 
 remain unchanged, P will vary directly as the left side 
 of the equation of exchange.^ 
 
 We choose, then, as one of the best index numbers of 
 prices, the average price of the goods sold, those goods 
 being measured in units worth a dollar in the base year; 
 in other words, the ratio of the value of sales at actual 
 prices to the value of the same sales if made at base 
 prices ; in still other words, the weighted arithmetical 
 average of all price ratios, each ratio being weighted 
 according to the values sold, reckoned at base prices. 
 
 We have still to consider the selection of the base. It 
 makes a difference to the above index numbers, not 
 only absolutely, but also relatively, whether the base 
 year is, for instance, 1900 or 1860. 
 
 Excepting Jevons's index numbers, which were 
 geometric averages, there are few index numbers which 
 are not vitiated in some degree by having a base remote 
 from the years for which comparisons are most needed. 
 As Professor Marshall has maintained and as Professor 
 Flux has emphasized, the best base for any year seems 
 to be the previous year. 
 
 Instead, then, of employing a fixed base year for which 
 all prices are called 100 per cent and in terms of which all 
 other prices are expressed in percentages, each year 
 may be taken as the base for the succeeding year. 
 Thus we obtain a chain of mdex numbers, each num- 
 ber being connected with the preceding year instead of 
 with a common base year. 
 
 The great advantage of this chain system is that it 
 yields its best comparison for the cases in which com- 
 parison is most used and needed. Each year we are inter- 
 
 ' See Appendix to Chapter II and the Appendix to (this) Chap- 
 ter X, §§ 5, 6, 7.
 
 204 THE PURCHASING POWER OF MONEY [Chap. X 
 
 ested in Sauerbeck's index number in order to compare 
 it with the number of the preceding year, and only to a 
 less extent with other years. The number, however, as 
 actually constructed, affords something quite different. 
 It gives us, as its best or most accurate comparison, 
 the ratio between the current year and the years 1867- 
 1877. This comparison is of little or no interest to 
 any one. What all users of these statistics actually do 
 is to compare two comparisons. The index numbers for 
 1909 and 1910 (each calculated in terms of 1867-1877) 
 are compared with each other. But direct comparison 
 between 1909 and 1910 would give a different and more 
 valuable result. To use a common base is like compar- 
 ing the relative heights of two men by measuring the 
 height of each above the floor, instead of putting them 
 back to back and directly measuring the difference of 
 level between the tops of their heads. The direct com- 
 parison is more accurate, although in the case of the 
 men's heights both methods would theoretically agree. 
 In the case of price levels, unfortunately, few index 
 numbers will even theoretically give consistent results 
 when the base is shifted ; ^ and those few will fail to 
 meet other equally important tests. 
 
 It may be said that the cardinal virtue of the suc- 
 cessive base or chain system is the facility it affords for 
 the introduction of new commodities, the dropping out 
 of obsolete commodities, and the continual readjustment 
 of the system of weighting to new conditions. A fixed 
 base system soon gets behind the times in every sense 
 of the word. 
 
 §2 
 
 Our next question is : What prices should be selected 
 in constructing an index number ? The answer to this 
 
 1 See Appendix to (this) Chapter X, § 5, test 7.
 
 Sec. 2] THE BEST INDEX NUMBERS 205 
 
 question largely depends on the purpose of the index 
 number. Hitherto we have considered only one purpose 
 of an index number, viz. to best meet the requirements 
 of the equation of exchange. But index numbers may 
 be used for many other purposes, of which the two 
 chief are to measure capital and to measure income. 
 Each of the three purposes mentioned (viz. exchange, 
 capital, and income) may be subclassified according as 
 the comparison desired is between places or times. Thus 
 mdex numbers may be used for comparisons between 
 places with respect to their exchange of goods, their 
 capital, or their income. When, for instance, the British 
 Board of Trade ^ tries to compare the cost of living in 
 various towns of England, Germany, and the United 
 States the comparison is with reference to the prices of 
 living (or income) of the working classes. 
 
 We thus have at least six large classes of purposes 
 for which index numbers may be used, viz. to compare 
 the prices, in different places, of the goods exchanged ; of 
 the capital goods; and of the income goods; and of the 
 same three groups of goods at different times. 
 
 In each of the six cases, prices of goods and quantities 
 of goods will be associated with each other, and an index 
 number (P) for one will imply an index number (T) for 
 the other (we here use T in the general sense of an index 
 of quantities of goods whether they are exchanged goods, 
 as hitherto, or capital goods, or income goods). 
 
 Evidently there will be a great difference in the selection 
 of the prices to be compared according to which of the 
 six comparisions we wish to make. Suppose, for in- 
 stance, that we wish to measure changes in the general 
 
 * See Report (to Parliament) of an Enquiry hy the Board of Trade 
 into Workinci Class Rents, Housing and Retail Prices, London 
 (Darling), 1908, 1909.
 
 206 THE PURCHASING POWER OF MONEY [Chap. X 
 
 level of prices of capital goods/ — railways, ships, real 
 estate, etc., — and also to measure the relative changes 
 in the amounts of those goods. The prices of some kinds 
 of capital may have increased, and of others decreased, 
 and some may have increased at different rates from 
 others. How shall we measure the general change in 
 prices of capital goods ? Again, the quantity of some 
 kinds of capital, as railroads, may have increased faster 
 than that of other kinds, as sailing ships. Still other 
 kinds of capital may have decreased. How shall it be 
 determined whether capital in general has increased, and 
 how much ? These two problems (of prices of capital 
 and quantities of capital) may be said to consist in 
 measuring the average change in the price of the same 
 quantity of capital, and the average change of quantity 
 of capital taken at the same prices. 
 
 For either index (since only capital is under considera- 
 tion, and not income or other designated goods, whether 
 stocks or flows), the index numbers should relate, not 
 to general prices and quantities, but only to prices and 
 quantities of capital goods. Thus, the prices and quan- 
 tities of all labor services should be omitted. The use 
 of capital and the rents paid for that use, such as the 
 rent paid for house shelter, should be omitted. Only 
 capital instruments, and not the services yielded by 
 these, should be included. We may obtain the price 
 index first and then obtain a quantity index by dividing 
 the value of capital in any year by the price index, or we 
 may proceed in the reverse direction.^ In making index 
 numbers of prices of capital and quantities of capital, we 
 
 1 This has been suggested by Nicholson, Journal of the Royal 
 Statistical Society, March, 1887. 
 
 2 Giffen, in his Growth of Capital, London (Bell & Sons), 1899, 
 pp. 50-54, makes correction for price changes although without 
 attempting to construct a special index number for capital.
 
 Sec. 2] THE BEST INDEX NUMBERS 207 
 
 naturally select for our list articles which are important 
 as capital, and weight them accordingly. 
 
 To determine this general change in prices of capital, 
 we should weight each ratio by the value of the partic- 
 ular capital to which that ratio relates. In this case 
 each ratio should be weighted, not according to the 
 annual sales, but according to the existing capital. 
 Obviously, the difference between these two modes of 
 weighting may be great. Thus, real estate forms a 
 large part of all existing capital, but sales of real estate 
 are a relatively unimportant part of all sales. Food 
 products, on the other hand, contribute little to capital 
 and much to exchange. Consequently, prices and quan- 
 tities of food products would not figure in capital index 
 numbers, but would figure largely in the index numbers 
 relating to the equation of exchange. 
 
 Again, suppose the purpose of the index numbers of 
 prices is to measure the quantities and prices of income, 
 not of elements of capital. In this case the list of 
 articles and their weights will be quite different from 
 those in a capital index. 
 
 If the income of workingmen is under consideration, 
 we have to deal with index numbers for prices of those 
 goods entering into workingmen's budgets, and with 
 index numbers of the quantities of such goods. The 
 first will show the cost of living of the workingman, 
 or the purchasing power of a workingman's dollar; 
 the second will show what is called his "real wages" 
 or ''consumption." In this case the aim is to compare, 
 not stocks existing at two points of time, but flows 
 through two periods of time. One way to obtain an 
 index of real wages is to correct the nominal or money 
 wages by using the index number of prices of goods 
 for which wages are spent. Thus, if money wages for
 
 208 THE PURCHASING POWER OF MONEY [Chap. X 
 
 1908 were twice those for 1900, but money prices of the 
 necessaries and comforts of life had also doubled, real 
 wages would be unchanged. 
 
 Evidently the index numbers used in the case of 
 quantities and prices of workmen's living are not the 
 same as those used in the case of capital. Goods should 
 have each an importance in the index number, depend- 
 ent upon its importance in workingmen's budgets. 
 The goods in this case are flows, while in the case of 
 capital the goods considered were stocks. In compar- 
 ing capital, the index numbers must relate to capital ; 
 and in comparing income, the index numbers must 
 relate to income. 
 
 §3 
 
 Perhaps the most important purpose of index num- 
 bers is to serve as a basis of loan contracts.^ It is 
 
 ^ An early attempt to construct a series of index numbers ex- 
 pressing the general change in prices was made by Sir George 
 Shuckburgh Evelyn, Bart., F.R.S. and A.S. in 1798 in an article 
 entitled "An Account of Some Endeavors to Ascertain a Standard 
 of Weight and Measure," in the Philosophical Transactions of the 
 Royal Society of London, Vol. LXXXVIII, pp. 133-182, inclusive. 
 
 Bishop William Fleetwood in 1707 in Chronicon Preciosum, an 
 Account of English Money, the Price of Corn and Other Commodities 
 for the Last Six Hundred Years, raises and discusses the question 
 whether the holder of a fellowship founded between 1440 and 14G0 
 and open only to persons having an estate of less value than £5 a 
 year may rightly swear that he has less than that, if he has £6, the 
 value of money, however, having meanwhile greatly depreciated. 
 
 The idea of using an index number or tabular standard of money 
 value was later put forth by Joseph Lowe, The Present State of Eng- 
 land in regard to Agriculture and Finance, London, 1822 (see pp. 
 261-291, Appendix, pp. 89-101), and afterwards by G. Poulett 
 Scrope, Principles of Political Economy . . . applied to the Present 
 State of Britain, London, 1833, pp. 405-408, although, as we have 
 seen, the idea of an index number itself antedated them. See Correa 
 Moylan Walsh, The Measurement of General Exchange Value, New 
 York and London (Macmillan), 1901 ; Bibliography, p. 555.
 
 Sec. 3J THE BEST INDEX NUMBERS 209 
 
 desirable to determine the particular forra and weighting 
 best suited to this purpose as well as the best selection 
 of prices to be included. 
 
 An index number which serves the purpose of measur- 
 ing the appreciation or depreciation of loan contracts — 
 or what is called " deferred payments " — evidently be- 
 longs to the time rather than the place group of com- 
 parisons. But to which if any of the three sub-groups 
 (exchange, capital, or income) it most properly belongs 
 is not at first clear. But, before considering this ques- 
 tion and as a preliminary to finding the best index 
 number for contracts between borrower and lender, we 
 must arrive at some opinion as to what is the ideal 
 basis for loan contracts. 
 
 In the first place, it should be pointed out that 
 though there is a gain and loss there is not necessarily 
 any ''injustice" wrought because of a change in the 
 level of prices. Thus, if a man borrows $1000, con- 
 tracting to pay it back with $40 additional as interest 
 at the end of five years, and meanwhile prices unex- 
 pectedly double, he is a decided gainer. Though he 
 has to pay, to be sure, the same number of dollars, he 
 needs to sell only about half as much of his stock of 
 goods as he expected. He pays back, in the princi- 
 pal, only half of the real purchasing power borrowed. 
 The lender, on the other hand, is a loser by the change. 
 
 Yet the contract was perfectly fair. Each party 
 knew or should have known that the price level might 
 change, and took the risk. There was no fraud any 
 more than when wheat has been ordered for future 
 delivery at a certain price and the market unexpectedly 
 turns; or when an insurance company loses a ''risk" 
 prematurely. 
 
 Indeed, for a government to attempt by legislation
 
 210 THE PURCHASING POWER OF MONEY [Chap. X 
 
 to deprive the gainer of his profit would itself be in 
 general unfair.^ To protect themselves from losses 
 the risk of which they took upon themselves, the losing 
 parties cannot justly betake themselves to legislation 
 after the making of contracts. 
 
 The unfairness of so doing becomes the more manifest, 
 when it is considered that, if the change in price level 
 is at all expected, there is apt to be some compensation 
 by means of an adjustment in the" rate of interest.^ 
 If the price level is rising, the nominal rate of interest 
 will probably be a little higher, compensating the 
 lender somewhat for the loss of part value in his prin- 
 cipal ; while, if the price level is falling, the borrower 
 is likely to be partly compensated for his loss by a 
 lower nominal rate of interest. It is not right that 
 either side should use its influence with government 
 to impair the obligations of contracts already made.^ 
 It is, however, sound public policy to lessen in advance 
 the risk element, as rapidly as may be, so that future 
 contracts may be made by all parties on the most cer- 
 tain basis possible. In the problem of time contracts 
 between borrowers and lenders, the ideal is that neither 
 debtor nor creditor should be worse off from having 
 been deceived by unforeseen changes. Experience 
 shows that the rate of interest will seldom adjust itself 
 perfectly to changes in price level, because these changes 
 are only in part foreseen. The aim should be to make 
 the currency as certain or dependable as possible. 
 Practically speaking, this means that it shall be as 
 nearly constant as possible. 
 
 ^ Cf. Irving Fisher, "Appreciation and Interest," Part 3, Publican 
 tions of the American Economic Association, 1896. 
 ^ Rate of Interest, Chapter XIV. 
 ' Appreciation and Interest, Part 3, § 4.
 
 Sec. 3] THE BEST INDEX NUMBERS 211 
 
 In an ideal standard of value, the index number of 
 prices would continually register 100 per cent.^ But 
 as long as an absolutely stable currency does not exist, 
 and cannot be had, the index number is itself a possible 
 standard for long-time contracts. It is called the 
 ''tabular standard," as it depends on a table of prices. 
 Thus, if a man borrows $1000 when the index number 
 is 100, he might agree to pay back, not the same dollars, 
 but the same general purchasing power, with interest. 
 If, at the time of repayment, the index number had gone 
 to 150, the principal of the debt would be understood 
 to be $1500, since this represents the same purchasing 
 power that was borrowed. If, on the other hand, the 
 level of prices had fallen to 80, the principal would 
 automatically become $800. Thus, both parties would 
 be protected against fluctuations in the value of money. 
 The same correction would apply to the interest pay- 
 ments, each of which would be adjusted according to 
 the index number relating to the time of payment. 
 
 We are now ready to consider the question of what 
 are the goods the prices of which should be included in 
 an index number to serve the purposes of measuring 
 changes in loan contracts. 
 
 ' It has been argued that an ideal standard ought to be such 
 as to keep constant not objective, but subjective, prices, so that a 
 debt would be repaid in a given amount of "labor" or "utility." 
 But, aside from the practical difficulties of measuring such subjec- 
 tive magnitudes — which are insuperable and therefore render their 
 discussion purely academic — there are even more serious theo- 
 retical objections because of the fact that the standard would in- 
 crease with some persons and decrease with others as they grow 
 poorer or richer and that these changes are anticipated in making 
 loan contracts — in fact, are the instigating causes of such contracts. 
 See § 4 infra and Irving Fisher, "Appreciation and Interest," 
 Chapter XII, § 2, Publications of the American Economic Associa' 
 Hon, 1896.
 
 212 THE PURCHASING POWER OF MONEY [Chap. X 
 
 If all goods kept the same ratios of prices among 
 themselves, it would make no difference whether a 
 loan contract were made in terms of one index number or 
 another or even whether it were made in terms of wheat, 
 tons of coal, or pounds of sugar. But because prices 
 do not vary in the same, but in different proportions, an 
 index number measuring the general level of prices is 
 necessary. If repayment is made in equivalent pur- 
 chasing power (plus interest), over one kind of goods, 
 this may be either more or less than equivalent purchas- 
 ing power over other kinds. Hence, one party or the 
 other is a loser according to the kind of goods he handles 
 as a producer or prefers to use as a consumer. Even 
 if each contracting party could arrange to receive or pay 
 back purchasing power over an amount of goods of the 
 kinds which most concerned him, equivalent to what he 
 lent or borrowed, with interest, the speculative element 
 resulting in gain or loss to one or the other, though de- 
 creased, would not be entirely removed.^ 
 
 Suppose, for example, that a lender receives back 
 purchasing power over an amount of goods of the kinds 
 he wished to use, equivalent to what he lent plus in- 
 terest.2 Suppose also that, during the period of the 
 loan, these goods appreciate relatively to others. 
 Then the lender really gains, since he can now get more 
 of other goods in exchange for those it was his original 
 purpose to use, — a course which he may now be 
 tempted to take while otherwise he would not. To the 
 borrower, however, the appreciation of the goods on 
 
 1 Cf. Kinley, Money, New York (Maemillan), 1904, p. 267. 
 
 ^ The argument of the remainder of this section is substantially 
 the same as that in a paper by Harry G. Brown, in the Quarterly 
 Journal of Economics, August, 1909, entitled, "A Problem in De- 
 ferred Payments and the Tabular Standard."
 
 Sec. 3] THE BEST INDEX NUMBERS 213 
 
 the basis of which repayment is made, relatively to the 
 goods he is engaged in producing, might be regarded 
 as causing him loss. The same purchasing power over 
 the goods, on the basis of which he is to make pay- 
 ment, means in such a case, a greater purchasing power 
 over the goods he is engaged in producing. 
 
 It is clear that no one kind of goods is a fair stand- 
 ard. An index number intended to serve as a standard 
 for deferred payments must have a broad basis. 
 
 Were all borrowers and all lenders interested merely 
 as consumers — lenders denying themselves in immedi- 
 ate consumption in order to lend, with the idea of con- 
 suming more on repayment, and borrowers planning to 
 consume more immediately with the intention of later 
 consuming less — an exactly satisfactory index number 
 for each individual would seem impossible. The goods 
 which interested a lender in any given case might not be 
 those of most importance to the borrower. Only a 
 rough average could be struck and an index number 
 found to be used by all parties in their contracts. Such 
 an average would doubtless be one in which each price 
 ratio would be weighted according to the total con- 
 sumption of the goods to which it related, — the total 
 consumption of all borrowers and all lenders in the 
 country considered. 
 
 The case is even more complicated, however; for many 
 borrowers and lenders are interested less in consumption 
 than in investment.^ The choice is as much between 
 lending and other investing as between lending and con- 
 suming. Similarly, the borrower may borrow to invest 
 as well as to consume and may raise the money for repay- 
 ment by curtailing investment rather than by curtailing 
 consumption. Borrowers and lenders, in other words, 
 
 * Cf. Kemmerer, Quarterly Journal of Economics, August, 1909.
 
 214 THE PURCHASING POWER OF MONEY [Chap. X 
 
 may be more interested in purchasing factories, railroads, 
 land, durable houses, etc., which yield services during 
 a long future, than in purchasing more or better food, 
 shelter and entertainments, which yield immediate 
 satisfactions. To base our index number for^ time con- 
 tracts solely on services and immediately consumable 
 goods would therefore be illogical. Though the prac- 
 tical differences may amount to little, yet, in theory at 
 least, they are important. 
 
 Let us suppose each price ratio to be weighted by 
 the value (at standard prices) of the services of quickly 
 consumable goods enjoyed during a given period, pur- 
 chases of durable capital being omitted. Suppose also 
 that before the time of repayment arrives the rate 
 of interest has risen. With higher interest, the value 
 of land, railroads, and other durable capital will be lower 
 because the value depends on future earnings or future 
 services, and these are now discounted at a higher rate.^ 
 The borrower, in paying back an equal purchasing 
 power over consumable goods and services, is pay- 
 ing back a much higher purchasing power over such 
 things as land, houses, and factories — a much higher 
 purchasing power over future income — than he bor- 
 rowed. The lender is receiving back, therefore, a larger 
 purchasing power over these durable items of capital 
 than he loaned, though not a larger purchasing power 
 (except for the interest) over inmiediately consumable 
 goods and services. He gets back no more control over 
 present income, but he gets a purchasing power over 
 a greater amount of deferred income. Had he invested 
 
 ^ For a discussion of the effect of a change in the rate of interest 
 on prices, see Irving Fisher, Nature of Capital and Income, New 
 York (Macmillan), 1906, p. 227, and Rate of Interest, New York 
 (Macmillan), 1907, pp. 226 and 227.
 
 Sec. 3] THE BEST INDEX NUMBERS 215 
 
 in land at the start, instead of lending, the rise of interest 
 would have left him with the same amount of land, but 
 a less value. As it is, he gets back a purchasing power 
 over a greater amount and the same value of land. An 
 accident has made the lender better off than he ex- 
 pected, and better off than he would have been had he 
 invested instead of loaning. 
 
 If, on the other hand, the rate of interest should fall, 
 the borrower will be benefited, and the lender injured. 
 The value of land and of any other property, the income 
 of which extends far into the future, would rise in 
 comparison with the value of food, shelter, and so on. 
 The value of a house is the discounted value of its 
 future rent or service in affording shelter. The rate 
 of interest having fallen, the value of the house will be 
 higher, in comparison with the yearly rental value, 
 than before. To repay the same amount of purchasing 
 power over shelter as was borrowed is to repay less than 
 the same amount of purchasing power over houses. 
 The borrower is benefited to the extent that he has to 
 curtail investments to repay, since he repays a less 
 investing power although as great a spending power. 
 He need not, therefore, curtail his investments in land 
 and machinery quite so much as he otherwise would 
 have to do. The lender, on the other hand, is in the 
 same degree injured. If he wishes to invest in durable 
 capital, such as an office building, a mine, or shares in 
 a railroad, he cannot purchase as much of these with 
 the returned principal as he could have purchased with 
 the same principal at the time of the loan. Had he 
 foreseen the fall in interest, he might have refused to 
 make the loan and invested instead. He would then 
 have had, in place of interest on a loan, a return on his 
 investment and a larger amount of capital on which
 
 216 THE PURCHASING POWER OF MONEY [Chap. X 
 
 to realize future income. The effect of the fall in in- 
 terest would then have been, not to decrease the re- 
 turns on his investment, but to increase the capitalized 
 vahie of the investment. 
 
 It appears, then, that while an index number based 
 on services and the less durable commodities may be 
 adapted to time contracts between a borrower intend- 
 ing to indulge in immediate consumption, and a lender 
 intending to postpone consumption until the repay- 
 ment of the loan, such an index number is not entirely 
 suited to contracts one or both parties to which are 
 interested in more permanent investment. 
 
 Instead, therefore, of basing our index number on 
 consumable goods and services enjoyed during a period, 
 we ought rather to base it partly on these and partly on 
 the amount of durable capital. Each borrower and 
 each lender may wish to make a different distribution 
 in time of his income stream.^ One man, that he may 
 have a large income in the future, wants to invest ; 
 another, that he may enjoy a large income soon, does 
 not want to invest. One lender is, 'therefore, interested 
 in getting back as much durable capital as he lent ; 
 another lender is interested in receiving as great pur- 
 chasing power over services and consumable goods 
 as he lent. 
 
 Now different persons, with different intentions as 
 to the spending of their money, nevertheless make 
 loan contracts with each other. Even if a separate 
 index number, specially weighted, could be used for 
 each couple, such a standard would not be equally 
 fitted to both parties. Yet the same debt cannot be 
 paid in two different standards. Therefore, absolute 
 equalization is out of the question. We can mitigate 
 
 1 Rate of Interest, pp. 121-125.
 
 Sec. 4] THE BEST INDEX NUMBERS 217 
 
 the evils of a fluctuating money standard, but we cannot 
 entirely remove the element of speculation from time 
 contracts. 
 
 Although different persons and different classes 
 might establish different standards for special contracts, 
 yet for the great mass of business contracts involving 
 postponed payments, a single series of index numbers 
 including articles used and purchased by all classes, 
 and including also services, would probably be found 
 advisable. This index number would be best suited 
 to contracts between different classes, between in- 
 dividuals of differing habits of consumption, and to fix 
 the money payments on bonds which are securities 
 sold to the public in general. 
 
 Without attempting to construct index numbers 
 which particular persons and classes might sometimes 
 wish to take as standard, we shall merely inquire re- 
 garding the formation of such a general index number. 
 It must, as has been pointed out, include all goods and 
 services. But in what proportion shall these be 
 weighted? How shall we decide how much weight 
 should be given, in forming the index, to the stock of 
 durable capital and how much weight to the flow of 
 goods and services through a period of time, — the flow 
 to individuals, which mirrors consumption? The two 
 things are incommensurable. Shall we count the rail- 
 ways of the country as equally important with a month's 
 consumption of sugar, or with a year's? 
 
 §4 
 
 To cut these Gordian knots, perhaps the best and 
 most practical scheme is that which has been used in 
 the explanation of the P in our equation of exchange, 
 an index number in which every article and service
 
 218 THE PURCHASING POWER OF MONEY [Chap. X 
 
 is weighted according to the value of it exchanged at 
 base prices in the year whose level of prices it is desired 
 to find.^ By this means, goods bought for immediate 
 consumption are included in the weighting, as are also 
 all durable capital goods exchanged during the period 
 covered by the index number. What is repaid in con- 
 tracts so measured is the same general purchasing 
 power. This includes purchasing power over every- 
 thing purchased and purchasable, including real estate, 
 securities, labor, other services, such as the services 
 rendered by corporations, and commodities. 
 
 There has been much discussion as to the propriety 
 of the inclusion of services of human beings, or so-called 
 ''labor." In one way the question solves itself, since 
 the inclusion or exclusion on the basis of piece work will 
 make little or no difference to the results. 
 
 It is well known that we may measure wages either 
 " by the piece " or by "time." In either case they enter 
 into and affect the general index number expressing 
 the price level, but the influence is different in the 
 two cases. If we take hours of labor as the basis and 
 measure the wages paid by the hour or by the day, 
 then we are likely to find that, during a period of 
 improvement in the arts, money wages are rising while 
 the prices of goods are falling, or that money wages are 
 rising faster than the prices of goods, or are falling more 
 slowly. But if we measure wages by the piece, we shall 
 find less inconsistency of results. If goods increase 
 faster than currency, so that prices tend to fall, piece 
 
 1 The same conclusion as to the best standard for deferred pay- 
 ments is reached by Professor H. S. Foxwell by a somewhat differ- 
 ent Hue of reasoning. See remarks of Professor F. Y. Edgeworth 
 (as Secretary of the Committee on Variations of the Monetary 
 Standard). Report of the British Association for the Advancement 
 of Science, for 1889, pp. 134-139.
 
 Sec. 4] THE BEST INDEX NUMBERS 219 
 
 wages will tend to fall, on the average, in very much 
 the same proportion. As improvements in machinery 
 make the output per hour of labor, i.e. the piece work, 
 increase, the price per piece may decrease. 
 
 The two methods of measurement giving these differ- 
 ent results for price indexes make opposite differences 
 in the volume of trade. The volume of piece work 
 increases with progress in invention faster than the 
 volume of time work. 
 
 In considering the index number as a standard for 
 deferred payments, the desirability of assuming piece 
 wages to change like commodity prices is based largely 
 on the difficulty and consequent impracticability of 
 including wages on a time basis. On the piece-wage 
 basis, changes in money prices of other goods furnish 
 an approximate measure of changes in money prices 
 of labor. 
 
 Those who make time contracts on the basis of 
 such an index number know that they will pay back, 
 or receive back, purchasing power over the same 
 quantities of goods, the purchasing power over which 
 they borrowed or lent. This form of index number is 
 an objective standard of goods. 
 
 If an index number were to be constructed from time 
 wages alone (not including goods at all), debtors would 
 pay back and creditors receive an equivalent purchas- 
 ing power over hours of labor. When the time wages 
 and prices of goods are both included, the problem is 
 how much weight to give to each. Kemmerer weights 
 wages 3 per cent out of a total of 100 per cent. Its 
 influence, therefore, would in any case not be felt 
 greatly, while, if we take piece wages, it will not be felt 
 at all; that is, it will not greatly matter whether 
 wages are included or not. Since practically we have
 
 220 THE PURCHASING POWER OF MONEY [Chap. X 
 
 no statistics of relative piece wages, and few good 
 statistics for time wages, we may, in general, as well 
 omit wages altogether. 
 
 This procedure has another advantage. In an index 
 number intended to serve as a basis for deferred pay- 
 ments for wage earners, it is clear that wages should 
 be excluded. A wage earner does not judge his pur- 
 chasing power on the basis of how much labor he can 
 buy.^ 
 
 In this connection it may be well to call attention 
 to another standard of purchasing power of money 
 which has sometimes been suggested for adjusting 
 contracts. This is the utility standard. According 
 to this, each person would be expected to receive or 
 pay back marginal utility equivalent to what he had 
 lent or borrovred. But the marginal utility of the 
 same goods is different for different persons and different 
 for the same person at different periods of his life. 
 Hence, no such standard could be practically applied. 
 
 A price is an objective datum, susceptible of measure- 
 ment, and the same for all men. Marginal utilities, 
 on the other hand, not only are impossible to meas- 
 ure, but are unequal and vary unequally among in- 
 dividuals. The purchasing power of money in the 
 objective sense is, therefore, an ascertainable magnitude 
 with a meaning common to all men. It is of course true 
 that marginal utility of money is a fundamental magni- 
 tude and that it depends in part on the purchasing 
 power of money. But it depends also on each man's 
 income. The marginal utilities of money will vary 
 directly with the purchasing power of money if aU 
 prices and all money incomes change in the same ratio, or 
 
 1 Cf. Edgeworth, in Palgrave's Dictionary of Political Economy^ 
 "Index Numbers."
 
 Sec. 4] THE BEST INDEX NUMBERS 221 
 
 (roughly at least) if incomes change in the ratio of the 
 average price change. Ideally, this fixed ratio between 
 marginal utilities and purchasing power should hold 
 true when the quantity of money varies (assuming that 
 deposits vary equally and that velocities of circulation 
 and volume of trade remain unchanged) after transi- 
 tion periods are over. Practically, however, all these 
 elements vary, and vary unequally. Money incomes 
 sometimes increase faster, often more slowly, than 
 prices. The result is that changes in the purchasing 
 power of money do not correspond to changes in mar- 
 ginal utilities of money. 
 
 Society may become more prosperous, or it may be- 
 come less so, during the time a contract has to run. 
 This fact, it may be thought, should influence the re- 
 lation of the amount repaid to the amount borrowed. 
 It has been claimed that the benefits of progress 
 should be equably distributed between borrowers and 
 lenders.^ 
 
 But while loan contracts are made with reference to 
 marginal utilities, it is here contended that corrections 
 in a monetary standard not only cannot, but should not, 
 include variations in the subjective value of money 
 due to changes in incomes, but should be confined to 
 variations in objective purchasing power. At any rate, 
 to obtain a measure of objective purchasing power is 
 
 ^ See, for example, paper by Professor J. B. Clark, "The Gold 
 Standard in Recent Theory," Political Science Quarterly, Septem- 
 ber, 1895. Compare with this "The Standard of Deferred Pay- 
 ments," by Professor Edward A. Ross, Annals of the American 
 Academy of Political and Social Science, November, 1892 ; Lucius S. 
 Merriam, " The Theory of Final Utility in its Relation to Money 
 and the Standard of Deferred Payments," ibid., January, 1893 ; Pro- 
 fessor Frank Fetter, " The Exploitation of Theories of Value in the 
 Discussion of the Standard of Deferred Payments," ibid., May, 1895.
 
 222 THE PURCHASING POWER OF MONEY [Chap. X 
 
 a step which may properly be taken by itself before 
 any step more ambitious is considered. The search for 
 a standard of deferred payments which shall auto- 
 matically provide for the just distribution of the " ben- 
 efits of progress " seems as fatuous a quest as the search 
 for the philosopher's stone. Since we cannot measure 
 utility statistically, we cannot measure the corrections 
 in utility required to redistribute the " benefits of prog- 
 ress." In the absence of statistical measurement, any 
 practicable correction is out of the question. The 
 ''utility standard" is therefore impracticable, even if 
 the theory of such a standard were tenable. 
 
 Somewhat similar theories of a perfect standard of 
 deferred payments are based on the idea that a dollar 
 should require always the same amount of labor to pro- 
 duce it. In one sense, since marginal utility and mar- 
 ginal effort are normally equal, the labor standard is 
 identical with the marginal utility standard. But in 
 whatever sense ''labor" is defined, it is an elusive mag- 
 nitude, quite impracticable as a measurable basis for 
 statistics of purchasing power. Seemingly labor may 
 be measured in terms of time and, on such a basis, " a 
 day's labor " has been suggested as a proper unit for 
 measuring deferred payments. But even " a day's 
 labor" is not a sufficiently definite unit in which to 
 measure with any considerable degree of accuracy the 
 purchasing power of money. Days' labor differ in 
 hours, in intensity, and disagreeability of effort as well 
 as in the quality of labor performed — whether it be 
 manual, mental, etc. A magnitude which offers so 
 many theoretical difficulties in measurement can never 
 serve as a practical standard of deferred payments. 
 
 We see then that the attempt to set up a utility 
 or labor standard is too ambitious to be practica-
 
 Sec. 4] THE BEST INDEX NUMBERS 223 
 
 ble.^ We should content ourselves with securing the 
 maximum attainable improvement in the standard of 
 deferred payments, without attempting to secure an 
 ideal distribution of " the benefits of progress." 
 
 It will also simplify our problem if we remember that 
 our ideal is not primarily constancy of • the dollar but 
 rather dependability. Fluctuations which can be fore- 
 seen and allowed for are not evils. Each man may 
 presumably be depended on to allow for changes in his 
 own fortunes, utility, and labor, and perhaps even to a 
 large extent on the general effects of invention and prog- 
 ress. At any rate he should not expect the monetary 
 unit to insure him against every wind that blows. 
 
 The manner in which each person allows for such 
 future changes as he can foresee is by adjusting the 
 size of loans he makes or takes and the rate of interest 
 thereon. If the average income is rising, the borrower 
 can afford to repay more and the lender should receive 
 more ; while, if the average income is falling, the 
 amount paid should be less. The fact is that such are 
 the tendencies where the rise or fall of average income 
 is foreseen. If the average income is rising, the lender 
 will be less anxious to deplete his present income, which 
 is relatively meager, in order to increase his future in- 
 come, which he sees will probably be larger anyway. 
 Thus, increasing prosperity (by which is meant, not 
 great prosperity, but growing prosperity) tends to re- 
 strict the supply of loans. At the same time, it tends to 
 increase the demand and so raise interest. Conversely, 
 a decreasing average income will tend to lower interest.^ 
 
 * Cf. Charles A. Conant, The Principles of Money and Banking, 
 Vol. II, Chapter VII. 
 
 ^ Rate of Interest, pp. 95-98 and 304-306. This position is taken 
 by Correa Moylan Walsh, The Fundamental Problem in Monetary 
 Science, New York (Macmillan), 1903, p. 345, footnote.
 
 224 THE PURCHASING POWER OF MONEY [Chap. X 
 
 All this follows only in case the rise or fall of incomes 
 is foreseen. If not foreseen, it can exercise no influence 
 of importance on the interest rate. To the extent 
 that such changes come unexpectedly after loan con- 
 tracts have been entered into which take no account 
 of them, — to that extent loan contracts are speculative. 
 If incomes fall, the lender has gained relatively to the 
 borrower, because he has realized a higher interest than 
 he could have realized had the change been foreseen. 
 The chief burden of the change falls on the borrower. 
 If incomes experience an unexpected rise, the relative 
 positions are reversed ; the whole gain goes to the 
 borrower. The normal effect of continuous extension 
 of income is to raise the rate of interest. 
 
 Our present problem, however, is not to safeguard 
 the interests of debtors and creditors against all pos- 
 sible elements of change, but only against those ele- 
 ments which are purely monetary. Industrial changes 
 are in a class by themselves, and contracting parties 
 must be trusted to work out their own salvation. We 
 are merely concerned in providing them with a stable 
 or reliable monetary standard. A secure monetary 
 standard cannot guarantee against earthquake nor in- 
 sure the equable distribution of prosperity. It can, 
 however, mitigate the losses now suffered from changes 
 in the relation of money to other goods. 
 
 Statistics of nominal or money interest rates and 
 virtual or commodity interest rates prove that the 
 latter fluctuate much more than the former.^ The 
 effects of this lack of compensation are evil. In the 
 first place, the situation interferes with the normal dis- 
 tribution of wealth and income. If the level of prices 
 is rising, since nominal interest does not for a con- 
 
 1 Rate of Interest, Chapter XIV.
 
 Sec. 5] THE BEST INDEX NUMBERS 225 
 
 siderable time rise enough to compensate, the lender 
 gets back a less amount of wealth or services than he 
 might reasonably have expected. Creditors lose and 
 debtors gain. It should be noted also that all persons 
 with relatively fixed money salaries lose by this rise 
 of prices. When the level of prices falls, on the other 
 hand, creditors and persons with relatively fixed in- 
 comes gain at the expense of debtors. The distribu- 
 tion of wealth is changed in either case from purely 
 monetary causes, and the change can be averted by 
 making the standard of deferred payments more stable. 
 
 §5 
 
 We are brought back again, therefore, to the conclusion 
 that on the whole the best index number for the purpose 
 of a standard of deferred payments in business is the 
 same index number which we found the best to indicate 
 the changes in prices of all business done ; — in other 
 words, it is the P on the right side of the equation of 
 exchange.^ 
 
 It is, of course, utterly impossible to secure data for 
 all exchanges, nor would this be advisable. Only 
 articles which are standardized, and only those the use 
 of which remains through many years, are available 
 and important enough to include. These specifica- 
 tions exclude real estate, and to some extent wages, 
 retail prices, and securities, thus leaving practically 
 nothing but wholesale prices of commodities to be in- 
 cluded in the list of goods, the prices of which are to be 
 
 1 This is really the same conclusion as that reached by Walsh, 
 The Fundamental Problem in Monetary Science, in which, after a 
 thorough and critical review of the literature of the subject, the 
 author concludes that the kind of stability desirable in the standard 
 of deferred payment is "stability of exchange value.'' 
 Q
 
 226 THE PURCHASING POWER OF MONEY [Chap. X 
 
 compounded into an index number. These restrictions, 
 however, are not as important as might be supposed. 
 The total real estate transactions of New York City 
 (Manhattan and the Bronx) in 1909 (an active year) 
 measured by assessed valuations (probably | of the 
 market valuation) amounted to only $620,000,000. 
 This is utterly insignificant if compared only with the 
 104 billions of bank clearings in New York City. Yet 
 real estate transactions probably constitute a higher 
 percentage of total transactions in New York than in 
 the United States.^ In the United States we feel safe, 
 therefore, in saying that they amount only to a fraction 
 of 1 per cent of the total transactions. As to exchanges 
 in securities, Kemmerer estimates, on the basis of the 
 transactions of the New York Stock Exchange, that 
 about 8 per cent of the total transactions of the coun- 
 try consist in the transfer of securities.^ As already 
 stated, he also estimates that wages amount to about 
 3 per cent.^ As to the comparative importance of 
 retail as compared with wholesale prices, we have 
 some figures of Professor Eanley, of the Monetary 
 Commission.^ On this basis, and because wholesale 
 and retail prices roughly correspond in their move- 
 
 ^ At any rate the impression is strong that real estate is more 
 "active" in New York than in most other cities, because of the 
 rapid change in the character of sites on account of the narrowness 
 of Manhattan Island and the consequent acceleration of growth 
 in one direction (northward) and that, in general, cities have more 
 trade in real estate than the country, not only absolutely, but rela- 
 lively to other trade. 
 
 * Money and Prices, 2d ed.. New York (Holt), 1909, p. 138. 
 « Ibid., p. 138. 
 
 * Credit Instruments, 1910, 61st Congress, 2d Session, Senate Docu- 
 ment 399, pp. 69, 73, 134, 136, would indicate that wholesale trade 
 requires something like twice as much exchange work as retail 
 trade.
 
 Sec. 5] THE BEST INDEX NUMBERS 227 
 
 ments,^ we may omit retail prices altogether. It is true 
 that retail prices usually lag behind wholesale prices ; but 
 part of the lagging is more apparent than real. Expert 
 testimony of those who have collected such statistics 
 shows that when, as at present, prices are rising rapidly, 
 retailers obviate the necessity of confronting their 
 customers with too frequent and rapid increases in 
 prices by quoting the same prices and substituting in- 
 ferior grades or, in some instances, smaller loaves or 
 packages. 
 
 It is true that wholesale transactions constitute 
 a minority of all transactions, perhaps only a fifth. ^ 
 Nevertheless, wholesale prices are more typical than 
 any other. 
 
 They are to a large extent typical of producers' 
 prices which precede them, and of retail prices which 
 succeed them. They are typical of many large and 
 often nondescript groups which go to make up the total 
 transactions, such as are classed together in Kinley's 
 Report to the Monetary Commission under the head 
 ''other deposits," including hotel charges, fees of pro- 
 fessional men, etc., as well as wages. Among items of 
 which wholesale prices may not be very typical are 
 the transactions in securities (speculative and other), 
 railway and other transportation charges, and insurance. 
 Latterly, prices of stock securities have advanced faster 
 than wholesale prices, while transportation and insur- 
 ance charges have not advanced as fast. The attempts 
 
 1 The studies of the Bureau of Labor in retail prices seem to show 
 a general sympathy in movement between retail or wholesale prices, 
 as indeed might be expected. 
 
 2 See, in Report of National Monetary Comviission on Credit 
 Instruments, the figures of aggregate sums deposited in banks by 
 wholesale merchants and others. While these do not afford an ex- 
 act comparison, they aid in making a rough guess.
 
 228 THE PURCHASING POWER OF MONEY [Chap. X 
 
 of Kemmerer and myself (Chapter XII) to combine in 
 one average wholesale prices and prices of stocks and 
 wages yield results differing only slightly from those 
 based on wholesale prices. From a practical stand- 
 point, wholesale prices of commodities are the only 
 prices which are yet sufficiently standardized, and the 
 use of the goods sufficiently stable through a long 
 period of time, to make them serviceable for general 
 use. 
 
 Not only may we consider that wholesale prices 
 roughly represent all prices, but we may, with even more 
 confidence, confine our statistics for wholesale prices 
 to a relatively small number. Edgeworth and others 
 have shown, both practically and theoretically, that 
 a large number of articles is needless and may even 
 be detrimental. The 22 commodities employed by 
 ''The Economist" afford an index number of con- 
 siderable value; the 45 of Sauerbeck have given us a 
 standard of great value; and the 200 and more com- 
 modities used in the Aldrich Report and the bulle- 
 tins of the Bureau of Labor are certainly numerous 
 enough, if not too numerous, to give a most accurate 
 index number of prices. 
 
 The recommendations of the Committee of the 
 British Association for the Advancement of Science 
 were that the index number should include six groups, 
 comprehending twenty-seven classes of articles, and 
 that the prices should be weighted in round numbers 
 representing approximately the relative expenditures 
 of the community in these objects. The groups and 
 classes with weighting were as follows : ^ — 
 
 ^ See Report of the Committee in Report of the British Associa- 
 tion for the Advancement of Science, for 1888, p. 186.
 
 Sec. 5] THE BEST INDEX NUMBERS 229 
 
 Breadstuffs (wheat 5, barley 5, oats 5, potatoes, rice, etc., 5) . . 20 
 
 Meat and dairy (meat 10, fish 21, cheese, butter, milk, 71) ... 20 
 Luxuries (sugar 2i, tea 2z, beer 9, spirits 2i, wine 1, tobacco 
 
 2i) 20 
 
 Clothing (cotton 2i, wool 2i, silk 2i, leather 2i) 10 
 
 Minerals (coal 10, iron 5, copper 2j, lead, zinc, tin, etc., 2^) . . 20 
 Miscellaneous (timber 3, petroleum 1, indigo 1, flax and linseed 
 
 3, palm oil 1, caoutchouc 1) 10 
 
 This report was made after very thorough considera- 
 tion by a remarkably competent committee consisting 
 of Mr. S. Bourne, Professor F. Y. Edgeworth (Sec), 
 Professor H. S. Foxwell, Mr. Robert Giffen, Professor 
 Alfred Marshall, Mr. J. B. Martin, Professor J. S. 
 Nicholson, Mr, R. H. Inglis Palgrave, and Professor 
 H. Sedgwick. The report also gives the precise techni- 
 cal description of the articles the price quotations of 
 which are to be used (the iron, for instance, being 
 ''Scotch pig iron"), and also the price list or other source 
 for price quotations (the wheat, for instance, being the 
 ''Gazette Average"). 
 
 With slight modifications this recommendation of 
 the British Committee could be made to apply to 
 American figures. In America we have had a number 
 of index numbers of wholesale prices, the most im- 
 portant being (1) those of Roland P. Falkner in the 
 Aldrich Senate Report, covering a period from 1840 
 to 1891, in which, beginning with 1860, there were 223 
 commodities included, the results being given in two 
 ways, viz., weighted, the weighting being arranged accord- 
 ing to relative expenditures on these articles or their 
 congeners used by workmen, and also unweighted ; 
 (2) those of the United States Labor Bureau for 251 to 
 261 commodities beginning with 1890, and now, it is 
 understood, to be published every year; (3) Dun's
 
 230 THE PUKCHASING POWER OF MuNEY [Chap. X 
 
 index numbers from 1860 to 1906 continued recently 
 for Gibson by Dr. J. P. Norton ; and (4) Bradstreet's 
 index numbers since 1895 for 96 commodities. 
 
 We need not go into detailed criticism of these index 
 numbers. On the whole they seem to include too many 
 commodities, while they all employ the objectionable 
 fixed-base system. It would be a great advantage if we 
 could fix upon a system in America which would be not 
 only authoritative, but would give out its results at 
 least yearly and promptly. 
 
 For practical purposes the median is one of the best 
 index numbers. It may be computed in a small fraction 
 of the time required for computing the more theoret- 
 ically accurate index numbers, and it meets many of 
 the tests of a good index number remarkably well. 
 It also has the advantage of easily exhibiting (by means 
 of the ''quartiles") the tendency to dispersion of prices 
 (from each year as a base to the next) on either side 
 of the median. The median should be weighted in 
 round numbers analogously to the weighting already dis- 
 cussed for the more theoretically perfect index numbers.^ 
 The median of a series of numbers is a number such 
 that there are as many numbers above as below it in 
 the series. If the number of terms in the series is odd, 
 the median is the middle term of the series of numbers 
 arranged in the order of magnitude. If the number of 
 terms is even, the median falls between two terms. If 
 these are equal, the median is identical with them both; 
 if they are unequal, the median lies between them and 
 may then be taken as their simple arithmetical, geo- 
 metric, or any other average. Practically the two 
 middle terms are almost inevitably so close together 
 that it would make no appreciable difference what 
 \See Appendix to (this) Chapter X, § 8.
 
 Sec. 6] THE BEST INDEX NUMBERS 231 
 
 method of averaging the two middle terms is adopted. 
 The method of weighting the terms from which a 
 median is computed consists in counting each term the 
 number of times indicated by its weight. To illustrate 
 these statements, it is evident that the median of the 
 numbers 3, 4, 4, 5, 6, 6, 7, arranged in order of magni- 
 tude is 5 ; and the median of 3, 4, 4, 5, 6, 6 is 4^. 
 If the weights to be attached to these latter numbers are 
 
 for number 3 weight 1 
 for number 4 weight 2 
 for number 4 weight 3 
 for number 5 weight 4 
 for number 6 weight 2 
 for number 6 weight 1 
 
 the median is then found from the following : — 
 
 Series 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6 
 
 The weights being 12 3 4 2 1 
 
 of which the median is 5. The arithmetical averages 
 corresponding to the three medians mentioned (5, 4J 
 and 5) are 5., 4.67 and 4.69 respectively. 
 
 Practically it is not necessary to arrange the terms 
 in exact order of size. Terms easily recognized as low 
 can readily be paired off against those easily recognized 
 as high and only the remaining few central terms need 
 be arranged in exact order. The terms near the middle 
 being usually almost or quite equal, make the selection 
 of the median extremely easy. 
 
 In order to use the median for an index number of 
 prices, we first arrange our yrice ratios and then select 
 the median ratio. 
 
 § 6 
 
 In this chapter we have aimed to show that an excel- 
 lent form of index number of prices is the ratio of real
 
 232 THE PURCHASING POWER OF MONEY [Chap. X 
 
 values to ideal values at base prices ; and that the ele- 
 ments entering into the construction of index numbers 
 differ according to the different purposes for which they 
 are desired. If the purpose is to measure capital, the 
 prices of services should not be included, but only the 
 prices of the different articles of wealth existing at any 
 point of time. If the purpose is to obtain means to 
 measure real wages, only those things should be in- 
 cluded which workingmen buy ; and they should be 
 included according to the values bought during a given 
 period, these values being measm-ed at standard prices. 
 
 The question of justice between borrower and lender, 
 where the purpose is to fix on the best index number as 
 a standard for deferred payments, was also considered. 
 It was seen to be not an infringement of justice that one 
 man should gain from another on account of fluctuations 
 in the money standard ; for the contract is a free one 
 in which normally each should assume whatever risk 
 there may be of loss for the sake of whatever chance 
 there may be of gain. It was maintained, also, that 
 it would be wrong for the government deliberately to 
 take his gain away from a person who had assumed a 
 risk of loss in the first place. Nevertheless, it was urged 
 that a means by which contracts made in the future 
 could be made less speculative, is desirable. 
 
 It was urged that it is no part of the function of an 
 index number of general prices to guard against rising 
 and falling real income. The function of such an index 
 number is to measure the change in the level of prices, 
 in order that, in contracts involving deferred payments, 
 there shall be no element of risk so far as money is con- 
 cerned. Without the index number as a standard, such 
 contracts are quite highly speculative. The adjustment 
 of the rate of interest compensates to some extent, but
 
 Sec. 6] THE BEST INDEX NUMBERS 233 
 
 not nearly enough, for the fluctuations in the value of 
 money. These fluctuations influence the distribution 
 of wealth among persons and classes, and bring about 
 crises and business depressions. It is desirable that 
 some basis for time contracts should be fixed upon, 
 which will remedy these evils. It is believed that an 
 index number expressing the price level entering into 
 the equation of exchange might be adopted as such 
 a basis. The ideal set forth is that neither debtor 
 nor creditor should be the worse off by being deceived 
 through changes in the level of prices of goods bought 
 and sold. Some system is to be sought, therefore, by 
 which the actual results of the contract should closely 
 approximate the expected results in nearly all cases. 
 
 It was shown that different persons and dift'erent 
 classes might be interested in having for their time con- 
 tracts index numbers somewhat differently constructed, 
 because different persons are interested in consuming 
 different kinds of commodities and because they desire 
 to invest larger or smaller proportions of their earnings. 
 But for general purposes, as the best compromise to 
 fit the needs of different classes, what was suggested 
 was an index number based on the prices of all goods 
 exchanged during a given period. It was pointed out, 
 however, that the different forms of index numbers 
 which had gained reputation lead to practically the 
 same results. 
 
 Finally, it was shown that for rough and ready com- 
 putations the median has advantages over all other 
 forms of index numbers.
 
 CHAPTER XI 
 
 STATISTICAL VERIFICATION. GENERAL HISTORICAL 
 
 REVIEW 
 
 § 1 
 
 Since both the level of prices and the quantity of 
 money in circulation cannot in practice be perfectly 
 measured, and since the level of prices depends upon 
 other factors besides the quantity of money, — viz. 
 the quantity of circulating credit, the velocities of cir- 
 culation of that credit and of money, and the volume of 
 business, — it would be absurd to expect any exact 
 correspondence between variations in the quantity of 
 circulating money and variations in the price level ; 
 and it is likewise absurd to state, as some have stated, 
 
 that the absence of exact statistical correspondence 
 
 * 
 
 proves the absence of any influence of quantity of money 
 on price level. Nevertheless, when the volume of money 
 changes greatly and quickly, the effect on prices from 
 this cause is usually so great as to make itself manifest. 
 The general trend of prices has usually been upward, 
 as Figure 10 ^ shows. According to the diagram prices 
 are now about five times as high as a thousand years 
 ago and are from two to three times as high as in the 
 period between 1200 and 1500 a.d.' Beginning with 
 the last-named date, or shortly after the discovery of 
 America, prices have almost steadily risen. 
 
 1 This diagram shows the changes in price level according to the 
 separate estimates of D'Avenel, Hanauer, and Leber as given in 
 Aupetit's Essai sur la theorie generale de la Tnonnaie, Paris (Gnillau- 
 min), 1901, p. 245. 
 
 2 These figures are found by supplementing those of D'Avenel, 
 Hanauer, and Leber by those of Jevons and Sauerbeck in the 
 19th century. Without such supplementing the rise is still more, 
 being tenfold in a thousand years and four to six times since 
 1200-1500. 
 
 234
 
 Sec. 1] 
 
 STATISTICAL VERIFICATION 
 
 235 
 
 The discovery of America was followed in 1519 by 
 the invasion of Mexico under Cortez and, twenty years 
 later, by Pizarro's conquest of Peru. From these 
 conquests and the consequent development of New 
 World mining of precious metals, dates the tremendous 
 production of gold, and especially of silver, during the 
 sixteenth century. From the discovery of America 
 until the after effects of its discovery began to be felt, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 160 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 •40 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 \ 
 
 
 
 
 
 
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 \/ 
 
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 \ 
 
 
 
 
 
 
 
 
 
 
 
 HANAUER 
 
 LEBER. 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
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 i 
 
 s\ 
 
 
 
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 \ 
 
 Z' 
 
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 40 
 
 
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 Sv, 
 
 
 
 V 
 
 
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 4 
 
 / 
 
 
 
 
 
 L 
 
 
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 *" 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 650 /eOO 1300 lAOO 1300. l&iO 1700 1800 1900 
 
 Fig. 10. 
 
 or, to be exact, through the year 1544, the average 
 annual output of gold was less than five million dollars, 
 and of silver about the same.^ The rich mines of Potosi 
 
 1 These and the following figures are from "The World's Pro- 
 duction of Gold and Silver from 1493-1905," J. D. Magee, Journal 
 of Political Economy, January, 1910, p. 50 ff. Mr. Magee's figures 
 to 1885 are based on Soetbeer's, and since that date, on the Reports 
 of the Director of the United States Mint. For Soetbeer's figures, 
 see Adolf Soetbeer, Edelmetall-Produklion und Werthverhdltniss 
 zunschen Gold und Silber seit der Entdcckung Amerika's bis zur 
 Gegenwart, Cotha (Justus Perthes), 1879, p. 107. These figures 
 and others to follow are given also in the same author's Materialien 
 and are quoted, and their significance discussed, in L. L. Price,
 
 236 THE PURCHASING POWER OF MONEY [Chap. XI 
 
 in Bolivia were discovered in 1546. From 1545 to 1560 
 the annual production of silver averaged eighteen mil- 
 Uons, which was over fourfold the previous rate. The 
 product of gold also increased, though slightly. The 
 rates of production for both metals rose steadily (with 
 slight interruption, 1811-1840) up to the present time. 
 
 These new world mines began to pour their product 
 into Europe : first into Spain, the chief owner of the 
 mines, then, by trade, into the Netherlands and other 
 parts of Europe, and then into the Orient — that great 
 ''sink of silver." Accordingly, as Cliff e Leslie^ has 
 shown, prices rose first in Spain, then in the Nether- 
 lands, and then in other regions. 
 
 But, though the new supphes of the precious metals 
 distributed themselves very gradually through Europe, 
 and the rise of prices was consequently in some regions 
 delayed, there can be no doubt that they rose or that 
 the rise was great. The rise between the discovery of 
 America and the beginning of the nineteenth century 
 was several hundred per cent. This rise was simul- 
 taneous with an increase of the stock of the precious 
 metals, because production outran consumption. 
 
 Although the total production of the precious metals 
 continued to increase until 1810, the ratio of the yearly 
 production to the existing stock became gradually less. 
 Corresponding to this slackening of production, and 
 presumably because of it, prices did not continue to rise 
 at the same rapid rate as at first. Furthermore, with 
 the development of trade with the East, more and more 
 of the new supplies found their way thither. The 
 most rapid rise occurred during the sixteenth century. 
 
 Money and its Relation to Prices, London (Sonnenschein), 1900, 
 New York (Scribner's), p. 82 ff. 
 
 ^ Essays in Political Economy, 2d ed., No. 19.
 
 Sec. 2] 
 
 STATISTICAL VERIFICATION 
 
 237 
 
 §2 
 
 The stock of money metals at any time in any country 
 is evidently the difference between the total product and 
 the sum of the consumption and the net export. Jacob^ 
 has estimated roughly the stock in Europe at various 
 dates. The following table compares the estimated me- 
 talUc stocks in Europe with the estimated price levels : — 
 
 Money and Prices 
 
 Estimated Product, Consumption, and Stock of Precious Metals in 
 Europe, expressed in Millions of Dollars, and Price Levels ^ 
 
 Date 
 
 Product 
 
 Consumption 
 AND Export 
 
 Stock 
 
 Prices 
 
 1500 .... 
 1600 .... 
 1700 .... 
 1800 .... 
 1900 .... 
 
 J 670 
 1 1640 
 1 4280 
 1 13,000 
 
 290 
 
 740 
 
 3880 
 
 8960 
 
 170 
 
 550 
 
 1450 
 
 1850 
 
 5890 
 
 35 
 
 75 
 
 90 
 100 
 125 (?) 
 
 1 William Jacob, F.R.S., An Historical Inquiry into the Produc- 
 tion and Consumption of the Precious Metals, 2 vols., London (Mur- 
 ray) 1831 ; Vol. II, p. 63. See also Price, Money and its Relation 
 to Prices, p. 78. 
 
 * The estimates of the product and stock are those of Jacob and 
 Soetbeer (op. cil.) and Del Mar, History of the Precious Metals, 
 New York (Cambridge Encyclopaedia Co.), 1902, p. 449. The price 
 levels (except that for 1900) are the averages of those of Vicomte 
 D'Avenel, Histoire Economique de la Propriety des Salaires et des 
 Denrees, Vol. I, pp. 27 and 32, Leber and Hanauer (see A. Aupetit, 
 Essai sur la theorie generate de la monnaie, Paris (Guillaumin), 1901, 
 p. 245), the three estimates being each reduced to 100 per cent for 
 the last quarter of the eighteenth century, or rather 1770-1790. 
 The figure for each century year is taken as the average of the 
 figures given by the three authorities for the preceding and succeed- 
 ing quarter century. The figure for 1900 is given as 125 as a com-
 
 238 THE PURCHASING POWER OF MONEY [Chap. XI 
 
 With the enormous increase in the quantity of the 
 precious metals, small wonder if prices have risen ! 
 
 We see that there has been a general increase (1) in the 
 stock of money metals, and (2) in the price level, and 
 that the greatest increase of each was in the sixteenth 
 century. We find also that the prices did not increase 
 as fast as the quantity of money. This relative slow- 
 ness on the part of prices was to be expected, because of 
 the increased volume of business. This, we know, must 
 have come Vvdtli increased population and with progress 
 in the arts — especially the arts of trade — and with 
 development in transportation. As to changes in the 
 velocity of circulation of money we know absolutely 
 nothing. 
 
 §3 
 
 During the last century the price movements have 
 been more carefully recorded and show many ups and 
 downs. The most complete statistics (those of Sauer- 
 beck) are for England. They are represented in Figure 
 11.^ As is well known, English prices were inflated by 
 
 promise between widely conflicting results. Leber, Hanauer, and 
 D'Avenel agree fairly well and D'Avenel (^\Titing in 1890 to 1894) 
 finds (p. 32) the "present" price level in France to be double what it 
 was for 1776-1790, which would make the required figure 200. The 
 figures for England, however, of Jevons for 1782 to 1818, Investi- 
 gations in Currency and Finance, London (Macmillan), 1884, p. 144, 
 combined with those of Sauerbeck from 1818 to the present, Course 
 of Average Prices in England, London (King), 1908, indicate an actual 
 fall of prices, the figure for 1900 being on the above basis from 75 
 to 80. The English figures are so m.uch more com-plete than the 
 continental figures of D'Avenel, Leber, and Hanauer, that they are 
 given more weight, and 125 seems a fair rough average for Europe. 
 But the wide discrepancies between the various figures make this, 
 or any other figure which might be chosen, extremely uncertain. 
 
 ^ The figures are taken from various numbers of the Joiirnal oj 
 the Royal Statistical Society. For many years Sauerbeck has pub- 
 lished yearly his index number in the March issue of this journal.
 
 Sec. 3] 
 
 STATISTICAL VERIFICATION 
 
 239 
 
 the issue of irredeemable paper during the Napoleonic 
 wars. This period of the paper standard extended 
 from 1801 to 1820. But prices in paper were only 
 shghtly higher than prices in gold, and the chief price 
 
 fX 
 
 1(9 
 
 
 1 
 
 
 'ia 
 
 
 
 
 
 I 
 
 ■ 
 
 ;:; 
 
 :i 
 
 ^\ 
 
 
 m 
 
 :::: 
 
 ;^: 
 
 prt 
 
 Ih 
 
 i 
 
 :: 
 
 ii 
 
 ::::: 
 
 s 
 
 1 
 
 } 
 
 
 1 
 
 i 
 
 ; 
 
 1 
 
 ;; 
 
 ^;; 
 
 1 
 
 i 
 
 1 
 : + 
 
 i 
 
 MO 
 
 n 
 
 •e 
 ■«s 
 
 1 
 
 i 
 
 
 5::::1 
 
 i 
 
 m 
 
 i 
 
 : 
 
 i; 
 
 
 
 l\\\ 
 
 
 1 
 
 h 
 
 r.i 
 
 m. 
 
 -+fT^ 
 
 T 
 
 t 
 
 
 1 
 
 1 
 
 ■J 
 
 1 
 
 I 
 
 :: 
 ::: 
 
 1 
 
 17^9 '&0O *80S l6tO 1513 ISSO ISSS 1 
 
 ■ 1635 1840 I 
 
 Fig. 11. 
 
 movements (except in a few years) were but slightly 
 affected by the existence of a paper standard. The 
 main periods of price movements in England since 
 1789 may be stated as follows: — 
 
 Prices rose 1789-1809, stock increasing. 
 Prices fell 1809-1849, stock stationary. 
 Prices rose 1849-1873, stock increasing. 
 Prices fell 1873-1896, stock increasing slightly. 
 Prices rose 1896-present, stock increasing. 
 
 In each case is cited the movement in the stock of 
 money metals in Europe as given in the table of Del Mar.^ 
 
 The only period which does not, at first glance, agree 
 with what we might expect if our theory of price levels 
 
 1 History of the Precious Metals, p. 449. The data given by Del 
 Mar are based on the estimates of King, Humbolt, Jacob, Tooke, 
 Newmarch, McCulIoeh, and himself. The dates correspond ap- 
 proximately with the ends of the periods of price movements as 
 above given. The following figm-es summarize those of Del Mar 
 as to stock (expressed in billions of dollars) : — 
 
 1776 
 
 1808 
 1838 
 1850 
 
 1.4 
 1.9 
 1.3 
 2.0 
 
 1870, 
 1876, 
 1893 , 
 1896, 
 
 3.6 
 3.7 
 3.7 
 4.5
 
 240 THE PURCHASING POWER OF MONEY [Chap. XI 
 
 in relation to money is correct, is the period 1873-1896. 
 Of the other four periods, three are periods of rising 
 prices and increasing stocks. The fourth is a period of 
 a stationary stock ; and since the volume of trade un- 
 doubtedly increased, a fall of prices was naturally to 
 be expected. 
 
 The exceptional period 1873-1896 — a period of 
 falling prices — is probably to be accounted for by the 
 increasing volume of trade and the successive demone- 
 tization of silver by various countries. 
 
 The foregoing parallelism between monetary stocks 
 and prices is somewhat remarkable in view of the in- 
 completeness of the data.^ In the table there are lack- 
 ing, not only exact statistics as to the volume of trade 
 and all statistics whatever of velocity of circulation, 
 but also statistics of the volume of bank notes, govern- 
 ment notes, and deposit currency. We know, however, 
 that modern banking, which had scarcely developed at 
 all before the French Revolution, developed rapidly 
 throughout the nineteenth century. It is also known 
 that banking and deposit currency developed more 
 rapidly during the third period in the table (1849-1873) 
 than during the fourth (1873-1896),2 which fact con- 
 tributes somewhat to explain the contrast between the 
 price movements of these two periods. 
 
 §4 
 
 We may, therefore, summarize the course of price 
 movements during the nineteenth century by the fol- 
 lowing probable statements : — 
 
 1. Between 1789 and 1809 prices rose rapidly, the 
 
 * Cf . Albert Aupetit, Essai sur la theorie ginirale de la monnaiet 
 Paris (Guillaumin), 1901, pp. 271-285. 
 
 * See Mulhall, Dictionary of Statistics, article on "Banks.!!
 
 Sec. 4] STATISTICAL VERIFICATION 241 
 
 index numbers of Jevons moving from 85 to 157 when 
 prices are expressed in the gold standard, or 161 when 
 expressed in paper.^ That is, prices practically doubled 
 in twenty years. This rise was due to the increased 
 stock of gold and silver, which in turn was due to their 
 large production during this period as compared with 
 the periods before and after. The production of silver 
 was especially great. ^ The Napoleonic wars with their 
 destruction of wealth and interference with trade prob- 
 ably exercised some influence in the same direction.^ 
 
 2. Between 1809 and 1849 prices fell. The fall was 
 measured by Jevons as a fall from 157, gold (or 161 , paper) , 
 to 64. That is, in forty years prices were reduced to 
 less than half, or, to be more exact, to two fifths. This 
 fall in prices was presumably due to the lull in the pro- 
 duction of the precious metals, which prevented the 
 aggregate stock from keeping pace with the volume of 
 business. Indeed, the aggregate stock remained station- 
 ary while the volume of business increased. Even the 
 development of bank currency was insufficient to offset 
 the continued increase in the volume of business. It is 
 interesting to observe that this period of falling prices 
 was interrupted by a temporary rise after 1833, which 
 Jevons was at a loss to account for, but which was ap- 
 parently due to the inflow of Russian gold after the 
 discoveries of gold in Siberia in 1830.* 
 
 3. Between 1849 and 1873 (although with two nota- 
 ble interruptions) prices rose. They rose, according 
 
 * Jevons, Investigations in Currency and Finance, London (Mae- 
 millan), 1884, p. 144. 
 
 ''See Magee, "World's Production of Gold and Silver," Journal 
 of Political Economy, January, 1910, pp. 54, 56. 
 
 ' See Harrison H. Brace, Gold Production and Future PriceSf 
 New York (Bankers' Publishing Co.) 1910, pp. 16 and 17. 
 
 * Price, Money and its Relation to Prices, p. 112.
 
 242 THE PURCHASING POWER OF MONEY [Chap. XI 
 
 to Jevons's figures supplemented by Sauerbeck's/ from 
 64 to 86, and according to Sauerbeck's alone, from 74 
 to 111. That is, in 24 years prices increased, according 
 to one calculation, by one third; according to another, 
 by one half. This rise was presumably in consequence 
 of the gold inflation following the famous California gold 
 discoveries in 1849 and Australian discoveries in 1851 
 and 1852. The simultaneous rapid development of 
 banking contributed to the same result in spite of the 
 continued increase in trade. 
 
 4. Between 1873 and 1896 prices fell. This fall was 
 presumably due to the slackening in the production of 
 gold ; to the adoption of the gold standard by nations 
 previously on a silver basis, and the consequent with- 
 drawal of gold by these new users from the old ; to the 
 arrest of the expansion of silver money consequent on 
 the closure of mints to silver ; to the slackening in the 
 growth of banking; and to the ever present growth of 
 trade.^ 
 
 During the long fall of prices from 1873 to 1896, coun- 
 try after country adopted the gold standard. We have 
 already seen that Germany adopted the gold standard 
 
 ^ This rise is found by adding to Jevons's table, which ends in 
 1865, a fictitious figure (86) for 1873, calculated to be in the ratio 
 to the 1865 figure (78), which Sauerbeck's figure for 1873 (111) 
 bears to his figure for 1865 (101). 
 
 - It is not that the left-hand side of the equation did not increase, 
 but that it did not increase so fast as trade ; therefore prices fell. 
 Laughlin seems to think he is overthrowing Mill's position that 
 credit acts like money on prices (an increase of credit raising prices, 
 other things equal), by appealing to the fact of an enormous growth 
 of deposit currency in this period which had not raised prices nor 
 prevented their fall. But if trade increased even faster (and Laugh- 
 lin himself asserts an increase of trade, though he denies that it is a 
 satisfactory answer), then a fall of prices was not opposed to, but 
 entirely consistent with. Mill's theory. See Laughlin, The Principles 
 of Money, New York (Scribner), 1903, pp. 319 and 320.
 
 Sec. 4] STATISTICAL VERIFICATION 243 
 
 in 1871-1873, thus helping to render impossible the 
 maintenance of bimetallism by the Latin Union. The 
 Scandinavian monetary union adopted the gold stand- 
 ard in 1873. Between that date and 1878 the countries 
 of the Latin Union suspended the free coinage of silver 
 and came practically to a gold basis. In the United 
 States the legislation of 1873 signified that with re- 
 sumption (which took place in 1879), the country would 
 come to a gold basis, although no considerable amount 
 of silver, except for small change, had been coined here 
 for several decades previously. The Netherlands virtu- 
 ally adopted the gold standard in 1875-1876, Egypt in 
 1885, Austria in 1892, India in 1893, Chih in 1895, 
 Venezuela and Costa Rica in 1896, Russia, Japan, and 
 Peru in 1897, Ecuador in 1899, and Mexico in 1905. In 
 fact, most countries of importance have now definitely 
 adopted the gold standard. 
 
 The preceding figures apply only to gold countries. 
 But in 1873 gold and silver countries, as it were, fell 
 asunder. It is interesting, therefore, to inquire whether 
 the movement of prices in gold countries was parallel 
 or antithetical to that in silver countries. As might be 
 expected, we find it antithetical. The demonetization 
 of silver in gold countries made a greater amount of that 
 metal available for silver countries. Accordingly, we 
 find that prices rose in India from 107 in 1873 to 140 in 
 1896,' in Japan from 104 in 1873 to 133 in 1896,^ and in 
 
 ^ F. J. Atkinson, "Silver Prices in India," Journal of the Royal 
 Statistical Society, March, 1897, p. 92. The figures for 1893, 1894, 
 1895, and 1896 were lowered by the closure of the Indian mint to 
 silver in 1893. 
 
 2 The figures from 1873 to 1893 are from Japanese Monetary 
 Reports, 1895, translated for me by Mr. Sakata of Yale University. 
 The figures for 1894, 1895, 1896 were also from official Japanese 
 soxirces provided by Japanese students.
 
 244 THE PURCHASING POWER OF MONEY [Chap. XI 
 
 China from 100 in 1874 to 109 in 1893.i These figures, 
 although not as reliable and representative as the figures 
 for gold countries, agree in indicating a rise of prices. 
 The amount of rise is differently indicated, ranging 
 roughly from 10 per cent to 35 per cent. The following 
 table shows the contrast between the gold and silver 
 countries as between 1873-1876 and 1890-1893, the 
 last year being that of the closure of the Indian mint to 
 silver.^ 
 
 Prices in Gold and Silver Countries ' 
 
 
 Gold 
 
 Silver 
 
 1873-1876 
 
 100 
 
 78 
 
 100 
 
 1890-1893 
 
 117 
 
 
 
 We see that gold prices fell a little more than 20 per 
 cent and that silver prices rose a little less than 20 per 
 cent.^ 
 
 If some way had been contrived by which gold and 
 silver could have been kept together (say by world-wide 
 
 ^ From the Japanese Report mentioned in the above note. 
 
 ^ The figures for prices in India are, of course, too meager and 
 local to be of as great value as the corresponding index numbers for 
 Europe and America. Cf. figures cited by J. Barr Robertson's 
 article (1903), Report of Commission on International Exchange, 58th. 
 Congress, 2d Session, H. R. Document 144, Washington, 1903^ 
 pp. 357-378. 
 
 ^ Irving Fisher, "Prices in Silver Countries," Yale Review, May, 
 1897, p. 79. The index numbers for gold countries are based on 
 those of Sauerbeck for England, Soetbeer, Heintz, and Conrad for 
 Germany, and Falkner (Aldrich Report) for the United States. 
 Those for silver countries are from Atkinson for India and the 
 Report of the Japanese Currency Commission above referred to. 
 
 * We may remark in passing that this divergence between the 
 two sets of prices is somewhat more than the divergence between 
 gold and silver themselves.
 
 Sec. 4] STATISTICAL VERIFICATION 245 
 
 bimetallism), prices would not have fallen so much in 
 gold countries, or risen so much (if at all) in silver coun- 
 tries, but would probably have fallen in gold countries 
 slightly — probably about 10 per cent up to 1890-1893 
 and more up to 1896. This is because the stocks of 
 specie in silver countries were less than half those in gold 
 countries ^ (including those with the " limping stand- 
 ard " from left-over silver) ; so that had there been a 
 transfer of a given amount of silver from the silver 
 Orient to the gold Occident, this would have affected 
 Oriental prices about twice as much as Occidental. 
 
 The transition of India from the silver to the gold 
 side has left about nine tenths ^ of the specie (gold and 
 overvalued silver) in the gold column. In other words, 
 the world is now practically on a gold basis. The result 
 has been to make Indian prices move in sympathy with 
 European prices,^ instead of in opposition. 
 
 5. From 1896 to the present, prices have been rising 
 because of the extraordinary rise in gold production and 
 the consequent increase in money media of all kinds. 
 The gold of South Africa combined with the gold from 
 the rich mines of Cripple Creek and other parts of the 
 Rocky Mountain Plateau, and reenforced by gold from 
 the Klondike, caused, and is still causing, a repetition 
 of the phenomenon of half a century ago. 
 
 That there has been a distinct rise in prices is evident 
 from the figures of all index numbers. Those of The 
 Economist, Sauerbeck, Dun, the Labor Bureau Reports, 
 and Bradstreet are given on the following page. 
 
 1 See Muhleman, Monetary Systems of the World, New York 
 (Nicoll), 1897, p. 177. 
 
 2 See Muhleman, ibid. 
 
 ' See J. B. Robertson, "Variations in Indian Price Levels since 
 1861 expressed in Index Numbers," Department oj Commerce and 
 Industry (Government of India).
 
 246 
 
 THE PURCHASING POT\^R OF MONEY [Chap. XI 
 
 English 
 
 American 
 
 Close of Dec. 
 
 Economist 
 
 Sauerbeck 
 
 Dun 
 
 Labor Bureau 
 
 Bradstreet 
 
 1896 . . 
 
 1950 
 
 61 
 
 74 
 
 90 
 
 59 
 
 1897 . . 
 
 1890 
 
 62 
 
 72 
 
 90 
 
 61 
 
 1898 . . 
 
 1918 
 
 64 
 
 77 
 
 93 
 
 66 
 
 1899 . . 
 
 2145 
 
 68 
 
 85 
 
 102 
 
 72 
 
 1900 . . 
 
 2126 
 
 75 
 
 91 
 
 111 
 
 79 
 
 1901 . . 
 
 1948 
 
 70 
 
 91 
 
 109 
 
 76 
 
 1902 . . 
 
 2003 
 
 69 
 
 102 
 
 113 
 
 79 
 
 1903 . . 
 
 2197 
 
 69 
 
 99 
 
 114 
 
 79 
 
 1904 . . 
 
 2136 
 
 70 
 
 97 
 
 113 
 
 79 
 
 1905 . . 
 
 2342 
 
 72 
 
 98 
 
 116 
 
 81 
 
 1906 . . 
 
 2499 
 
 77 
 
 105 
 
 123 
 
 84 
 
 1907 . . 
 
 2310 
 
 80 
 
 
 130 
 
 89 
 
 1908 . . 
 
 2197 
 
 73 
 
 
 123 
 
 80 
 
 1909 . . 
 
 2373 
 
 74 
 
 
 127 
 
 85 
 
 The high points of 1900 and 1907, as compared with 
 the low level of 1896, must be regarded as at least partly 
 due to expansion of credit. The fairest comparison (to 
 eliminate the effects of undue changes in credit) is per- 
 haps that of the years 1896, 1903, and 1909. That the 
 rise of prices has been world wide is evidenced not only 
 by index numbers, which are only available for a limited 
 number of countries, but by general impressions of con- 
 sumers and by special reports and investigations.^ 
 
 The period 1896-1909 for the United States will be 
 studied in more detail in the following chapter. 
 
 §5 
 
 It will be seen that the history of prices has in sub- 
 stance been the history of a race between the increase in 
 media of exchange (M and M') and the increase in 
 trade (T), while (we assume) the velocities of circulation 
 
 ^See Report of the Select Committee on Wages and Prices of Comr- 
 modities. Senate Report 912, 61st Congress, 2d Session, 1910.
 
 Sec. 5] STATISTICAL VERIFICATION 247 
 
 were changing in a much less degree. Knowing Uttle of 
 the variations in the development of trade, we may ten- 
 tatively assume a steady growth, and pay chief atten- 
 tion to the variations of circulating media. Sometimes 
 the circulating media shot ahead of trade and then prices 
 rose. This was undoubtedly the case in the periods 
 numbered 1, 3, and 5 of the five periods just considered. 
 Sometimes, on the other hand, circulating media lagged 
 behind trade and then prices fell. This must have 
 been the case in the periods numbered 2 and 4. 
 
 It is important to emphasize at this point a fact 
 mentioned in a previous chapter ; namely, that the 
 breakdown of bimetallism and the consequent division 
 of the world into a gold section and a silver section 
 have made each section more sensitive than before to 
 fluctuations in the production of the precious metals. 
 The present flood of gold can spread itself only over 
 the gold section of the world, and not over the whole 
 world as was virtually the case with the Calif ornian gold 
 immediately after 1849. At that time gold displaced 
 silver in bimetallic France and sent it to the Orient. 
 In this way the Orient afforded relief for bimetallic 
 countries by draining off silver and making room for 
 gold; and the bimetallic countries thereby afforded 
 relief to gold countries also. 
 
 Since 1873, therefore, the gold reservoir of Europe 
 and America has been separated from the silver reser- 
 voir of the East, with the consequence that the Euro- 
 pean and American reservoir level has been made more 
 sensitive to either a scarcity or a superabundance of 
 gold. The result has been to aggravate both the fall of 
 prices from 1873 to 1896 and the present rise, although 
 the later effect is mitigated by the previous extension 
 of the gold standard.
 
 248 THE PURCHASING POWER OF MONEY [Chap. XI 
 
 §6 
 
 The outlook for the future is apparently toward a 
 continued rise of prices due to a continued increase in 
 the gold supply. To-day almost as much gold is pro- 
 duced every year as was produced in the whole of the 
 16th century. 
 
 The most careful review of present gold-mining con- 
 ditions shows that we may expect a continuance of gold 
 inflation for a generation or more. 'Tor at least 
 thirty years we may count on an output of gold higher 
 than, or at least comparable to, that of the last few 
 years." ^ This gold will come from the United States, 
 Alaska, Mexico, the Transvaal, and other parts of 
 Africa and Australia, and later from Colombia, Bolivia, 
 Chili, the Ural Province, Siberia, and Korea. It must 
 be remembered that it is the stock of gold and not the 
 annual production which influences the price level; 
 and that the stock will probably continue to increase 
 for many years after the production has begun to 
 decline, — as long, in fact, as production keeps above 
 consumption. 
 
 A lake continues to rise long after the freshet which 
 feeds it has reached its maximum. So the stock of 
 gold will continue to increase long after the annual 
 production of gold has stopped increasing. Whether 
 or not prices will continue to rise depends on whether 
 the increase in gold and the circulating media based 
 on gold continues to exceed the growth of trade. It is 
 the relation of gold to trade that chiefly affects prices. 
 Even if the stock of gold should increase for many years, 
 prices may not rise ; for trade may increase still faster. 
 
 1 L. de Launay, The World's Gold, English translation, New York 
 (Putnam), 1908, p. 227.
 
 Sec. 6] STATISTICAL VERIFICATION 249 
 
 If the annual additions of gold to the total stock remain 
 constant and consequently the stock continually in- 
 creases, the ratio between the constant annual addi- 
 tion and the increasing stock will evidently decrease, 
 and the increase in stock will count for less and less in 
 raising prices.^ 
 
 It is difficult to predict the future growth of trade and 
 therefore impossible to say for how long gold expansion 
 will keep ahead of trade expansion. That for many 
 years, however, gold will outrun trade seems probable, 
 for the reason that there is no immediate prospect of 
 a reduction in the percentage growth of the gold stock, 
 nor of an increase in the percentage growth of trade. 
 Not only do mining engineers report untold workable 
 deposits in outlying regions (for instance a full billion 
 of dollars in one region of Colombia alone), but any 
 long look ahead must reckon with possible and probable 
 cheapening of gold extraction. The cyanide process 
 has made low grade ores pay. If we let imagination 
 run a little ahead of our times, we may expect similar 
 improvements in the future whereby still lower grades 
 may be worked or possibly the sea compelled to give 
 up its gold. Like the surface of the continents, the 
 waters of the sea contain many thousand times as much 
 gold as all the gold thus far extracted in the whole 
 history of the world. It is to be hoped that the knowl- 
 edge of how to get this hidden treasure may not be 
 secured. To whatever extent inventors and gold 
 miners might be enriched thereby, scarcely a worse 
 economic calamity can be imagined than the resulting 
 
 ' Cf. Jevons, Investigations in Currency and Finance, London 
 (Macmillan), 1884, pp. 64, 65, 66; also Harrison H. Brace, Gold 
 Production and Future Prices, New York (Bankers' Publishing Co.), 
 1910, p. 113.
 
 250 THE PURCHASING POWER OF MONEY [Chap. Xl 
 
 depreciation. It may be, however, that only by such a 
 calamity can the nations of the world be aroused to the 
 necessity of getting rid of metallic standards altogether. 
 
 §7 
 
 We have briefly summarized the history of price 
 movements since the discovery of America and shown 
 their relation to the stock of the precious metals. But, 
 as we have emphasized in previous chapters, the pre- 
 cious metals do not include all forms of circulating 
 media. Paper money and bank deposits have come 
 during the nineteenth century to occupy very important 
 places in currency systems. 
 
 We shall not attempt any complete review of the 
 effects of paper money on prices. The best that can 
 be done is to mention briefly the most striking cases of 
 paper money inflation and contraction. These are all 
 cases of irredeemable paper money. When paper 
 money is redeemable, its possible increase is restricted 
 by that fact and, what is more important, the effects of 
 the increase are dissipated over so large an area as to 
 have little perceptible effect on prices. This dissipa- 
 tion takes place through the export of specie from the 
 country in which the paper issues occur. Though 
 the paper cannot be itself exported, it can displace 
 gold or silver, which amounts to the same thing so far 
 as spreading out the effect on prices is concerned. 
 
 But when the paper is irredeemable, after specie has 
 been expelled from circulation (whether by export, 
 melting, or hoarding in anticipation of disaster) there 
 is no such spreading-out effect. The effects on prices 
 are then entirely local and therefore greatly magnified.^ 
 
 1 See Ricardo, Essay on the "High Price of Bullion," Works, 
 2d ed., London (Murray), 1852, p. 278.
 
 Sec. 7] STATISTICAL VERIFICATION 251 
 
 The consequence is that the most striking examples 
 of price inflation are cases of irredeemable paper money. 
 The rise of prices is often still further aggravated by 
 the gradual substitution of other and better money 
 or resort to barter, which further restricts the sphere 
 in which the paper is used and within that sphere makes 
 it the more redundant. Where the paper money is 
 looked upon with disfavor, for whatever reason — 
 whether because its promised redemption has been 
 indefinitely postponed, or simply because of the bare 
 fact that it is depreciating, or because of any other 
 consideration — its sphere of use is restricted.^ Credi- 
 tors and tradesmen avoid taking it if they can, by 
 "contracting out" in advance; by barter; by fixing 
 a double set of prices, one in paper and the other in 
 some other money; and by outright refusal. In the 
 end it may happen that the paper ceases to be used at 
 all. In that case its value depreciates indefinitely and 
 therefore prices (so far as still expressed in terms of 
 paper) rise indefinitely. 
 
 Whatever the situation, the equation of exchange 
 continues to hold true though its significance becomes 
 of less importance, because T, instead of comprising 
 practically all trade, comes to mean only that disappear- 
 ing portion of trade still transacted by means of paper 
 money. 
 
 The value of irredeemable paper money is, therefore, 
 extremely precarious. If once it starts depreciating — 
 from whatever cause — it is likely to depreciate further, 
 not simply because of the ever present temptation to 
 further issue, but also because of a growing public 
 
 1 See Francis A. Walker, Money, New York (Holt), 1878, p. 199. 
 Cf. Joseph French Johnson, Money and Currency, Boston (Ginn), 
 1906, p. 269.
 
 252 THE PURCHASING POWER OF MONEY [Chap. XI 
 
 sentiment against it which sooner or later restricts its 
 use.^ In many cases the irredeemable paper money- 
 continues to be used with sufficient acceptability to give 
 it a virtual monopoly as a medium of exchange. 
 
 Although theoretically irredeemable paper money 
 may be the cheapest and most easily regulated form 
 of currency, and although, in some cases, it has remained 
 a stable currency for a considerable period, the lesson 
 of history is emphatically that irredeemable paper 
 money results in monetary manipulation, business dis- 
 trust, a speculative condition of trade, and all the evils 
 which flow from these conditions. 
 
 §8 
 
 One of the early paper-money schemes was that of 
 John Law, who established a bank of issue in France 
 in 1716. Two years later (December 4, 1718), the bank 
 was taken over by the Crown. Soon shrewd traders 
 were acquiring specie for notes and exporting the 
 specie secretly, although exportation of specie was illegal. 
 May 27, 1720, only four years after its establishment, 
 the bank stopped payment of specie. By November of 
 the very same year the paper had fallen to one tenth of 
 its par value, and after this it became utterly worthless. 
 
 The case of the assignats of the French Revolution is 
 classic.^ It was in December, 1789, that the first issue, 
 four hundred million francs, was ordered, based osten- 
 sibly on the landed property of the nation. The notes 
 were issued in April, 1790, and bore 3 per cent interest. 
 According to the original plan, all of the assignats received 
 
 1 Cf . the mention of this influence on depreciation in the Bxxllion 
 Report, III. 
 
 2 For the following facts, see Andrew D. White, Paper Money 
 Inflation in France, Economic Tracts, No. VII, No. 3 of Series, 1882.
 
 Sec. 8] STATISTICAL VERIFICATION 253 
 
 in payment for land were to be burned. But original 
 plans seem never to be carried out with respect to paper 
 money. Instead, a hundred millions were reissued in 
 the form of small notes. Prices began to rise. In 
 June of the year 1791, six hundred millions more were 
 issued. Depreciation to the extent of 8 to 10 per cent 
 immediately followed. Specie was rapidly disappear- 
 ing. Another three hundred millions of francs were 
 ordered in December, 1791. By February, the assig- 
 nats were over 30 per cent below par. In April, 1792, 
 came a decree for the issue of three hundred millions 
 more, and in July for the same amount additional. 
 Most prices were very high, but wages seem to have 
 still remained at the level of 1788. By December 14 
 of 1792, thirty-four hundred million francs had been 
 issued in assignats, of which six hundred millions had 
 been burned, leaving twenty-eight hundred millions in 
 circulation. Laws were enacted to fix maximum prices, 
 but were evaded. By 1796, forty-five billion francs had 
 been issued, of which thirty-six billions were in circula- 
 tion. In February of that year the gold louis, of 25 
 francs, was worth 7200 francs in assignats ; and the 
 assignats were worth ^Is of P^-^- A. new kind of paper 
 money, the mandats, was next issued, but soon fell to 
 5 per cent of its nominal value. In the end the twenty- 
 five hundred million mandats and the thirty-six billion 
 assignats were repudiated and became entirely worth- 
 less. 
 
 §9 
 
 England's experience with irredeemable paper money 
 was more temperate. Under the stress of the Napole- 
 onic wars, the Bank of England suspended cash pay- 
 ments in 1797. This nullified the force which auto- 
 matically limited overissue. The bank resumed cash
 
 254 
 
 THE PURCHASING POWER OF MONEY [Chap. XI 
 
 payments in 1821. During much of the intervening 
 period of paper money, prices in paper were very high. 
 The following table of Jevons shows the relative prices 
 in notes and specie from 1801 to 1820 : ^ — 
 
 Ybae 
 
 Gold Standard 
 
 Paper Standard 
 
 1801 
 
 140 
 
 153 
 
 1802 
 
 110 
 
 119 
 
 1803 
 
 125 
 
 128 
 
 1804 
 
 119 
 
 122 
 
 1805 
 
 132 
 
 136 
 
 1806 
 
 130 
 
 133 
 
 1807 
 
 129 
 
 132 
 
 1808 
 
 145 
 
 149 
 
 1809 
 
 157 
 
 161 
 
 1810 
 
 142 
 
 164 
 
 1811 
 
 136 
 
 147 
 
 1812 
 
 121 
 
 148 
 
 1813 
 
 115 
 
 149 
 
 1814 
 
 114 
 
 153 
 
 1815 
 
 109 
 
 132 
 
 1816 
 
 91 
 
 109 
 
 1817 
 
 117] 
 
 120 
 
 1818 
 
 132 
 
 135 
 
 1819 
 
 112 
 
 117 
 
 1820 
 
 103 
 
 106 
 
 The causes of the rise of prices were discussed in 
 the famous BuUion Report. The general conclusion 
 reached was that a "rise of the market price of gold 
 above its mint price will take place," if the local cur- 
 rency of any particular country, ''being no longer con- 
 vertible into gold, should at any time be issued to excess. 
 That excess cannot be exported to other countries, and, 
 not being convertible into specie, it is not necessarily 
 returned upon those who issued it; it remains in the 
 channel of circulation, and is gradually absorbed by 
 
 1 Investigations in Currency and Finance, London (Macmillan), 
 1884, p. 144.
 
 Sec. 10] STATISTICAL VERIFICATION 255 
 
 increasing the prices of all commodities. An increase 
 in the quantity of the local currency of a particular 
 country will raise prices in that country exactly in the 
 same manner as an increase in the general supply of pre- 
 cious metals raises prices all over the world. By means 
 of the increase of quantity, the value of a given portion 
 of that circulating medium, in exchange for other com- 
 modities, is lowered. In other words, the money prices 
 of all other commodities are raised — that of bulhon 
 with the rest." This is an excellent statement of the 
 philosophy of irredeemable paper money when that 
 money is sufficiently within bounds to remain in general 
 use. No mention is made of partial or complete aban- 
 donment of use because of worthlessness. The reason 
 is doubtless that in England the paper money never 
 reached this pass, as it undoubtedly did in many in- 
 stances in France, Austria, America, and elsewhere. 
 
 §10 
 
 Austrian experience with paper money is instructive.* 
 Like so many of the European banks, that of Austria 
 was used by the government as an instrumentality for 
 obtaining loans. This was done by allowing the bank 
 to issue large sums in notes. The wars with Napoleon 
 demanded supplies, and during these wars the issue was 
 largely increased. In 1796 the note issue was 47,000,000 
 gulden; in 1800 it was 200,000,000; in 1806, it was 
 449,000,000. The notes were much below par. In 
 1810 the bank notes fell successively to ^, | and about 
 ^of par. In 1811 a proclamation openly valued them 
 at one fifth of their nominal value and decreed their 
 exchange at this rate for redemption notes, called the 
 
 * See W. G. Sumner, History of American Currency, New York 
 (Holt), 1874, Chapter III.
 
 256 THE PURCHASING POWER OF MONEY [Chap. XI 
 
 Viennese legal tender, which became the Austrian 
 legal-tender currency. But even these new issues soon 
 fell to 2 16 of their face value (May, 1812) and 3^^ of their 
 face value (June, 1812), while the bank notes were at 
 1G90 to 100 in silver. New issues were added under a 
 difTerent name until, in 1816, the amount of paper 
 money was over 638,000,000, with prices, of course, 
 tremendously inflated. In 1816 was founded the Aus- 
 trian national bank, which was intended to draw in the 
 paper money. From time to time thereafter the amount 
 of paper circulation was reduced, but not without occa- 
 sional relapses. At the present time Austria has no 
 paper money which is not at par. 
 
 §11 
 Many of the American colonies had experience with 
 paper money. In fact, one of the grievances against 
 England was the parliamentary prohibition of paper 
 money issues ! In practically all cases ^ there was over- 
 issue and depreciation. This was true, for example, in 
 Massachusetts, where paper money was issued to pay 
 the expenses of the expeditions against Canada,^ and 
 in Rhode Island,^ which suffered more, perhaps, from 
 paper money than any of the others. Following are 
 figures for Rhode Island taken from the account book 
 of Thomas Hazard (the entries and memoranda ex- 
 tending from 1750 to 1785), which show the height and 
 variabihty of prices.^ 
 
 ^ Pennsylvania seems to have been an exception. 
 
 2 W. G. Sumner, History of American Currency, Chapter I. 
 
 » Ibid. 
 
 * Rowland Hazard, Sundry prices taken from Ye Account Book 
 of Thomas Hazard, son of Robt. Wakefield, R.I. (Times Print), 
 1892.
 
 Sec. 11] 
 
 STATISTICAL VERIFICATION 
 
 257 
 
 1755. Hay £20 per Load 
 Corn per Bushel Butter per Pound 
 
 1751 
 1758 
 1762 
 
 25 s. 
 
 50 s. 
 
 100 s. 
 
 Wool per Pound 
 
 1751 
 1760 
 
 1752 
 1756 
 1759 
 1768 
 
 8 s. 
 
 12 s. 
 
 28 s. 
 
 32 s. 
 
 1750 
 1753 
 
 1774 
 
 7 s. 
 16 s. 
 
 Potatoes per Bushel 
 
 10 s. 
 20 s. 
 35 s. 
 
 We had also during the Revolution a national expe- 
 rience with Continental paper money which gave rise 
 to the derogatory phrase, still current, "not worth a 
 continental." Depreciation began almost from the 
 moment of issue (1775), and finally the money was 
 recognized by Congress itself to have reached -^q of the 
 nominal value. ^ All prices, of course, were tremen- 
 dously high. Even the new tenor paper given for the 
 old emissions at the rate of a dollar for forty ^ declined 
 rapidly in value. A bushel of wheat was worth, at 
 one time, seventy-five dollars, coffee four dollars a 
 pound, and sugar three dollars a pound.^ It is inter- 
 esting to observe that, in this case, the depreciation 
 seems to have been accentuated far beyond what mere 
 overissue tended to produce, by a distrust of the money 
 and a refusal to receive it in trade. Several classes were 
 disinclined to receive it to begin with, and as confidence 
 waned, the number who were unwilling to receive it 
 increased. Barter frequently took the place of trade 
 with money.^ 
 
 The depreciation was doubtless much greater because 
 
 ^ See Albert S. BoUes, Financial History of the United States, 
 Vol. I, from 1774 to 1789, New York (Appleton), 1879, p. 135. 
 » Ibid., pp. 137 and 138. » Ibid., p. 141. * Ibid., Chapter IX 
 
 8
 
 258 THE PURCHASING POWER OF MONEY [Chap. XI 
 
 the paper money of various colonies helped to overflow 
 the circulation, competing with the congressional money 
 and limiting its sphere of circulation. 
 
 §12 
 
 The effects were so disastrous that, in the Constitu- 
 tion of the United States, a provision was incorporated 
 prohibiting any state from issuing "bills of credit." 
 But, during the Civil War, the temptation again came 
 to resort to this easy way of securing means of pay- 
 ment ; and the federal government itself issued United 
 States notes or "greenbacks." The banks had already 
 suspended specie payments so that gold was at a slight 
 premium in bank paper. ^ 
 
 These greenbacks were issued from time to time dur- 
 ing the war with resulting depreciation as their quantity 
 increased, — a depreciation greater or less also accord- 
 ing as failure or success of the Union armies affected 
 confidence in the paper money. The amounts issued 
 were: $150,000,000 by the act of February 25, 1862; 
 $150,000,000 by act of July 11, 1862; $150,000,000 
 authorized by acts of January 17 and March 3, 1863. 
 Besides the greenbacks (issued in denominations in no 
 case under a dollar), there was some issue of fractional 
 currency and of interest-bearing notes running for a 
 brief period, both of which were also made legal tender.^ 
 The rise in prices is shown by the following table :^ — 
 
 1 Davis Rich Dewey, Financial History of the United States, New 
 York (Longmans), 3d ed., § 29. 
 
 - For a brief account of the greenbacks, see Dewey, Financial 
 History of the United States, Chapter XII. The most complete 
 account is found in Wesley Clair Mitchell, A History of the Green- 
 backs, Chicago (University of Chicago Press), 1903. 
 
 * Aldrich Senate Report on Wholesale Prices and Wages, 52d 
 Congress, 2d Session, table 24, p. 93.
 
 Sec. 12] 
 
 STATISTICAL VERIFICATION 
 
 259 
 
 Index Numbers of Prices during Greenback Depreciation 
 
 
 Price op 
 
 Index Nos. op Northern Prices (1860 = 100) 
 
 
 
 
 
 Yeab 
 
 Gold' in 
 
 Falkner^ 
 
 
 
 
 Greenbacks 
 
 In Gold 3 
 
 In Paper < 
 
 Dun 6 
 in Paper 
 
 Mitchell' 
 Median 
 in Paper 
 
 1861 . . 
 
 100 
 
 94 
 
 94 
 
 89 
 
 96 
 
 1863 . . 
 
 144 
 
 91 
 
 132 
 
 150 
 
 134 
 
 1865 . . 
 
 163 
 
 107 
 
 232 
 
 169 
 
 158 
 
 1867 . . 
 
 138 
 
 123 
 
 166 
 
 164 
 
 150 
 
 1869 . . 
 
 136 
 
 112 
 
 152 
 
 143 
 
 158 
 
 1871 . . 
 
 112 
 
 123 
 
 136 
 
 132 
 
 130 
 
 1873 . . 
 
 114 
 
 115 
 
 129 
 
 124 
 
 130 
 
 1875 . . 
 
 115 
 
 115 
 
 129 
 
 117 
 
 121 
 
 1877 . . 
 
 105 
 
 107 
 
 114 
 
 95 
 
 100 
 
 1879 . . 
 
 100 
 
 95 
 
 95 
 
 85 
 
 85 
 
 It has been asserted that the rise of prices during the 
 greenback depreciation was not due to the quantity 
 of the greenbacks, but to the pubHc distrust of green- 
 backs. The truth is probably that it was due to both. 
 Distrust was evident and restricted the sphere of 
 greenbacks very materially. California and, in fact, 
 all the region west of the Rocky Mountains, made 
 strenuous efforts to prevent the circulation of green- 
 backs, — efforts which were largely successful. And 
 naturally the greenbacks could not circulate in the 
 South. These restrictions alone would confine their 
 circulation to a population of about 20 millions out of a 
 total population in 1860 of 31 millions, that is, to less 
 
 * Average of quotations in January, April, July, October, from 
 Wesley Clair Mitchell, Gold Prices and Wages under the Greenback 
 Standard, Berkeley (University Press), March, 1908. 
 
 2 Weighted arithmetical average of articles comprising 68.60 per 
 <3ent of total expenditure. ^ Aldrich Report, p. 100. * Ibid., p. 93. 
 
 * From Wesley Clair Mitchell, ibid., p. 59.
 
 260 
 
 THE PURCHASING POWER OF MONEY [Chap. XI 
 
 than two thirds of the entire population. Therefore 
 the volume of trade for which the greenbacks were used 
 must have been greatly reduced. The total circulating 
 currency during the war is not known with certainty ; 
 but the best estimates of the various forms of circu- 
 lating media are those compiled by Mitchell.' Though 
 he modestly warns the reader against any attempt to 
 cast up sums, his results may be considered as at least 
 of some value. The totals, omitting money in the 
 Treasury and interest-bearing forms, which were known 
 to have only a very sluggish circulation, we find to be 
 as follows : — 
 
 
 
 
 Prices op all Articles aver- 
 
 ■1 
 
 J. 
 
 Roughly estimated Circula- 
 
 aged 3 according to Impor- 
 
 XtiiAJi 
 
 tion IN Loyal States ^ 
 
 tance, comprising 68.60 % op 
 
 
 
 
 Total Expenditure 
 
 1860 
 
 
 433 
 
 100 
 
 1861 
 
 
 
 
 490 
 
 94 
 
 1862 
 
 
 
 
 360 
 
 104 
 
 1863 
 
 
 
 
 677 
 
 132 
 
 1864 
 
 
 
 
 708 
 
 172 
 
 1865 
 
 
 
 
 774 
 
 232 
 
 1866 
 
 
 
 
 759 
 
 188 
 
 Considering the unreliability of the figures for cur- 
 rency ^ and the lack of data as to the other magnitudes in 
 the equation of exchange, there is here a rough corre- 
 spondence between the volume of the currency and the 
 level of prices. 
 
 1 Wesley C. Mitchell, History of the Greenbacks, Cliicago (Uni- 
 versity of Chicago Press), 1903, p. 179. 
 
 2 Mitchell, ibid., p. 179. 
 
 ^ Aldrich, Report on Wholesale Prices. 
 
 * The great reduction in 1862, for instance, is due to the assump- 
 tion that practically all gold was withdrawn from circulation ex- 
 cept in California. A more reasonable assumption would seem to 
 be that it was only partially withdrawn. Much of it may have
 
 Sec. 13] STATISTICAL VERIFICATION 261 
 
 §13 
 
 It is necessary to remember that the confidence with 
 which we have to deal is not primarily confidence in 
 redemption, but confidence in the paper money, — its 
 purchasing power. This confidence may rest on ex- 
 pectation of redemption or on other conditions, particu- 
 larly the expectation of further inflation or contraction. 
 The explanation of the value of the greenbacks appears 
 to me to be in brief as follows : — 
 
 The Redemption Act of 1875 announced the intention 
 of our government to redeem the greenbacks on and af- 
 ter January 1, 1879. Each greenback being thus kept 
 equal to the discounted value of a full dollar due Jan- 
 uary 1, 1879, they rose steadily toward par as that date 
 approached. Some of them were withdrawn from cir- 
 culation to be held for the rise. The value of a green- 
 back dollar could not be much less than this discounted 
 value of the gold dollar promised in 1879; otherwise 
 speculators might withdraw the greenbacks wholly. 
 This would pay them well provided they were certain 
 that the government's promise would be fulfilled. On 
 the other hand, the value of greenbacks could not, with 
 paper money redundant for trade, be greater than said 
 discounted value, because in that case speculators 
 would return it all to the circulation, the prospective 
 rise being 'Hoo small to repay the interest" lost in 
 carrying it. Thus speculation acted as a regulator of 
 the quantity of money. 
 
 been hoarded in coin form preparatory to export or melting. If 
 so, it probably circulated to some extent. "Hoarding" means a 
 longer retention in the same hands, but not necessarily failure to 
 be exchanged at all. Gold was a valuable form of bank "reserve" 
 at this time. While not paid out in meeting demand obligations, 
 it was a very quick asset and could be quickly realized upon.
 
 262 THE PURCHASING POWER OF MONET [Chap. XI 
 
 Thus the rise in value of the greenbacks, like other com- 
 ing events, cast its shadow before. It was ''discounted 
 in advance." It is quite true that confidence in redemp- 
 tion was here the ultimate cause of the appreciation of 
 the paper money; but the readjustments caused by 
 this confidence include a reduction in the quantity of 
 the money in circulation. Without such readjustment 
 the appreciation would be impossible, as the equation of 
 exchange plainly shows. We should note, however, that 
 if the price of the currency were already sufficiently high, 
 the prospect of future redemption would not further 
 raise it. It might happen that the value of the currency 
 was already above the discounted par value promised 
 at the time set for redemption. In such a case there 
 need not be any speculation or any immediate rise in 
 value until the date of redemption drew near enough 
 to make itself felt. On the other hand, when, during 
 the war, the government announced a further issue of 
 a paper currency already depreciated, the public antici- 
 pated its further depreciation by releasing such hoards 
 and stocks as were available ; in other words, by accel- 
 erating the circulation of money. Each man hastened 
 to spend his money before an expected rise of price, 
 and his very action hastened that rise. 
 
 Announcements of federal defeats in the war acted 
 in the same way, being signals that further issues of 
 greenbacks might be required; while announcement 
 of victories acted in the opposite way, being like signals 
 of probable redemption. 
 
 When appreciation is anticipated, there is a tendency 
 among owners of money to hoard or hold it back, and, 
 among owners of goods, to sell them speedily ; the result 
 being to decrease prices by reducing the velocity of circu- 
 lation and increasing the volume of trade. When, on the
 
 Sec. 141 STATISTICAL VERIFICATION 263 
 
 contrary, depreciation is anticipated, there is a tendency 
 among owners of money to spend it speedily and among 
 owners of goods to hold them for a rise, the result being 
 to raise prices by increasing the velocity of circulation 
 and decreasing the volume of trade. In other words, 
 the expectation of a future rise or fall of prices causes 
 an immediate rise or fall of prices. 
 
 These anticipations respond so promptly to every 
 sign or rumor that superficial observers have regarded 
 the rise and fall of the greenbacks as related directly 
 and solely to expected redemption and as having no 
 relation to quantity. These observers overlook the real 
 mechanism at work ; they fail to see that these effects, 
 though quick, are slight and limited. They are the 
 simple adjustments of transition periods described in 
 Chapter IV. It would be a grave mistake to reason, 
 because the losses at Chickamauga caused greenbacks 
 to fall 4 per cent in a single day, that their value had 
 no relation to their volume. This fall indicated a slight 
 acceleration in the velocity of circulation, and a slight 
 retardation in the volume of trade ; but, under ordinary 
 circumstances, it is only shghtly that the velocity of 
 circulation can thus be accelerated; while to make 
 trade stagnate long or completely would require a 
 cataclysm. 
 
 § 14 
 
 In the South it is ''impossible to state even approx- 
 imately how many Confederate treasury notes were 
 outstanding at any time." ^ Professor Schwab has, 
 however, given the value of gold in Confederate cur- 
 rency and index numbers of prices in the South. He 
 concludes : ^ — 
 
 ' J. C. Schwab, Confederate States of America, 1861-1865, New 
 York (Scribner), 1901, p. 165. * Ibid., pp. 167-169.
 
 264 THE PURCHASING POWER OF MONEY [Chap. XI 
 
 "This movement of the gold premium corresponds 
 roughly with the amount of government notes out- 
 standing in each period. The relatively rapid increase 
 in the issue of notes after August, 1862, during the last 
 months of 1863, and again during the last months of 
 the war, is reflected in the rapid increase of the gold 
 premium at those three times. When the amount of 
 outstanding notes remained stationary at the beginning 
 of 1863, there was a somewhat slower advance of the 
 gold premium during those months ; while the shrink- 
 ing of the outstanding notes during the first half of 1864 
 is distinctly reflected in a temporary decline of the 
 premium. 
 
 "In the North during the Civil War the course of gold 
 premium only remotely suggested the amount of notes 
 outstanding at any time. The premium rose most 
 rapidly, or, in other words, the notes sank in value most 
 rapidly, at the beginning of 1863, recovering again 
 during the second quarter of that year, declining after 
 August, 1863, to their lowest point in the summer of 
 1864, and rising again during the last months of the 
 war.^ The value of the 'greenback' was much more 
 a barometer of popular feeling as to the eventual out- 
 come of the war than a gauge of their amount in cir- 
 culation, for the latter did not materially increase after 
 July, 1863, and certainly not after July, 1864. In fact, 
 the gold value of the federal ' greenback ' ran closely 
 parallel with the gold value of the federal bonds during 
 the war. This is also true of the confederate bonds and 
 treasury notes. These two sets of parallel fluctuations 
 were evidently caused by the changing credit of the two 
 governments concerned. 
 
 1 J. C. Schwab, Confederate States of America, 1861-1865, Ne^V 
 York (Scribner), 1901, table on p. 167.
 
 Sec. 15] STATISTICAL VERIFICATION 265 
 
 "A general index number for either section, based 
 both on a simple and a weighted average, can be con- 
 structed. The hues plotted to indicate these two sets 
 of figures do not run parallel, but converge and diverge 
 during different periods of the war, converging at those 
 times when events in the military, the political, or the 
 financial field discouraged the South, and correspond- 
 ingly encouraged the North in the general belief that 
 the war was approaching an end ; diverging at those 
 times when federal reverses, or similar events in other 
 than the military field, raised the hopes of the South, 
 and led to behef on both sides that the war would be 
 protracted." ^ 
 
 We thus see that redundancy of issue produces a 
 rise of prices, not only because of increased quantity, but 
 because of decreased confidence,^ which affects the 
 sphere of use of the money and therefore the volume 
 of trade performed by the money, and accelerates its 
 velocity. 
 
 § 15 
 
 We have given historical instances of the effects on 
 prices of changes in the precious metals and in paper 
 money. 
 
 There remain to be considered historical instances 
 of the effects on prices of changes in deposit currency. 
 The price movements due to changes in deposit currency 
 usually include those culminations called crises and de- 
 pressions. 
 
 The economic history of the last century has been 
 
 1 J. C. Schwab, ibid., p. 179. 
 
 2 Cf. Wesley Clair Mitchell, History of the Greenbacks, pp. 208 and 
 210. Also Francis A. Walker, Political Economy, 3d ed., New York 
 (Holt), 1888, p. 164.
 
 266 THE PURCHASING POWER OP MONEY [Chap. XI 
 
 characterized by a succession of crises. Juglar in his de- 
 scription of the conditions preceding crises mentions the 
 signs of great prosperity, the enterprise and the specula- 
 tion of all kinds, the rising prices, the demand for labor, 
 the rising wages, the ambition to become at once rich, 
 the increasing luxury, and the excessive expenditure.^ 
 
 A crisis is, as Juglar in fact defines it, an arrest of 
 the rise of prices. At higher prices than those already 
 reached purchasers cannot be found. Those who had 
 purchased, hoping to sell again for profit, cannot dis- 
 pose of their goods.- 
 
 Our previous analysis has shown us that, before a 
 crisis, while prices are ascending, there is a great in- 
 crease in bank deposits ; and that these, being a cir- 
 culating medium, accelerate the rise. 
 fc It has been pointed out that, with trade international, 
 the rise of prices, resulting from expansion of deposits, 
 is also international. Even if, in some of the countries, 
 deposits should not expand, a rise of the price level 
 would nevertheless occur. The expansion of deposits 
 even in one country of considerable size would, by 
 tending to raise prices there, cause the export of gold. 
 Thus, in other countries the supply of money would 
 increase and prices rise also. This would tend to stim- 
 ulate expansion of deposits in these other countries and 
 bring about a further rise. Even, therefore, if credit 
 
 1 Clement Juglar, Des Crises Commerciales et de leur Retour 
 P6riodique en France, en Angleterre et aux Etats-Unis, 2 ed., Paris 
 (Guillaumin), 1889, pp. 4 and 5. See also translation of same deal- 
 ing with United States, by De Courcy W. Thom, A Brief History 
 of Panics in the United States, New York (Putnam), 1893, pp. 7-10. 
 Juglar is mistaken in adding that interest rates fall during rising 
 prices. The facts show that they rise, though not sufficiently to 
 check tke excessive lending. See Irving Fisher, The Rate of Interestf 
 Chapter XIV. 
 
 ' Juglar, ibid., p. 14.
 
 Sec. 16] 
 
 STATISTICAL VERIFICATION 
 
 267 
 
 expansion did not begin at the same time in all the prin- 
 cipal commercial countries, the beginning of it in one 
 country would be quickly communicated to others. 
 For the same reason the arrest of rising prices and the 
 beginning of falling prices would occur at about the 
 same time in most of the principal countries. As a 
 matter of fact this is what we find to be the case. Juglar 
 has made out a table showing the crises in England, 
 France, and the United States from 1800 to 1882.^ 
 With the addition of the dates of later crises the table 
 is as follows : — 
 
 France 
 
 England 
 
 United States 
 
 1804 
 
 1803 
 
 
 1810 
 
 1810 
 
 
 1813-1814 
 
 1815 
 
 1814 
 
 1818 
 
 1818 
 
 1818 
 
 1825 
 
 1825 
 
 1826 
 
 1830 
 
 1830 
 
 
 1836-1839 
 
 1836-1839 
 
 1837-1839 
 
 1847 
 
 1847 
 
 1848 
 
 1857 
 
 1857 
 
 1857 
 
 1864 
 
 1864-1866 
 
 1864 
 
 1873 
 
 1873 
 
 1873 
 
 1882 
 
 1882 
 
 1884 
 
 1889-1890 
 
 1890-1891 
 
 1890-1891 
 1893 
 
 1907 
 
 1907 
 
 1907 
 
 § 16 
 
 A study of Juglar's or Thom's tables will show that, 
 in general, bank note circulation and bank deposit cir- 
 culation increase before a crisis and reach a maximum 
 at the time of the crisis. Index numbers of prices show 
 the same general trend. 
 
 ^ Juglar, ibid., charts at end ; Thom's translation, p. 19, brings the 
 table to 1891.
 
 268 THE PURCHASING POWER OF MONEY [Chap. XI 
 
 Thus,^ for the United States, the crisis of 1837-1839 
 shows that circulation of state banks increased each year 
 from 61 milHons in 1830 to 149 in 1837 and fell to 116 
 in the next year ; that individual deposits rose each year 
 from 55 miUions in 1830 to 127 in 1837 and fell to 84 the 
 next year ; that from 1844 to 1848, the date of the next 
 crisis, circulation rose from 75 millions to 128, falling 
 back to 114 the next year, and that the deposits rose 
 from 84 millions to 103, falling back to 91 ; that from 
 1851 to 1857, the date of the next crisis, circulation rose 
 from 155 millions to 214, falling the next year to 155, and 
 that the deposits rose from 128 millions to 230, falling 
 the next year to 185. These facts — that prices and de- 
 posits rose, culminated, and fell together in reference to 
 the crises of 1837, 1846, and 1857 — are confirmed by 
 figures for per capita circulation and deposits given by 
 Sumner.^ These show the characteristic sharp check to 
 expansion in the crisis years, mild in the mild crisis of 
 1846 and pronounced in the more pronounced crises of 
 1837 and 1857. Corresponding phenomena occurred 
 at the next crisis, 1863-1864. After this time, the chief 
 statistics are for national banks, and these show simi- 
 lar results. Thus, from 1868 to 1873, national bank 
 circulation rose from 295 millions to 341 and then fell, 
 while in the same period deposits rose from 532 mil- 
 Uons to 656 and then fell. Similar, though less marked, 
 movements occurred in the milder crises of 1884 and 
 1890, which is the last included in Thom's tables. The 
 crisis of 1893 was exceptional and largely confined to 
 the United States, being chiefly due to the fear as to the 
 
 ' See Thorn, tables following p. 18. 
 
 2 History of Banking in the United States, Vol. I of History of Bank- 
 ing in all Nations, New York (Journal of Commerce), 1896, p. 456. 
 The figures are taken from 37th Congress, 3d Session, 5 Ex., 210.
 
 Sec. 16] STATISTICAL VEKIFICATION 269 
 
 stability of the gold standard without much reference 
 to currency and deposit expansion.^ Whereas in the 
 typical speculative cycle the ratio of deposits to re- 
 serves gradually increases until it reaches a maximum 
 just before the crisis, as it did in 1873, 1884, and 1907, 
 this did not happen in 1893. It is true that the deposits 
 of national banks were larger in 1892 than in 1890 or 
 1891, but they were no larger relatively to reserves, 
 though possibly this fact is to be accounted for by an in- 
 crease of reserves following the slight crisis of 1890-1891. 
 It is true, also, that the ratio of the deposits of national 
 banks to reserves was high in 1893, but this was due, not 
 to an expansion of deposits, for deposits decreased during 
 that year, but to the runs on the banks and consequent 
 depletion of their reserves.^ The crisis of 1907, on the 
 other hand, was, like that of 1857, typically a crisis of 
 currency expansion. The facts in reference to this crisis 
 will be discussed more fully in the following chapter. 
 
 In France the same tendency of circulation and de- 
 posits to reach a maximum at or about a crisis and recede 
 immediately afterward is illustrated fairly well,^ es- 
 pecially for deposits. 
 
 1 Lauck, Causes of the Panic of 1893, Boston (Houghton, Mifflin), 
 1907, p. 118. O. M. W. Sprague, in "History of Crises under the 
 National Banking System," National Monetary Commission Re-port, 
 Senate Document 538 (61st Congress, 2d Session), points out that 
 in the runs on banks there was no special demand for gold, and is 
 inclined to think that the influence of the currency expansion has 
 been exaggerated. 
 
 ^ For a statistical comparison of this with typical crises, see 
 article by Harry G. Brown, "Typical Commercial Crises versus a 
 Money Panic," Yale Review, August, 1910. 
 
 ' Juglar, op. cit., tables following p. 339 and charts at end. 
 Juglar calls the crisis of 1873 in France political rather than com- 
 mercial. The statistics of circulation and deposits and their velocity 
 of circulation (as shown by Pierre des Essars), however, reach a 
 maximum in 1873 and recede immediately after.
 
 270 THE PURCHASING POWER OF MONEY [Chap. XI 
 
 For the Bank of England we find the same general 
 correspondence between crises, circulation, and private 
 deposits.^ 
 
 §17 
 
 Not only do money and deposit currency {M and M') 
 'rise regularly to a maximum at the time of a crisis, but 
 their velocity of circulation, so far as statistics indicate, 
 goes through the same cycle. Pierre des Essars has 
 demonstrated this beyond peradventure, so far as 
 velocity of circulation of deposits is concerned.^ 
 
 For the United States we have scarcely any statistics 
 of velocity of circulation of deposits, but those for two 
 New Haven banks and for an Indianapolis bank, which 
 I have secured for the last few years, show a maximum 
 in the crisis year 1907. 
 
 After a crisis, a decrease occurs in M, M' , V, and F'. 
 Bank reserves are increased, and this causes a decrease 
 in M. 
 
 Since, then, currency and velocity both increase 
 before a crisis, reach a maximum at the crisis, and fall 
 after the crisis, it is small wonder that prices follow the 
 same course. That they do is the real meaning of a 
 crisis. In fact, as we have seen, Juglar defines a crisis 
 as an arrest of a rise of prices. The index numbers of 
 prices show the rise, maximum, and slump for almost 
 every crisis year for which price statistics exist.^ 
 
 * Juglar, op. cit., tables following p. 291. 
 
 2 "La vitesse de la circulation," Journal de la Societe de Statistique 
 de Paris, April, 1895, p. 148. From 1810 to 1892 in France, taking 
 the thirteen crisis years and the twelve years of "liquidation," Des 
 Essars finds that, unthout exception, the velocity of circulation of 
 deposits at the bank of France is a maximum in the crisis years 
 and a minimum in the years of liquidation. 
 
 ^ The detailed figures will be seen in the Appendix to the next 
 chapter (Chapter XII).
 
 Sec. 17] 
 
 STATISTICAL VERIFICATION 
 
 271 
 
 The following figures are designed to present a picture 
 of the crisis of 1907 in the United States as illustrating 
 the culmination of a typical credit cycle: — 
 
 
 
 
 ^ 1 
 
 
 
 
 
 
 
 
 C3 
 
 03 
 
 
 
 
 
 
 ^ 
 
 
 
 a 
 o 
 
 a 
 o 
 
 Is 
 
 a 
 
 o 
 
 
 "o 
 
 O V 
 
 
 
 Year 
 
 
 2.2 
 °3 
 
 o a 
 
 a § 
 
 3 
 
 1 
 
 3"^ 
 
 
 
 s 
 
 a 
 
 
 
 a^^ 
 
 - a „ 
 
 .s 
 
 
 ^a: 
 
 
 '-''Eo 
 
 z. 
 
 
 
 Pirn 
 
 .2.2 S 
 
 C3 
 
 t- 
 ^ 
 
 5S 
 
 OS 
 
 f5>< 
 
 > 
 
 1904 . 
 
 3.31 
 
 658 
 
 5.0 
 
 113 
 
 228 
 
 113.2 
 
 .7 
 
 4.2 
 
 3.5 
 
 1905 . 
 
 3.78 
 
 649 
 
 5.8 
 
 144 
 
 279 
 
 114.0 
 
 5.3 
 
 4.3 
 
 -1.0 
 
 1906 . 
 
 4.06 
 
 651 
 
 6.2 
 
 160 
 
 315 
 
 120.0 
 
 6.6 
 
 5.7 
 
 -0.9 
 
 1907 . 
 
 4.32 
 
 692 
 
 6.2 
 
 145 
 
 323 
 
 127.9 
 
 -1.7 
 
 6.4 
 
 8.1 
 
 1908 . 
 
 4.38 
 
 849 
 
 5.1 
 
 132 
 
 294 
 
 125.7 
 
 
 4.4 
 
 
 We notice, in the first column, a steady and rapid in- 
 crease in the deposits of national banks up to, and in- 
 cluding, the crisis year. Though deposits for 1908 do 
 not decrease, yet they remain almost stationary as 
 
 1 The figures for deposits and reserves of national banks are 
 those given in the Reports of the Comptroller of the Currency, and 
 represent the condition of the banks at their third report to the 
 Comptroller (generally about July 1) of each year. The ratio 
 column explains itself. 
 
 2 The figures for clearings are taken from the Financial Review 
 for 1910, p. 33. Those for M'V are constructed from the figures 
 for clearings by a method explained in § 5 of Appendix to Chapter 
 XII. 
 
 ' The index numbers of prices are those of the Bureau of Labor 
 (Bulletin 81, March, 1909), and relate to January of each year in 
 question. The next column, therefore, headed "Per cent rise of 
 prices during year" indicates the rise from January of the year in 
 question to January of the next. 
 
 * The figures for interest rates are taken from the Appendix of 
 The Rate of Interest, p. 418, brought through 1908 by computations 
 from the Financial Review. The per cent rise of prices is subtri"ted 
 from money interest to get virtual interest.
 
 272 THE PURCHASING POWER OF MONEY [Chap. XI 
 
 compared with those of the previous year. The second 
 column, that for reserves, shows, as we should expect, 
 a large increase in the year after the crisis, the banks 
 having fortified themselves against the decrease of busi- 
 ness confidence. We find, then (third column), an in- 
 crease in the ratio of deposits to reserves, the highest 
 ratio being reached in 1906 and 1907, not because re- 
 serves were depleted, — on the contrary, they were 
 expanding, — but because deposits were expanding 
 still more rapidly. If the theory presented in Chapter 
 IV is correct, it is precisely this high ratio of deposits to 
 reserves, brought about by failure of interest to rise 
 with rise of prices, which forced the banks to raise their 
 rates of discount and so check further expansion of 
 credit. Then came the crisis and the short succeeding 
 depression. The next column, headed " clearings," is 
 indicative of the volume of check transactions, the circu- 
 lation of deposit currency. As a fairly constant pro- 
 portion of checks is settled through the various clearing 
 houses of the country, clearings may fairly be regarded 
 as somewhat of a criterion of M'V. The fifth column 
 is derived from the fourth and from other data, and 
 is intended as an estimate of M'V. These two col- 
 umns increase through 1906, but (since they relate to 
 the whole year and not to a point in the middle of the 
 year) begin to show the effects of the credit slump in the 
 fall of 1907, so that their growth is arrested somewhat 
 in that year, and still more in the year after. We 
 should expect to find, then, a rise of prices reaching a 
 maximum with 1907 and falhng in 1908, and this we do 
 find in column six. Column seven shows the per cent 
 rise during each year. Thus, for January, 1904, the 
 index number or P is 113.2, and for January, 1905, it 
 is 114.0. The rise, therefore, is a little less than 1 per
 
 Sec. 17] STATISTICAL VERIFICATION 273 
 
 cent. The minus sign signifies a fall. The eighth col- 
 umn is for rates of interest and indicates, as we should 
 expect, a rise, culminating in 1907. Virtual interest — 
 that is, the interest in terms of commodities — was ex- 
 ceedingly low during the years immediately preceding 
 1907, because prices were rising so fast. This is shown 
 in column nine, where the nominal interest (measured 
 in money) is corrected by the rise or fall of prices to 
 give interest as measured in actual purchasing power. 
 With the culmination of the cycle in 1907 and the re- 
 sultant fall of prices, we find virtual interest suddenly 
 becomes very high. No wonder that borrowing enter- 
 prisers often found it hard to make both ends meet. 
 
 The facts as to credit cycles, then, completely con- 
 firm the analysis already given in previous chapters 
 and indicate that prices rise and fall with cycles of 
 currency and velocity. For the benefit of those who 
 doubt whether the expansion of deposit currency raises 
 23rices, or whether the rise of prices creates deposit cur- 
 rency, it may be added that facts, as well as theoiy, 
 show that the former relationship is the true one (al- 
 though temporarily, as during 1904-1907, there exists 
 a reaction of prices on deposits). Miss England has 
 shown, for instance, that loans and deposits expand be- 
 fore prices rise, and that, though prices often fall before 
 loans and deposits shrink, this anomalous order of 
 events is explainable by the revival of trade following 
 a crisis.^ 
 
 No attempt has been made in this chapter to review 
 all the phenomena or even all the typical phenomena 
 of crises. We are not here concerned with crises 
 
 1 Minnie Throop England, " Statistical Inquiry into the Influence 
 of Credit upon the Level of Prices," University Studies (University 
 of Nebraska), 1907. 
 
 T
 
 274 THE PURCHASING POWER OF MONEY [Chap. XI 
 
 except in relation to currency. Our concern is with 
 the magnitudes entering the equation of exchange, es- 
 pecially M, M', and V\ for these are the immediate 
 elements the variations in which affect the price level 
 and cause it to rise and fall. 
 
 §18 
 
 This chapter has been devoted to an historical study 
 of changes in the quantity of currency and of the effects 
 of these changes on prices. We have seen that, on the 
 whole, increases in the amount of money have tended 
 to raise prices from century to century during the last 
 thousand years, and especially since the discovery of 
 America. The changes in the last century, or more 
 exactly, from 1789 to 1909, have been considered in 
 somewhat more detail, covering five periods of alter- 
 nately rising and falling prices. We have seen evidence 
 to connect these price movements with changes in the 
 quantity of money and in the volume of business. The 
 periods 1789-1809, 1849-1873, and 1896-1909 were 
 periods of rising prices and large increases of the money 
 supply. In the period 1809-1849 prices fell presumably 
 because of a falling off in gold and silver production and 
 a continuing increase of business ; while between 1873 
 and 1896, although the world's stock of precious metals 
 was increasing slowly, prices in gold countries fell, 
 because in addition to the increasing volume of business 
 there was a stampede of nations to adopt the gold stand- 
 ard and demonetize or limit the coinage of silver. 
 
 We have observed the recent continual increase of 
 gold production and found reasons for the tentative 
 prediction that the gold production of the future would 
 continue excessive and probably cause the present rise 
 of prices to continue for some time in the future.
 
 Sec. 18] STATISTICAL VERIFICATION 275 
 
 We have described some of the chief examples of paper 
 money inflation and shown that the records for circula- 
 tion and price changes bear out in a general way the 
 principles set forth in previous chapters. The paper 
 money experiences of France during the French Revolu- 
 tion, of England during the Napoleonic wars, of Austria, 
 the American colonies, the United States, and the Con- 
 federacy have been briefly reviewed. We have noted 
 that in these cases, as in others, prices depended on the 
 quantity of money, its velocity, and the volume of busi- 
 ness. We have seen that the apparent exceptions 
 due to lack of confidence in paper money are not 
 really exceptions, because lack of confidence works it- 
 self out through the magnitudes in the equation of ex- 
 change. Distrust increases the velocity of circulation, 
 and decreases the trade performed by the money. We 
 have shown that the general effect of irredeemable paper 
 money issues, which are almost always in large quanti- 
 ties, despite pledges to the contrary, has been to raise 
 prices. 
 
 Finally, our study of deposit circulation and crises 
 has afforded further illustration. Preceding a typical 
 crisis, there is, in general, a tendency for deposits to 
 increase and also for their velocity of circulation to in- 
 crease, while prices tend to rise. Following the crisis 
 comes a decrease in bank deposits and their velocity of 
 circulation, an increase in bank reserves, with a corre- 
 sponding tendency to diminish money in circulation, and 
 a fall of prices. In the years of the principal crises 
 these took place simultaneously in different countries.
 
 CHAPTER XII 
 
 STATISTICS OF RECENT YEARS 
 §1 
 
 The last chapter was devoted to a brief sketch of price 
 movements and their causes, in so far as the scanty data 
 available make even a tentative interpretation possible. 
 From this telescopic view of the past we turn to a micro- 
 scopic view of the present. We shall confine it to a 
 study of the events of the last three decades in the 
 United States. In the study of the last chapter we 
 found the facts of history to be in accord with the a 
 priori principles already set forth in the equation of 
 exchange. But these facts of history were too general 
 and vague to constitute a quantitative fulfillment of the 
 equation of exchange. We shall find, however, much 
 fuller data in the last few decades. We shall see that 
 the equation of exchange, which has already been 
 proved a priori, may also be verified by actual statistics 
 — within at least the limit of error to which the statis- 
 tics are liable. 
 
 A good beginning of such a study is afforded by the 
 pioneer work of Professor Kemmerer, already often re- 
 ferred to. He has estimated ^ roughly the chief magni- 
 tudes of the equation of exchange and found that these 
 conform in a general way to the conditions which the 
 equation of exchange imposes. For each year, begin- 
 
 ^ Money and Credit Instruments in their Relation to General Prices, 
 New York (Holt), 1909, Book II. 
 
 276
 
 Sec. 1] STATISTICS OF RECENT YEARS 277 
 
 ning with 1879 (the year of resumption of the gold stand- 
 ard), and ending with 1908, he has estimated the total 
 monetary and check circulation (what we have called 
 MV and M'V) and the volume of trade {T), and from 
 these has calculated ^ what the price level ought to 
 
 be as determined by these factors, i.e. — ■. — ^ 
 
 This calculated magnitude, which Professor Kemmerer 
 calls the " relative circulation of money," he then com- 
 pares with the actual figures for price levels as given in 
 statistics of index numbers. 
 
 Professor Kemmerer's calculation is, I believe, the 
 first serious attempt ever made to test statistically the 
 so-called " quantity theory " of money. The results 
 show a correspondence which is very surprising when 
 we consider the exceedingly rough and fragmentary 
 character of the data employed. 
 
 Most other writers who have attempted to test the 
 quantity theory statistically seem to have been ani- 
 mated by a desire not to give it a fair test, but to 
 disprove it. They have carefully avoided taking ac- 
 count of any factors except money and prices. It is 
 not to be wondered at that they find little statistical 
 correlation between these two factors.^ The virtue 
 of Professor Kemmerer's work consists in giving due 
 attention to factors other than money. 
 
 The chief error in his investigation is the assumption 
 of 47 as the velocity of circulation of money. The true 
 value, as we shall see, is nearer 18 to 20. But the volume 
 
 1 For the details of Professor Kemmerer's calculations the reader 
 is referred to his book. A very brief summary and criticism are 
 given in § 1 of the Appendix to (this) Chapter XII. 
 
 ^ See e.g. Miss S. M. Hardy, "The Quantity of Money and 
 Prices, 1860-1891. An Inductive Study." Journal of Political 
 Economy, Vol. 3, pp. 145-168.
 
 278 THE PURCHASING POWER OF MONEY [Chap. XII 
 
 of money payments, even with Kemmerer's exaggerated 
 figure for velocity, is so small when compared with 
 check payments, that this weakness does not greatly 
 affect his final comparisons. At my request, Professor 
 Kemmerer has recalculated his curves on the basis of 
 18 instead of 47 as the velocity of circulation of money. 
 The results are given in Fig. 12. If these are com- 
 pared with those contained in Professor Kemmerer's 
 book, there will be seen to be little difference. It is 
 interesting to observe that when minute comparison is 
 
 Fig. 12. 
 
 made the selection of 18 as the estimate of velocity 
 gives a slightly better agreement between the two 
 curves than does 47. 
 
 The ''coefficient of correlation" between Professor 
 Kemmerer's results for P, as directly shown by statis- 
 tics and as indirectly calculated from the other factors 
 in the equation of exchange, is found, by Professor 
 Persons ^ of Dartmouth, to be only .23 (or 23 per cent 
 of perfect correlation), with a probable error of .13. 
 As Professor Persons says, this is a very low degree of 
 correlation. 
 
 ' " Quantity Theory as tested by Kemmerer," Quarterly Journal 
 of Economics, February, 1908, p. 287.
 
 Sec. 1] STATISTICS OF RECENT YEARS 279 
 
 But Persons's method of testing agreement by means 
 of a coefficient of correlation is not really applicable to 
 two curves representing magnitudes changing in time. 
 For it practically ignores a most essential factor, their 
 order in time. A year-to-year comparison is better. 
 If we consider the curves of prices and of ''relative cir- 
 culation," ^ we see at a glance that almost every succes- 
 sive change in direction in the one curve is matched by a 
 corresponding change in direction in the other. In fact, 
 out of 28 such possible coincidences, we find the actual 
 number to be 16 cases of agreement in the changes of 
 direction, 9 cases of disagreement, and 3 cases of a 
 neutral kind {i.e. cases which showed no change of 
 direction in one of the two curves). 
 
 The above figures relate to the curves in Professor 
 Kemmerer's book. The later curves employing 18 
 instead of 47 for money-velocity show about the same 
 results, there being 16 cases of agreement, 8 cases of dis- 
 agreement, and 4 cases of a neutral kind. The corre- 
 spondence here between prices and "relative circulation" 
 is very slightly greater than before. In both sets of dia- 
 grams the agreements are not only much more numerous 
 but much more pronounced than the disagreements. 
 
 Finally, some of the disagreements seem to be really 
 agreements, disguised by being shifted forward one year. 
 Thus, the inflections of 1899, 1900, 1901, for " relative 
 circulation," although all counted as cases of disagree- 
 ment, are strikingly similar respectively to the inflec- 
 tions of 1900, 1901, 1902, for "general prices." From 
 the fact that the statistics are partly for calendar and 
 partly for fiscal years, such one-year shifting of corre- 
 spondence is to be expected, as Professor Kemmerer 
 points out. 
 
 1 Kemmerer, op. cit., p. 149.
 
 280 THE PURCHASING POWER OF MONEY [Chap. XII 
 
 §2 
 
 I shall now attempt to make as precise statistical 
 estimates of the magnitudes in the equation of exchange 
 for the years 1896-1909 as the data available will allow. 
 This period — 1896-1909 — is selected chiefly because 
 its two end years afford the only known data making 
 possible an estimate of velocity of circulation of money 
 and of bank deposits. 
 
 The magnitudes will be considered in the order 
 M, M', V, V, T, P. For each the figures to be used 
 are new. 
 
 M. The following table gives the estimated amount of 
 money in circulation in the United States. By this 
 we mean the total amount of money (coin and paper) 
 outside of the federal treasury and outside the banks 
 of deposit and discount (national, state, private and 
 trust companies). The treasury stock is excluded be- 
 cause it is a hoard which does not become adjusted 
 to needs of payment in the sense — or at any rate in the 
 degree — that the stocks in merchants' tills and in 
 people's pockets become adjusted. The bank reserves 
 are excluded because, as we have shown, they are used 
 for banking operations, not commercial purchases. 
 
 Estimated Money in Circulation in the United States (M) 
 (in Billions of Dollars) 
 
 1896 
 
 1897 
 1898 
 1899 
 1900 
 1901 
 1902 
 
 .87 
 .88 
 .96 
 1.03 
 1.17 
 1.22 
 1.26 
 
 1903 
 1904 
 1905 
 1906 
 1907 
 1908 
 1909 
 
 1.38 
 1.37 
 1.45 
 1.59 
 1.63 
 1.63 
 1.63 
 
 This table is based on the oflScial estimate of money 
 in the United States, which includes money in banks and
 
 Sec. 2] STATISTICS OF RECENT YEARS 281 
 
 in the federal treasury. These official figures are then 
 corrected by means of recent revisions of the estimates 
 of the gold in the United States, and by deducting the 
 money in the federal treasury and the estimate of money 
 in banks reporting and unreporting.^ The results differ 
 somewhat from the official figures for so-called "money 
 in circulation," the chief reason for the discrepancy being 
 that these official figures include money in banks. The 
 figures here given are probably nearly correct ; the prob- 
 able error may, I believe, be assumed to be within 2 or 
 3 per cent. 
 
 The table shows that, during the space of thirteen 
 years between 1896 and 1909, the money in circulation 
 has nearly doubled and that its increase has been almost 
 uninterrupted. 
 
 M'. The following figures for M' are estimates of 
 individual deposits, subject to check. 
 
 Individual Deposits subject to Check (M') "^ (in Billions of 
 Dollars) 
 
 1896 2.68 
 
 1897 2.80 
 
 1898 3.19 
 
 1899 3.90 
 
 1900 4.40 
 
 1901 5.13 
 
 1902 5.43 
 
 1903 5.70 
 
 1904 5.80 
 
 1905 6.54 
 
 1906 6.84 
 
 1907 7.13 
 
 1908 6.60 
 
 1909 6.75 
 
 These figures are based on the official figures for 'in- 
 dividual deposits," but are much less than these, owing 
 to the fact that the official figures include deposits in 
 savings banks and other deposits not subject to check, 
 as well as to several other minor causes. The estimates 
 here given constitute the first attempt to give a series 
 
 ^ For details as to the construction of the table, see § 2 of Ap- 
 pendix to (this) Chapter XII. 
 
 2 For the method of estimating these figures see § 3 of Appendix 
 to (this) Chapter XII.
 
 282 THE PURCHASING POWER OF MONEY [Chap. XII 
 
 of figures for the bank deposits subject to check in the 
 United States. It was made possible through the kind 
 cooperation of the National Monetary Commission 
 and its expert, Mr. A. Piatt Andrew.^ 
 
 These figures give, therefore, the actual deposit cur- 
 rency of the United States. They show an enormous 
 growth of bank deposit currency. In the space of 
 thirteen years (between the beginning and the end of the 
 table) it has nearly trebled. Moreover, each year shows 
 an advance over the preceding year, excepting only the 
 year 1908 following the crisis of 1907. 
 
 §3 
 
 Having found M and M', the circulating media, we 
 next proceed to ascertain V and V, their velocity of cir- 
 culation. We shall find it convenient to consider the 
 latter first. 
 
 The velocity of circulation of bank deposits is found 
 by dividing respectively the total check circulation 
 (M'V) by the bank deposits (M'). The divisor, M', 
 has already been found. As to the dividend, M'V, this 
 is practically the total checks drawn in a year, for we 
 may reasonably assume that, on the average, each check 
 circulates against goods once and but once.^ 
 
 For two years, 1896 and 1909, thanks to the efforts of 
 Professor Kinley of the University of IlHnois, we have 
 voluminous and unique data collected originally for the 
 purpose of calculating the ratio of money-transactions 
 to check-transactions in the United States, i.e. the ratio 
 of MV to M'V. We shall see that these data, in con- 
 junction with other oflficial statistics, are sufiicient for 
 something more important than computing this ratio ; 
 
 1 For details see § 3 of Appendix to (this) Chapter XII. 
 * Cf. Kem merer, op. cit., p. 114.
 
 Sec. 3] STATISTICS OF RECENT YEARS 283 
 
 for they enable us to calculate with a tolerable degree 
 of exactness the magnitudes V andF' for both the years 
 mentioned. We shall find incidentally that, with the 
 aid of these magnitudes, it is possible to work out more 
 exactly than in the investigations above mentioned the 
 very magnitude for which these investigations were 
 undertaken, viz. the ratio of money-transactions to 
 credit-transactions. 
 
 We need first to estimate M'V. 
 
 M'V. Professor Kinley's special investigation of 
 1896 indicates that on ''the settling day nearest July 1, 
 1896," the value of the checks deposited was about 
 $468,000,000. If we could assume that this day was an 
 average day for the year, we should need, in order to 
 obtain the total year's deposits of checks, simply to 
 multiply this by the number of settling days in 1896, 
 which was 305.^ But it happens that July 1 is an excep- 
 tionally heavy day in the deposit of checks. Making 
 allowance for this fact, 2£> indicated by the clearings of 
 the New York clearing house, we conclude that the 
 total year's deposits of checks in 1896 was about 97 bil- 
 lions, with a probable error of some 5 or 6 per cent.^ 
 Similar calculations for 1909 make the total check trans- 
 actions of that year 364 billions.^ We have thus the 
 value of the total check circulation {M'V) in the two 
 years 1896 and 1909, and find them to be 97 and 364 
 billions respectively, indicating a prodigious growth in 
 thirteen years. We have still to interpolate figures for 
 intervening years. For the period between these two 
 years, we have, unfortunately, no such data as those of 
 
 » This multiplication gives $143,000,000,000, which figure is used 
 by Professor Kemmerer {op. cit., pp. 110-111). 
 
 * The method of reaching this result is described in § 4 of Appen- 
 dix to (this) Chapter XII. 
 
 » See § 4 of Appendix to (this) Chapter XII.
 
 284 THE PURCHASING POWER OF MONEY [Chap. XH 
 
 Professor Kinley for 1896 and 1909. However, we can 
 find an excellent barometer in the clearing house trans- 
 actions, — a barometer dependent partly on the clearings 
 in New York City, but more on those outside of New 
 York City. It is well recognized that, although the 
 clearings in New York deserve an exceedingly large 
 representation, their relative importance in the total 
 clearings is exaggerated.^ 
 
 On the question, therefore, ''What relative impor- 
 tance should be given respectively to clearings in New 
 York and to the outside clearings in order to get the best 
 barometer of the check transactions for the entire coun- 
 try?" we conclude that, if the out-lde clearings be 
 multiplied by five and the result added to the New York 
 clearings, we shall have a good barometer of check 
 transactions for the United States.- 
 I By means of this barometer of check transactions, 
 consisting of New York clearings plus five times the out- 
 side clearings, and our knowledge of the actual check 
 transactions of 1896 and 1909, we may easily derive 
 from the "barometer" an estimate of the actual check 
 transactions. The result is as follows : — 
 
 Estimated Check Transactions (M'V) (in Billions of 
 Dollars) 1896-1909' 
 
 1896 
 1897 
 1898 
 1899 
 1900 
 1901 
 1902 
 
 97 
 106 
 127 
 166 
 165 
 208 
 222 
 
 1903 
 1904 
 1905 
 1906 
 1907 
 1908 
 1909 
 
 223 
 
 233 
 282 
 320 
 320 
 300 
 364 
 
 * See e.g. the remarks on these clearings in Financial Review for 
 1910, p. 33, and in Babson's Business Barometers (Wellesley Hills, 
 Mass.), 1910, p. 188. 
 
 * See § 5 of Appendix to (this) Chapter XII. 
 ' See § 5 of Appendix to (this) Chapter XII.
 
 Sec. 4] 
 
 STATISTICS OF RECENT YEARS 
 
 285 
 
 The probable error of the figures between 1896 and 1909 
 may be set at some 5 to 10 per cent. 
 
 F'. Having obtained estimates of M'V and having 
 previously obtained estimates of M', it is easy, by simple 
 division, to obtain F'. The results are as follows : — 
 
 Estimated Velocity (F') of Circulation, by Checks, of De- 
 posits Subject to Check 
 
 1896 
 1897 
 1898 
 1899 
 1900 
 1901 
 1902 
 
 36 
 
 1903 
 
 38 
 
 1904 
 
 40 
 
 1905 
 
 43 
 
 1906 
 
 37 
 
 1907 
 
 41 
 
 1908 
 
 41 
 
 1909 
 
 39 
 40 
 43 
 47 
 45 
 46 
 54 
 
 The probable error in these figures may be set at some 5 
 to 10 per cent, being least for 1896 and 1909 and greatest 
 midway between. , 
 
 We note that the velocity of circulation has increased 
 50 per cent in thirteen years and that it has been sub- 
 ject to great variations from year to year. In 1899 and 
 1906 it reached maxima, immediately preceding crises. 
 These results correspond to those of Pierre des Essars 
 for the rates of turnover of deposits in continental 
 banks already noted, except that he usually finds the 
 maximum in the crisis year itself rather than the year 
 before. It is to be noted that the figure for 1909 is 
 much the highest in the table. Whether it portends an 
 approaching crisis, time will determine. 
 
 §4 
 
 MV. Our next quest is for the velocity of circula- 
 tion of money. The calculation of the velocity of circu- 
 lation of money presents great difficulties, — difficulties 
 which, in fact, have usually been considered insurmount-
 
 286 THE PURCHASING POWER OF MONEY [Chap. XII 
 
 able. This opinion was well expressed by Jevons/ 
 who wrote : 
 
 " I have never met with any attempt to determine in any coun- 
 try the average rapidity of circulation, nor have I been able to 
 think of any means whatever of approaching the investigation of 
 the question, except in the inverse way. If we know the amount of 
 exchanges effected, and the quantity of currency used, we might 
 get by division the average number of times the currency is turned 
 over; but the data, as already stated, are quite wanting." 
 
 As we shall see, however, data now exist, capable of 
 revealing the ''amount of exchanges effected," or, MV. 
 In fact, this is equal to the total money deposited 
 in banks, plus the total money-wages paid, plus a small 
 miscellaneous item. From MV and M it is of course 
 easy to obtain V by division. 
 
 The formula for obtaining MV is as simple as it may 
 at first seem mysterious. The chief peculiarity of the 
 method which this formula represents, and the feature 
 which adapts it to practical use, is that it utilizes bank 
 records and other ascertainable statistics as a means of 
 discovering the total value of money transactions. The 
 method is based on the idea that money in circulation 
 and money in banks are not two independent reservoirs, 
 but are constantly flowing from one into the other, and 
 that the entrance and exit of money at banks, being a 
 matter of record, may be made to reveal its circulation 
 outside. 
 
 It is obvious how the bank-record would be read, were 
 it true that every dollar withdrawn from banks cir- 
 culated once and only once before being redeposited. 
 Under these circumstances the annual flow of monetary 
 circulation would exactly equal the annual withdrawal 
 
 ' Money and the 'Mechanism of Exchange (London), p. 336.
 
 Sec. 4] STATISTICS OF RECENT YEARS 287 
 
 from banks prior to circulation, as well as the annual 
 deposits in banks subsequent to circulation. 
 
 Since we have a record of the first and last steps of 
 the three, viz. the withdrawals and the deposits, we 
 possess the means of knowing the intermediate step, 
 the exchange of money for goods. The ordinary circula- 
 tion of money, — excluding cases where it changes 
 hands more than once between withdrawal and rede- 
 posit, — is equal to the money-flow through banks. 
 
 The complete facts, however, are not so simple, for 
 the reason that money withdrawn from banks is often 
 circulated more than once. Yet the complications 
 involved follow definite laws. They do not destroy the 
 value of the bank record, but merely make it somewhat 
 more difficult to read. We propose to show (1) that in 
 actual fact much money circulates out of bank only once, 
 as in the hypothetical case just mentioned; (2) that when 
 it is paid for wages, it usually circulates twice ; and (3) 
 that only rarely does it circulate three or more times 
 before completing its circuit back to the banks. 
 
 This statement means that, like checks, money circu- 
 lates in general only once outside of banks; but that 
 when it passes through the hands of non-depositors 
 (which practically means wage-earners) it circulates 
 once more, thus adding the volume of wage payments to 
 the volume of ordinary money circulation, which, as we 
 have seen, is equal to the flow of money through banks. 
 
 We falsely picture the circulation of money in modern 
 society when we allow ourselves to think of it as consist- 
 ing of a perpetual succession of transfers from person to 
 person. Were it such a succession, it would be, as Jevons 
 said, beyond the reach of statistics. But we may 
 form a truer picture by thinking of banks as the home 
 of money, and the circulation of money as a temporary
 
 288 THE PURCHASING POWER OP MONEY [Chap. XII 
 
 excursion from that home. If this description be true, 
 the circulation of money is not very different from the 
 circulation of checks. Each performs one transaction 
 or, at most, a few transactions, outside of the bank, and 
 then returns home to report its circuit. 
 
 As is shown in the Appendix, the total money de- 
 posited in banks in 1896 amounted to nearly 10 billions of 
 dollars,^ and the total expenditures of non-depositors 
 to nearly 6 billions, of which 4| bilUons constituted 
 the expenditures of wage-earners ; the remaining item 
 in the formula for circulation amounted to less than 
 1 biUion, making about 16 billions for the total cir- 
 culation. 
 
 For 1909 the corresponding figures are: money de- 
 posited, 21 billions; expenditures of non-depositors, 13 
 billions; and the remaining item about 1 billion, making 
 35 billions in all. 
 
 The following table summarizes these results in bil- 
 lions of dollars : ^ — 
 
 
 1896 
 
 1909 
 
 1st term (money deposited in banks) . . . 
 2d term (expenditure of " non-depositors ") . 
 Remaining item 
 
 10- 
 6- 
 1- 
 
 16 + 
 
 21 
 
 13 
 
 1 
 
 Total 
 
 35 
 
 ' For a fuller account of the method of estimating the velocity 
 of circulation of money and its statistical application, see § 6 of the 
 Appendix to (this) Chapter XII, which consists, with revisions and 
 additions, of an article of mine published in December, 1909, in 
 the Journal of the Royal Statistical Society on "A New Method of 
 estimating the Velocity of Circulation of Money." The additions 
 incorporated in the Appendix (§§ 7, 8) include the statistical de- 
 tails of the calculations for the United States. 
 
 ' For details as to the figures in this table, see § 7 of Appendix 
 to (this) Chapter XII.
 
 Sec. 4] STATISTICS OF RECENT YEARS 289 
 
 V. In order to obtain the velocity of circulation, the 
 total circulation, MV (16 billions for 1896, or to be more 
 exact, 16.2 billions), must be divided by the amount of 
 money, M, circulating in 1896. This amount is estimated 
 at $870,000,000. Hence the velocity is 16,200,000,000 -4- 
 870,000,000 = 18.6, or about 19 tunes a year. In other 
 words, money was held on the average about 365 -^ 19, 
 which amounts to 19 or 20 days. If I have made as 
 full allowance for error as I believe has been made, the 
 error in this estimate does not exceed two or three days. 
 For 1909 the velocity of circulation is estimated as the 
 total circulation (35.1 billions) divided by the money in 
 circulation (1.63 billions), which is 21. 5+ ; that is, about 
 22 times a year, or once in 17 days. We conclude that 
 the velocity of circulation of money in 1896 and the 
 velocity in 1909 were about 19 and 22 times respec- 
 tively, with a probable error judged to be about 2 in 
 1896 and not much more than 1 in 1909. 
 
 These results would assign money a slower circulation 
 than most of the estimates or guesses which have been 
 made. We must remember, however, that such persons 
 as economists, who are most apt to think about the circu- 
 lation of money, have a rapid turnover. They are usu- 
 ally city dwellers and the comparatively well to do, who, 
 as we know, do not keep their cash inactive long. 
 Laborers, especially thrifty laborers and laborers paid 
 monthly, will keep cash on hand for several weeks with- 
 out spending it. Farmers and others living in sparsely 
 settled districts will even keep it for months. Probably 
 the velocity of circulation of money differs widely 
 among different classes and different localities. 
 
 We may now compare the years 1896 and 1909 in 
 respect to money in circulation, deposit currency, their 
 velocities, and their total circulation as follows: —
 
 290 THE PURCHASING POWER OF MONEY [Chap. XII 
 
 (1) 
 
 (2) 
 
 (3) 
 
 (4) 
 
 (5) 
 
 (6) 
 
 (7) 
 
 (8) 
 
 
 M 
 
 M' 
 
 V 
 
 V 
 
 MV 
 
 M'V 
 
 MV+M'V 
 
 1896 
 
 .87 
 
 2.68 
 
 19 
 
 36 
 
 16 
 
 97 
 
 113 
 
 1909 
 
 1.63 
 
 6.75 
 
 22 
 
 54 
 
 35 
 
 364 
 
 399 
 
 Our next task is to interpolate estimates for V between 
 19 in 1896 and 22 in 1909. The results are given in the 
 following table : — 
 
 Estimates of F, 1896 to 1909 * 
 
 1896 
 1897 
 1898 
 1899 
 1900 
 1901 
 1902 
 
 19 
 
 1903 
 
 19 
 
 1904 
 
 20 
 
 1905 
 
 22 
 
 1906 
 
 20 
 
 1907 
 
 22 
 
 1908 
 
 22 
 
 1909 
 
 21 
 
 21 
 
 22 
 22 
 21 
 20 
 22 
 
 § 5 
 
 We have now finished our statistical review of the 
 magnitudes M, M', V, V, on the left side of the equation 
 of exchange, and have remaining only the two magni- 
 tudes P, T, on the right side of the equation. 
 
 First we shall consider T. The results of our calcula- 
 tions are given in the following table, which expresses 
 the volume of trade in billions of dollars as reckoned at 
 the prices of 1909: — 
 
 Estimated Volume of Trade (in Billions op Dollars at Prices 
 
 OF 1909) 
 
 1896 
 1897 
 1898 
 1899 
 1900 
 1901 
 1902 
 
 209 
 
 1903 
 
 239 
 
 1904 
 
 260 
 
 1905 
 
 273 
 
 1906 
 
 275 
 
 1907 
 
 311 
 
 1908 
 
 304 
 
 1909 
 
 335 
 324 
 378 
 396 
 412 
 381 
 399 
 
 ^ For the method of calculating this table see § 8 of Appendix 
 to (this) Chapter XII.
 
 Sec. 5] STATISTICS OF RECENT YEARS 291 
 
 The table is constructed by averaging the index num- 
 bers of the quantities (not the values) of trade in various 
 lines. The figures representing trade are based on data 
 for 44 articles of internal commerce, 23 articles of im- 
 port and 25 of export, sales of stocks, railroad freight 
 carried, and letters through the post office. The final 
 figures are so adjusted that the figure for 1909 shall be 
 399 ; namely, the actual money value of transactions in 
 that year as worked out on the other side of the equa- 
 tion {i.e.MV +M'V'). Relatively to each other, the 
 numbers for T are independent of the other side of the 
 equation.^ 
 
 P. The only remaining factor in the equation of ex- 
 change is the index number of prices, P. Theoretically 
 this could be calculated from the other five magnitudes 
 already evaluated, provided all our previous calculations 
 could be depended upon for absolute accuracy. But 
 there are possible errors in all the magnitudes M, M', 
 V, V, T, and such errors, should they exist, would be 
 registered cumulatively in P. It is important, therefore, 
 to check such an indirectly calculated value of P by 
 directly calculated statistics. By so doing we are able 
 to compare the P directly calculated and the P in- 
 directly calculated. In like manner, we might, if desired, 
 compare the directly and indirectly calculated values 
 of M, M', Vj V, and T. We shall confine ourselves to 
 comparing the two values of P, since it is P which, as 
 we have seen, is really dependent on the five other fac- 
 tors in the equation of exchange. The values of P (in- 
 cluding prices of commodities, securities, and labor), 
 directly calculated in terms of the figures for 1909, as 
 100 per cent, are as follows: — 
 
 ' For the exact method (necessarily laborious) of constructing this 
 table see § 9 of the Appendix to (this) Chapter XII,
 
 292 THE PURCHASING POWER OF MONEY [Chap. XII 
 Index Numbers of General Prices 
 
 1896 
 1897 
 1898 
 1899 
 1900 
 1901 
 1902 
 
 63 
 
 1903 
 
 64 
 
 1904 
 
 66 
 
 1905 
 
 74 
 
 1906 
 
 80 
 
 1907 
 
 84 
 
 1908 
 
 89 
 
 1909 
 
 87 
 85 
 91 
 96 
 97 
 92 
 100 
 
 This table is based on the figures of the Bureau of 
 Labor for wholesale prices. It differs slightly from the 
 Bureau of Labor figures owing to the fact that we here 
 include prices of securities and wages. ^ 
 
 It remains to compare these actual statistics for P 
 with P as computed indirectly from the other magni- 
 tudes in the equation of exchange. This calculation 
 and comparison will be given in the following section. 
 
 §6 
 
 We have now calculated independently the six magni- 
 tudes of the equation of exchange for the fourteen years 
 1896-1909. But, as already stated, we know that these 
 six magnitudes are mutually related through the equa- 
 tion of exchange. The question arises whether the 
 magnitudeB as calculated will actually fulfill approxi- 
 mately the equation of exchange. 
 
 One way of testing this question is that adopted by 
 Professor Kemmerer ; namely, to compare the statis- 
 tics for any one factor (say P), as above directly calcu- 
 lated, with what it would be as indirectly calculated 
 from the five other magnitudes in the equation of ex- 
 change. The following table shows the value of P as 
 obtained in these two ways : — 
 
 * For the method of constructing this table se« § 10 of Appendix 
 to Cthis) Chapter XII.
 
 Sec. 6] 
 
 STATISTICS OF RECENT YEARS 
 
 293 
 
 Index Numbers of Prices as Calculated 
 
 
 DiREcrrLT 
 (P) 
 
 Indirectlt 
 /MV + M'V'\ 
 
 1896 
 
 63 
 64 
 66 
 74 
 80 
 84 
 89 
 87 
 85 
 91 
 97 
 97 
 92 
 100 
 
 54 
 
 1897 
 
 52 
 
 1898 
 
 56 
 
 1899 
 
 69 
 
 1900 
 
 68 
 
 1901 
 
 76 
 
 1902 
 
 82 
 
 1903 
 
 75 
 
 1904 
 
 81 
 
 1905 
 
 83 
 
 1906 
 
 90 
 
 1907 
 
 86 
 
 1908 
 
 87 
 
 1909 
 
 100 
 
 
 
 The agreement between the two sets of figures is 
 visuaUzed in Figure 13. 
 
 The two values as shown by the upper and lower 
 
 1^ 
 
 iSUt ISM'MW I^BO 004 iSOS 1903 )904 I9QS i3Q& iSST iaOS (909" 
 
 Fjq. 13.
 
 294 THE PURCHASING POWER OP MONEY [Chap. XII 
 
 curves agree with each other remarkably well.^ The 
 closeness of their agreement may be expressed in several 
 ways. One way is to count the agreements and dis- 
 agreements in their changes of direction or inflections. 
 Out of 12 inflections in each curve the two agree six 
 times, disagree three times, and are neutral three times. 
 Another method is that employed by Professor Pearson. 
 This method consists in calculating what Professor 
 Pearson calls a "correlation coefficient." It shows an 
 agreement of 97 per cent of perfection as compared 
 with 23 per cent which Professor Persons of Dart- 
 mouth found for Professor Kemmerer's figures^ for 
 1879-1901. But, as already stated, a coefficient of cor- 
 relation for successive data is apt to be misleading. If, 
 in the case of Professor Kemmerer's figures, the coeffi- 
 cient .23 was an understatement of the parallelism 
 between his curves, the coefficient .97 overstates the 
 parallelism between mine. This overstatement is 
 always likely to result when both of the curves to be 
 compared rapidly ascend or descend.^ 
 
 The proper method of applying a coefficient of cor- 
 relation to successive data appears to be to calculate 
 
 ^ The intermediate curve will be explained later. 
 
 ' "Quantity Theory as tested by Kemmerer," Quarterly Journal 
 of Economics, 1907-1908, p. 287. 
 
 3 E.g. Persons finds a coefficient of .98 for the correlation between 
 Kemmerer's figures for bank reserves and money in circulation 
 inclusive of bank reserves, although the two magnitudes do not show 
 any very great agreement between fluctuations in successive years, 
 but only a general agreement in the fact that both ascend rapidly. 
 The coefficient for Professor Kemmerer's figures for P will be much 
 higher, if instead of taking the period beginning with 1879, which 
 includes many years in which prices do not greatly change, we take 
 the period beginning at the same time as my own figures begin, viz. 
 1896. The correlation coefficient for Kemmerer's figures 1896-1908 
 is 83 per cent, which is far higher than that obtained by Persons for 
 the period beginning in 1879.
 
 Sec. 6] STATISTICS OF RECENT YEARS 295 
 
 the coefficient, not for the raw figures, but for their 
 successive year-to-year ratios. In other words, we 
 tabulate and compare the ratios of each year's P to the 
 
 preceding year's P and of each year's — to 
 
 the preceding year's — If the two sets of 
 
 ratios should rise or fall together, the curves would show a 
 close parallelism or agreement in their successive changes 
 of direction. As a matter of fact, the results of this 
 method show a coefficient of correlation of 57 per cent 
 (or .57 ± .10, where .10 is the probable error). This 
 figure, 57 per cent, is a moderately high coefficient of 
 correlation.^ We may conclude, therefore, that the 
 "quantity theory" is statistically verified to a high 
 degree of correlation.^ 
 
 It is to be emphasized that the coefficients of correla- 
 tion as just given compare the price level with what it 
 should be according to the statistics of the jive magni- 
 tudes on which, by the so-called quantity theory, it is 
 dependent. The correlation would be less if instead of 
 these five magnitudes only one were taken. Thus the 
 coefficient of correlation for 1896-1909 as between 
 money, M, and prices, P, by the year-to-year-ratio 
 
 1 For instance, no one would deny that the length and breadth 
 of nuts are highly correlated. The coefficient of their correlation is 
 57 per cent. The height of a man and the breadth of his face are 
 correlated to the extent of 35 per cent. 
 
 2 Incidentally we may here compare the relative degree of corre- 
 lation of Professor Kemmerer's figures and of my own. For this 
 purpose we take the period 1896-1908, which is the longest period 
 common to both investigations. For these years the coefficient for 
 my figures is 54 per cent (or .54 ± .11) as against 37 per cent (or 
 .37 ± .14) for Kemmerer's. These are by the method of year-to- 
 year ratios. By the method of raw figures my correlation is 95 per 
 cent and Kemmerer's, 83 per cent.
 
 296 THE PUKCHASING POWER OF MONEY [Chap. XII 
 
 method is 43 per cent (or .43 ± .13).^ Even this is a 
 moderately high degree of correlation. 
 
 If the opponents of the ''quantity theory" who at- 
 tempt to disprove any relation between money and 
 prices by pointing out the lack of statistical correspond- 
 ence between the two mean merely that other factors 
 besides money, M',V, V, T, change from time to time 
 and that therefore the level of prices does not in actual 
 fact vary exactly with the quantity of money, their 
 contention is sound. But the proposition involved is of 
 as little scientific consequence as the proposition that 
 the pressure of the atmosphere does not vary from day 
 to day in exact proportion to its density. We know 
 that, temperature being constant, the pressure of a gas 
 varies directly as its density ; but that, as a matter of 
 fact, temperature seldom is constant. Any critic of 
 Boyle's law who should attempt to dispute its validity 
 on such a ground, however, would merely betray his 
 ignorance of the real meaning of a scientific law ; and if 
 he should seriously attempt to ''disprove it statistically" 
 by plotting daily curves of barometric pressure and 
 atmospheric density, he would subject himself to scien- 
 tific ridicule. 
 
 If any one has ever really imagined that the price level 
 depends solely on the quantity of money, he should 
 certainly be corrected. But the really important 
 matter is that students of economics should appreciate 
 the existence of a law of direct proportion between quan- 
 tity of money and price level — a law as real,- as im- 
 portant, and as fundamental in the economic theory of 
 money, as Boyle's law of direct proportion between 
 density and pressure is real, is important, and is funda- 
 
 1 By the (misleading) direct comparison between M and P the 
 coefficient of correlation for 1896-1909 is 97 per cent.
 
 Sec. 61 STATISTICS OF RECENT YEARS 297 
 
 mental in the physical theory of gases. I beheve that 
 the frequent failure to realize the existence of this law is 
 due largely to the lack of any clear conception of the 
 magnitudes involved. M and P seem to be the only 
 magnitudes which some students really understand. 
 M', V, V, T are seldom discussed or even mentioned. 
 But not until the subject is put on a statistical basis, — 
 in figures which measure actual deposit currency, ve- 
 locities of circulation, and volume of trade, — will these 
 magnitudes be recognized as having a real existence and 
 significance. 
 
 But, to a candid mind, the quantity theory, in the 
 sense in which we have taken it, ought to appear suffi- 
 ciently secure without such checking. Its best proof 
 must always be a priori, not in the sense which applies 
 to the proof of abstract mathematical propositions, but 
 in the sense which applies to the proof of Boyle's law. 
 Thus, it is known by induction that the pressure of a 
 confined gas is caused by the bombardment of its mole- 
 cules on the containing walls. It is likewise known by 
 induction that the pressure must be proportional to 
 the frequency of impact, provided the velocities of 
 the molecules are constant. Finally, it is known that 
 frequency of impact must be proportional to the num- 
 ber of molecules, i.e. the density of the gas, and that 
 constancy of velocity implies constancy of tempera- 
 ture. Therefore, it follows that, temperature being 
 constant, pressure is proportional to density. Thus, 
 from knowledge gained inductively of the individual 
 pressures of the molecules which compose the gas, 
 we may reason out deductively the general pressure 
 of a gas. 
 
 Analogously, from knowledge gained inductively of 
 individual exchanges — molecules as it were — which
 
 298 THE PURCHASING POWER OF MONEY [Chap. XII 
 
 compose society's exchange, we may reason out deduc- 
 tively the general equation of exchange. 
 
 Fortunately, just as Boyle's law has been established 
 both deductively and inductively, we may now assert 
 that the equation of exchange has been sufficiently 
 established both deductively and inductively. 
 
 As previously remarked, to establish the equation of 
 exchange is not completely to establish the quantity 
 theory of money, for the equation does not reveal which 
 factors are causes and which effects. But this ques- 
 tion has been answered in Chapter VIII. 
 
 § 7 
 
 To those who have faith in the a priori proof of 
 the equation of exchange the real significance of the 
 remarkable agreement in our statistical results should 
 be understood as a confirmation, not of the equation 
 by the figures, but of the figures by the equation. 
 There are discrepancies in our inductive verification; 
 but these are all well within the limit of errors of meas- 
 urement. The discrepancies prove that slight errors 
 exist among the figures; otherwise, they would conform 
 exactly to the relation prescribed by the equation of 
 exchange. 
 
 Our next task is to examine the discrepancies and lo- 
 cate, so far as possible, the errors involved. The degree 
 of total mutual discrepancy between the independently 
 calculated magnitudes is best expressed by the degree 
 of inequality between the calculated values of MF + 
 M'V and PT, which should be equal. That is, PT 
 divided by MV + M'V should always be unity. Ac- 
 tual division gives the figures in the column headed 
 " original" in the following table. The other column 
 will be explained presently.
 
 Sec. 7] 
 
 STATISTICS OF RECENT YEARS 
 
 299 
 
 Ratio of PT to MV + M' V as Calculated 
 
 
 Original 
 
 RjCDUCSD 
 
 (1) 
 
 (2) 
 
 (3) 
 
 1896 
 
 1.17 
 
 1.06 
 
 1897 
 
 1.24 
 
 1.13 
 
 1898 
 
 1.18 
 
 1.07 
 
 1899 
 
 1.06 
 
 .95 
 
 1900 
 
 1.17 
 
 1.06 
 
 1901 
 
 1.11 
 
 1.00 
 
 1902 
 
 1.08 
 
 .97 
 
 1903 
 
 1.16 
 
 1.05 
 
 1904 
 
 1.06 
 
 .95 
 
 1905 
 
 1.09 
 
 .98 
 
 1906 
 
 1.08 
 
 .97 
 
 1907 
 
 1.13 
 
 1.02 
 
 1908 
 
 1.05 
 
 .94 
 
 1909 
 
 1.00 
 
 .89 
 
 The figures in column (2) show that the calculated 
 values oi PT are always larger than the calculated 
 values of MV + M'V, the excess varying from 24 
 per cent to and averaging 11 per cent. 
 
 But these discrepancies between PT and MV + M'V 
 can be substantially diminished merely by changing the 
 base for measuring prices. This base we have thus far 
 taken as the price level of 1909. But as the index num- 
 bers have only a relative significance, we are free to 
 choose any other set of numbers so long as they maintain 
 the same relative magnitudes. In accordance with this 
 prerogative we choose to reduce all the numbers for P 
 by 11 per cent, this being the average of the original 
 discrepancies. The result will be to decrease PT by 11 
 per cent and to change the series of discrepancies from 
 those shown in column (2) to (approximately) those 
 shown in column (3). These numbers vary from 13 per 
 cent above to 11 per cent below unity. These errors
 
 300 THE PURCHASING POWER OF MONEY [Chap. XII 
 
 are very small — far smaller in fact than might have 
 been expected in view of the incomplete and unreliable 
 character of some of our data. 
 
 The question remains, Where shall we place the blame 
 for the errors which the small existing discrepancies 
 indicate? Is the fault with M, M' , V, V, P, or T? 
 
 , 46^7 l^^e 1099 J^OO IgOi 1902 1903 1904 4eg» 1906 i.9Q? 190& (^9 
 
 FiQ. 14. 
 
 How shall we correct our calculated jfigures ? We may 
 conclude on general principles that the smallest correc- 
 tions are the most likely to be right. The smallest cor- 
 rections imply a mutual adjustment between the six 
 factors, each adjustment being in the direction which 
 will diminish the existing discrepancy. In this way 
 each factor, as calculated, is regarded as having some 
 value, and is given some influence in correcting the
 
 Sec. 7] 
 
 STATISTICS OP RECENT YEARS 
 
 301 
 
 others ; so that any one factor requires extremely Uttle 
 change. The changes made in the various factors are 
 made in proportion to their assumed relative liability to 
 error. 
 
 The results are shown in Figures 14, 15, 16, and the 
 previous Figure 13, each of which relates to one of the 
 factors in the equation of exchange as originally calcu- 
 lated and as finally adjusted (dotted lines). When they 
 
 ' ■ rr ' •]- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ,,-.«:;,, ::=^I.^ ^--->? 
 
 . _ _ _L. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 : |~"P 'tT^ n^t^t' itl — 1 i4^f "1'f 
 
 3E1 cp :» 1 ■"" : d ; ; 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ol1 , 1 1 
 
 
 1897 t%S» IS99 ISCxi I3CU 1902 1903 1904- 1903 1806 I907 IS08 1909 
 
 Fig. 15. 
 
 are all thus adjusted, they conform exactly to the equa- 
 tion of exchange.^ 
 
 In Figure 14 we see that the alterations made in the 
 figures for M and M' are so trifling as to be almost negli- 
 gible, being usually much less than 1 per cent. The al- 
 terations in V and V, which are shown in Figure 15, 
 though somewhat greater, are also small, being usually 
 
 1 For the method of adjustment, see § 11 of Appendix to (this) 
 Chapter XII.
 
 302 THE PURCHASING POWER OF MONEY [Chap. XII 
 
 less than 2 per cent. The alterations in T, as shown in 
 Figure 16, though still greater than the preceding, are 
 nevertheless so small and uniform as to preserve an 
 almost perfect parallelism between the original and the 
 altered curve. The differences rarely exceed 10 per cent. 
 The alterations in P are shown in the previous Figure 
 13, the upper curve representing the original and the 
 
 
 
 
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 :::] 'la \ 
 
 M 
 
 5 :ti[i:::]i:-:5n:i^K::-::::::::::::: ;::::::::::::;: 
 
 
 
 
 
 " ~ 3 
 
 ■::::ni 
 
 1 ■ 
 
 TT iTm ' n 't'lr 'mT t 1 ' 1 itl 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 iks 
 
 « i0vy 1 
 
 ito 
 
 ma 
 
 i«o 
 
 ft iMt 1 
 
 to 
 
 Z leOS I9<H leoS 1906 )907 Id08 I909 
 
 Fig. 16. 
 
 dotted, or middle, curve representing the altered fig- 
 ures for P. Here also an extremely close parallelism 
 between the original and the altered curves is evident. 
 The differences rarely exceed 3 per cent. 
 
 Certainly the most exacting of critics could not ask 
 for any greater consistency of results and conformity 
 to the theory of the equation of exchange than these 
 statistics show. The corrections which have been found 
 necessary to bring the six figures as first calculated into 
 perfect agreement are smaller than the probable error
 
 Bec. 7] STATISTICS OF RECENT YEARS 303 
 
 in those figures themselves. I had — quite antecedently 
 to any knowledge of how closely the final results would 
 harmonize — assigned certain rough estimates of the 
 probable errors. These are noted in the Appendix. The 
 probable error of M is adjudged to be 2 or 3 per cent ; of 
 M', 2 or 3 per cent ; of F, 5 to 10 per cent ; of V, 5 to 
 10 per cent ; of P, 5 to 10 per cent ; and of T, 5 to 10 per 
 cent. In other words, our statistical data were regarded 
 as only rough or approximate ; yet the final "doctor- 
 ing" needed to make them agree with each other was, as 
 has been seen, seldom over 2 per cent, being less than 1 per 
 cent for M and M' ; less than 2 per cent for V and V ; less 
 than 3 per cent for P; and less than 4 per cent for T. We 
 conclude then that the figures fit each other better than 
 might be expected from their known lack of precision. 
 
 The corrections which we have assigned to the va- 
 rious factors are so insignificant that it would be haz- 
 ardous to attempt to explain them specifically. The 
 errors which they presumably represent might be due 
 to numerous sources, such as the varying ingredient in 
 the New York clearing house transactions of bank trans- 
 fers as distinct from ordinary check transactions; or 
 such as errors or defects in the statistics of trade in grain, 
 etc. ; or such as an over or underestimate of the devia- 
 tion from normal of the particular days in 1896 and 1909 
 on which the statistics of deposits made in banks were 
 gathered; or such as over or underestimates of the un- 
 reported deposits, or over or underestimates of the gold 
 in the United States, or over or underestimates of wages 
 and of other numerous minor though often conjectural 
 elements in our calculations. 
 
 The sources of error just mentioned were named 
 in the order of their probable importance. It is, per- 
 haps, significant that the greatest discrepancies are in
 
 304 THE PURCHASING POWER OF MONEY [Chap. XII 
 
 the years 1896-1898, whose data for T were most defect- 
 ive, and in 1900, 1903, and 1907, which were years of 
 crises or of impending crises. 
 
 §8 
 
 After making the above named mutual adjustments 
 among the six magnitudes in the equation of exchange, 
 we reach the following figures, constituting our final 
 table of values for M, M', V, V\ P, and T; they are the 
 figures plotted in the dotted curves above given : — 
 
 Finally Adjusted Values of Elements of Equation of 
 Exchange (as to 1910-1912, see p. 492) 
 
 
 
 
 
 
 
 
 
 
 MV + M'V 
 
 
 M 
 
 M' 
 
 V 
 
 v 
 
 P 
 
 T 
 
 MV 
 
 M'V 
 
 PT 
 
 1896 . 
 
 .88 
 
 2.71 
 
 18.8 
 
 36.6 
 
 60.3 
 
 191 
 
 16 
 
 99 
 
 115 
 
 1897 . 
 
 .90 
 
 2.86 
 
 19.9 
 
 39.4 
 
 60.4 
 
 215 
 
 18 
 
 112 
 
 130 
 
 1898 . 
 
 .97 
 
 3.22 
 
 20.2 
 
 40.6 
 
 63.2 
 
 237 
 
 20- 
 
 131- 
 
 150 
 
 1899 . 
 
 1.03 
 
 3.88 
 
 21.5 
 
 42.0 
 
 71.6 
 
 259 
 
 22 
 
 163 
 
 185 
 
 1900 . 
 
 1.18 
 
 4.44 
 
 20.4 
 
 38.3 
 
 76.5 
 
 253 
 
 24 
 
 170 
 
 194 
 
 1901 . 
 
 1.22 
 
 5.13 
 
 21.8 
 
 40.6 
 
 80.5 
 
 291 
 
 27 
 
 208 
 
 235 
 
 1902 . 
 
 1.25 
 
 5.40 
 
 21.6 
 
 40.5 
 
 85.7 
 
 287 
 
 27 
 
 219 
 
 246 
 
 1903 . 
 
 1.39 
 
 5.73 
 
 20.9 
 
 39.7 
 
 82.6 
 
 310 
 
 29 
 
 227 
 
 256 
 
 1904 . 
 
 1.36 
 
 5.77 
 
 20.4 
 
 39.6 
 
 82.6 
 
 310 
 
 28 
 
 228 
 
 256 
 
 1905 . 
 
 1.45 
 
 6.54 
 
 21.6 
 
 42.7 
 
 87.7 
 
 355 
 
 31 + 
 
 279+ 
 
 311 
 
 1906 . 
 
 1.58 
 
 6.81 
 
 21.5 
 
 46.3 
 
 93.2 
 
 375 
 
 34 
 
 315 
 
 349 
 
 1907 . 
 
 1.63 
 
 7.13 
 
 21.3 
 
 45.3 
 
 93.2 
 
 384 
 
 35 
 
 323 
 
 358 
 
 1908 . 
 
 1.62 
 
 6.57 
 
 19.7 
 
 44.8 
 
 90.3 
 
 361 
 
 32 
 
 294 
 
 326 
 
 1909 . 
 
 1.61 
 
 6.68 
 
 21.1 
 
 52.8 
 
 100.0 
 
 387 
 
 34 
 
 353 
 
 387 
 
 1910 . 
 
 1.69 
 
 7.23 
 
 21. 
 
 52.7 
 
 104.0 
 
 399 
 
 34 
 
 381 
 
 415 
 
 1911 . 
 
 1.64 
 
 7.78 
 
 21. 
 
 49.9 
 
 102.2 
 
 413 
 
 34 
 
 388 
 
 422 
 
 1912 . 
 
 1.71 
 
 8.17 
 
 22. 
 
 53.4 
 
 105.3 
 
 450 
 
 38 
 
 436 
 
 474 
 
 This table, combining as it does the virtues of all the 
 independent calculations of M, M', V, V, P, T, with 
 the corrections of each necessary to make it conform to 
 the others, may be considered to give the best available 
 data concerning these magnitudes. 
 
 These figures, or the dotted curves in the preceding 
 diagram, show that money in circulation (M) has nearly
 
 Sec. 8] STATISTICS OF RECENT YEARS 305 
 
 doubled in thirteen years ; that its velocity of circular 
 tion (F) has increased only 10 per cent; that the de- 
 posit currency has nearly tripled and its velocity of 
 circulation (V) has increased 50 per cent; that the 
 volume of trade has doubled; and that prices have risen 
 two thirds. 
 
 These results are not surprising, but are, I believe, just 
 such as we might expect. Nevertheless, almost all are 
 new. The figures for money in circulation (M) are not 
 greatly different from those given in official documents 
 and used by Professor Kemmerer. Likewise the figures 
 for index numbers of prices are based chiefly on, and are 
 very similar to, the index numbers for wholesale prices 
 of the United States Labor Bureau. The statistics for 
 volume of trade are constructed entirely anew and differ 
 somewhat from Kemmerer's, which were their only pre- 
 cursors. The statistics for deposits subject to check 
 (M') are here published for the first time. The statis- 
 tics of velocities of circulation of bank deposits (V) are 
 the first statistics of their kind, excepting the statistics 
 for the activity of bank accounts of European banks. 
 Finally the statistics of velocity of circulation of money 
 (F) are the first of their kind. 
 
 With these data we are able to form a fairly correct 
 statistical picture of the circulatory system in the United 
 States. According to the records of 1909, the money in 
 actual circulation (M) is 1.6 billions of dollars or $18 per 
 capita (much less than the official figure given for circu- 
 lation, $35) ; its velocity of circulation (F) is twenty-one 
 times a year ; the deposit currency (ilf' ) is 6.7 billions or 
 $74 per capita — fourfold that of money ; its velocity of 
 circulation (F'), 53 times a year — two and a half 
 times that of money ; the total circulation of, or pay- 
 ments by, money (MV), 34 billions a year ; the circula-
 
 306 THE PURCHASING POWER OF MONEY [Chap. XII 
 
 tion of deposits subject to check or payments by check 
 (M'V), 353 bilHons — ten times as much or nearly a 
 bilUon a day. This makes a grand total for business 
 done at present prices (MV + M'V or PT) of 387 bil- 
 lions, or more than a billion a day. The size of this 
 aggregate will probably astonish most readers. In the 
 absence of actual statistics we have heretofore little real- 
 ized the colossal proportions of our trade. Probably few 
 persons outside of statisticians would have imagined 
 that our import and export trade, which has filled so 
 large a place in our political vision, sinks into utter insig- 
 nificance as compared with the internal trade of the 
 country. The total exports and imports amount only 
 to a paltry 3 billions as compared with a total national 
 trade of 387 billions. 
 
 We are now ready to represent the entire set of figures 
 given in the last table by means of the mechanical illus- 
 tration adopted in previous chapters. This is done in 
 Figure 17, which shows at a glance the course of all the 
 six magnitudes for fourteen years, making 84 statistical 
 figures in all. This mechanical picture visualizes the 
 increase in prices (lengthening in right arm) which has 
 been going on during these fourteen years, and at the 
 same time exhibits the changes in all the five factors on 
 which that increase of prices depends. All of the six 
 magnitudes represented are, of course, the corrected ones, 
 so as to exactly harmonize with each other and make 
 the two sides of the scales balance. The steady 
 growth of the money in circulation is shown in the in- 
 crease in the size of the hanging purse ; the similar but 
 more rapid growth of deposits subject to check is shown 
 by the increase in the size of the bank book ; the lesser 
 growth in the velocities of these two media of exchange is 
 shown by the lengthening of the two arms at the left
 
 ■^. 
 
 (usually from |^I^,U three to eight billions). 
 
 The leverage of this bank book represents V, the velocity of circulaliao ("activity^ of these deposits The < 
 
 The leverage of this Iray represents P, the inc 
 
 s T, ^e voluma of t 
 (or $1 in 1909, 
 
 r 
 
 ^T 
 
 Eia"" g w'- nr isz 
 
 frf)"""7a' a'o }!ir 
 
 jEIZmsissse!: 
 
 -^i bi'-'/iT 
 
 -*^ a^""a'o yo""Bb"'"Bi»"' 'itjn ;;b ;^ 
 
 jo' ^ ' i I ' o ' ii; ' 'T"i ";k""s""x"" ' s«""x z a ' fe" ' ;x"" 
 
 ■x-^-m, .a ' a}'",i'o'' a^ t ' im 
 
 "T SB 'SS X jK-aj^'-'^ ' ;,J' o'o ■ Jo ' b^n 
 
 ^ 
 
 J & g sa'-iK s-.«;""sti- 
 
 
 :1L 
 
 ""li a, ^t.""ix^' 
 
 'j' °''"> 
 
 ^ M lb' i^i^""'^'-'^' '--j^i^-'-j^^^''' 
 
 ;^. .^.i' fc"'''-X' 
 
 :.h k •jr'n s8 '''X' 
 
 Jb iW '"W ,j,-.-g-i"»g'Ti;;(;iii™|; '^gjT'^ X 
 
 w
 
 Sec. 9] STATISTICS OF RECENT YEARS 307 
 
 of the fulcrum. These four factors have all conspired 
 to increase prices. The only cause resisting the rise is 
 the growth of trade, which is shown by the increasing 
 size of the hanging tray at the right and which has 
 tended to reduce prices. 
 
 We have here a complete quantitative picture of the 
 causes affecting the price level during the last fourteen 
 years, or, at any rate, of all the 'proximate causes; 
 for, as we have noted, back of the five proximate causes 
 lie innumerable antecedent causes. 
 
 What then, in brief, are the facts of history ? They 
 are that prices have increased by about two thirds be- 
 tween 1896 and 1909, that this has been in spite of a 
 doubling in the volume of trade, and because of (1) a 
 doubling of money, (2) a tripling of deposits, and (3 
 and 4) slight increases in the velocities of circulation. 
 
 §9 
 
 There has been much discussion as to the most im- 
 portant causes which have increased prices during re- 
 cent years. It is, therefore, interesting to compare the 
 four proximate causes which, as we have seen, have alone 
 tended to increase prices in the period 1896-1909. Per- 
 haps the simplest and best method is to compare the 
 actual rise of prices with what it would have been if 
 any one cause of that rise had been absent. That is, 
 we test the importance of any price-raising factor by 
 answering the question. What difference does it make 
 to prices whether that factor is present or absent? 
 We shall find that the growth of money is by far the most 
 important cause. The growth of deposits is less impor- 
 tant than appears at first glance. The growth of deposits 
 would have to be regarded as the most important cause 
 if deposits could be considered as independent of money.
 
 308 THE PURCHASING POWER OF MONEY [Chap. XII 
 
 But they are not independent. We have seen that, 
 normally, deposits rise or fall with money in circulation. 
 Therefore, if deposits had increased just as fast as money 
 and no faster, we should ascribe the whole increase to 
 money alone. In that case no part of the rise of prices 
 would be ascribable to any increase in deposits; for 
 there would have been no increase except what was due 
 to the increase in money. The increase of deposits 
 subject to check can be considered independently of the 
 increase of money only in so far as the deposits have 
 increased relatively to money. We have seen that mere 
 increase of money would of itself normally cause a pro- 
 portionate increase of deposits ; only the c^isproportion- 
 ate increase of deposits should therefore be considered 
 apart from the increase in money as a cause of rising 
 prices. Therefore the true method of considering de- 
 posits as a separate cause appears to be to reckon them 
 
 M' 
 
 relatively to money. That is, not M', but -jtt is 
 
 the magnitude to be considered.^ 
 
 We may therefore consider as the only causes tending 
 to raise prices during the period 1896-1909, the follow- 
 ing four : — 
 
 (1) The increase in money in circulation, i.e. the in- 
 crease in M. 
 
 (2) The increase in relative deposits, i.e. the increase 
 . AI' 
 
 M 
 
 (3) The increase in the velocity of circulation of 
 money, i.e. the increase in V. 
 
 (4) The increase in the velocity of circulation of de- 
 posits, i.e. the increase in V. 
 
 1 See § 1 of Appendix to Chapter III, where this magnitude (rela- 
 tive deposits) is treated and represented by the letter k.
 
 Sec. 9] STATISTICS OF KECENT YEARS 309 
 
 The fifth factor determining the price level, viz. 
 the factor T has, as we have seen, tended to lower 
 prices. 
 
 We shall now proceed to note what would be the sepa- 
 rate effects on prices of these four price-raising causes 
 and of the one price-depressing cause. 
 
 We wish, then, to know what the price level would 
 have been in 1909 under the following five conditions : — 
 
 (1) If the money in circulation {M) had not grown 
 at all since 1896, 
 
 M' 
 
 (2) If the relative deposits — had not grown at all 
 
 since 1896, 
 
 (3) If the velocity of circulation of money (F) had 
 not grown at all since 1896, 
 
 (4) If the velocity of circulation of deposits {V) had 
 not grown at all since 1896, 
 
 (5) If the volume of trade {T) had not grown at all 
 since 1896, 
 
 assuming in each case that all the other four factors 
 had grown in exactly the way they did grow. We have 
 taken the actual price level in 1909 as 100 per cent and 
 shall continue to do so, expressing on this basis what 
 the price level would have been under each of the five 
 hypotheses above named. We reach the following 
 results : ^ — 
 
 1 The calculations needed are obvious and simple. They consist 
 of substituting, for all the factors but one in the right side of the 
 
 equation P = — "^ = ^^^ '- — . the statistics already 
 
 obtained for 1909, and for that one factor remaining, the figure for 
 1896. This one factor remaining is, for the first hjrpothesis, M ; 
 for the second, M' / M ; for the third, V ; the fourth, V \ and the 
 fifth T.
 
 310 THE PURCHASING POWER OF MONEY (Chap. XH 
 
 Were it not for the growth of 
 
 (1) Money (M), the price level of 1909 would have 
 been 55 instead of 100; 
 
 (2) Relative deposits [jir], the price level of 1909 
 
 would have been 77 instead of 100; 
 
 (3) Velocity of circulation of money (F), the price 
 level of 1909 would have been 99 instead of 100; 
 
 (4) Velocity of circulation of deposits (F'), the price 
 level of 1909 would have been 72 instead of 100; 
 
 (5) Volume of trade (T), the price level of 1909 would 
 have been 206 instead of 100. 
 
 In other words, were it not for the growth of 
 
 (1) Money (M), prices would have been 45 per cent 
 lower; 
 
 (2) Relative deposits (77- J, prices would have been 
 
 23 per cent lower; 
 
 (3) Velocity of money (V), prices would have been 1 
 per cent lower; 
 
 (4) Velocity of deposits (V), prices would have been 
 28 per cent lower. 
 
 (5) Volume of trade (7^, prices would have been 106 
 per cent higher. 
 
 The four price-raising causes may, therefore, be 
 arranged in the following order of relative impor- 
 tance : — 
 
 Except for the growth of V, prices would have been 
 
 1 per cent lower than they were. 
 
 M' 
 Except for the growth of — -, prices would have been 
 
 23 per cent lower than they were. 
 
 Except for the growth of F', prices would have been 
 28 per cent lower than they were.
 
 Sec. 10] STATISTICS OP RECENT YEARS 311 
 
 Except for the growth of M, prices would have been 
 45 per cent lower than they were. 
 
 We conclude, therefore, that the growth of the velocity 
 of circulation of money was a negligible factor in raising 
 prices ; that the relative growth of deposits and their 
 velocity were large factors ; and that the growth of 
 money was the largest. The importance of the growth 
 of money as a price-raising factor was, according to the 
 above figures, almost exactly double that of relative 
 deposits and a little over 50 per cent greater than that 
 of their velocity of circulation. 
 
 §10 
 
 But the full effect of the increase in the quantity of 
 money is really greater even than these figures indicate ; 
 for we have not included the effect of the overflow of 
 money abroad, caused by the great increase in Ameri- 
 can bank deposits. Evidently this overflow must be 
 taken into account; for the other three price-raising 
 factors, by crowding out money and usurping its place, 
 have given themselves an exaggerated appearance of 
 importance. In other words, there has been a greater 
 increase in money than appears from the United States 
 figures by the amount which has overflowed into foreign 
 lands. The United States is only a small part of the 
 world's market, and its price level is largely determined 
 by the world's price level. Whatever raises prices in 
 one country tends to raise prices in all countries, and in 
 the last analysis the only correct way to measure the 
 relative importance of price-raising causes is to consider 
 the world as a whole. If the statistics we have worked 
 out for the United States were typical of the world, 
 the resulting estimate of the relative importance of the 
 four price-raising causes would be true of the world.
 
 312 THE PURCHASING POWER OF MONEY [Chap. XII 
 
 But there is strong reason to believe that the growth of 
 deposits and of their velocity played a far greater 
 part in raising prices in the United States than anywhere 
 else. The reason is that banking is in its infancy in 
 France and most other countries. It is so unimportant 
 that even if its rate of growth there were prodigious, it 
 would still be a relatively insignificant price-raising 
 factor. We may therefore be certain, humanly speak- 
 ing, that outside of the United States the increase of 
 prices is even more largely due to the growth of money 
 (gold) than in the United States. 
 
 We conclude, therefore, with much confidence, that 
 the increase in the world's gold is chiefly responsible for 
 the increase in the world's prices. What has been said 
 probably explains why, in the last three years, there has 
 been no actual increase in the quantity of money in cir- 
 culation in the United States. It has been crowded out 
 or prevented from increasing by the excessively great 
 increase of our deposits and of their velocity of circula- 
 tion. 
 
 But besides the world movements of prices there are 
 special local movements as well. Anything which in- 
 terferes with trade, like a tariff, tends to make the rise 
 of prices unequal. There remains, therefore, the ques- 
 tion of such special influences on the American price 
 level as the tariff, — working out its effects through M. 
 
 As we have seen in a previous chapter, the effect of en- 
 acting a protective tariff is to raise the price level of 
 the "protected" country by creating temporarily a 
 ''favorable" balance of trade and thus stimulating im- 
 ports of the money metal and discouraging its export. 
 This effect ceases as soon as the price level at home has 
 been elevated enough, relatively to the price levels abroad, 
 to restore the equilibrium of trade and stop the relative
 
 Sec. 10] STATISTICS OF RECENT YEARS 313 
 
 accumulation of gold in the protected country. There- 
 after the tariff ceases to affect the price level, 
 except as it interferes with trade and thereby prevents 
 the price level at home from adjusting itself to the price 
 levels abroad. This interfering effect may be in either 
 direction; that is, the price level at home will be ren- 
 dered more independent of foreign price levels than it 
 would be if trade were free. The tariff merely isolates 
 the protected country. 
 
 During the period under investigation, 1896-1909, 
 there have been two changes in the tariff, that of 1897, 
 and the more recent law of 1909. The first represented 
 an advance over the rates of 1894. This law of 1897 
 must have tended, therefore, somewhat to restrict im- 
 ports and to raise prices. So far as our prices have 
 risen faster than prices have risen in other countries, 
 like England, in the period here considered, it seems 
 fair to attribute a part of this additional rise to our 
 tariff system. 
 
 We come finally to the tariff of 1909. This act is 
 so recent as scarcely yet to have had much perceptible 
 influence, even if that influence be assumed to have 
 begun as soon as the act was planned, early in 1909. 
 There has waged a bitter political controversy over the 
 question whether it was a revision upward or downward. 
 The best unbiased opinion seems to be that it was 
 slightly upward but was chiefly a mere rearrangement 
 by which some duties were raised and others lowered. 
 These conclusions of Professor Taussig, Professor Willis, 
 and others are based on an intensive study of the tariff 
 schedules. 
 
 A review of the statistics of the equation of exchange is 
 entirely consistent with these conclusions. This consist- 
 ency may not be evident at first glance. On the con-
 
 314 THE PURCHASING POWER OF MONEY [Chap. XII 
 
 trary, those who claim that duties have been greatly 
 increased might point to the fact that since the tariff 
 American prices have risen faster than English prices ;* 
 while those who claim that the revision was distinctly 
 downward might point to the increase in our imports of 
 commodities, and the increase in our exports of gold. 
 But these seemingly discordant facts are reconcilable. 
 
 American statistics show that there has been an enor- 
 mous expansion in bank deposits and in their velocity 
 of circulation in 1909 as compared with 1908. This 
 would naturally have the effect of raising American 
 prices, displacing gold, and checking the increase of 
 money in circulation in the United States, which would 
 otherwise occur, and correspondingly of encouraging the 
 import of commodities. The facts agree precisely with 
 these known tendencies. Prices in the United States have 
 risen more than in England, the increase in the quantity 
 of money in circulation has been checked, the export of 
 gold and the import of commodities have been increased. 
 Thus we may explain all the facts without assuming 
 the tariff as a disturbing element.^ 
 
 It would take us too far afield to discuss all the other 
 factors which have been held more or less responsible for 
 the increase in prices. We have already made it clear 
 
 * Beyond 1909 only American figures are available. Those in 
 the Bulletin of the United States Bureau of Labor show an uninter- 
 rupted rise in prices from January, 1909, to March, 1910. Between 
 these dates the index numbers for wholesale prices rose from 124.0 
 to 133.8. For a good English-American comparison, see Report of the 
 (Mass.) Commission on the Cost of Living. Boston, 1910, pp. 26, 56. 
 
 2 But, although we cannot justly convict the tariff of raising our 
 price level in recent years, it is of course true that a reduction in the 
 tariff would tend powerfully to reduce that level ; for, as we have seen, 
 a tariff wall acts like a dam in keeping up the high level accumulated 
 by the original imposition of duties.
 
 Sec. 11] STATISTICS OF RECENT YEARS 315 
 
 that none of these could influence prices except by in- 
 creasing the quantity of money in circulation, the rela- 
 tive deposits, or their velocities, or by decreasing trade. 
 As trade has increased greatly, the last possibility may 
 be ignored. 
 
 As to the causes which have increased money and de- 
 posits and their velocities, the most important seem to 
 be the following : — 
 
 ( 1 ) The chief cause of the increase of money has been the 
 increase in gold mining. Bank notes have only slightly 
 more than kept pace with other money in circulation. 
 
 (2) The chief causes of the relative increase in 
 bank deposits seem to have been those which 
 have extended banking especially in the South. 
 The recent banking laws, encouraging the establish- 
 ment of small banks, may have had some part in this 
 extension. 
 
 (3) The chief cause of the increase of velocity of cir- 
 culation, especially of bank deposits, seems to have been 
 the concentration of population in cities. We have 
 seen that the larger the town the greater the velocity of 
 circulation of bank deposits. 
 
 § 11 
 Throughout this book we have aimed at explaining 
 the general purchasing power of money, not its purchas- 
 ing power over any particular goods or class of goods. 
 The problem of the rise in " the cost of living " is partly 
 a general problem of the purchasing power of money, 
 and partly a special problem of the prices of food, cloth- 
 ing and other costs of " living." With the special 
 problem we have here nothing to do. But it so hap- 
 pens that the special changes in the cost of living are 
 very small as compared with the general change in
 
 316 THE PURCHASING POWER OF MONEY [Chap. XII 
 
 prices. At any rate this is true of the wholesale prices 
 of food. The index number of food rose between Jan- 
 uary, 1909, and March, 1910, from 122.6 to 130.9, while 
 general wholesale prices rose from 124.0 to 133.8; that 
 is, the special prices of food rose about evenly with the 
 general rising tide of prices. So far as there was any 
 difference it was such that the special prices rose slightly 
 less than general prices. The "general prices" here 
 referred to are only wholesale prices and do not include 
 prices of labor and securities; but the inclusion of these 
 elements, judging from the statistics as already given 
 up to 1909, and market reports since that date, would 
 not materially change the result. 
 
 j We conclude that the "rise in the cost of living" is 
 no special movement of food prices nor, presumably, of 
 other particular prices, but is merely a part of the gen- 
 eral movement of prices. The cost of living is swept 
 along with the general rising tide of prices of all sorts. 
 It indicates little or no special change in the supply 
 or demand of special classes of goods, but simply 
 reflects the fall in the general purchasing power of 
 money. These remarks apply not simply to the 
 months beginning w th January, 1909, but back to 
 1908. Back of 1908 food prices move somewhat ir- 
 regularly as compared with general prices, but on the 
 whole maintain an approximately even pace from 1897 
 to 1909. 
 
 The following table gives some interesting by-prod- 
 ucts of our study for the period 1896-1909. 
 
 We note from column (2) that deposits {M') have 
 grown, not only absolutely, but relatively to money 
 (M), changing, from a little over threefold to a little 
 over fourfold the money in circulation. The figure for 
 the panic year, 1907, was the highest but one, and
 
 Sec. Ill 
 
 STATISTICS OF RECENT YEARS 
 
 317 
 
 the drop in the succeeding year was the largest drop 
 in the table. 
 
 Column (3) shows the "virtual" velocity of money, 
 based on the idea that the total work of exchange, even 
 that performed by checks, is really the work, indirectly, 
 of money. It is simply the quotient of the total ex- 
 change work done, divided by the total money in circula- 
 tion and in banks. 
 
 (1) 
 
 (2) 
 
 (3) 
 
 (4) 
 
 (5) 
 
 
 Ml 
 
 M 
 
 Virtual 
 Velocity 
 
 MV 
 
 M'V 
 
 
 MV+M'V 
 
 MV+M'V 
 
 1896 
 
 3.1 
 
 80 
 
 .14 
 
 .86 
 
 1897 
 
 3.2 
 
 84 
 
 .14 
 
 .86 
 
 1898 
 
 3.3 
 
 89 
 
 .13 
 
 .87 
 
 1899 
 
 3.8 
 
 103 
 
 .12 
 
 .88 
 
 1900 
 
 3.6 
 
 99 
 
 .12 
 
 .88 
 
 1901 
 
 4.2 
 
 114 
 
 .11 
 
 .89 
 
 1902 
 
 4.3 
 
 115 
 
 .11 
 
 .89 
 
 1903 
 
 4.1 
 
 113 
 
 .11 
 
 .89 
 
 1904 
 
 4.2 
 
 107 
 
 .11 
 
 .89 
 
 1905 
 
 4.5 
 
 125 
 
 .10 
 
 .90 
 
 1906 
 
 4.3 
 
 132 
 
 .10 
 
 .90 
 
 1907 
 
 4.4 
 
 129 
 
 .10 
 
 .90 
 
 1908 
 
 4.0 
 
 107 
 
 .10 
 
 .90 
 
 1909 
 
 4.1 
 
 124 
 
 .09 
 
 .91 
 
 1910 (see p. 492) . . 
 
 4.4 
 
 134 
 
 .08 
 
 .92 
 
 1911 " " " . . 
 
 4.7 
 
 131 
 
 .08 
 
 .92 
 
 1912 " " " . . 
 
 4.8 
 
 144 
 
 .08 
 
 .92 
 
 We note that this virtual velocity of circulation of 
 monej^, or its efficiency in providing for exchanges, has 
 grown about 50 per cent. Its growth has been inter- 
 rupted by occasional slumps, but all of these were trifling 
 excepting that following the crisis of 1907. 
 
 The fourth and fifth columns give the solution of the 
 much mooted question of the relative importance of 
 check transactions {M'V) and money transactions
 
 318 THE PURCHASING POWER OF MONEY [Chap. XII 
 
 (MV), — a question to which many writers, including 
 Professor Kinley, have given much attention. We find 
 that in 1896 about 14 per cent of the business in the 
 United States was performed by money and in 1909 
 about 9 per cent. In other words, checks performed in 
 1896 about 86 per cent of the total exchange work, and 
 in 1909 about 91 per cent.^ 
 
 These figures appear to afford the first fairly precise 
 determination of the relative importance of check and 
 money transactions. They confirm the belief ^ that the 
 relative part played by checks in the country's trans- 
 actions has substantially increased. The prevailing im- 
 pression that they constitute nine tenths of all transac- 
 tions is also seen to be correct. 
 
 ^ For discussion of these figures, see § 12 of the Appendix to (this) 
 Chapter XII, where comparison is made with Professor Kinley 's 
 results. 
 
 * See e.g. Cannon on Clearing Houses among the Reports of the 
 Monetary Commission, 1910.
 
 CHAPTER XIII 
 
 THE PROBLEM OF MAKING PURCHASING POWER MORE 
 
 STABLE 
 
 §1 
 
 We have seen that the purchasing power of money 
 (or its reciprocal, the level of prices) depends exclu- 
 sively on five factors, viz. : the quantity of money in cir- 
 culation, its velocity of circulation, the quantity of 
 deposits subject to check, its velocity, and the volume 
 of trade. Each of these five magnitudes depends on 
 numerous antecedent causes, but they do not depend 
 on each other except that: — 
 
 (1) Deposits subject to check depend on money in 
 circulation, the two normally varying in unison. 
 
 (2) The velocities of circulation of money and deposits 
 tend to increase with an increase in the volume of trade. 
 
 (3) Any two or more of the five factors may be in- 
 directly related by virtue of being dependent on a com- 
 mon cause or causes. Thus, the same invention may 
 cause an increase in both velocities, or in both money 
 and trade, or in both deposits and their velocity. To 
 take an historical case, we know that the growing 
 density of population has operated to increase all of 
 the five factors. 
 
 (4) During transition periods certain temporary dis- 
 turbances or oscillations occur in all six magnitudes, the 
 extremes of which are crises and depressions. Normally, 
 the price level is an effect and not a cause in the equation 
 
 319
 
 320 THE PURCHASING POWER OF MONEY [Chap. XIII 
 
 of exchange; but during such transition periods its 
 fluctuations temporarily react on the other five factors, 
 and especially on deposits. A rise will thus temporarily 
 generate a further rise, while a fall temporarily operates 
 in the opposite direction. 
 
 The price level, then, is the result of the five great 
 causes mentioned, normally varying directly with the 
 quantity of money (and with deposits which normally 
 vary in unison with the quantity of money), provided 
 that the velocities of circulation and the volume of 
 trade remain unchanged, and that there be a given 
 state of development of deposit banking. This is one 
 of the chief propositions concerning the level of prices 
 or its reciprocal, the purchasing power of money. It 
 constitutes the so-called quantity theory of money. 
 The qualifying adverb " normally"; is inserted in the 
 formulation in order to provide for the transitional 
 periods or credit cycles. Practically, this proposition is 
 an exact law of proportion, as exact and as fundamental 
 in economic science as the exact law of proportion be- 
 tween pressure and density of gases in physics, assum- 
 ing temperature to remain the same. It is, of course? 
 true that, in practice, velocities and trade seldom re- 
 main unchanged, just as it seldom happens that tem- 
 perature remains unchanged. But the tendency repre- 
 sented in the quantity theory remains true, whatever 
 happens to the other elements involved, just as the 
 tendency represented in the density theory remains true 
 whatever happens to temperature. Only those who fail 
 to grasp the significance of what a scientific law really 
 is can fail to see the significance and importance of the 
 quantitative law of money. A scientific law is not a 
 formulation of statistics or of history. It is a formula- 
 tion of what holds true under given conditions. Sta-
 
 Sec. 1] IS THE PRICE LEVEL CONTROLLABLE ? 321 
 
 tistics and history can be used to illustrate and verify 
 laws only by making suitable allowances for changed 
 conditions. It is by making such allowances that we 
 have pursued our study of the last ten centuries in the 
 rough and of the last decade and a half in detail. In 
 each case we found the facts in accord with the princi- 
 ples previously formulated. 
 
 From a practical point of view the most serious prob- 
 lem revealed by this historical and statistical study is 
 the problem of stability and dependability in the pur- 
 chasing power of money. We find that this purchasing 
 power is subject to wide variations in two ways: (1) It 
 oscillates up and down with the transitional periods 
 constituting credit cycles; and (2) it is likely to suffer 
 secular variations in either direction according to the 
 incidents of industrial changes. The first transition is 
 connected with the banking system; the second depends 
 largely upon the money metal. 
 
 One method of mitigating both of these evils is the 
 increase of knowledge as to prospective price levels. 
 As we have seen, the real evils of changing price levels 
 do not lie in these changes per se, but in the fact that 
 they usually take us unawares. It has been shown that 
 to be forewarned is to be forearmed, and that a fore- 
 known change in price levels might be so taken into 
 account in the rate of interest as to neutralize its evils. 
 While we cannot expect our knowledge of the future 
 ever to become so perfect as to reach this ideal, viz. 
 compensations for every price fluctuation by corre- 
 sponding adjustments in the rate of interest — never- 
 theless every increase in our knowledge carries us a 
 little nearer that remote ideal. Fortunately, such in- 
 crease in knowledge is now going on rapidly. The edi- 
 tors of trade journals to-day scan the economic horizon
 
 322 THE PURCHASING POWER OF MONEY [Chap. XIII 
 
 as weather predictors scan the physical horizon; and 
 every indication of a change in the economic weather 
 is noted and commented upon. Within the past year a 
 certain firm has instituted a statistical service to supply 
 bankers, brokers, and merchants with records, or "busi- 
 ness barometers," and forecasts based thereon, with the 
 avowed object of preventing panics. Yet it is probably 
 in regard to the fundamental mechanism by which such 
 forecasts are based that there is the greatest need of a 
 wider diffusion of knowledge. The range of the ordi- 
 nary business man's theoretical knowledge is extremely 
 narrow. He is even apt to be suspicious of such 
 knowledge, if not to hold it in contempt. The conse- 
 quences of this narrowness are often disastrous, as, for 
 instance, when, in pursuance of the advice of New York 
 business men. Secretary Chase issued the greenbacks, or 
 when the ill-advised legislation to close the Gold Room 
 was enacted. And it is not altogether in unusual pre- 
 dicaments such as those brought by the Civil War that 
 the business man's Umitations in knowledge react in- 
 juriously upon him. Every day he is hampered by a 
 lack of understanding of the principles regulating the 
 purchasing power of money; and in proportion as he 
 fails to understand these principles he is apt to fail in 
 predictions. The prejudice of business men against 
 the variability of, and especially against a rise of the 
 rate of interest, probably stands in the way of prompt 
 adjustment in that rate and helps to aggravate the far 
 more harmful variability in the level of prices and its 
 reciprocal, the purchasing power of money. The busi- 
 ness man has, in fact, never regarded it as a part of 
 the preparation for his work to understand the broad 
 principles affecting money and interest. He has rather 
 assumed that his province was confined to accumu-
 
 Sec. 2] IS THE PRICE LEVEL CONTROLLABLE ? 323 
 
 lating a technical acquaintance with the nature of the 
 goods he handles. The sugar merchant informs him- 
 self as to sugar, the grain merchant as to grain, the 
 real estate trader as to real estate. It scarcely occurs 
 to any of them that he needs a knowledge as to gold; 
 yet every bargain into which he enters depends for 
 one of its two terms on gold. I cannot but beUeve 
 that the diffusion among business men of the fuller 
 knowledge of the equation of exchange, of the relation 
 of money to deposits, of credit cycles and of interest, 
 which the future is sure to bring, will pay rich returns 
 in mitigating the evils of crises and depressions which 
 now take them so often unawares. 
 
 §2 
 
 But while there is much to be hoped for from a greater 
 foreknowledge of price changes, a lessening of the price 
 changes themselves would be still more desirable. Va- 
 rious preventives of price changes have been proposed. 
 We shall first consider those which are more particularly 
 applicable to secular price changes, and afterward con- 
 sider those more particularly applicable to the price 
 changes involved in credit cycles. The secular price 
 changes are, as we have seen, chiefly due to changes in 
 money and in trade. There has been for centuries, and 
 promises to be for centuries to come, a race between 
 money and trade. On the results of that race depends to 
 some extent the fate of every business man. The com- 
 mercial world has become more and more committed to 
 the gold standard through a series of historical events 
 having little if any connection with the fitness of that or 
 any other metal to serve as a stable standard. So far as 
 the question of monetary stability is concerned, it is 
 not too much to say that we have hit upon the gold
 
 324 THE PURCHASING POWER OF MONEY [Chap. XIII 
 
 standard by accident just as we hit on the present rail- 
 way gauge by the accident of previous custom as to 
 road carriages ; and just as we hit upon the decimal 
 notation by the accident of having had ten fingers, and 
 quite without reference to the question of numerical 
 convenience in which other systems of numeration 
 would be superior. Now that we have adopted a gold 
 standard, it is almost as difficult to substitute another 
 as it would be to establish the Russian railway gauge 
 or the duodecimal system of numeration. And the 
 fact that the question of a monetary standard ■ is to- 
 day so much an international question makes it all 
 the more difficult. Yet, as Professor Shaler, the geol- 
 ogist, has said, '' It seems likely that we shall, within 
 a few decades, contrive some other means of measur- 
 ing values than by the ancient device of balancing 
 them against a substance of which the supply is ex- 
 cessive." ^ 
 
 I shall not attempt to offer any immediate solution 
 of this great world problem of finding a substitute 
 for gold. Before a substitute for gold can be found, 
 there must be much investigation and education of 
 the public. The object here is to call attention to 
 the necessity for this investigation and education, 
 to examine such solutions as have been already pro- 
 posed and, very tentatively, to make a suggestion which 
 may possibly be acted upon at some future time, 
 when, through the diffusion of knowledge, better statis- 
 tics, and better government, the time shall become 
 ripe. 
 
 One suggestion has been to readopt bimetallism. This 
 has already been discussed in Chapter VII. We were 
 then concerned, however, chiefly with the "mechanics 
 ^ Man and the Earth, New York (Duffield), 1906, p. 62.
 
 Sec. 2] is THE PRICE LEVEL CONTROLLABLE ? 325 
 
 of bimetallism" and not its influence on price levels. 
 We have now to note the claim of advocates of a 
 bimetallic standard that such a standard would tend 
 to steady prices.^ As we have seen, by connecting the 
 currencies of both gold and silver countries, bimet- 
 allism, as long as it continues in working order, has 
 the effect of spreading any variation of one particular 
 metal over the combined area of gold, silver, and bime- 
 tallic countries. If variations occur simultaneously in 
 both metals, they may be in opposite directions, and 
 neutralize each other more or less completely; while, 
 even if they happen to be in the same direction, the 
 combined effect on the whole world united under bi- 
 metallism would be no greater than on the two halves 
 of the world under silver and gold monometallism re- 
 spectively. Even if bimetallism did not enlarge the 
 monetary area, it might reduce monetary fluctuations. 
 Thus a world-wide gold standard might prove more 
 variable than bimetallism.^ But if the amount of one 
 metal used in coinage increases faster or more slowly 
 than business, while the amount of the other maintains 
 a constant ratio to business, then the use of the two 
 metals results in less steadiness than would result from 
 the less variable of the two, though in somewhat more 
 steadiness than would result from the use of the more 
 variable. 
 
 Two variable metals joined through bimetallism 
 may be likened to two tipsy men locking arms. To- 
 gether they walk somewhat more steadily than apart, 
 although if one happens to be much more sober 
 
 * See Jevons, Investigations in Currency and Finance, London 
 (Macmillan), 1884, pp. 331-333. 
 
 *Cf. F. Y. Edgeworth, "Thoughts on Monetary Reform," 
 (British) Economic Journal, September, 1895, p. 449.
 
 326 THE PURCHASING POWER OP MONEY (Chap. XIII 
 
 than the other, his own gait may be made worse by 
 the union. ^ 
 
 The table in the footnote shows that in the seven- 
 teenth and nineteenth centuries the two metals were 
 about equally unsteady. In the eighteenth century 
 gold was the more steady. During the first half of the 
 nineteenth century silver was the more steady, while 
 for 1851-1890 gold was the more steady. Since then, 
 silver has been the more steady. On the whole, there 
 is not much to choose between the behaviors of the two. 
 
 Bimetalhsm, then, even could it be maintained, would 
 offer but an indifferent remedy for the variations in the 
 price level, and, moreover, there is always the objection 
 previously noted that the system may break down. 
 We then saw that whatever the ratio at which both 
 metals are to circulate, one metal is Hkely, sometime, to 
 be produced in such abundance as completely to fill 
 the money reservoir, driving the other metal altogether 
 out of circulation. Such a result may be long in com- 
 ing, but eventually it is practically sure to come. 
 
 1 The variabilities of gold and silver production have been calcu- 
 lated by one of my students, Mr. Morgan Porter. He finds the 
 following mean percentage variations from the mean productions for 
 each period named : — 
 
 
 Gold 
 
 SiLVBH 
 
 1601-1701 5 periods of 20 years each 
 
 1701-1800 5 periods of 20 years each 
 
 1801-1900 5 periods of 20 years each 
 
 % 
 
 7.8 
 15.6 
 69.0 
 
 % 
 
 7.7 
 27.4 
 67.0 
 
 1801-1850 5 periods of 10 years each 
 
 1851-1885 7 periods of 5 years each 
 
 1886-1890 5 periods of 1 year each 
 
 1891-1895 5 periods of 1 year each 
 
 1896-1900 5 periods of 1 year each 
 
 1901-1905 5 periods of 1 year each 
 
 52.4 
 8.1 
 5.9 
 13.3 
 12.3 
 10.7 
 
 22.3 
 
 40.8 
 
 10.5 
 
 6.3 
 
 3.4 
 
 1.9
 
 Sec. 2] IS THE PRICE LEVEL CONTROLLABLE ? 327 
 
 A more important objection remains to be noted. 
 Since bimetallism, as usually proposed, would greatly 
 overvalue one of the two metals, the first great effect 
 of its adoption might be not to steady prices but to 
 disrupt them and upset the relation of debtor and 
 creditor. While the great overvaluation of one metal 
 is not a necessary feature of bimetallism, it has always 
 been the feature which has made it politically popular. 
 Thus, the bimetallism advocated in the United States 
 during the last twenty or thirty years has been a bimet- 
 allism which would grossly overvalue silver. It pro- 
 posed that 16 ounces of silver should circulate as the 
 equivalent of an ounce of gold, when during much of 
 this time it really required 30 or 35 ounces of silver to 
 be equivalent to one of gold. Such an overvaluation 
 of silver would mean that silver would be imported 
 from Mexico, India, China, and other silver countries, 
 as well as mined in larger quantities and coined in the 
 United States, thus depreciating the currency both 
 greatly and suddenly. The proposal was well satirized 
 by a cartoon in the "free silver" campaign of 1896 
 representing the United States as a ship sailing over 
 Niagara Falls in order to reach smooth sailing below 
 the falls, — if only it survive the shock of the fall ! 
 
 Bimetallism is the only scheme of steadying the 
 monetary standard which has ever secured political 
 momentum; and even its popularity lay far less in its 
 potency for ultimately steadying than in its potency 
 for immediately unsteadying the standard. We now 
 pass on to consider schemes which have never reached 
 the stage of practical proposals, but are still wholly 
 academic. 
 
 The first is polymetallism, a generalization of bimet- 
 allism. The theory of bimetallism contemplates the
 
 328 THE PURCHASING POWER OF MONEY [Chap, XIIl 
 
 circulation side by side of two metals; that of poly- 
 metallism looks to the contemporaneous circulation of 
 more than two. So long as several metals could be 
 maintained in circulation together, the price level might 
 fluctuate less than if one metal only were used. But 
 all of the theoretical objections against bimetallism 
 apply also against polymetalhsm. One metal would 
 eventually drive all the others out of a country, or, — 
 if polymetalhsm were international, — into the arts. 
 
 §3 
 
 Recognizing the force of the arguments against bi- 
 metalhsm (and polymetalhsm). Professor Marshall has 
 suggested as a substitute a system which has been called 
 symmetalhsm. Under ttiis scheme — symmetallism — 
 two (or more) metals would be joined together physically 
 in the same coin or in "linked bars." Evidently any 
 ratio could be used, and neither metal could push the 
 other out of circulation. The value of the composite 
 coin would be the sum of the values of its two constit- 
 uents, and the fluctuations in its value would be the 
 mean of the fluctuations of its constituents.^ 
 
 Many other schemes for combining metals have been 
 suggested. Among them are the "joint-metallisms" of 
 Stokes and Hertzka, which are kinds of bimetallism at 
 a variable instead of at a fixed ratio. Another, advo- 
 cated by Walras,^ is the gold standard with a "silver 
 regulator," which is simply the limping standard such 
 as now prevails in the United States, France, or India 
 
 'See F. Y. Edgeworth, "Thoughts on Monetary Reform," 
 (British) Economic Journal, September, 1895, p. 448. 
 
 2 " Monnaie d'or avec billon d'argent regulateiir," Revue de droit 
 international, December, 1884 ; reprinted in Etudes d' Economie 
 politique appliquee, Lausanne (Rouge), 1898, pp. 3-19.
 
 Sec. 3] IS THE PRICE LEVEL CONTROLLABLE ? 329 
 
 except that the quantity of silver in circulation, instead 
 of being fixed, would be systematically manipulated by 
 the government in such a manner as to keep prices 
 steady. But these, like symmetallism and bimetallism, 
 offer a remedy which at best is only partial. For in- 
 stance, in Walras's scheme, in order to maintain prices, 
 the amount of silver might need to be reduced to zero 
 — after which no further regulation would be possible; 
 or it might need to be increased so far as to expel all 
 gold, after which the system would be no longer a gold 
 standard, but would become an inconvertible silver 
 standard. Worst of all, every one of these proposed 
 remedies would be subject to the danger of unwise or 
 dishonest political manipulation. 
 
 It is true that the level of prices might be kept almost 
 absolutely stable merely by honest government regula- 
 tion of the money supply with that specific purpose in 
 view. One seemingly simple way by which this might 
 be attempted would be by the issue of inconvertible 
 paper money in quantities so proportioned to increase 
 of business that the total amount of currency in circu- 
 lation, multiplied by its rapidity, would have the same 
 relation to the total business at one time as at any 
 other time. If the confidence of citizens were pre- 
 served, and this relation were kept, the problem would 
 need no further solution. 
 
 But sad experience teaches that irredeemable paper 
 money, while theoretically capable of steadying prices, 
 is apt in practice to be so manipulated as to pro- 
 duce instability. In nearly every country there exists a 
 party, consisting of debtors and debtor-like classes, 
 which favors depreciation. A movement is therefore 
 at any time possible, tending to pervert any scheme for 
 maintaining stability into a scheme for simple inflation.
 
 330 THE PURCHASING POWER OF MONEY [Chap. XIII 
 
 As soon as any particular government controls a paper 
 currency bearing no relation to gold or silver, excuses 
 for its over-issue are to be feared. 
 
 Even if, in times of peace, these persistent pleas for 
 inflation could be resisted, it is doubtful if they could 
 be resisted in time of war. In time of war many 
 plausible defenses can be given, notably the need of 
 government supphes. The history of our own country 
 in this respect is not reassuring. It is natural, there- 
 fore, that such schemes should have gotten in bad 
 odor. Indeed, their odor has been so bad that many 
 have impulsively concluded that the "quantity theory" 
 which has been appealed to as making possible govern- 
 ment manipulation of prices must be fundamentally 
 unsound. Experience has shown, however, that the 
 evil feared need not always be realized, 
 i Another method by means of which government could 
 theoretically keep the price level more stable is by 
 confining the primary money to a precious metal, say 
 gold, and regulating the quantity of this metal in the 
 currency by means of a system of seigniorage. Thus, 
 as the supply of gold from the mines increased, and 
 gold tended to depreciate in value, the value of gold 
 coin could be kept up by making a continuously higher 
 charge for coinage, in the shape of seigniorage. This 
 charge would become higher as gold bullion became 
 cheaper, in such proportion as to keep the currency in 
 the same relation with the volume of business, and thus 
 to keep the level of prices stable. If, later, the annual 
 production of gold should become very small, and gold, 
 in consequence, should begin to appreciate in value, 
 stability might be maintained by a reversal of this 
 pohcy, i.e. by gradually reducing the seigniorage so 
 as to prevent appreciation of the currency. There
 
 Sec. 3] IS THE PRICE LEVEL CONTROLLABLE ? 331 
 
 would, however, be a Kmit to the power to regulate in 
 this direction similar to the hmit we noted in the case 
 of Walras's scheme. The seigniorage could never be 
 reduced to less than zero. Money can never be ma- 
 terially cheaper than the metal composing it, since the 
 slightest tendency in this direction will result in coin 
 being exported or melted into bullion. In a period of 
 rising prices, regulation would be easy ; in a period of 
 falling prices, regulation might be quite impossible.^ 
 
 Another plan is a convertible paper currency, the 
 paper to be redeemable on demand, — not in any re- 
 quired weight or coin of gold, but in a required pur- 
 chasing power thereof. Under such a plan, the paper 
 money would be redeemed by as much gold as would 
 have the required purchasing power. Thus, the amount 
 of gold obtainable for a paper dollar would vary in- 
 versely with its purchasing power per ounce as com- 
 pared with commodities, the total purchasing power 
 of the dollar being always the same. The fact that a 
 paper dollar would always be redeemable in terms of 
 purchasing power would theoretically keep the level of 
 prices invariable. The supply of money in circulation 
 would regulate itself automatically. Should money 
 tend to increase fast enough to impair its purchasing 
 power, the notes would be presented for redemption 
 in gold; for under the arrangement assumed, the gold 
 
 ^ For the effect of the legal prohibition of exportation see Kem- 
 merer, Money and Credit Instruments in their Relation to General 
 Prices, 2d Edition, New York (Holt), 1909, p. 39 n. Cf. Kemmerer, 
 " The Establishment of the Gold Exchange Standard in the Philip- 
 pines," in the Quarterly Journal of Economics. Vol. XIX, 600-605 
 (August, 1905) ; Second Annual Report of the Chief of the Division 
 of Currency, etc., 14, 15, 21-28; and "A Gold Standard for the 
 Straits," II, in the Political Science Quarterly. Vol. XXI, p. 665-677 
 (December, 1906).
 
 332 THE PURCHASING POWER OF MONEY [Chap. XIII 
 
 which would be given would always have the same 
 purchasing power. Should the money tend to become 
 scarce and thus to appreciate, the amount of gold hav- 
 ing unchanged purchasing power would be exchanged 
 for the notes. 
 
 It is true that this scheme, like a simple paper-money 
 scheme, would be liable to abuse, — but it would have 
 two practical advantages. Having a metallic basis, it 
 would inspire more confidence than a pure paper-money 
 plan, while it would offer less excuse for abuse and less 
 chance to delude the public. Every change in the 
 weight of the gold dollar would be definitely measurable, 
 and would have to be justified to the pubhc. A reduc- 
 tion in weight not fully explained by a fall in prices 
 would be a clear confession of depreciation. 
 
 §4 
 
 The next plan to be considered is that advocated by 
 Professor Marshall and the Committee of the British 
 Association.^ It is, in essence, the revival of the tabu- 
 lar standard proposed and discussed by Lowe,^ Scrope,' 
 Jevons,^ and others; a standard which is relatively in- 
 dependent of special legislation. This involves the 
 passing of a law — first merely permissive — by which 
 contracts could be expressed in terms of an index num- 
 ber. Such a law would not be necessary, but it might 
 serve to draw attention to the index method. The 
 
 ^ See Report of the British Association for the Advancement of 
 Science, 1890, p. 488, containing a draft of a proposed Act of Par- 
 liament for this purpose. 
 
 2 Present State of England in regard to Agriculture, Trade, and 
 Finance. London, 1622. 
 
 ' Principles of Political Economy, London, 1833, p. 406. 
 
 * Investigations in Currency and Finance, London (Macmillan), 
 1884, p. 122 ; also Money and the Mechanism of Exchange, London, 
 (Kegan, Paul), 1893, Ch. XXV.
 
 Sec. 4] is THE PRICE LEVEL CONTROLLABLE ? 333 
 
 money of the country would continue to be used as a 
 medium of exchange and as a measure of value, but 
 not as a standard for all deferred payments. The 
 standard of deferred payments, when advantage was 
 taken of the law, would be the index number of general 
 prices; and contracts involving deferred payment could, 
 when desired, call for the exchange of a given purchas- 
 ing power, or of an amount of money varying directly 
 with the index number. To facilitate such a change, 
 it might be well for the government to inaugurate an 
 authorized system of index numbers, but government 
 action would not have to go farther than this, or in- 
 deed, necessarily, so far. The aim would no longer be 
 to keep the level of prices absolutely stable. Gold or sil- 
 ver or both would furnish the primary money, and their 
 value would consequently fluctuate with that of the con- 
 stituent metal or metals. But the contracts based on 
 index numbers would not be affected because made 
 in terms of the index number. Doubtless the plan 
 would encounter much opposition,^ but it would ap- 
 peal strongly to certain classes.^ For instance, those 
 ''living on their incomes" would like to be guaranteed 
 a stable purchasing power. A widow, or a trustee, 
 or other long-time investor, would prefer to buy bonds 
 which guaranteed a regular yearly purchasing power over 
 subsistence, rather than those which merely promised a 
 given sum of money of uncertain value. A few prece- 
 dents already exist, suggestive, at least, of what the new 
 system would be. In England, the ''tithe averages" 
 have been made to vary with the value of grain, so that 
 the tithe was in effect so much grain, not so much money ; 
 
 1 Cf. Francis Walker, Money, New York (Holt), 1891, pp. 157-163. 
 
 2 See Joseph French Johnson, Money and Currency, Boston 
 (Ginn), 1906, p. 175.
 
 334 THE PURCHASING POWER OP MONEY [Chap. XIII 
 
 also the Scotch fiars prices have existed for more than 
 two centuries for similar purposes, establishing the price 
 of grain on the basis of which rents contracted in grain 
 should be paid in money. ^ 
 
 As has been already indicated, government action 
 looking to this result need not necessarily be i taken. 
 The beginnings of such a plan for "a tabular standard 
 of value" could be made at any time by private con- 
 tracting parties, some index number already in vogue, 
 such as Sauerbeck's or the Bureau of Labor's, being 
 used as a standard. Should the results of such experi- 
 ments, on the whole, satisfy the contracting parties, 
 others might follow their lead. At first contracts 
 would be interpreted as having been made in terms 
 of money except when otherwise provided. A specific 
 proviso would therefore be required in contracts made in 
 terms of the index number. If the latter form of con- 
 tract should become more general, however, legislation 
 could be passed, making the index number the standard 
 in all cases, except where specifically provided that 
 payment should be based on a different standard. 
 
 It is to be noted that such a custom, however general 
 it might become, would not do away with the desir- 
 ability of having an elastic currency to respond to 
 seasonal variations of business. Seasonable readjust- 
 ments of wages, for instance, and of many other prices, 
 are difficult. Custom tends to establish standards hold- 
 ing through successive seasons. Since there is more 
 business at some seasons than others, there will be an 
 element of strain unless there is also an expansion of 
 credit. An elastic banking system, facilitating credit- 
 expansion, would, therefore, remain a desideratum. 
 
 ^ See Edgeworth, Reports of the British Association for the Ad- 
 vancement of Science for 1888, p. 182. .'
 
 Sec. 4] is THE PRICE LEVEL CONTROLLABLE ? 335 
 
 The system of making contracts in terms of the price 
 level is not intended directly to prevent fluctuations 
 in price level. Its purpose is rather to prevent these 
 fluctuations from introducing a speculative element into 
 business. But an incidental result of the system would 
 be that fluctuations in the level of prices would be less 
 than before, because credit cycles would no longer be 
 stimulated. The alternate abnormal encouragement 
 and discouragement of loans would cease. Hence, credit 
 fluctuations would become less, and the level of prices 
 would be comparatively unaffected by them.^ Even if 
 panics should occur, accompanied by sharp falls of prices, 
 they would not be as severe as now. At present, loans 
 must be liquidated in terms of a given amount of money, 
 though that money may buy more (or less) at the time 
 of liquidation than when the loan was contracted, and 
 though the borrower must dispose of more (or less) com- 
 modities to raise the given amount. He is compelled to 
 pay, when prices have fallen, on the same basis in terms 
 of money, and a much higher value in terms of goods, 
 than when prices ranged higher. Hence failure often 
 results, credit currency contracts still further because 
 of the general distrust, and depression becomes more 
 severe. With payment in terms of purchasing power, 
 the situation would be altogether different. Falling 
 prices would neither injure borrowers nor benefit lenders. 
 
 On the whole, the "tabular standard" seems to have 
 real merit.^ Certainly there could be no material harm 
 in trying a "permissive " law. But the tabular standard 
 is subject to serious if not fatal objections : One is the 
 
 ^ See Jevons, Money and the Mechanism of Exchange, London 
 (Kegan Paul), 1893, p. 333. 
 
 2 See J. Allen Smith, " The Multiple Money Standard," Annals oj 
 the American Academy of Political and Social Science. March, 1896.
 
 336 THE PURCHASING POWER OF MONEY [Chap. XIII 
 
 fact that it would involve the trouble of translating 
 money into the tabular standard and would therefore 
 fail to attract the public sufficiently to warrant its com- 
 plete adoption by any government. Another objection 
 is that its halfway adoption would really aggravate 
 many of the evils it sought to correct, and therefore 
 discourage, rather than encourage, its further extension. 
 Even were the system adopted in its complete form for 
 any one country, it would have the disadvantage of 
 isolating that country commercially, and thus reintro- 
 ducing the inconveniences of an uncertain rate of inter- 
 national exchange. An analogous inconvenience would 
 arise by its partial adoption in any one country. Busi- 
 ness men naturally and properly prefer a uniform system 
 of accounts to two systems warring with each other. 
 They would complain of such a double system of ac- 
 counts in exactly the same way, and on exactly the same 
 grounds, as they have always complained of the double 
 system of accounts involved in international trade be- 
 tween gold and silver countries. A business man's 
 profits constitute a narrow margin between receipts and 
 expenses. If receipts and expenses could both be reck- 
 oned in the tabular standard, his profits would be more 
 stable than if both were reckoned in money. But if he 
 should pay some of his expenses, such as interest and 
 wages, on a tabular basis, while his receipts remained 
 on the gold basis, his profits would fluctuate far more 
 than if both sides, or all items of the accounts, were in 
 gold. In fact, his expected profits would often turn into 
 losses by a slight deviation between the two standards, 
 in precisely the same way as the importer or exporter of 
 goods between China and the United States may have 
 his profits wiped out by a slight variation in the ex- 
 change. In either case, he would prefer to have the
 
 Sec. 5] is THE PRICE LEVEL CONTROLLABLE ? 337 
 
 same standard on both sides of the account, even if this 
 standard fluctuated, rather than have two standards, 
 only one of which fluctuated; for his profits depend 
 more on the parallelism between the two sides of his ac- 
 count than on the stability of either. It was to escape 
 the evils from having two standards that, after lengthy 
 debate and experiment, the present gold-exchange stand' 
 ard was adopted in India, the Philippines, Mexico, 
 Straits Settlement, Siam, and Panama. 
 
 §5 
 
 The mention of the gold-exchange standard brings 
 us to the proposal which is here tentatively suggested, — • 
 a proposal M'hich, it is believed, may one day be found 
 both practicable and advisable. This plan involves a 
 combination of the tabular standard with the principles 
 of the gold-exchange standard. 
 
 We have already described briefly the gold-exchange 
 standard, and given references to other and fuller 
 sources of information. While the gold-exchange stand- 
 ard purports to be a system of redemption, or partial 
 redemption in gold of the native coin, yet as a matter 
 of fact, no gold is necessarily required in the country 
 itself where the system is in operation. Thus, the 
 Philippine government does not offer gold for silver 
 pesos, even when gold is wanted for export to New 
 York. Instead, it keeps a reserve of gold in New 
 York, and "redeems" the Filipino's pesos in merely a 
 draft upon this gold. As this draft may be forwarded 
 to New York, it serves the purpose of gold redemption 
 for export. The price of the sale includes a premium 
 on exchange corresponding to the usual excess above 
 the "gold point"; that is, the government charges the 
 Filipino the equivalent of freight, insurance, and other 
 expenses on gold to New York.
 
 338 THE PURCHASING POWER OF MONEY [Chap. XIII 
 
 It will be evident that the gold-exchange system is 
 only nominally a redemption system. In actual fact, 
 it is a system of manipulating the silver currency in such 
 a manner as to prevent its value from diverging from 
 par with gold by more than the usual premiums on 
 exchange between gold countries. This manipulation 
 consists in contracting the currency when the rate of 
 exchange reaches a certain point above par, and ex- 
 panding the currency when it reaches a certain point 
 below par. The contraction of the currency is secured 
 by selling foreign bills of exchange and locking up the 
 currency received therefor, while the expansion of the 
 currency is secured by releasing this currency to circula- 
 tion, or, if necessary, by coining more currency. 
 
 The successful operation of the system is not only 
 compatible with, but actually requires, an overvalua- 
 tion of the metallic content of the silver currency. In 
 fact, in the Philippines it was found necessary to reduce 
 the silver pesos from 374 grains to 247 grains, to prevent 
 their disappearance. Without a margin between the 
 coin-value and the bullion-value of the peso, the power 
 to regulate its circulation would exist only in one direc- 
 tion — contraction; with such a margin, the power 
 exists to expand as well as to contract. 
 
 After once becoming familiar, the system would 
 operate just as successfully if the weight of the silver 
 coins were still further reduced, or, in fact, if a paper 
 currency were substituted instead. It will be seen, 
 therefore, that at bottom the gold-exchange standard is 
 practically the same standard as that which is now in 
 operation for paper currency in Austria. In that 
 country the paper is really irredeemable, but is kept 
 at par by the sale of exchange on London. 
 
 The plan by which the buUion content of the coins
 
 Sec. 51 IS THE PRICE LEVEL CONTROLLABLE? 339 
 
 is kept below their value as coins not only prevents 
 melting and exportation, and the consequent loss of 
 control of their quantity and value, but also has the 
 advantage of economy. The reduction of the weight 
 of the pesos was, in fact, used as a means of defraying 
 the expense of maintaining the gold reserve and the 
 other expenses of inaugurating and operating the 
 system in the Philippines. 
 
 The gold-exchange standard was at first regarded 
 with great suspicion, and its advocates scarcely dared 
 claim for it any better virtue than that of a practical 
 makeshift, affording, as it did, a means of easy transi- 
 tion from the previously existing system to the gold 
 standard, without shock, or introducing an unfamiliar 
 coinage. 
 
 But the results have been so satisfactory that it 
 may well be asked whether those who devised the 
 gold-exchange standard did not build better than they 
 knew. While the system bears a close, though some- 
 what superficial, resemblance to a fiat money system, 
 it has now little or none of the odium or suspicion 
 attached to it which we associate with that name. 
 So simple are the duties of maintaining the gold- 
 exchange par, and so unfailingly has the system been 
 faithfully executed, that even those who at first most 
 strenuously opposed it seem now inclined to trust it 
 implicitly. There is, indeed, no reason why, under 
 almost any conceivable circumstances, there should be 
 €ven the fear of this system being abused. 
 
 Now that there has been actually constituted a new 
 form of governmental machinery, which can be as fully 
 trusted to perform its functions of regulation as the 
 mint, there seems to be no reason why the system 
 should not be extended. It is well known that the par of
 
 340 THE PURCHASING POWER OF MONEY [Chap. XIII 
 
 exchange which has been adopted for the gold-exchange 
 standard is quite arbitrary, and it must be evident that 
 this par could be changed. The par of exchange be- 
 tween the English and Indian system is 16<i. per rupee. 
 This par could be easily changed to 15c?. or 17 d., and 
 gradually changed further in either direction. By such 
 changes of the gold par of exchange, the currency of 
 those countries now having a gold-exchange standard 
 could, if desired, be kept at par with a tabular stand- 
 ard. Thus, when it is found practicable to measure 
 by index numbers the exact shifting of the gold stand- 
 ard, a corresponding shifting of the par of exchange or 
 price of rupees in gold could be effected. 
 
 As the system is now operated, the coinage is manip- 
 ulated to keep it at par with gold, that is, to follow the 
 fluctuations of the gold standard wherever they may 
 lead. We have, therefore, the spectacle of India, and 
 other countries formerly having a silver standard, now 
 clinging to the skirts, as it were, of the gold standard 
 countries, and following that erratic standard where- 
 ever it may lead them, although it is within their power, 
 by exactly the same machinery, to keep their course 
 steady. 
 
 I would not, however, for a moment suggest that these 
 countries should give up their par of exchange with gold 
 standard countries. Although much might be said in 
 favor of such a course, it would, to a large extent, be a 
 step backward by again restoring the uncertainties of 
 international exchange which have been mentioned. 
 What is needed is to induce the entire civilized world 
 to do what is now within the power of the gold-exchange 
 countries to do, viz. to keep pace with a tabular stand- 
 ard. It is a little anomalous that these gold-exchange 
 standard countries now have a power to regulate their
 
 Sec. 5] IS THE PRICE LEVEL CONTROLLABLE ? 341 
 
 price level, which is not possessed by the gold standard 
 countries themselves. The latter are, by their present 
 system, kept absolutely at the mercy of the accidents 
 of gold mining and metallurgy, while the former can 
 keep or change the par of exchange with gold countries 
 at will. 
 
 But evidently the gold countries could do precisely 
 what the silver countries have done, namely, inaugu- 
 rate the system of a gold-exchange standard by closing 
 their mints to gold, reducing, if need be, the weight of 
 gold coins (although with the depreciation now going 
 on in gold, this would probably not be necessary), 
 and operating an exchange standard system in pre- 
 cisely the same way that the Phihppines and the other 
 countries mentioned now operate their gold-exchange 
 system. 
 
 To make this clear we shall suppose, at first, that one 
 country, say Austria, would continue on the gold stand- 
 ard while England, Germany, France, the United States, 
 and the other chief countries of the world should close 
 their mints to the free coinage of gold. They could 
 then maintain a gold-exchange standard with a (vary- 
 ing) par of exchange with Austria. By suitably chang- 
 ing the par of exchange from time to time, the whole 
 commercial world, excepting Austria, could then keep 
 the purchasing power of money stable, instead of allow- 
 ing it to fluctuate with gold. The same relation which 
 India now bears toward England would then be held 
 by both India and England toward Austria. But 
 it would not even be necessary that one country like 
 Austria should hold aloof in commercial isolation. The 
 system, when put in operation, should include all the 
 countries concerned and sufficiently interested to enter 
 into a treaty agreement. Instead of sacrificing its own
 
 342 THE PURCHASING POWER OF MONEY [Chap. XIH 
 
 interests by serving as a gold standard country in 
 terms of which all the other countries of the world 
 should in common adjust their pars of exchange, 
 Austria could itself adjust its currency by buying and 
 selling gold. In other words, precisely the same prin- 
 ciples which regulate the currency of India or the 
 Philippines, by buying and selling exchange on gold 
 abroad, could be operated more directly through buying 
 and selling gold itself at home. Austria might be a 
 good country in which to do this, because it has long 
 operated substantially this system, and by it kept its 
 irredeemable paper money at a fixed par with gold. 
 Should suitable treaty arrangements be effected, 
 Austria might maintain a par, not with a fixed weight 
 of gold, but with such a weight of gold as should have a 
 fixed purchasing power, and could do this by buying 
 and selling gold at these adjusted prices, selling gold 
 bullion for gulden to contract the currency, and buying 
 gold bullion for gulden to expand the currency. All 
 other countries could maintain their par with Austria, 
 or each other, by the methods by which now India 
 maintains its par with England, or, if they chose, by 
 exactly the same process as proposed for Austria. In 
 fact, it is evident that the method of maintaining par 
 by selling exchange on other countries, and by exchang- 
 ing currency directly for some commodity, such as 
 gold, are at bottom much the same thing. 
 
 In order that such an international system should 
 work, we might imagine three separate functions : 
 (1) the function of maintaining an exchange par with 
 the Austrian gulden to be performed by Foreign Ex- 
 change Offices exactly as at present in the Philippines 
 under the gold-exchange system; (2) the similar func- 
 tion of regulating the currency in at least one country,
 
 Sec. 5] IS THE PRICE LEVEL CONTROLLABLE ? 343 
 
 say Austria, by a Bureau of Currency Regulation 
 through buying or selhng gold, at the option of the 
 pubUc, at an official price, changing from time to time 
 according to the decisions of the Statistical Office about 
 to be mentioned; (3) the function of fixing this official 
 price of gold according to the price level. An inter- 
 national Statistical Office at, say. The Hague, could be 
 estabUshed to do this in a purely clerical manner; its 
 duties would consist in ascertaining the index number 
 of prices in the usual way and then dividing the 
 market price of gold by that number. 
 
 For instance, if, a year after the system was started, 
 it were found by the Statistical Office that prices had 
 risen one per cent, this Office would, in order to neutral- 
 ize the rise, issue an official declaration to the Bureau 
 of Currency Regulation fixing the official price of gold 
 at substantially one per cent lower than the ruling 
 market price. At this cheap price the public will buy 
 gold bullion of the government and surrender currency 
 in return. Therefore the currency will be contracted 
 and general prices will fall until no more gold is called 
 for, or until there is declared a new official gold price. 
 Should the next official gold price be set above the 
 market price, the government would become a buyer 
 of gold and would thus reissue some of the currency 
 previously called in, or if need be, issue new currency. 
 
 The plan, as above outlined, fixes a single price of gold 
 at which the government must be ready either to buy 
 or sell. There would be practical advantages, however, 
 in fixing a pair of prices differing slightly from each 
 other, the higher for selling and the lower for buying. 
 The device of a pair of prices was proposed by Ricardo.* 
 
 ^ Proposals for an Economical and Secure Currency, 2d Edition, 
 London (Murray), 1816, p. 26.
 
 344 THE PURCHASING POWER OF MONEY [Chap. XIII 
 
 It is also employed, as we have seen, in the gold-exchange 
 standard to simulate the "gold-points." The Austrian 
 paper currency, although usually called irredeemable, is 
 kept at par with gold by a similar arrangement under 
 which the Austro-Hungarian bank stands ready to buy 
 gold at k. 3, 278 ^ per kilo and to sell gold-exchange on 
 London at a sHghtly higher rate. 
 
 It will be seen that the plan here proposed requires 
 no revolution of the world's currencies. It requires Ut- 
 tle more than to assemble, into one working whole, 
 operations already existing separately, viz. (1) cal- 
 culating Index Numbers as done at present by our 
 Bureau of Labor; (2) buying and selHng exchange, as 
 done at present by the PhiUppine Government; (3) 
 buying and selling gold, as done at present in Austria; 
 (4) periodically readjusting the gold pars as was done 
 at least once when the present system was inaugurated 
 in India, the Philippines, Panama and Mexico. The 
 readjustment of par is the only feature which could be 
 called new, and this should not be condemned as caus- 
 ing fluctuations in values; for its only object is to prevent 
 the fluctuations from which we now suffer. Neither 
 this periodic readjustment nor any other feature of the 
 plan would require changes in the circulating medium. 
 Each nation would continue to use its old familiar cur- 
 rency, whether gold, silver, or paper. The ordinary 
 man would be unaware of any change. 
 
 The cost of maintaining the gold-exchange system has 
 been slight and the cost of maintaining the system here 
 proposed, whatever it might be, could be as nothing 
 compared with the benefits it would render the entire 
 civilized world. 
 
 ^ See L. V. Mises, " The foreign exchange policy of the Austro- 
 Hungarian Bank," Economic Journal, June, 1909, p. 201.
 
 Sec. 5] IS THE PRICE LEVEL CONTROLLABLE ? 345 
 
 One incidental benefit which could easily be secured 
 would be the oft-proposed readjustment of relative 
 values of various coins; for the first adjustment of pars 
 would naturally make the sovereign equivalent to five 
 dollars, the ruble to fifty cents, the Japanese yen to 
 fifty cents, the Dutch florin to forty cents, the mark 
 to twenty-five cents, the franc to twenty cents, the 
 Austrian crown to twenty cents, and the Portuguese 
 crown to ten cents. 
 
 The plan as above outlined contemplates the regu- 
 lation of the world's currencies by buying and selling 
 gold; but of course silver or any other commodity 
 could be used instead. The less variable the commod- 
 ity relatively to commodities in general, the less would 
 be the readjustments needed and the less active the 
 buying or selling of that commodity by the govern- 
 ment. 
 
 The objections which could be urged against this sys- 
 tem are doubtless many, but they do not seem to be as 
 serious as the objections which have already been urged 
 against the adoption of the gold-exchange standard, 
 and which have been satisfactorily answered by the 
 course of events. In fact, there would seem to be no 
 greater danger in trusting Austria, under treaty agree- 
 ment, to maintain her gulden at an ideal par with com- 
 modities in accordance with an index number, than to 
 trust her, as at present, to maintain stable exchange 
 with London, or than to trust the Indian, Mexican, 
 Panama or PhiHppine governments to maintain their 
 overvalued silver at par with gold. The functions in- 
 volved are clerical; the acts required are specific. De- 
 partures from a strict compliance with the law or treaty 
 would be instantly recognized, and would bring upon 
 the culprit wrath and punishment proportionate to the
 
 346 THE PURCHASING POWER OF MONEY [Chap. XIII 
 
 international gravity of the offense. The plan does not 
 require and would not permit any experimental dosing 
 of the circulation dependent on the judgment of an 
 official. The official who regulates does so merely by 
 buying and selling at specific prices fixed by others; 
 and he must buy or sell at the pleasure of the public. 
 He would have no more choice than a broker who is 
 ordered to buy or sell at prices specified by his custom- 
 ers, or than his prototype, the present official in the 
 Phihppines, who now buys or sells foreign exchange. 
 The danger of abuse or fraud in the Statistical Office, 
 the work of which is based on published market prices 
 and is necessarily done in the light of day, would seem 
 negligible. 
 
 Not only would the scheme seem to be entirely free 
 from the possibility of mismanagement by individual 
 officials, but it would seem also to be fully safeguarded 
 against the danger of inflationistic legislation. No in- 
 dividual nation could inflate the currency without 
 withdrawing from the international arrangement and 
 isolating itself accordingly, while it is quite inconceiv- 
 able that all the civilized nations of the world should 
 voluntarily and simultaneously commit the folly of 
 inflationistic legislation. 
 
 But, before any control of the price level be 
 undertaken, the public must learn to realize its neces- 
 sity. So long as the rank and file even of business 
 men fail to realize that they are daily gambling* in 
 changes in the value of money, a fact of which they 
 are blissfully unaware, they will exert no demand for 
 preventing those changes. They are the parties whose 
 interests are chiefly involved, and the first essential 
 step in the reform process is that they shall be made 
 to comprehend the benefits of a stable purchasing
 
 Sec. 6] is THE PRICE LEVEL CONTROLLABLE? 347 
 
 power.^ Until this time arrives, any political proposals 
 will be premature. 
 
 §6 
 
 At the beginning of this chapter we reviewed the 
 principles determining the purchasing power of money 
 and the practical problems involved. We then consid- 
 ered the possible methods of avoiding the evils of varia- 
 bility in purchasing power. Among these, one of the 
 most feasible and important was found to be an increase 
 of knowledge, — both specific knowledge of conditions 
 and general knowledge of principles. Next, the claims 
 of bimetallism and polymetallism as means of maintain- 
 ing a stable level of prices were considered. It was seen 
 that there was no guarantee of keeping two or more 
 metals in circulation indefinitely at an agreed ratio, and 
 it was pointed out that, even could this be done, the 
 gain in stability of prices would be likely to be incon- 
 siderable. The latter objection was brought also 
 against symmetallism — the proposal to have more 
 
 ^ A recent popular pamphlet by A. C. Lake, Currency Reform the 
 Paramount Issue, Memphis (28 N. Front St.), Tenn., proposes to 
 stop the free coinage of gold. As I write, other evidences of the 
 spread beyond academic circles of the idea that gold is an unstable 
 standard come to hand. The rapid rise in the cost of living has of 
 course thrust the subject on the attention of the magazine and news- 
 paper press. Mr. Edison, in a recent interview, predicts the further 
 downfall of gold, through the discovery, — sure to be made sooner 
 or later, — of cheap methods of extracting immense quantities of gold 
 from some Southern clays. He asks the pertinent question : " Is it 
 not absurd to have, as our standard of values, a substance, the only 
 real use of which is to gild picture frames and fill teeth?" Mr. 
 Carnegie, in his last gift of ten millions of dollars to the Carnegie 
 Institution of Washington, stipulates that a certain part of the in- 
 come shall be set aside as a sinking fund against " the diminishing 
 purchasing power of money." This is significant as one of the first 
 cases in which a business man has taken cognizance, in a practical 
 way, of the instability of gold.
 
 348 THE PURCHASING POWER OF MONEY [Chap. XIII 
 
 than one precious metal in each standard coin — as 
 well as against joint metallism, etc. 
 
 Several methods were next considered by which a 
 government might regulate the quantity of money rel- 
 atively to business so as to keep the level of prices con- 
 stant. One such method was to make inconvertible 
 paper the standard money, and to regulate its quantity. 
 Another was to regulate the supply of metallic money 
 by a varying seigniorage charge. Still another was to 
 issue paper money, redeemable on demand, not in fixed 
 amounts of the basic precious metal, but in varying 
 amounts, so calculated as to keep the level of prices 
 unvarying. Lastly was considered the proposal of the 
 writer, — to adopt the gold-exchange standard combined 
 with a tabular standard. 
 
 It was suggested that the first step in this needed 
 reform would be to persuade the public, and especially 
 the business public, to study the problem of monetary 
 stability and to realize that, at present, contracts in 
 money are as truly speculative as the selling of futures, 
 — are, in fact, merely a subdivision of future-selling. 
 
 The necessary education once under way, it will then 
 be time to consider schemes for regulating the purchas- 
 ing power of money in the light of public and economic 
 conditions of the time. All this, however, is in the 
 future. For the present there seems nothing to do 
 but to state the problem and the principles of its 
 solution in the hope that what is now an academic 
 question may, in due course, become a burning issue. 
 
 For a fuller explanation of the above described plan 
 to " standardize the dollar," the reader is referred to 
 pages 494 ff.
 
 APPENDIX TO CHAPTER II 
 
 § 1 (to Chapter II, § 3) 
 
 The Concept of an Average 
 
 The subject of averages or means is so important — both 
 theoretically and practically — and so little upon it is readily 
 available for economic readers that a short statement of its 
 fundamental principles may be fitly inserted here.^ 
 
 There are numerous kinds of averages or means. Among 
 them are the arithmetical, geometrical, and harmonical ; and 
 of each of these there are many different varieties. The 
 simple arithmetical mean of a specific series of terms is found 
 by adding the terms together and dividing by their number. 
 Thus, suppose it is desired to find a mean of 2 and 8. It is 
 
 evidently ^ ~J' ' = — - = 5. This is, as a matter of fact, the 
 
 mean most commonly employed. 
 
 The simple geometrical mean is obtained by multiplying all 
 the terms together and extracting that root of the product 
 which corresponds to the number of terms. Thus, the geo- 
 metrical mean of 2 and 8 is V2 X 8 or 4. 
 
 The simple harmonical mean of any number of terms is 
 the reciprocal of the arithmetical average of their reciprocals. 
 1_ 
 
 For 2 and 8 it is t-t-t or 3^ 
 
 2 
 
 The weighted arithmetical mean is a modification of the 
 simple arithmetical mean. Suppose it is desired to find the 
 mean height of two groups of trees, one tall, the other short. 
 
 ^ For discussion of certain statistical averages, see Dr. Franz 
 Zizek, Die Statistischen Mittelwerte, Leipzig (Duncker & Humblot), 
 1908, in which (p. 2) will be found further references. 
 
 349
 
 350 THE PURCHASING POWER OF MONEY [Append. H 
 
 The tall group is 8 yards high, the short, 2. The simple 
 arithmetical mean as we have seen is 5. But this mean treats 
 both groups as of equal importance. Let us suppose that 
 there are twenty of the two-yard trees and ten of the eight- 
 yard trees, and let us seek a mean of the two heights, such 
 as will give equal importance to each tree. This will give 
 the short group of twenty trees twice the importance of the 
 tall group of ten trees. We shall be giving equal importance 
 to each tree if we take the simple arithmetical mean of the 
 thirty trees. But this simple mean of thirty trees will be a 
 weighted mean of the two groups of trees. It is to be found 
 by adding their heights together (twenty heights of two 
 yards plus ten of eight) and dividing by the number of trees 
 
 (20 + 10). That is, the mean height is 20 X 2 +10X8 ^ . 
 K -r J , 6 20+10 ' 
 
 and this (considered as an average of the two groups instead 
 of that of the thirty trees) is said to be the weighted arith- 
 metical mean of 2 and 8, the 2 being weighted twenty times, 
 and the 8, ten times. The weighted mean of the two groups 
 means the simple mean of the thirty trees. In other words 
 when we " weight " the various terms averaged, we no longer 
 count these terms once each, but we count one term as though 
 it were (say) twenty, and another as though it were (say) 
 ten and the number of times we count a term is its " weight." 
 In the same way we may define the weighted geometrical 
 and weighted harmonical means. Taking the same example 
 of the trees, we find the results to be respectively V22° • 8^° 
 
 °' ^-^^^ ^^^ 20(^) 1 10(1) ^^ 2|. 
 30 
 
 The same results would have been obtained in each case 
 if, instead of the weights 20 and 10, we had taken, as weights, 
 2 and 1. 
 
 Since there are so many different kinds of means, the ques- 
 tion arises, What is the meaning of an average or mean in gen- 
 eral ? We answer : Any mean of a series of terms must be 
 obtainable from them by a mathematical rule such that,
 
 Sec. 1] APPENDIX TO CHAPTER II 351 
 
 when applied to a series of identical terms, it will make their 
 mean identical with each of them. Any rule of averaging is 
 admissible which is consistent with this condition (that the 
 average of identical terms must be identical with each). 
 We know that the simple arithmetical mean A, of a, b, and c 
 
 is A = • It is easy to see that this formula meets 
 
 o 
 
 the required test. Substituting A for each of the three 
 
 n-X-h -I- c A \ A \ A 
 
 magnitudes a, b, and c in ' ' , we obtain — — — — — , 
 
 o o 
 
 which is evidently equal to A ; thus the test is satisfied. 
 
 Again, let G be the geometrical mean of a, b, and c ; so 
 that G=wabc. This formula also conforms to the defini- 
 tion of a mean because G = VGGG. 
 
 Similarly, the harmonical average (which we may call H) 
 
 of a, b, and c'ls H= - — - — j • This also conforms, because 
 a c 
 
 1 + 1 + 1 
 H H H 
 
 3 
 
 For a weighted arithmetical average A to of a, b, c, the 
 
 weights being a /3, y, we have the formula A«, = — \, ~r Y' ^ 
 which conforms to our test, since evidently 
 . _ aAy,-\-(3Ay,-\-yAy, _ 
 
 By applying this general rule, we can make at will in- 
 numerable kinds of averages. It is only necessary to write 
 any formula twice, . once using the terms to be averaged 
 and once using, instead, the required average, and then 
 equate the two. Thus, let us take the complicated formula 
 
 (a + a^ + Ka')(b+j^ 
 
 3^^ • This may be employed to obtain a 
 
 c-f- v6c
 
 it with the similar form .-= • That x as 
 
 ■5/ o 
 
 352 THE PURCHASING POWER OF MONEY [Append. II 
 
 new species of average {x) of a, b, and c, simply by equating 
 
 (x + x^-{-Kx^)(x-\-^^ 
 
 x-{-Vx^ 
 
 determined by this equation will conform to our definition of 
 an average is evident, since substituting x for a, h, and c, 
 the equation becomes a truism, showing that the proposed 
 new average of the identical terms a; is a:. 
 
 A special case of the definition, requiring particular men- 
 tion, is that in which two or more means (not necessarily of 
 the same kind) are related to one another. In order that 
 A should be a mean of ai, 02, as, ••• when we know that B is 
 a mean of 61, 62, bz, ••■ it is only necessary to have a deter- 
 mining formula such that if ai = 02 = Ui ••• and at the same 
 time 61 = 62 = 63 • • • (each of which by hypothesis must be 
 equal to B), then A shall also be equal to each of the magni- 
 tudes Gi, (h, as, etc. Many examples of pairs of means Uke 
 A and B will be given in Chapter X (on the construction of 
 index numbers). The following is a simple example : — 
 
 Let nAB = aybi -\- 0262 + «3&3 H and let B be the arithmeti- 
 cal mean = ^ ^ — (n being the number of terms). 
 n 
 
 Then A is a. (new) sort of mean of ai, a^, as; for, substituting 
 A for ai, 02, as, ••• and B for 61, 62, bs, in the equation nAB 
 — fli&i + •••, the equation is satisfied. 
 
 § 2 (to Chapter II, § 5) 
 
 The Concept of Velocity of Circulation 
 
 The velocity of circulation of money has been defined as a 
 ratio of the money expended to the average money on hand, 
 that is, as a rate of turnover. A rate of turnover differs from 
 the popular concept of velocity. The latter regards velocity 
 as the average number of times money changes hands from 
 one person to another ; whereas, the concept we have em- 
 ployed treats velocity as the average number of coins which
 
 Sec. 21 APPENDIX TO CHAPTER II 353 
 
 pass through one man's hands, divided by the average amount 
 held by him. The difference between the two concepts is 
 very similar to that between two methods of obtaining the 
 velocity of a railway train. One method is to follow the 
 train for a certain number of miles, and note how long a time 
 it takes to travel those miles. The other is to stand on a 
 certain spot beside the track and note the time consumed by 
 a given length of train in passing that spot. Following the 
 train from place to place is like following a coin from person 
 to person, while watching the train pass one point is like ob- 
 serving the rate of turnover of one person's purse. We may 
 distinguish the two methods as the " coin-transfer " method 
 and the '' person-turnover " method. Both methods, if cor- 
 rectly employed, yield the same result. But in the coin-trans- 
 fer method, an important distinction is usually overlooked, 
 the distinction between the gross and net circulation of money. 
 What is desired is the rate at which money is used for pur- 
 chasing goods, not for " making change." The result is the 
 difference between the number of times each piece changes 
 hands against goods, and the number of times it changes 
 hands with goods. If a $10 bill is transferred in purchase of 
 goods and $2 is given back " in change," the actual money 
 expended for goods is measured, not by S12, the gross trans- 
 fer of money, nor yet by $10, the gross amount transferred 
 against goods, but by $8, the net amount paid for goods. 
 
 If it is desired .n the coin-transfer method, to learn the 
 average velocity x circulation of two pieces of money, such 
 as a dollar and a ten-cent piece, we must not only find the 
 net rate of turnover of each coin, but also take account of 
 the discrepancy between the buying efficiencies of the two 
 coins. Let it be assumed that during the year the dollar is 
 passed 115 times against goods and 15 times with goods, so 
 that its net velocity of circulation is 115 — 15 or 100. If we 
 suppose the velocity of the ten-cent piece to be 290 — 90 or 
 200, the average velocity of the two must somehow take 
 account of the different values of different denominations. 
 A dollar is the equivalent of ten dimes. Its rapidity of cir- 
 2a
 
 354 THE PURCHASING POWER OF MONEY [Append. II 
 
 culation should therefore be "weighted" tenfold in order 
 
 to get the real average, that is, the average of the service 
 
 performed by the two. The net rate of circulation of 100 
 
 for the dollar is equivalent to a net velocity of circulation 
 
 of 100 for each and every one of ten dimes. It follows that 
 
 XI 1 •* f +u + . • lOX 100 + 200 
 the average velocity of the two coms is ' , a 
 
 result much closer to the velocity of the dollar than to that 
 of the dime. With these two safeguards against error ap- 
 plied to the coin-transfer method, it is easy to see that the 
 coin-transfer method will yield the same results as the per- 
 son-turnover method.^ 
 
 There is yet another magnitude which should be considered 
 in connection with the velocity of monetary circulation. 
 This may be called the average time of turnover, i.e. the 
 average amount of time consumed by all the given money, 
 in being turned over once. This is the " reciprocal " of 
 velocity. If money changes hands twenty times in a year, 
 it turns over, on the average, once in ^V of a year, or once in 
 somewhat over 18 days. This is its average time of turnover. 
 If the average velocity of circulation or rate of turnover is 
 forty times a year, then the average time of turnover is ^ of 
 a year or about 9 days. Or, instead of considering all the 
 given money directly, let us come at it through a component 
 part of it. If a man having, on the average, $10 in his 
 pocket every day, expends on the average $1 a day, he evi- 
 dently turns over yjj of his money each day. Since to turn 
 over yV of tiis average stock each day is to turn over the 
 whole of it 36|^ times a year or once in 10 days, the time of 
 turnover will be 10 days. If the man under consideration 
 had a pocketbook arranged with a series of ten one dollar 
 bills, and every day, as one was taken from the top to be 
 expended, another were added at the bottom, evidently any 
 and every bill would remain in his hands just ten days 
 traveling from the bottom to the top of the pile. 
 
 * For mathematical statement, see § 5 of this Appendix.
 
 Sec. 3] 
 
 APPENDIX TO CHAPTER II 
 
 355 
 
 § 3 (to Chapter II, § 5) 
 
 *^ Arrays " of p's, Q's, and pQ's 
 Let us assume that the year is divided into an indefinite 
 number of periods, or moments, and distinguish the prices 
 and quantities relating to those successive periods by the 
 subscripts 1, 2, 3, etc., at the left ; and that we are deaUng 
 with a community of an indefinite number of persons, dis- 
 tinguished likewise by subscripts at the right. Thus the 
 quantity of a particular kind of goods purchased by individ- 
 ual No. 1 in moment No. 3 is represented by sQi and the price 
 of the sale by sPi- The entire system of quantities and prices 
 is represented by the two following " arrays." 
 
 
 Pkesons 
 
 Periods 
 
 Total 
 
 Persons 
 
 Periods 
 
 Average 
 
 1 
 
 1 
 
 3... 
 
 1 
 
 2 
 
 
 1 
 
 2 
 3 
 
 l9l 
 
 l93 
 
 2qi 
 
 293 
 
 3?1... 
 392--- 
 3?3-.. 
 
 «3 
 
 1 
 2 
 3 
 
 lP2 
 
 IPs 
 
 2P\ 
 2i)2 
 2^3 
 
 zP\--- 
 
 3P2-- 
 3i>3... 
 
 P\ 
 
 i>2 
 
 Total 
 
 iQ 
 
 2Q 
 
 zQ 
 
 Q 
 
 Average 
 
 \P 
 
 2P 
 
 ZP.: 
 
 P 
 
 
 We have just stated the meaning of the letters inside these 
 arrays. Those outside are as follows : Qi is the total quantity 
 bought by person 1 and is the sum dgi + 2^1 + 3?i + •••) of all 
 quantities purchased by him in all the different periods of time. 
 Like definitions apply to Q2, Qs, etc. iQ is the total quantity 
 purchased in moment 1 and is the sum (151 + 152 + 153+ •••) 
 of all quantities purchased in that moment by all the differ- 
 ent persons. Like definitions apply to 2Q, sQ, ••• Finally 
 Q is (as ah-eady employed in the text) the grand total of quan- 
 tities bought by all persons in all periods of time. Evidently, 
 
 Q = iQ + 2Q-\-zQ-\-"- 
 
 = Ql + (?2 + Q3+ - 
 
 = i^i + 251 + etc. + 152 + 252 + etc. 
 
 + etc.
 
 356 
 
 THE PURCHASING POWER OF MONEY [Append. H 
 
 Like definitions apply to the letters outside the p array, but 
 the relations to the letters inside are here averages instead of 
 sums. We may best derive the form of these averages from 
 a third or intermediate array for -pQ indicating the money 
 values of the purchases. 
 This last named array is 
 
 
 Persons 
 
 Peeiods 
 
 Total 
 
 1 
 
 2 
 
 3 
 
 1 
 
 2 
 3 
 
 \P2 1?2 
 1^3 153 
 
 2Pl2?l 
 2i'2 29-2 
 2i53 2?3 
 
 3 Pi 3?1 
 3^2 3(/2 
 3^3 3^3 
 
 PlQl 
 P2Q2 
 P3Q3 
 
 Total 
 
 iPlQ 
 
 iP 2§ 
 
 zP sQ 
 
 pQ 
 
 
 In this array the same relations must evidently hold as in 
 the Q array. That is, pQ, the entire sum spent on the given 
 commodity by all persons in the community during all periods 
 of the year, must be equal to (1) the sum of the column above 
 it, (2) the sum of the row at its left, and (3) the sum of the 
 interior terms of the array. In other words, it must be equal 
 to (1) the sum of the total yearly amounts spent by the many 
 different persons, (2) the sum of the total amounts spent in 
 the community at the many different periods of the year, and 
 (3) the sum of the purchases of all the individuals in all the 
 periods. 
 
 The nature of the p array is now determined by the Q and 
 the pQ arrays. It must namely be such as to permit the 
 summation just described for the pQ array. That is, each of 
 the average prices (such as pi) must conform to the type of 
 formula: — 
 
 Pi Qi = iPi igi + 2P1 291 + •••, that is 
 
 ^ i??i igi + 2P1 2<7l I ,- 
 _ i??i iQ'i + 27>i 2<7i + •••
 
 Sec. 3] APPENDIX TO CHAPTER II 357 
 
 Hence, p is a weighted average of ipi, 2P1, etc., the weights 
 being i^i, 291, etc. That is, the average price paid by person 
 No. 1 is the weighted arithmetical average of the prices paid 
 by him at different moments through the year, the weights 
 being the quantities bought. The same principle obtains for 
 all other persons. 
 
 Similarly, the average price, ip, may be shown to be 
 
 iViiqi-^iP2iq2+ ••• 
 iQ(= iqi-\-iq2-\ ) 
 
 That is, the average price in period No. 1 is the weighted 
 arithmetical average of all prices paid by different per- 
 sons at moment No. 1, the weights being the quantities 
 bought by each. The same principles obtain at all other 
 moments. 
 
 Finally, the average price, p, in the lower right corner of 
 
 the p array, is either p = >. / 'X ^ 1 , ' — r (that is, p is a 
 
 weighted arithmetical average of pi, p^, etc., the weights 
 being Q\, Q2, etc.) ; or (using the row instead of column), p is 
 the like weighted arithmetical average of ip, 2P, etc., the 
 weights being iQ, 2Q, etc.; or lastly, either of these two ex- 
 pressions for p, combined with the preceding expression for 
 Vh P2, etc., or with that for ip, 2P, etc., may be used to show 
 that p is a weighted arithmetical average of all the p's 
 within the array, the weights being the corresponding q's. In 
 short, the price of each commodity for the year is its aver- 
 age at all times and for all purchases in the year weighted 
 according to the quantities bought. 
 
 This principle covers the method of averaging prices in 
 different localities. Thus the average price of sugar in 1909 
 in the United States is the weighted arithmetical average of 
 all prices of sales by all individuals throughout the United 
 States, and at all moments throughout the year, the weights 
 being the quantities bought. Thus, if there are large local 
 or temporal variations in price, it is important to give chief 
 weight to the largest purchases.
 
 358 THE PURCHASING POWER OF MONEY [Append. II 
 
 What has been said as to Q and p arrays relates only to 
 one commodity. But the same principles apply to each com- 
 modity yielding separate arrays corresponding to each of the 
 total quantities, Q, Q', Q", etc., as well as corresponding to 
 each of the average prices, p, p', p", etc. 
 
 § 4 (to Chapter II, § 5) 
 
 " Arrays " of e's, m's, and Vs 
 
 In the preceding section we have seen that there exists an 
 " array " of p's, pQ's and Q's for each commodity. These 
 relate to the right side of the equation of exchange. Similar 
 arrays relate to the left side. 
 
 If, as before, we assume a community of any number of 
 persons, distinguished respectively by subscripts at the right, 
 and if we divide the year into moments, distinguished by 
 subscripts at the left, we may designate the amount of money 
 expended in the first moment by the first person as iCi, the 
 average amount of money he has on hand at that moment 
 as iWi and his velocity of circulation at that moment (reck- 
 oned at its rate per year) as iFi. The expenditure in the 
 moment being iCi, that moment's rate per annum is iWnei, 
 there being n moments in the year, so that the velocity of 
 
 circulation or rate of turnover per annum, iFi, is n^-^ • A 
 
 similar notation may be used to express the amounts ex- 
 pended and held and the velocity of circulation for each 
 member of the community during each moment of the 
 year as shown in the following three " arrays " (inside the 
 lines). 
 
 In the first table, Ei at the right of the first line is the 
 sum expended by the first person, being the sum of iCi, 
 261, 3C1, • • • in the first line representing the amounts expended 
 by him at successive moments during the year. Likewise, 
 E2 is the sum expended by the second person during the 
 year, and E3 is the sum expended by the third. lE at the foot 
 of the first column is the amount expended by all persons in
 
 Sec. 4J 
 
 APPENDIX TO CHAPTER II 
 
 359 
 
 the first moment ; that is, it is the sum of all the amounts 
 in the column above it ; 2E is likewise the amount expended 
 by all persons in the second moment; 3^, the amount ex- 
 pended in the third, etc. Finally, E, in the lower right-hand 
 corner, is, as employed in the text, the grand total expended 
 by all persons in all moments of the year. Evidently E can 
 be obtained by adding the row to the left of it, or by adding 
 the column above it. It is also the sum of all the elements 
 inside the hnes, i.e. E = 'ZiE = "ZEy = SiCi. 
 
 Amottnt Expended 
 
 Monet on Hand 
 
 Pkbsons 
 
 Periods 
 
 Total 
 
 Persons 
 
 Periods 
 
 AVERAGS 
 
 
 1 
 
 2 
 
 3... 
 
 1 
 
 2 
 
 3 ••• 
 
 
 1 
 
 lei 
 
 2*1 
 
 3C1 ••• 
 
 ^1 
 
 1 
 
 iVfli 
 
 2n»i 
 
 zm-i ■■' 
 
 nil 
 
 2 
 
 1«2 
 
 2«2 
 
 3*2 ••• 
 
 ^2 
 
 2 
 
 lW»2 
 
 2WI2 
 
 3W2 ••• 
 
 »l2 
 
 3 
 
 1*3 
 
 2«S 
 
 3*3 ••• 
 
 Ez 
 
 3 
 
 Ittlz 
 
 2W3 
 
 3«»3 ••• 
 
 TMa 
 
 — 
 
 — 
 
 — 
 
 
 — 
 
 — 
 
 — 
 
 — 
 
 
 — 
 
 Total 
 
 lE 
 
 2-fi 
 
 zE ••• 
 
 E 
 
 Total 
 
 iM 
 
 iM 
 
 sM- 
 
 M 
 
 Velocity of CiRcnLATioN 
 
 Pbbboms 
 
 Periods 
 
 Average 
 
 
 1 
 
 2 
 
 3 
 
 
 1 
 
 2 
 
 3 
 
 imi 
 im2 
 
 1*3 TT 
 
 lW»3 
 
 ^ 2*1 T;r 
 " ^ =2Fl 
 
 2mi 
 
 ^ 2*2 T^ 
 n = 2 K 2 
 2m2 
 
 « 2*3 -p- 
 
 2n»3 
 
 « 3^1 T7- 
 " ^ =8Fl 
 
 8n»i 
 
 « 3*2 TA 
 " »„ =3F2 
 
 3n»2 
 
 " ^ =8F3 
 3WJ3 
 
 nil 
 
 ^=F2 
 
 m-z 
 ^=F, 
 
 Average 
 
 "ri-^ 
 
 ^ 2-^ jr 
 2iH 
 
 „ 3^ T;r 
 
 ^=F 
 
 In the second table, M in the lower right corner is a sum 
 of the average amounts held by the different members of
 
 360 THE PURCHASING POWER OF MONEY [Append. II 
 
 the community during the year, i.e. it is the sum of the 
 elements in the column above it, mi, rrh, W3, etc., each of 
 which is by hypothesis a simple average of the row to its 
 left. 
 
 Or, again, ilf is a simple average of the row to its left, \M, 
 zM, zM, etc., the average amounts of money in the com- 
 munity, in the successive moments of the year, each of which 
 averages is in turn the sum of the column above it, i.e. 
 
 M = 'Xmi = — — . Thus M is both the sum of averages and 
 n 
 
 the average of sums. That the two are equal follows by 
 
 expressing both in terms of the elementary quantities iWi 
 
 by means of the equations 
 
 mx = ^^^+^^^ + ^^^+- ,etc., 
 n 
 
 and the equations iM = imi + 1^2 + 1W3 + •••. It is, of course^ 
 easy also to express M directly in terms of imi, etc., within 
 
 the table. Thus expressed, it is — ^— \ 
 
 n 
 
 The third table (that for velocities) is derived from the 
 other two. As just explained, i7i is the velocity of circula- 
 tion (considered as a per annum rate) for the first person in 
 the community in the first moment. 
 
 There remain to be shown the relations of the elements in 
 the V table. 
 
 Evidently, F = — 
 
 M 
 
 __ Ei-\- E2-\- ••• 
 'mi-\-mz-\- ••• 
 
 ^ miVi-\-nhV2-\- '" Qx 
 
 Wi+m2+ ••• 
 
 Form (1) shows that F is a weighted average of the yearly 
 velocities of the different persons, the velocity of each person 
 being for the entire year and weighted according to his aver- 
 age amount of money on hand.
 
 Sec. 4] APPENDIX TO CHAPTER II 361 
 
 Following an analogous but slightly different sequence, we 
 have 
 
 M 
 
 iM + zAf + - 
 
 n 
 \E -\- oE -\- •" 
 
 — n 
 
 1M + 2M + 
 
 xM{n^]+.M[n^^-\- 
 
 ^ iMiF + 2M2y + 
 1M + 2M+ - 
 
 ("fi)_ 
 
 (2) 
 
 Form (2) shows that V is also the weighted average of the 
 yearly velocities of the successive moments into which the 
 year is divided, the velocity of each moment being for the 
 entire community and weighted according to its average 
 amount of money then in circulation. 
 
 Thus form (1) gives V in terms of the column above it, 
 while form (2) gives V in terms of the row at its left. A 
 formula similar to (1) maybe constructed to express each of 
 the magnitudes \V, 2V, 3V, etc., in terms of the column 
 above it, while a formula similar to (2) may be constructed 
 to express each of the magnitudes Fi, F2, F3, etc., in terms 
 of the row at its left. That is, the velocity in the entire 
 community at any particular moment is a specific form of 
 average of the velocities of different persons at that moment; 
 and the velocity for the entire year of any particular person 
 is a specific form of average of the velocities at different 
 moments for that person. 
 
 Finally, F may be expressed, not only as an average of its
 
 362 THE PURCHASING POWER OF MONEY (Append. II 
 
 column and row as in formula (1) and (2), but also as an 
 average of the magnitudes in the interior of the table. This 
 last result may be obtained in several ways, of which the 
 most direct may briefly be expressed as follows : We know 
 that E is the sum of the interior of the first or E table, that 
 
 is, ^ = Siei; and that M is equal to - SiWi. Hence, we have 
 
 n 
 
 V = — 
 M 
 
 n 
 
 2 
 = n— 
 
 \ xmiJ 
 
 2iWi 
 
 That is, V is the weighted arithmetical average of the yearly 
 velocities pertaining to different persons in different mo- 
 ments, each velocity being weighted by the amount of money 
 on hand in that instance. The mathematical reader will 
 perceive that an alternative treatment would derive the re- 
 sult in terms of an harmonic average. 
 
 § 5 (to Chapter II, § 5) 
 
 The Coin-transfer Concept of Velocity and the Concept of 
 Time of Turnover 
 
 We now turn to the coin-transfer concept of velocity of 
 circulation. To show what kind of an average V is of the 
 velocity of circulation of individual coins, or rather of in- 
 dividual pieces of money in general, let us denote the values 
 of the individual pieces of money circulating in the commu- 
 nity by the letters a,h,c, d, etc., and let us denote the net ve- 
 locity of circulation of these (the number of times exchanged
 
 Sec. 5] APPENDIX TO CHAPTER II 363 
 
 against goods minus the number of times exchanged with 
 goods or " in change ") by h, i, j, k, respectively, etc. Then 
 E, the total amount expended, is denoted by ha -\- ih -\r jc -\- 
 kd-]- •••; and the amount of money, M, in the community 
 is a + 6 + c + d. 
 
 Hence ^ ^ /^g + ^•& + jc + A:rf^+ '- 
 
 M a-\-b + c + d-\- ■■• 
 
 That is, — is a weighted average of the net velocities of cir- 
 culation of the different pieces of money, the velocity of each 
 piece being weighted according to its denomination. But ■—- 
 
 is also V, which we have already seen is the velocity of circu- 
 lation in the person-turnover sense. 
 
 It is clear, therefore, that the coin-transfer method of aver- 
 aging is the same in results as the person-turnover method, 
 if all the pieces of money in the community are included. 
 
 Finally, we come to the concept of '' time of turnover." 
 
 If velocity of circulation is represented as V, then — repre- 
 sents the time of turnover. Similarly, the reciprocals of iV, 
 zV, •••, Vi, V2, •••, iFi, 1V2, •", 2F1, •••, are corresponding times 
 of turnover. Using W for the reciprocal of V and applying 
 the appropriate subscripts, we may write an array of W's 
 analogous to the previous array of F's, and we may show 
 that W is an average of Wi, W2, or of iW, 2W, ••■ or of JVi, 
 
 lW2,-,2Wi, -. 
 
 But these averages are all harmonic averages. To see this, 
 we need only remember that V has already been analyzed ^ 
 as a weighted average of the elementary F's, and that W has 
 been defined as the reciprocal of V. That is, W is the re- 
 ciprocal of this weighted average of elementary F's. But 
 the elementary IF's are reciprocals of the elementary F's. 
 In other words, W is the reciprocal of the weighted arith- 
 metical average of the reciprocals of elementary W's. This 
 
 * In § 4 of this Appendix.
 
 364 THE PURCHASING POWER OF MONEY [Append. II 
 
 makes W, by definition, a weighted harmonic average of 
 these elementary magnitudes. 
 
 § G (to Chapter II, § 5) 
 Algebraic Demonstration of Equation of Exchange 
 
 It is clear that the equation of exchange, MV = ^pQ, is 
 derived from elementary equations expressing the equiva- 
 lence of purchase money and goods bought. The money 
 expended by any particular person at any particular mo- 
 ment is, by the very concept of price, equal to the quanti- 
 ties of all commodities bought in that moment by that 
 person multiphed by the prices, i.e. 
 
 \e\ = ipi iqi + ip'i iq\ + ip'\ iq"i + •-. 
 
 From this equation and others like it, for every person in 
 the community and for every moment in the year, simply 
 by adding them together, we obtain, for the left side of the 
 equation, the sum of the e's which we call E ; and for the 
 right side the sum of all the pq's. We have already seen in 
 the text how the left side, E, may be converted (by multiply- 
 ing and dividing by M) into MV, and we have also just seen 
 (§ 3 of this Appendix) how the sum of all the terms relating to 
 each particular commodity represented on the right side may 
 be converted (by similar simple algebraic operations) into one 
 term of the form pQ so that the whole sum becomes ^pQ. 
 The final result is, therefore, MV = ^pQ. This reasoning 
 constitutes, therefore, a demonstration of the truth of this 
 formula, based on the simple elementary truth that in every 
 exchange the money expended equals the quantity bought 
 multiplied by the price of sale. 
 
 § 7 (to Chapter II, § 5) 
 
 P must be a Specific Form of Average in order to vary 
 directly as M and V and inversely as the Q's 
 
 Let us assume that V and the Q's remain invariable while 
 M changes to Mo and p, p', p", etc., to po, p'o, p"o, etc.
 
 Sec. 6] APPENDIX TO CHAPTER II 365 
 
 (The subscripts '' " refer to a year called the base year 
 other than the original year.) We have for the two years 
 respectively the two equations : — 
 
 Mo7 = poQ + p'oQ'+- 
 
 whence by division, we obtain 
 
 M vQ-\-v'Q'+"- \Po. 
 
 J \VoJ 
 
 Mo PoQ + p'oQ' + - PoQ + p'oQ" + - 
 
 The last expression is evidently a weighted arithmetical 
 
 average of ( — ), f-^l, etc., the weights being poQ, p'oQ\ 
 \PoJ \poJ 
 
 etc. We conclude that, if the velocity of circulation and the 
 
 quantities of goods exchanged remain unaltered, while the 
 
 quantity of money is altered in a given ratio, then prices will 
 
 change in this same ratio " on the average," the average 
 
 being exactly defined as a weighted arithmetical average, in 
 
 which the weights are the values of goods sold, reckoned at 
 
 the prices of the base year. The ratio may evidently also be 
 
 written: — 
 
 M ^ pQ + p'Q'+-' ^ 1 
 
 Mo poQ-\-p'oQ'+- PoQ + p'oQ'+ - 
 
 pQ + p'Q'-h-\ 
 1 
 
 ° (^>o+(^°>'o-+- 
 
 PQ + P'Q'+'- 
 
 which is a weighted harmonic average of ^, -^> etc., in 
 
 Po Po 
 which the weights are pQ, p'Q', etc., that is, the values, not 
 in the base year, but the other year. 
 
 If M and the Q's remain invariable, while V changes from 
 
 V to Vi, evidently the ratio — will be expressed by pre- 
 
 Vi 
 
 cisely the same formulae as above.
 
 366 THE PURCHASING POWER OP MONEY [Append. II 
 
 K the Q's remain invariable, while M and V both change, 
 
 evidently the ratio -z-rTr will be expressed by the same 
 MiVi 
 
 formulae. 
 
 Again the same formulae apply if M and V remain invari- 
 able while the Q's all vary in a given ratio, or if the Q's all 
 vary in a given ratio in combination with any variation in 
 ilf or F or both. In short, the formulae apply perfectly in all 
 cases of variation, except when the Q's vary relatively to each 
 other. 
 
 These formulae, it should be noted, are those later discussed 
 as the formulae numbered (11) in the large table of formulae 
 in the Appendix to Chapter X.
 
 APPENDIX TO CHAPTER III 
 
 § 1 (to Chapter III, § 2) 
 
 ''Arrays" of k's andr's 
 Let k be the ratio of deposits to money in circulation f — j 
 
 which, on the average, the public prefers to keep ; k will then 
 be derivable from the like ratios for the different persons 
 and business firms in the community in the successive mo- 
 ments of the year, and we may, therefore, form an array on 
 the analogy of previous arrays, of the form : — 
 
 
 Pekiods 
 
 
 Pebbons 
 
 
 
 AVKEAGK 
 
 1 
 
 2 
 
 1 
 
 1*1 
 
 2*1 
 
 *1 
 
 2 
 
 1*2 
 
 2*2 
 
 *2 
 
 
 
 
 
 Average 
 
 1* 
 
 2* 
 
 * 
 
 Each letter outside the array is a weighted arithmetical aver- 
 age either of the row to its left or of the column above it. 
 k (in the lower right corner) also is both of these as well as 
 the weighted arithmetical average of all the elements inside 
 the Unes (the weights being in all cases the amounts of money 
 in circulation, which are the denominators of the ratios repre- 
 sented in the arrays). The same proportions hold true if 
 "harmonic" be substituted for "arithmetic" (provided the 
 weights be changed from the denominators to the numerators 
 
 367
 
 368 THE PURCHASING POWER OF MONEY [Append. Ill 
 
 of the ratios, viz. the deposits) . These theorems can be easily 
 
 proved analogously to those in § 7 of the Appendix to Chapter 
 
 M' 
 II, remembering that k = 
 
 Similarly, we may let r stand for the average ratio, for the 
 year, of the reserves of all banks (ft) to their deposits (M'). 
 
 This ratio (r, or -^j is resolvable into an array expressing 
 the ratios for different banks at different moments, viz.: — 
 
 
 Periods 
 
 
 
 
 
 AVEKAQE 
 
 
 1 
 
 2 
 
 1 
 
 iri 
 
 ari 
 
 ri 
 
 2 
 
 1>'2 
 
 2r2 
 
 ri 
 
 
 
 
 
 
 
 
 
 Average 
 
 ir 
 
 2r 
 
 r 
 
 Here each element outside the lines is a weighted arithmetic 
 (or harmonic) average of the terms in the row to its left or 
 the column above it, while r is both of these as well as a 
 weighted arithmetic (or harmonic) average of all the terms 
 inside, the weights being (for the arithmetic average) the 
 deposits in each case or (for the harmonic average) the 
 money in each case. The total currency of the community 
 is /i+ikf +M', although only M + M' is actually in circulation. 
 
 § 2 (to Chapter III, § 4) 
 
 Algebraic Demonstration of Equation of Exchange Including 
 Deposit Currency 
 
 The money expended for goods by individual 1 at moment 
 1 is iCi and his check expenditure is le'i. His total expendi- 
 ture for goods by money and checks is, therefore, iCi + le'i =
 
 Sec. 2] APPENDIX TO CHAPTER III 369 
 
 By adding together all such equations for all persons in 
 the community and all moments of the year, we obtain the 
 equation 
 
 E+E' = %pQ 
 which becomes 
 
 MV -\- M'V = :S,pQ 
 
 since, by definition, V = tt and V = — • 
 
 2s
 
 APPENDIX TO CHAPTER V 
 
 § 1 (to Chapter V, § 5) 
 
 Effect of Time Credit on Equation of Exchange 
 
 It is important to note that, though the system of book 
 credit has a great influence on prices indirectly, it does not 
 enter into the equation of exchange hke circulation or bank 
 credit. We may properly include in the discussion with 
 book credit, those cases of credit where the record of the 
 debt is not simply on the books of one of the two parties, but 
 in which an explicit record exists in the form of a promissory 
 note given by the purchaser to the seller. In either case, 
 goods are bought by a promise to pay at a later time ; in 
 the one case, the promise is exphcit ; in the other, implied. 
 
 Such an exchange of goods against a later payment may 
 be resolved into two successive exchanges. The first occurs 
 at the start when the credit is given for the goods. The pur- 
 chaser then buys goods in exchange for a promise to pay. 
 The second exchange occurs at the close of the transac- 
 tion, when the debt is Uquidated. The original purchaser 
 may then be said to buy back his book credit or promissory 
 note with money. Unlike bank credit, then, time credit 
 does not directly save the use of money. Its immediate effect 
 is simply to postpone ^ that use, since, to eventually extin- 
 guish the credit, as much money or checks must be expended 
 as though cash were paid in the first instance. Dr. Andrew, 
 now Assistant Secretary of the Treasury, points out that if 
 time credit is being contracted faster than it is being ex- 
 
 ' See A. Piatt Andrew, "Credit and the Value of Money," Pro' 
 ceedings Seventeenth Annual Meeting, American Economic Associa- 
 tion, December, 1904. 
 
 370
 
 Sec. 1] APPENDIX TO CHAPTER V 371 
 
 tinguished, prices tend to become higher, but that as soon as 
 the paying of these debts becomes as rapid as the making of 
 them, prices will fall back to their old level.^ The excess of 
 credit contracted over credit extinguished acts just as does 
 so much money or bank deposits offered for goods. 
 
 In order to show how these considerations as to book credit 
 affect the equation of exchange, let us denote the creation of 
 all book credits and other time loans by the letter E", and 
 their extinguishment by the letter E'". The left side of our 
 equation of exchange — or the total of money payments, 
 check payments, and book charges and promissory notes 
 for goods bought in the course of the year — will now be 
 MV -\- M'V -\- E" ; and the right side, including the value 
 of (1) goods bought and (2) debts maturing and extin- 
 guished during the year by payment of money or check, 
 will be represented by 2pQ -\- E'". Transposing for con- 
 venience £"", the equation of exchange may now be written 
 MV + M'7' + E" - E'" = 2pQ. Since E" will be approxi- 
 mately equal to E'", these equal and opposite terms nearly 
 cancel, i.e. E" — E'" becomes zero, and the equation virtually 
 becomes again MV -{- M'V = ^pQ. 
 
 Before leaving the subject it may be noted that book credit 
 tends to increase prices by creating offsetting debts and thus 
 diminishing the volume of trade which must be done by money 
 or checks. Thus, the farmer buys on account at the village 
 store, occasionally selling farm produce there, also on account. 
 The account is balanced at long intervals when the difference 
 only is paid in money.' And, of course, as pointed out in the 
 text of this chapter, book credit tends also to increase 
 velocity.' 
 
 » Andrew, loe. cit. » Ihid, p. 10. ' Chapter V, § 4.
 
 APPENDIX TO CHAPTER VI 
 
 § 1 (to Chapter VI, § 1) 
 
 Modification of Equation of Exchange required by Inter- 
 national Trade 
 
 We have already seen that there are two equations of ex- 
 change, one for purchases, and the other for sales. In a closed 
 community, these two are necessarily identical, for every 
 purchase by one member of the community is a sale by an- 
 other member. But in a community with international trade 
 they will be slightly different. The equation of exchange as 
 developed in this book relates to the expenditure of money 
 for the purchase of goods, and not to the receipt of money 
 for the sale of goods. This equation of exchange at its last 
 stage of elaboration was 
 
 MV + M'V + E" - E'" = -%pQ 
 
 where the letters have the meanings previously given to them, 
 E" relating to the debts contracted in the given period in 
 book accounts and promissory notes used in purchase of 
 goods, and E'" relating to the extinguishment of such debts 
 during the same period. Since MV was developed from E, 
 and M'V from E', this equation may be written as follows: — 
 
 ' E + E' + E"-E"'=^p,Q^ 
 
 where the letters E on the money side of the equations are 
 used to indicate that the money is expended money and the 
 subscripts h on the goods side are used to indicate that the 
 goods are goods bought ; likewise, if the letter R is used to in- 
 dicate received money, and the subscript s to indicate that the 
 
 372
 
 Sec. 1] APPENDIX TO CHAPTER VI 373 
 
 goods are goods sold, the following equation expresses the re- 
 ceipt of money, etc., in exchange for the sale of goods: — 
 
 If there is no external trade, the several magnitudes in these 
 two equations will evidently be identical on each side. If 
 external trade exists, each equation may be resolved into an 
 equation in which are distinguished the home trade and the 
 outside trade. Thus, for the first equation, relating to ex- 
 penditures, the E, E', etc., may be replaced hyH -{-0,11' -\- 0', 
 etc., where the JY's relate to the purchases at home and the 
 O's to money spent outward. On the other side of the equa- 
 tion the SpftQft may be replaced by '^pnQh + "^piQi where the 
 subscripts h relate to the goods purchased at home and the 
 subscripts i to those coming inward. The equation will then 
 become : — 
 
 {H + H'-{- H" - H'") + {0-^0'-\- 0" - 0'") 
 
 which, for brevity, we may write %H + 20 = ^phQh + '^ViQu 
 Similarly, the second equation, relating to sales, may be 
 written : — 
 
 That is, the net sum of the receipts at home (of money, bank 
 credit, and book credit) plus the sum of pa3Tnents for goods 
 coming inward, is equal to the sum of the value of the goods 
 sold at home plus the value of those sent out of the country. 
 The last two equations, one relating to purchases and the 
 other to sales, may be added together so as to give in a com- 
 mon equation the total trade in which the given community 
 is concerned, that is, the total sales and purchases within 
 itself and the sales and purchases with respect to the outside 
 world. The combined equation will be: — 
 
 2 2jy + 20 + 27 = 2 ^pnQn + ^PiQi + SpoQo. 
 
 Here the internal trade is counted twice, because every trans- 
 action occurs both as a sale and as a purchase. This expresses
 
 374 THE PURCHASING POWER OF MONEY [Append. VI 
 
 the equation of exchange for the total trade (domestic and 
 foreign) in which the country under consideration engages. 
 If, instead of adding, we subtract one equation from the 
 other, we obtain the following : — 
 
 20 - 27 = %ViQi - 2poQo 
 
 which is the equation of the balance of trade in its most 
 general form, taking account, as it does, of credit as well as 
 of money. The flow of money, as to or from a nation, depends 
 upon this last equation. 
 
 The right-hand side of the penultimate equation, depends 
 on three sets of prices, — the home prices (the p^'s), the prices 
 of goods which come into the country (the p/s), and the 
 prices of goods which go out (the po's) . 
 
 If, for instance, thep/,'s are extremely high, the consequence 
 will be a stimulus to goods coming in (Qj) and a discouragement 
 to goods going out (Qo), thus tending to make the right side of 
 the last equation large and, therefore, also increasing the left 
 side. In other words, there will be a so-called unfavorable 
 balance of trade and a tendency for media of payments to go 
 out rather than to come in; that is, there will be an outflow of 
 money (indicated by 0) , or a transfer of bank credit to foreigners 
 (0'), or a charging on the books of the foreigners (0")> or a less- 
 ening of the liquidations of previous book accounts {0'") ; or 
 else there will be opposite changes in 7, I', I", 7'"; or finally, 
 a combination of both tendencies, while temporarily there 
 will be fluctuations between these various magnitudes. In 
 the long run and in the last analysis, the changes will relate 
 largely to the actual export and import of money, that is, 
 will concern the unprimed magnitudes and 7. 
 
 For a large country like the United States, the outside 
 trade is so small, compared with the internal trade, as to be 
 negligible. As we shall see in Chapter XII, the foreign 
 trade of the United States is only a fraction of one per cent 
 of the internal trade. And, because the export and import 
 sides of the various magnitudes (O's, 7's, Qo's and Q<'s)
 
 Sec. 1] APPENDIX TO CHAPTER VI 375 
 
 nearly cancel each other, the net balance remaming on either 
 side of the equation of exchange seldom amounts to more 
 than one eighth of one per cent of the internal trade of the 
 United States. 
 
 Almost equally insignificant is the difference, E" — E'", 
 between debts annually contracted and liquidated, if we may 
 judge from estimates of that indebtedness, such as Hohnes's. 
 We are at any rate safe in saying that the corrections to our 
 equation of exchange which have been discussed in this and 
 the previous section are needless complications so far as the 
 United States is concerned. We may therefore consider the 
 equation MV + M'V = 2pQ as practically a precise form of 
 the equation.
 
 APPENDIX TO CHAPTER VII 
 
 § 1 (to Chapter VII, § 2) 
 
 Money Substitutes Unlike Other Substitutes 
 
 Much reasoning has been based upon the assumption that 
 the price determination of two commodities used as money 
 is analogous to that of any other two commodities. It is 
 clear, however, that two forms of money differ from a random 
 pair of commodities in being substitutes.^ Two substitutes 
 proper are regarded by the consumer as a single commodity. 
 This lumping together of the two commodities reduces the 
 number of demand conditions, but does not introduce any 
 indeterminateness into the problem because the missing 
 conditions are at once supplied by a fixed ratio of substitution. 
 Thus, if ten pounds of cane sugar serve the same purpose as 
 eleven pounds of beet-root sugar, their fixed ratio of substitu- 
 tion is ten to eleven ; or if a bushel of India wheat can replace 
 a bushel of Dakota wheat, the substitution ratio is unity. 
 In these cases, the fixed ratio is based on the relative capaci- 
 ties of the two commodities to fill a common need, and is 
 quite antecedent to their prices. Ten pounds of cane sugar 
 can replace eleven pounds of beet-root sugar so long as human 
 taste marks no other ratio. India and Dakota wheat have 
 the same desirability or utility because they have the same 
 relation to man's tastes. No change of market conditions, 
 
 ^ Substitutes merely in the sense of Gresham's Law that the 
 cheaper will be substituted for the dearer. It does not deny that 
 the metals are differently preferred for different monetary uses. 
 We cannot compare gold and silver to independent commodities as 
 "copper and wheat," or "beef and shoes," but only to some other 
 pair of substitutes, or quasi substitutes, such as iron and steel, 
 cotton and wool, oats and maize, molasses and sorghum, cane and 
 beet-root sugar, India and Dakota wheat. 
 
 376
 
 Sec. 1] APPENDIX TO CHAPTER VII 377 
 
 no change of price, could make a consumer regard one bushel 
 of India wheat as equivalent to two of Dakota. The sub- 
 stitution ratio is fixed by nature, and in turn fixes the price 
 ratio. 
 
 In the single case of money, however, there is no fixed 
 ratio of substitution. In one age, ten ounces of silver may 
 circulate as the equivalent of one of gold ; in another, twenty 
 ounces. No human taste or need will interfere. We have 
 here to deal, not with relative sweetening power, nor relative 
 nourishing power, nor with any other capacity to satisfy 
 wants — no capacity inherent in the metals and independent 
 of their prices. We have instead to deal only with relative 
 purchasing power. We do not reckon a utihty in the metal 
 itself, but in the commodities it will buy. We assign their 
 respective desirabilities or utilities to the sugars or the wheats 
 before we know their prices, but we must first inquire the 
 relative circulating value of gold and silver before we can 
 know at what ratio we ourselves prize them. To us the ratio 
 of substitution is identically the price ratio and therefore can 
 have no influence in fixing that ratio. The case of two forms 
 of money is unique. They are substitutes, but have no natural 
 ratio of substitution, dependent on consumers' preferences. 
 
 The foregoing considerations are emphasized for the reason 
 that they are overlooked by those writers who imagine that a 
 fixed legal ratio is merely superimposed upon a system of 
 supply and demand already determinate, and who seek to 
 prove thereby that such a ratio is foredoomed to failure. This 
 is the monometallist's favorite analogy. It is unsound, 
 though its unsoundness does not necessarily involve the un- 
 soundness of the monometalhst's general conclusions. Gold 
 and silver or any other two commodities which serve the 
 purposes of money are not analogous to two ordinary and 
 unrelated articles and are not completely analogous even to 
 two substitutes, because, for two forms of money, there is no 
 consumer's natural ratio of substitution. There seems, 
 therefore, room for an artificial ratio. We shall see, however, 
 that there are limits beyond which an artificial ratio will fail.
 
 378 THE PURCHASING POWER OF MONEY [Append. VII 
 
 § 2 (to Chapter VII, § 2) 
 
 Limits for Ratios within which Bimetallism is Possible 
 
 A change of ratio is represented by a reconstruction of our 
 reservoirs in new units, but we can, without the trouble 
 of such a transformation, exhibit on the mechanism as it 
 stands the limiting ratios between which bimetallism is pos- 
 sible. Suppose the film in Figure 76 to be forced, firstly to 
 its extreme right limit, and secondly to its extreme left, and 
 in each case permanent equilibrium to be attained. In the 
 one case there is a premium on gold, in the other, a premium 
 on silver. These premiums mark the divergences from the 
 given ratio which are possible without destroying bimetallism. 
 Thus suppose the legal ratio and that for which the mecha- 
 nism is constructed is 32 of silver to 1 of gold and that, when 
 the film is moved to the left limit, the level of gold will be be- 
 low 00 a distance ^ as great as the silver level, while at the 
 right limit it will be |. Then the ratio 32 to 1 can be varied 
 between the factors | of 32 to 1 and f of 32 to 1 and bimetal- 
 lism would succeed at any ratio between 32 X i to 1 and 
 32 X I to 1, i.e. between 28 to 1 and 40 to 1. A ratio below 
 28 to 1, such as the famous 16 to 1, would ultimately convert 
 gold monometallism into silver monometallism, but would 
 be inoperative in the opposite direction. A ratio above 40 
 to 1, such as 50 to 1, would ultimately convert silver mono- 
 metallism into gold monometalUsm. A ratio between the 
 two extremes would result in neither sort of monometallism 
 but in bimetallism. The statistical determination of these 
 limits is, of course, a problem which cannot with present 
 knowledge be solved. The figures 28 and 40 are not intended 
 as guesses, but purely as illustrations.
 
 APPENDIX TO CHAPTER VIII 
 
 § 1 (to Chapter VIII, § 6) 
 
 Statistics of Turnover at Yale University 
 
 The rate of turnover of money varies with the amount of 
 money expended at a given level of prices. In other words, it 
 varies with the volume of trade of the individual. The statis- 
 tics of turnover among Yale students form two series, the 
 first or earlier showing an average velocity or rate of turn- 
 over of 34 per year, the second or later, of 66. The differ- 
 ence is probably due in part to the higher expenditure of the 
 second group of students, although it is probably chiefly ac- 
 counted for by the fact that the first series were not ac- 
 curate. Each student in the first series was simply asked 
 to estimate roughly his annual cash expenditure and the 
 average cash on hand. The quotient of the first divided by 
 the second showed his rate of turnover. Estimates were 
 received from 128 men. The average annual expenditure in 
 cash was $514 and the average cash on hand, $15, yielding 
 the quotient 34 times a year as the average rate of turnover. 
 These estimates, being usually little more than guesses, may 
 have been wide of the mark. In order to obtain a more 
 exact estimate the second series was undertaken. The plan 
 was adopted of asking volunteers to keep an exact account 
 for one month of the daily cash expenditures and balances 
 at the beginning and end of each day. It was found from 
 these statistics that for the 113 individuals who contributed 
 these new data, the average annual rate of expenditure was 
 $660 and an average cash on hand was almost exactly $10, 
 giving the quotient 66 times a year. The rougher estimates, 
 the average of which was 34, have so little weight compared 
 with the accurate records, the average of which was 66, that 
 we may place the general average at 60, the nearest round 
 number below 66. Besides the two student series, returns 
 
 379
 
 380 THE PURCHASING POWER OF MONEY [Append. VIII 
 
 were received from five other persons. One was a stenogra- 
 pher who, during a month, spent at the rate of $435 a year 
 and had an average cash balance of $7.86, making her turn- 
 over rate 55 times a year. Another was a young hbrarian 
 whose cash expenditures, kept carefully for six months, 
 showed a rate of $854 a year and whose average cash bal- 
 ance was $10.41, making a rate of 82 times a year. A third 
 was a lawyer who made a practice of paying all bills in cash, 
 and as these amounted to some $4000 a year, he carried in his 
 pocket an average cash balance estimated at $175, This 
 figure he regarded as correct within $15. His velocity of 
 circulation, on the basis of 4000 divided by 175, shows 23 
 times a year. The other two cases were of professors. The 
 first, from careful records, found that he turned over his cash 
 37 times a year and turned over his bank account 52 times a 
 year. The second roughly estimated his rjite of cash turnover 
 at 175 and of bank deposits at 25. 
 
 Of the total 2 46 persons whose records were collected, only 
 116 had kept careful accounts. Of these 116, all except three 
 were students. The reason for believing that the lower veloc- 
 ity of the first series is not wholly accounted for by its being 
 erroneously estimated, but is partly due to the smaller ex- 
 penditures of that group, is based on the fact that we find a 
 distinct relation between amount of expenditure and rate of 
 turnover within each group. Thus, if we separate the 113 
 students who gave careful returns into two groups, one, 
 those who spend less than $50 a month and the other those 
 who spend $50 and over, we find the following figures : — 
 
 Expending less than $600 a 
 year 
 
 Expending $600 and over a 
 year 
 
 No. OF 
 
 Cases 
 
 72 
 41 
 
 Average 
 Annual 
 Rate of 
 Expendi- 
 ture 
 
 i 367 
 1175 
 
 Average 
 
 Cash 
 Balance 
 
 5 8.60 
 12.70 
 
 Vel. op 
 Circu- 
 lation 
 
 43 
 93
 
 Sec. 1] 
 
 APPENDIX TO CHAPTER VIII 
 
 381 
 
 Here we see that the richer men averaged about three times 
 as great an expenditure as the poorer, but carried only 50 
 per cent more cash on hand. In consequence, the velocity 
 of the richer was 93 as against 43 for the poorer, or more than 
 double. The progressive relation between expenditure and 
 rate of turnover may be seen by arranging the 113 cases into 
 five groups according to expenditure. 
 
 No. OF 
 
 Cases 
 
 Average 
 Expendi- 
 ture 
 
 Vel. of 
 Circu- 
 lation 
 
 Expending less than $300 a year 
 Expending over $300 and under 
 
 a year 
 
 Expending over $600 and under $900 
 
 a year 
 
 Expending over $900 and under $1200 
 
 a year 
 
 Expending over $1200 a year . . . 
 
 22 
 50 
 19 
 
 10 
 
 12 
 
 179 
 450 
 
 781 
 
 1012 
 1936 
 
 17 
 
 59 
 
 61 
 
 96 
 137 
 
 The number of cases is small, but the results are uniformly 
 consistent. They show that velocity and expenditure are 
 directly correlated. Even the other series (of rough esti- 
 mates) show the same general relation. Taking the same 
 classifications for expenditure, we find that the velocities are 
 22, 30, 44, 88, 32. Here the only exception is the last figure, 
 which, as it is the average of only five individuals, is an ex- 
 ception of httle importance. We conclude, therefore, with 
 at least a moderate degree of confidence, that for a given 
 price level, the greater the expenditure the higher the rate of 
 turnover. In other words, persons who spend money faster 
 absolutely than others also spend it faster relatively to the 
 amount kept on hand. The amount kept on hand by the 
 rich, though larger absolutely than that kept on hand by 
 the poor, is smaller relatively to the expenditure. 
 
 This law of increasing velocity with increasing expenditure 
 agrees with the general fact that the larger the scale of any 
 business operation, the greater the economy. Small stores 
 have to keep a larger stock relatively to their business than
 
 382 THE PURCHASING POWER OF MONEY [Append. VIII 
 
 larger stores. Likewise, small banks have to keep a larger 
 reserve in proportion to business transacted. Professor 
 Edgeworth has shown a mathematical basis for the fact that 
 the larger the bank, the smaller relatively the reserve needed. 
 Hence, we need not be surprised to find that the small pur- 
 chaser finds it well to keep on hand a relatively larger stock 
 of money than the large purchaser. 
 
 The data are too meager to state any exact quantitative 
 relation between velocity and expenditure. They show that 
 velocity increases as expenditure increases. But beyond 
 this we cannot safely go. The data seem to point to the 
 conclusion, however, that the velocity increases in a smaller 
 ratio than expenditure. 
 
 § 2 (to Chapter VIII, § 8) 
 
 Four Types of Commodities Contrasted 
 
 Let us assume four sorts of commodities which we may, 
 for convenience, designate as wine, sugar, beef, and salt. 
 We shall suppose that a reduction in the respective prices 
 of these will have in each case a different effect on the sale. 
 Accordingly we shall witness four possible effects on the 
 general price level, following a reduction in the price of the 
 four commodities respectively. 
 
 First, wine. This is assumed to be a commodity of such a 
 sort that a reduction in its price will be accompanied by a 
 more than proportionate increase in its sale. Thus the total 
 amount of money expended for wine will be increased. This 
 leaves a less amount with which to buy other commodities. 
 In consequence, the prices of these other commodities, as well 
 as of the wine itself, must fall. 
 
 Next, as to sugar. This is assumed to be such a commodity 
 that a reduction in its price will be accompanied by an 
 exactly proportionate increase in sales ; so that the total 
 money expended upon sugar will be unchanged. Under these 
 circumstances the amount of money to be expended in ex-
 
 Sec. 2] APPENDIX TO CHAPTER VIII 383 
 
 change for other things will be neither increased nor de- 
 creased, and other prices will remain unchanged ; but the 
 general level of prices, including that of sugar itself, will be 
 slightly lowered because the fall of one commodity, when 
 others do not change, must produce some decrease in the 
 average. 
 
 Third, as to beef. This typifies what is called a "neces- 
 sary." We assume that a reduction in its price will be ac- 
 companied by an increase in consumption, but not sufficient 
 to absorb all the money that was previously spent for it. 
 The total expenditure for beef will thus be reduced, and in 
 consequence there will be set free a certain amount of money 
 to be expended for other goods, the prices of which will, 
 therefore, in general, rise slightly. The net effect, however, 
 will be an infinitesimal fall of general prices, including beef ; 
 for to the slight extent that there has been an increase of 
 the total of goods sold by reason of the increase in the sales 
 of beef, without any increase in the total amount of money spent, 
 there must be a fall in the average prices.^ 
 
 Lastly, as to salt. This is assumed to be an "absolute 
 necessary," so that a reduction in its price will not affect the 
 amount sold. The result will be that the general price level 
 will be unaffected, the fall in the price of salt being exactly 
 offset by a compensatory rise in other prices, and the total 
 volume of trade remaining unchanged. 
 
 We see then that the degree of fall in price level due to 
 the fall in a single price may be great or small or nothing at 
 all, according to circumstances. 
 
 In all of the four foregoing illustrations, it was assumed 
 that the fall in the individual price originated in a change in 
 the supply curve or schedule. If the fall in price originates 
 
 ^ The mathematical necessity of this result can be seen from the 
 formulae in the Appendix to Chapter X, where the right side of the 
 equation of exchange is transformed into the product of two factors, 
 the volume of trade (T) and the price level (P). If their product 
 remains the same, an increase in the volume of trade, however small, 
 must cause a decrease in the price level.
 
 384 THE PURCHASING POWER OF MONEY [Append. VIII 
 
 in a change in the demand curve or schedule, there will in 
 general be a rise in other prices and in the general price 
 level, for, there being less of the particular commodity bought 
 and that at a less price, there will be less spent upon it and 
 therefore more on other commodities, the price of which will 
 be higher and, as the reduction in the amount bought of the 
 particular commodity will, in general, imply a reduction in 
 the total volume of trade, the general price level will be 
 raised.^ 
 
 ^See Irving Fisher, "Mathematical Investigations in the Theory 
 of Value and Prices," Transactions of the Connecticut Academy of 
 Arts and Sciences, 1892, p. 51.
 
 APPENDIX TO CHAPTER X 
 
 § 1. Each Form of Index Number for Prices implies a Cor- 
 relative Form of Index Number for Quantities 
 
 We have seen that the number of possible forms of aver- 
 ages is infinite. Since an index number, as Pi, is an average, 
 it follows that there exists an infinite number of possible 
 forms of index numbers. Forty-four of the simplest and 
 most important forms are given in the table which follows. 
 In this table the subscript " i " relates to any specified year 
 called for convenience "year 1," while the subscript "0" 
 likewise relates to " year 0," called the " base " year. The 
 headings of the columns in the table give the formula for 
 the index number. Pi, for the year 1 relatively to the base 
 year 0. By substituting "2" for " 1," each formula could 
 be made to refer to a second year, 2, considered relatively to 
 the base year 0. Likewise, substituting " 3," "4," etc., for 
 " 1," we have an entire series of index numbers. Pi, P2, P3, 
 P4, etc., for different years, all relative to the same base year 
 0. Since the formulae are all aUke and differ only in sub- 
 scripts, it is unnecessary to waste space by expressing P2, 
 P3, etc., in the headings. Consequently, in each column 
 heading, only the formula for Pi is expressed. 
 
 Also to save space, the column headings omit the formulae 
 for Ti, etc., correlative to those for Pi. Each form of price 
 index, Pi, applicable to the equation of exchange, implies a 
 correlative trade index, Ti, such that the product of the two 
 is equal to SpiQi, the right side of the equation of exchange. 
 
 Since PiT^i = %piQi, 
 
 it foUows that Ti = ?^^ 
 Pi 
 
 Hence, given a particular formula for Pi, we have a result- 
 ant and particular formula for Ti. For instance, if Pi is a 
 2 c 385
 
 386 THE PURCHASING POWER OF MONEY [Append. X 
 
 ,(re) 
 
 simple arithmetic average of ^, ^, ^-r^, ••• ~^, i.e. if 
 
 Po Po p p^ ^0 
 
 1 'n 
 
 Pi = - 2— (formula 3 of the table), where n is the num- 
 n po 
 
 ber of commodities of which the price ratios are included, 
 
 then the correlative formula for Ti will evidently be 
 
 rp _ SpiQi _ SpiQi 
 
 * Pi 1 2Pi" 
 
 n po 
 
 Again, if Pi is the geometric average \/— * ^ " ^-rr '" ^-r^ 
 
 ^Po Po p p%i 
 
 (formula 7 of the table), then Ti has the correlative form 
 
 "/pTTpT 
 
 ^Po p'o 
 
 Conversely any particular formula for Ti implies a correl- 
 ative particular formula for Pi. For, since 
 
 PiTi = SpiQi, 
 it follows that p _ SpiQi 
 
 By means of this equation, if we have given any particu- 
 lar formula for Ti, we may obtain a resultant particular 
 formula for Pi. 
 
 The examples already given of Pi (the arithmetical and geo- 
 metric average) illustrate how to obtain the correlative formula 
 for Ti. If we work backward from these somewhat compli- 
 cated formulae for Ti, we may in turn derive as the correla- 
 tive formulae for Pi the arithmetic and geometric averages. 
 
 As a third example illustrating the derivation of the 
 formula for Pi from a given formula for Ti, let Ti be 
 defined as SpoQi," then 
 
 ' Ti SpoQi' 
 (Formula 11 of the table.)
 
 Sec. 11 APPENDIX TO CHAPTER X 387 
 
 We may consider, then, that each column heading, though 
 stating only the formula for Pi, implies also a corresponding 
 formula for Ti ; that is, Pi and Ti occur in correlative pairs. 
 Pi and Ti are such that if one of them (say Pi) is given 
 independently of the equation, SpiQi = PiTi, the other is 
 then defined by means of that equation. 
 
 The two magnitudes Pi and Ti are not, however, abso- 
 lutely symmetrical. There is this important distinction 
 between them: that, while Pi is an abstract number, Ti is 
 concrete, being expressible in dollars and cents. 
 
 It thus appears that, although the p's and Q's enter sym- 
 metrically into the expression SpiQi, yet, when this expression 
 is replaced by PiTi, the first factor, Pi, represents the p's in 
 a somewhat different manner from that in which the second 
 factor, Ti, represents the Q's. Pi is a pure number, an aver- 
 age of pure numbers — the ratios the p's bear to the base 
 
 prices, po's, whereas Ti, being -^~' is a concrete number, 
 
 Pi 
 
 being a value found by dividing the value ^piQi by the 
 pure number Pi. 
 
 Thus, while the p's and Q's occur symmetrically in the 
 original formula 2piQi, the process by which we convert 
 2piQi into PiTi treats them asymmetrically. But evidently 
 we can reverse the asymmetry in their treatment; for, in- 
 stead of putting SpiQi equal to PiTi, we may put it equal to 
 AiQi, in which ^i is now a quantity index, that is, an average 
 of the ratios which the Qi's bear to the Qo's or base quanti- 
 ties (i.e. an average of ^^ • Mr * ^77 •" ), and Ai, being 
 \ Qo Q Q J 
 
 therefore -£^, is the "aggregate price," that is, the value 
 
 found by dividing the value SpiQi by the pure number Qi. 
 Here, if the form of Qi is given independently of the equa- 
 tion SpiQi = ^4.1^, the form of Ai is defined by means of this 
 equation, and conversely. 
 
 Thus we may convert SpiQi into either PiTi or AiQi. In 
 the first, the p's are represented by a ratio. Pi ; in the second,
 
 388 THE PURCHASING POWER OF MONEY [Append. X 
 
 by a value, Ai; in the first, the Q's are represented by a value, 
 Ti ; in the second, by a ratio, ^i. The asymmetry of each of 
 the two formulae PiTi and AiQi is the reverse of the other. 
 
 Finally we may, if we wish, treat both the p's and Q's 
 alike by putting SpiQi equal to ('^poQo)PiQi, where Pi and Qi 
 are, both of them, index numbers for the pi's and Qi's 
 respectively. That is (as we shall prove). Pi and ^i are 
 
 averages respectively of price ratios like ^' and of quantity 
 
 Po 
 
 ratios like ^- The equation ^piQi= {^poQo)PiQi may be 
 
 said to define either one of the two averages (Pi and ^i) in 
 terms of the other. One or the other must be defined irre- 
 spective of the equation. 
 
 Thus there are three ways of resolving ^piQi, as follows : — • 
 
 MQi = PiTi = AiQi = (2poQo)Pi(?i. 
 
 The third form becomes, dividing the equation through by 
 ^PoQo, 
 
 We wish now to prove that if either Pi or Qi is first de- 
 termined in any way conformably to the definition of an 
 average, leaving the other to be determined by the above 
 equation, then the latter also necessarily conforms to the 
 definition of an average. We have to prove that if Qi is 
 
 O O' 
 taken as an average of ^, xr"*' ^^^n the correlative ex- 
 
 pression for Pi derived from (1), viz.: — 
 
 is an average of ^,^'". It is, therefore, only necessary to 
 Po p 
 
 show (in accordance with the most general definition of an
 
 Sec. 11 APPENDIX TO CHAPTER X 389 
 
 average as given in the Appendix to Chapter II) that ex- 
 pression (2) shall be equal to k when 
 
 Po p'o 
 (and when at the same time 
 
 Qo Q'o / 
 
 We therefore suppose that 
 
 Pl-P'i = J. 
 
 — —J. — Kf 
 
 Po Po 
 so that pi = kpo ; p\ = kp'o', ••• ; 
 
 and also that ^ = ir = - = ^'» 
 
 Qo Q 
 
 so that Qi = k'Qo; Q\ = k'Q\; -. 
 
 Then SpiQi = 2(fcpo X k'Q^) = kk' ^poQo. 
 
 Now, since ^^^=""^^'» 
 
 it follows that (av. ^, ^,..-) = k' 
 \ Qo Q / 
 
 by the definition of an average. 
 
 Hence the expression (2) may now be written 
 
 kk' SpoQo 
 
 which is evidently equal to k. 
 
 Therefore expression (2) is, by definition, an average of 
 
 2l, 2j...^ By the same reasoning we may show conversely 
 Po Po 
 
 2poQo 
 
 that 
 
 fAv. 21, HJ...^ 
 
 V Po Po J 
 
 is a true average of ^S ^•••- We conclude that if either
 
 390 THE PURCHASING POWER OF MONET [Append. X 
 
 Pi or Oi in the formula PiQi = -z^— is an average of the p or 
 
 SpoQo 
 
 Q ratios respectively, then the other is also an average re- 
 spectively of the Q or p ratios. 
 
 § 2. Index Numbers for Prices occur in Antithetical Pairs as 
 also do Index Numbers for Quantities 
 
 We have seen that, given any special form of average for 
 Pi, there results therefrom a correlative form for ^i and vice 
 
 versa. Thus if Pi is the simple arithmetical average - 2^> 
 
 n po 
 SpiQi 
 
 then Q\ is . Again, if we start with Qi as the simple 
 
 n po 
 
 arithmetical average - 2 ^ then we discover in its correlate 
 n Qo 
 
 SpiQi 
 
 a new formula for Pi, viz. ° . In this way any given 
 
 n Qo 
 formula for Pi leads to another formula for Pi which may be 
 called its antithesis. This second formula for Pi is identical 
 in form with the formula for ^i correlative to the first for- 
 mula for Pi, dififering merely in the fact that the pi's and Qi's 
 are interchanged. 
 
 The four forms and their relations are best seen by placing 
 them in a square, as in the following example : — 
 
 221 SpiQi 
 
 Pi = -^ antithetical to Pi = ^^ 
 
 correlative to correlative to 
 
 SpiQi ^Qi 
 
 ^1 = ^ antithetical to Pi = -^- 
 
 l^Pi n 
 
 n Po
 
 Sec. 2] APPENDIX TO CHAPTER X 391 
 
 The pair of formulae in the left vertical column express 
 correlative formulae, one for Pi and the other for Qi. The 
 formula diagonally opposite each of these has the p's and 
 Q's interchanged. The right pair thus formed are evidently 
 also correlates of each other and each is the antithesis of that 
 in the same horizontal line at its left. Since any formula 
 for Pi involves an antithetical formula for Pi, we have here 
 a means of devising new formulae from old and also of noting 
 certain unsuspected relationships between formulae already 
 in use. 
 
 In the table of index numbers for Pi which follows, the 
 antithetical formulae are in each case placed side by side 
 and joined by a bracket. The two together represent, in 
 each case, the upper half of a square like the above. The 
 omitted lower half, giving the correlative forms for ^i, can 
 be readily suppUed in every case; but, to save space, each 
 column heading in the table only includes the formula for 
 Pi, omitting its correlate for ^i as well as the corresponding 
 formulae for Ti and Ai. The formula for ^i is, as above 
 explained, easily written by interchanging p's and Q's in the 
 formula given in the neighboring (antithetical) columns; 
 that for Ti is found by dividing SpiQi by Pi; that for Ai by 
 dividing SpiQi by ^i. Practically Pi and Ai serve the same 
 purpose, namely, that of indicating price changes; likewise 
 Qi and Ti serve the same purpose, namely, that of indicating 
 quantity changes. For any series of years the numbers for 
 Pi and for Ai will be proportional, the only difference being 
 that Pi is expressed in percentages, the figure for the base year 
 being 100 per cent, whereas Ai is expressed in dollars, the fig- 
 ure for the base year being the actual exchanges 2poQo in 
 that year. Likewise Qi and Ti differ merely as percentage 
 and dollar measurements, the base figure being 100 per cent 
 and SpoQo dollars respectively.
 
 d92 THE PURCHASING POWER OF MONEY [Append. X 
 
 § 3. General Meanings of p's and Q's 
 
 We may here pause to point out that the whole present 
 discussion relates purely to the form of an index number of 
 p's and Q's without reference to the meaning to be assigned 
 to these p's and Q's. These meanings may be far wider 
 than simply the prices and quantities in the equation of 
 exchange. For example, an index number of prices may be 
 constructed with reference to the purchasing power of a 
 workman's wages. In this case, the same formula as be- 
 fore, 2piQi, may be employed, but the terms have different 
 meanings. The p's now relate to the prices of goods enter- 
 ing into the workmen's budgets, and the Q's to the quantities 
 of workmen's goods entering into their consumption. In this 
 case, the price index, P, indicates the price level of work- 
 men's consumption, and the index, T, means an index for 
 workmen's real-wages. Any special form of price index now 
 implies a correlative special form of real-wages index. 
 
 Again, if we are studying statistics of capital such as in 
 Giffen's Growth of Capital, we have 2pQ as the value of capi- 
 tal, the p's being the prices of different forms of capital and 
 the Q's, their quantities. For every special form of price 
 index number, P, representing the price level of capital, 
 there will be a correlative special index of capital showing 
 the real "growth of capital" as distinct from its mere money 
 value. Such an index seems seldom to have been employed.^ 
 Yet it is evidently advisable to distinguish between an ap- 
 parent increase of capital due to inflated prices and a real 
 increase, as would be shown by such an index as here 
 suggested. 
 
 * See Giffen, Growth of Capital, London (George Bell and Sons), 
 1889, pp. 50-54, where allowance is made for changes in the price 
 level. Index numbers of the Economist, of Sauerbeck, and of 
 Soetbeer are cited. Professor J. S. Nicholson has advocated such 
 a capital-standard in the Journal of the Royal Statistical Association, 
 March, 1887, pp. 152 ff. This method is discussed by Edgeworth, 
 Report of the British Association, 1887, p. 276.
 
 Sec. 3] APPENDIX TO CHAPTER X 393 
 
 We see, therefore, that wherever prices and quantities are 
 united, we have the requisite conditions for constructing 
 correlative pairs of index numbers, one index in each pair 
 relating to prices, and the other to quantities. 
 
 We shall, however, for convenience, continue to employ 
 the magnitude 7", rather than Q, and to refer to it as a 
 "trade" index. 
 
 § 4. Review of 44 Formulce, heading the Table Columns 
 
 We shall now briefly review the formulae of the table of 
 selected index numbers. Each even-numbered formula is 
 best regarded as derivable from the odd-numbered formula 
 at its left as its antithesis. The odd formulae are those con- 
 structed directly for the p's without reference to any average 
 for the Q's; the even are constructed indirectly by refer- 
 ence to some average first assumed for the Q's. The latter 
 are what Walsh had in mind under the name of " double 
 weighting." 
 
 Formula (1) is simply the ratio of the sums of prices. It 
 may also be considered as the ratio of the averages of prices 
 in the two years considered, as is evident by writing it, — 
 
 — -, where n is the number of commodities employed. 
 n 
 
 This formula was used by Dutot in 1738,^ and has been 
 used recently by Bradstreet,^ who applied it practically. 
 
 Although it is a ratio of average prices, it may also be 
 thrown into the form of a weighted arithmetical average of 
 
 the price ratios, ^, ^, ^, etc., as the following transfor- 
 Po Po p 
 
 mation shows : — 
 
 1 See Walsh, Measurement of General Exchange Value, New York 
 (Macmillan), 1901, pp. 534, 553. 
 * BradstreeV s Journal from 1895.
 
 + 
 
 394 THE PURCHASING POWER OF MONEY [Append. X 
 
 Spi ^ pi + p'l + p''i + — 
 2po Po + p'o + p"o+ ••• 
 
 Po + p'o + p"o+ ••• 
 
 The formula in this last form is evidently the weighted arith- 
 metical average of the ratios in parenthesis, the weights be- 
 ing the prices po, p'o, p"o, ••• of the year 0. A change in 
 the units of quantity for the various goods would change 
 these prices; thus a change from ounces to pounds would 
 multiply the number expressing price by sixteen. Such a 
 change in any price, such as po, would entirely change the 
 relative importance of the " weights," po, p'o, etc. Conse- 
 quently this system of weighting is, as Walsh says, quite 
 accidental or haphazard.^ 
 
 The same formula is also a harmonic average, as the follow- 
 ing transformations show : — 
 
 2pl 
 
 Spo 
 
 _P1 + P'l+ 
 
 Po + p'o + 
 
 Pl + P 
 
 'l+ 
 
 
 
 ' P'©+P' 
 
 'fp' 
 
 V 
 
 1 
 
 0.1... 
 
 
 ~<f>^' 
 
 <^^ 
 
 ")- - 
 
 Pl + p'l+ ••• 
 
 The last expression is evidently the reciprocal of a weighted 
 arithmetical average of the price ratios in parenthesis. But 
 
 these price ratios are the reciprocals of (— )> (/)> ( /T )> ^*^' 
 In other] words, the formula is the reciprocal of a weighted 
 * Walsh, op. cit., pp. 81 and 82.
 
 Sec. 41 APPENDIX TO CHAPTER X 395 
 
 arithmetical average of the reciprocals of the ratios — , etc. 
 
 It is therefore the weighted harmonic average of these ratios 
 
 — , etc., the weights being pi, p/, etc., or the prices of the 
 Po 
 
 year 1. 
 
 In short, formula (1) is both an arithmetical and a har- 
 monic average of ^, ^\ etc., the weights being, in the first 
 Po p 
 
 case, the terms of the denominator, and in the second, those 
 of the numerator. 
 
 We have seen that formula (1) in the table, although 
 primarily a ratio of averages of prices, may be also con- 
 sidered as an average of ratios of prices with arbitrary 
 weighting. 
 
 Conversely we may, if we choose, regard every average of 
 ratios as a ratio of averages by assuming arbitrary units for 
 measuring commodities. It is evident that, if the unit of 
 measure is increased in any ratio, the number expressing 
 the price is decreased in the inverse ratio. If, therefore, we 
 change the unit of measure of a commodity the price of 
 which is at first expressed by pi by dividing by the ratio po, 
 
 this price becomes ^. Thus ^ may be considered to be a 
 Po Po 
 
 price as well as a price ratio. Hence an average of ^, ^, ^, 
 
 Po Po p 
 
 etc., may be regarded as an average of prices. The new 
 
 units, instead of being pounds, yards, etc., are dollars-worth-in- 
 
 the-hase-year. With these units, the price in the base year is 
 
 unity, for dividing the price, po, in the original units by the 
 
 factor Po, we obtain unity. 
 
 Hereafter, however, we shall treat all index numbers as 
 averages of price ratios. 
 
 It is interesting to note that the antithesis of Dutot's or 
 Bradstreet's formula (No. 2), found by dividing the frac- 
 
 tioJi -^^ by the correlative formula for Qi, viz., -^, turns 
 SpoQo 2^0
 
 396 THE PURCHASING POWER OF MONEY [Append. X 
 
 out to be that advocated by Drobisch,^ and earlier by Sir 
 Rawson-Rawson . "^ 
 
 Formula (3)' is evidently the familiar simple arithmetical 
 average, — 
 
 ^W or Po^P^o^ ^Vr' 
 
 Formula (4), the antithesis of formula (3), gives, as the 
 average price ratio, the ratio of total values SpiQi / SpoQo 
 corrected for change in the Q's by division by the arith- 
 metical average ratio of the Q's. 
 
 Hereafter the even-numbered formulae, being antitheses of 
 the preceding odd formulae, will be passed over unless there 
 is, in any case, special reason for mention. 
 
 ^ See M. W. Drobisch, "Ueber Mittelgrossen und die Anwend- 
 barkeit derselben auf die Bereehnung des Steigens und Sinkens des 
 Geldwerthes " (Berichte liber die Verhandlungen der Koniglich sdchs- 
 ischen Gesellschaft der Wissenschaften zu Leipsig ; Mathematisch- 
 physische Classe, Band XXIII, 1871, pp. 25-48). Also " Ueber die 
 Bereehnung der Veranderungen der Waarenpreise und des Geld- 
 werthes " (Jahrbiicher fur N ational-oekonomie und Statistik, 1871, 
 Band XVI, pp. 143-156) ; and " Ueber einige Einwiirfe gegen die in 
 diesen Jahrbiichern veroffentlichte neue Methode, die Verander- 
 ungen der Waarenpreise und des Geldwerthes zu berechnen '* 
 (ibid., 1871, Band XVI, pp. 416-427). See also Walsh, op. ciL, 
 pp. 97-99, where the method is explained. 
 
 2 See Edgeworth, Report of the British Association for the Ad- 
 vancement of Science, 1889, p. 152. Sir Rawson-Rawson' s sug- 
 gestion, as developed by Edgeworth, was to divide the value of 
 exports (or imports) by the tonnage of exports (or imports) and 
 consider the result as an index number of prices of exports (or im- 
 ports). The suggestion was made not for any theoretical virtues, 
 but because of the practical ease of computation. Edgeworth 
 compares the results of Rawson's rough and ready method with the 
 more exact method of Giffen by actual figures for 1886 compared 
 with 1885, and finds substantial agreement. 
 
 " For a statement of the history of this formula from Carli to the 
 present, see Walsh, op. cit., p. 534.
 
 Sec. 4] APPENDIX TO CHAPTER X 397 
 
 Formulae (5), (7)\ and (9)^ are respectively the simple 
 harmonic, simple geometric, and simple median averages. 
 We note that the antithesis of (7), viz. (8), is one proposed by 
 Nicholson and Walsh .^ 
 
 Formula (11)* resembles Bradstreet's, except that the in- 
 troduction of the Q's as multipliers prevents the weighting 
 from being arbitrary ; for the weights poQi, etc., unlike the 
 weights po, etc., are uninfluenced by a change in the units 
 of measurement for commodities. Whether an article be 
 measured in pounds or ounces will not affect the value of a 
 given amount of it. The following transformations show 
 that the formula is a weighted arithmetic mean : — 
 
 ^PiQ^ _ PiQi + p'^Q\+ ••• 
 SpoQi PoQi-\-p'oQ'i+ '•• 
 
 + 
 
 The last expression is evidently a weighted arithmetic 
 average of the price ratios in the parentheses, the weights 
 being poQi, p'oQ'i, etc., i.e. the values of the quantities in the 
 year 1 reckoned at the prices of year 0. 
 
 But the same formula is also a harmonic average, as may 
 be seen by transforming the denominator instead of the 
 numerator as was done for formula (1). It is a weighted 
 harmonic average, the weights being piQi, p\Q'i, etc., or the 
 values in the year 1. 
 
 In short, formula (11) or —^ is, like formula (1), both a 
 
 SpoQi 
 
 weighted arithmetical and a weighted harmonic average of 
 
 ^ See Jevons, Investigations in Currency and Finance, London 
 (Maemillan), 1884 ; Edgeworth, Reports British Association, 1887, 8, 
 9; Walsh, op. cit., pp. 229 ff. 
 
 2 See Edgeworth, Reports British Association, 1887, 8, 9, esp. 
 1888, pp. 206 ff. 
 
 ' Walsh, op. cit., p. 548. 
 
 * For Formulae 11 and 12 there exists a large literature. See 
 Walsh, op. cit., esp, pp. 191 ff., and pp. 539 ff.
 
 398 THE PURCHASING POWER OF MONEY [Append, X 
 
 ^> / > ^> 6tc., but the weights are different in the two 
 Po Po p 
 
 cases. 
 
 (11) has the interesting property that its antithesis (12) is 
 of the same form except that the subscripts for Q are now 
 in place of 1. Similar reasoning shows that this formula (12) 
 is also both an arithmetical and an harmonic average, weighted 
 according to the terms in its denominator and numerator 
 respectively. 
 
 These two formulae, (11) and (12), seem to be the favorites 
 among writers on Index Numbers. Since the shortcomings 
 of one are, in some cases, not shortcomings of the other, there 
 have been many attempts to combine them into some com- 
 posite. No. (13),^ for instance, is their simple arithmetical 
 average. The antithesis of (13), viz. (14), turns out to be the 
 simple harmonic average of (11) and (12). Number (15) is the 
 simple geometric average of (11) and (12). This formula (15) 
 has the distinction of being identical with its own antithesis 
 (16). Numbers (17), (19), (21), and (23) are other attempts 
 at combining (11) and (12), not by averaging them, as was 
 the case with (13) and (15), but by averaging their coefficients, 
 viz., Qi and Qq, Q\, and Q'o, etc. Two antitheses of these, 
 namely (18) and (22), turn out to be formulae proposed by 
 Walsh, and a third (24) to be one proposed by Julius Lehr.^ 
 
 We have seen that the formulae (11) and (12) considered 
 as arithmetical averages have for weights 
 
 PoQi, p'oQ'i, p"oQ"i, etc., for No. (11), 
 
 and poQo, p'oQ'o, p"oQ"o, etc., for No. (12). 
 
 We next use weights 
 
 PiQi, p'lQ'i, p'\Q'\, etc., for No. (25), 
 
 and piQo, p'xQ'o, p"iQ"q, etc., for No. (27), 
 
 ^ For references to literature concerning this and many others 
 among the remaining formulae of the table (col. 13-44), see Walsh, 
 op. cit. 
 
 ^ Beitrdge zur Statistik der Preise, Frankfurt-a.-M, 1885 (p. 11 and 
 pp. 37-42 for the method). The method is explained in Walsh, 
 Measurement of General Exchange-Value, pp. 386-388.
 
 Sec. 4] APPENDIX TO CHAPTER X 399 
 
 thus completing the four permutations of the subscripts, 01, 
 00, 11, 10. Number (29) represents a weighted arithmetical 
 average in which the weights are derived from other con- 
 siderations than the product of the prices and quantities of 
 the base year (1). An instance is the method employed in 
 some of the tables in the "Aldrich Report," ^ the weights 
 being the percentage of consumption of various kinds in 
 workingmen's budgets without reference to the base year or 
 any other particular year. 
 
 Numbers (31) and (33) are weighted harmonic means in 
 which the weights instead of being 
 
 PiQi, etc., as in (11), 
 or piQo, etc., as in (12), 
 
 are poQi, etc., for (31), 
 
 and poQo, etc., for (33), 
 
 thus completing for harmonic averages the same permuta- 
 tions of subscripts as before for arithmetical averages. We 
 see then that the odd formulae (11) to (33) inclusive are 
 
 merely arithmetical averages or harmonic averages of ^, 
 
 etc., or else averages or mixtures of such averages. 
 
 Numbers (35), (37), (39), (41) are various forms of 
 weighted geometric averages of those price ratios, the 
 weights being 
 
 PiQi, etc., for (35). 
 
 poQo, etc., for (37). 
 
 PiQo, etc., for (39). 
 
 PoQi, etc., for (41). 
 
 Number (43) is the ratio of the weighted geometric aver- 
 age of the prices in years 1 and 0, the weights being piQi, etc., 
 for year 1 and poQo, etc., for year 0. 
 
 * Report on Wholesale Prices, Senate Report 1394, 2d Sessioiii 
 52d Congress, 1893.
 
 400 THE PUKCHASING POWER OF MONEY [Append. X 
 
 It will be seen that all of the 44 formulae selected for the 
 table are based on a few simple principles of averaging. 
 Most are arithmetic, harmonic, or geometric averages or 
 their combinations. Needless to say, numerous other and 
 more complicated forms might be constructed. 
 
 § 5. Review of Eight Tests, heading the Table Rows 
 
 Having reviewed the headings of the vertical columns of 
 the table, we have next to note the headings of the horizon- 
 tal rows. These headings are the eight tests of index num- 
 bers. The first six tests are arranged in pairs, the odd being 
 expressed in terms of prices and the even in terms of 
 quantities. 
 
 The Eight Tests for a Good Index Number 
 
 The eight tests are intended to include all the tests which 
 have been hitherto applied in the study of index numbers 
 and some others. They are: 
 
 1. Test of proportionality, as to prices. 
 
 2. Test of proportionaUty, as to trade. 
 
 3. Test of determinateness, as to prices. 
 
 4. Test of determinateness, as to trade, 
 
 5. Test of withdrawal or entry, as to prices. 
 
 6. Test of withdrawal or entry, as to trade. 
 
 7. Test by shifting base, both as to prices and as to trade. 
 
 8. Test by shifting unit of measurement, both as to prices 
 and as to trade. 
 
 We shall first define each of these tests in general terms 
 and then proceed to illustrate them by actual applications. 
 
 1. Test of proportionality as to prices. A formula for the 
 price index should be such that the price index will agree 
 with all individual price ratios when these all agree with 
 each other. Thus, if in 1910 the price of everything is 10 per 
 cent higher than in 1909, the index number should register 
 10 per cent higher.
 
 Sec. 51 APPENDIX TO CHAPTER X 401 
 
 2. Test of proportionality as to trade. Likewise the cor- 
 relative formula for the trade index should be such that the 
 trade index will agree with all individual trade ratios when 
 these all agree with each other. 
 
 3. Test of determinateness ac to prices. A price index should 
 not be rendered zero, infinity, or indeterminate by an individ- 
 ual price becoming zero. Thus, if any commodity should in 
 1910 be a glut on the market, becoming a " free good," that 
 fact ought not to render the index number for 1910 zero. 
 
 4. Test of determinateness as to trade. The correlative trade 
 index should not be rendered zero, infinity, or indeterminate 
 by an individual quantity becoming zero. Thus, if any com- 
 modity should go completely out of use in 1910 so that its 
 quantity exchanged becomes zero, that fact ought not to 
 render the trade index for 1910 indeterminate. 
 
 5. Test of withdrawal or entry as to prices. A price index 
 should be unaffected by the withdrawal or entry of a price 
 ratio agreeing with the index. Thus, if the price index of a 
 certain number of goods, not including sugar, should be 105 
 in 1910 as compared with 1900, and the price of sugar itself 
 should be 105 in 1910 as compared with 1900, then the in- 
 clusion of sugar in the calculation of the index number ought 
 not to change the index from 105. 
 
 6. Test of withdrawal or entry as to trade. The correlative 
 trade index should be unaffected by the withdrawal or entry 
 of a quantity ratio agreeing with the index. 
 
 7. Test hy changing base. The ratios between various price 
 indexes (and therefore also, as we shall see, the ratios between 
 the correlative trade indexes) should be unaffected by revers- 
 ing or changing the base. Thus, if the index number for 1910 
 is twice that for 1900, when calculated on the basis of 1860, 
 it should remain twice, when calculated on the basis of 1870. 
 
 8. Test hy changing unit of measurement. The ratios be- 
 tween various price indexes (and therefore also, as we shall 
 see, the ratios between the correlative trade indexes) should 
 be unaffected by changing any unit of measurement. Thus, 
 if the index number for 1910 is twice that for 1900 when coal 
 
 2d
 
 402 THE PURCHASING POWER OF MONEY (Append. X 
 
 is measured by the ton, it should remain twice, when coal is 
 measured by the pound. 
 
 The statements of tests 7 and 8 are expressed in each case 
 both as to prices and quantities; in these cases it was im- 
 plied that what holds true of price indexes holds true also of 
 trade indexes, and vice versa. To show this reciprocal rela- 
 tion for test 7 (base shifting), let the price index for year 1 
 in terms of year be designated by Pi, o instead of by Pi as 
 heretofore, in order that the base year may be specifically 
 designated, and let us compare years 1 and 2 by using first 
 year as a base and then (say) year 8. If the base-shifting 
 
 P P 
 
 test is fulfilled for the P's, i.e. if — ^^ = — ^ , we are to prove 
 
 P2, P2, 8 
 
 that the corresponding relation is also true for the T's, viz. 
 that 
 
 Ti, _ Ti, s 
 
 Tz, T2, 8 
 
 We know that Ti, = %^ • (1) 
 
 PljO 
 
 m _ -*/'2V2 
 i 2, p 
 
 ■t 2, 
 
 (2) 
 
 Jt lj8 ' 
 
 (3) 
 
 i 2, 8 - p 
 
 X^2, 8 
 
 (4) 
 
 Divide (1) by (2) and (3) by (4). The quotients are 
 
 
 Ti,o_fMQyYP2,o\ 
 2^2,0 \.MQ2APi,oJ' 
 
 
 ^2,8 y^PiQiAPuJ 
 
 
 Comparing the right sides of these equations, we find that 
 the " 2 " ratios are identical in the two cases, and we know 
 that the P ratios are equal by hypothesis. Consequently
 
 Sec. 5] APPENDIX TO CHAPTER X 403 
 
 the entire right sides of the two equations, and therefore 
 the left sides, are also equal, and this is what was to be 
 proved. The converse reasoning is also evident. 
 
 Like the base-shifting test, the unit-shifting test, No. 8, 
 cannot apply to prices without applying also to quantities, 
 and vice versa. To show this we employ the equation T = 
 
 -^^' Evidently the numerator of the right side of this 
 
 equation is unaffected by a change of unit. For instance, 
 if coal should be measured in ounces instead of tons, thus 
 greatly increasing the number (say Q) representing its quan- 
 tity, the value {pQ) will not be disturbed, since the number 
 (p) representing the price will be correspondingly diminished. 
 Consequently, if the denominator (P) meets the correspond- 
 ing test, i.e. is likewise unaffected by a change in unit, the 
 quotient (T) must be unaffected. That is, if the unit-shift- 
 ing test is met for P, it must be met for T. As the con- 
 verse reasoning also apphes, the proposition is proved. 
 
 As will have been noted, the first six tests are expressed 
 alternately in terms of prices and in terms of quantities. 
 We now wish to point out that those expressed in terms of 
 prices have a significance for quantities also, and that those 
 expressed in terms of quantities have a significance for prices 
 as well. That is, all the tests have significance both as to 
 prices and as to quantities. 
 
 To emphasize this fact, which is important, let us note the 
 price significance of each test. Since the price significance 
 of tests 1, 3, 5, 7, 8 is evidently expressed in the statement 
 of the test, we have left merely to express the price signifi- 
 cance of tests 2, 4, 6. 
 
 Test 2 tells us that if all the trade ratios agree, their index 
 should agree with them ; that is, 
 
 if Qi _ Q 1 _ Q 1 _ ... _ t 
 
 T 
 then also should — ^ = k.
 
 404 THE PURCHASING POWER OF MONEY [Append. X 
 
 The question now before us is, assuming this condition to hold 
 as to the Q's, what condition holds true as to the p's. The 
 answer evidently is: — 
 
 ^PiQ 
 
 
 [obtained by substituting kQz for Qi, kQ'2 for Qi, etc., and kTi 
 for Tx] = ^PiQa = SpiQi _ 
 
 2P2Q2 SpoQi 
 The last form is derived from the next to the last by multi- 
 plying both numerator and denominator by k and then sub- 
 stituting Qi for kQi, Q'l for kQ'2, etc. 
 
 The resulting two formulae for — ^ express test No. 2 in 
 
 terms of the conditions to which prices must conform. 
 These formulae will be recognized as those discussed in § 7 
 of the Appendix to Chapter II, the significance of which was 
 there explained. It was there shown that a change in M, or 
 a change in F, or a uniform change in all the Q's, or any 
 combination of these changes will, through the equation of 
 exchange, affect the price level in the maimer expressed by 
 the formula: — 
 
 El ^ SpiQi ^ SpiQz . 
 
 P2 27?2Qi ^paQo 
 
 Thus the equation of exchange itself prescribes test No. 2; 
 for the fundamental theorems which the equation of ex- 
 change has taught us are that prices vary directly as M and 
 as the F's and inversely as the Q's; and the only forms of 
 index numbers which will faithfully reflect these changes, i.e. 
 will vary directly with M and inversely with the Q's (assum- 
 ing that all Q's vary in unison), are those forms of index 
 numbers which conform to test No. 2. Any other form of in- 
 dex number, when M (and M') increased 50 per cent and there 
 was no change in F's or Q's, might register a rise of 49 per cent
 
 Sec. 5] APPENDIX TO CHAPTER X 405 
 
 or 51 per cent. That is, no other forms of index numbers will 
 enable us to say that when the quantity of money changes, the 
 velocity of circulation and the Q's remaining the same, the 
 index number of prices will vary proportionately. No other 
 forms will enable us to state the corresponding theorem 
 as to the effect of a change in velocity or of a (uniform) 
 change in the Q's. But these theorems are fundamental. The 
 very concept of an index number is that it shall replace the 
 divergent individual variations and enable us to state of its 
 proportionate changes the same theorems which hold true 
 when prices all change alike. 
 
 Test No. 2 is therefore of such fundamental importance 
 that we may profitably pause a moment to restate it in 
 words. To be concrete, let us suppose two years, 1900 and 
 1910. Let us assume that the quantity of every kind of 
 goods sold in 1910 is (say) exactly double the quantity sold 
 in 1900. Then the only proper ndex number showing 
 the level of prices in 1910 (year 1) as compared with the 
 
 level of prices in 1900 (year 0) is ^ ^ the ratio of the total 
 
 value of the goods sold in 1910 to what that value would 
 have been at the prices of 1900 ; or, what amounts to the 
 
 same thing, it is ~~^ the ratio of what the total value of 
 
 the goods sold in 1900 would have been at the prices of 1910 
 to what it actually was at the prices of 1900. 
 
 Of the 44 formulae in the table, only the following reduce 
 to the required formula when the Q's change uniformly: 
 (2) of Drobisch, (4), (6), (8), (10), (11), (28), (30), (34), (38), 
 (40). All these are even-numbered except formula 11. 
 Several others will reduce to the required formula, provided 
 one of the years compared is the base year. 
 
 The formulae of the tables which fail to meet test 2 at all 
 would not even allow us to say of MV+M'V'=PT that if 
 all the Q's remain the same, T will remain constant and 
 P will vary as the other side of the equation. For these 
 formulae T fails as a true index of the Q's, and its error
 
 406 THE PURCHASING POWER OF MONEY [Append. X 
 
 in one direction implies a corresponding error in P in the 
 opposite direction. 
 
 Test 2 seems therefore in some respects the most important 
 of all the eight tests for prices; although primarily it was 
 not stated in terms of prices, but in terms of quantities. It 
 is the only test which indicates the kind of weighting re- 
 quired. It completely prescribes the conditions which, 
 while permitting any individual changes in prices, however 
 divergent, enable us to say that a change in M or the two 
 F's or in all the Q's in a given ratio will affect prices " on 
 the average " in that same ratio (directly, of course, for the 
 ilf' s and F's and inversely, for the Q's). 
 
 Test 2 in fact points out the true form of the index num- 
 ber of prices as prescribed by the equation of exchange under 
 all possible circumstances except when the Q's vary in un- 
 equal proportions. It also points to the proper weights 
 required. These weights may be said to depend either on 
 the Qi's or on the QqS, interchangeably. The formula sug- 
 gested by the Q\S is formula 1 1 ; that suggested by the QqS 
 is formula 12. Either will be perfectly satisfactory when the 
 Qi's and Qo's are proportional, while when they are not, their 
 discrepancy is negligible. When the Q's vary unequally, 
 however, there seems to be no perfectly satisfactory formula. 
 Under these circumstances the two systems of weights — 
 one in terms of Qi's, the other in terms of Qo's — conflict 
 with each other. But the conflict has been shown by Edge- 
 worth ^ to be slight. In fact, the weights are of much less 
 importance in determining an index number of prices than 
 the prices themselves. 
 
 The discussion of test 2 will be resumed later when in § 7 
 we come to compare the various forms of index numbers. 
 
 * Report of the British Association for the Advancement of Science 
 for 1887, pp. 288-292 and for 1888, pp. 197-198, 200, 202, 203, 206. 
 Edge worth shows in the case specified by him that an "error" in the 
 iseights only makes an "error" one twentieth as great in the re- 
 sultant index number, while an "error" in the prices themselves 
 makes an "error!! in the resultant index number one fourth or fifth 
 as great.
 
 Sec. 5] 
 
 APPENDIX TO CHAPTER X 
 
 407 
 
 Tests Algebraically Stated for the General Case of any 
 
 TWO YEARS compared AS TO PRICES AND TRADE. (FOR THE 
 
 Special Case when one of the two years is a base year, 
 substitute "0" for "2.") 
 
 Test 1, 
 Proportionality as 
 top's 
 
 Test 2, 
 Proportionality as 
 to C'8 
 
 Test 3, 
 Determinateness 
 as to p's 
 
 Test 4, 
 Determinateness 
 as to Q's 
 
 Test 5, 
 By withdrawal or 
 entry as top's 
 
 Test 6, 
 By withdrawal or 
 entry as to Q's 
 
 Teat 7, 
 By changing base 
 
 Test 8, 
 By changing units 
 of measurement 
 
 Pi = or 
 Pi = 0, etc. 
 
 $, = or 
 Qj = 0, etc. 
 
 Pz Pi 
 
 Pi P't ' 
 
 Base changed from 
 "0" to "8" Chang 
 ing: 
 
 A. to Pi,, 
 A, to P„ , 
 Tx, to 2\, , 
 Ti, to r,, , 
 
 Qjand pi changed in 
 inverse ratio 
 
 A 
 
 Pj and Pj determinate 
 and not zero nor in 
 finity 
 
 P-i and P, determinate 
 and not zero nor in- 
 finity 
 
 Th« Test Kkqttibes that 
 (as top's) (as to Q'&) 
 
 (Primes signify that 
 Pi. Pi> Qi, Qi are 
 excluded ; absence of 
 primes signifies they 
 are included.) 
 
 P\_ ^P\Q\ . 7\ 
 P\ '^P\Q\ ' 7i 
 (Primes and their 
 absence signify as 
 above.) 
 
 
 -^ unchanged 
 
 
 
 Tj and 7*, determinate 
 and not zero nor 
 
 infinity 
 
 Ti and T, determinate 
 and not zero nor 
 infinity 
 
 T'i ^p\Q\ . Pt 
 
 T\ S-p'tQ't ■ P, 
 (Primes signify p,. 
 Pi, Q\, Qt are ex- 
 cluded ; absence of 
 primes signifies they 
 are included.) 
 
 = k 
 
 T'._ 
 
 (Primes and their 
 absence signify as 
 above.) 
 
 
 
 p unchanged
 
 408 THE PURCHASING POWER OF MONEY [Ai pend. X 
 
 As to test 4, this states that if an individual quantity be- 
 comes zero this fact should not render the quantity or trade- 
 index zero, infinity, or indeterminate. But according as the 
 index does or does not become zero, infinity, or indetermi- 
 nate, will the price index become or not become infinity, zero, 
 or indeterminate respectively. This is clear from the rela- 
 tion Pi = -VMl . Hence test 4 possesses a significance as to 
 
 prices similar to that which it possesses as to quantities. 
 
 The price significance of test 6 is more complex and of no 
 apparent importance. Its statement is included in the ex- 
 planatory table on page 407. In the preceding table of 
 44 index numbers the " score " for test 6 is bracketed to 
 indicate that it has no important price significance, and is 
 to be omitted in the totals. 
 
 Mutatis mutandis, each of the tests expressed in terms of 
 prices (tests 1, 3, 5) has a significance as to quantities also. 
 
 The preceding explanatory table exhibits in algebraic terms 
 both hjrpothesis and conclusion for each of the eight tests 
 with respect both to prices and quantities. 
 
 § 6. The Interior of the Table; Column 11 in Particular 
 
 We have reviewed briefly the headings of the table, includ- 
 ing both those of the vertical columns and those of the hori- 
 zontal rows. Their relations to each other are contained in 
 the interior of the table. The object of the table is to show 
 the degree of conformity of the 44 various formulae for P 
 (and their correlates for T) to the eight tests. In spite of 
 all the mathematical ingenuity spent by many writers in 
 devising index numbers, no known formula and apparently 
 no possible formula will meet all eight of the tests. 
 
 For each test we note three possible degrees of conformity. 
 It may be fulfilled by any particular formula in three de- 
 grees of conformity or nonconformity: (1) completely, (2) 
 partially, or (3) not at all. These three degrees are indicated 
 in the table which follows, by the numbers 1, |^, respec-
 
 Sec. 6] APPENDIX TO CHAPTER X 409 
 
 tively. A test is completely fulfilled by index numbers for 
 any two years whatever (as year 1 and year 2). A test is 
 partially fulfilled if it is fulfilled by index numbers for two 
 years, one of which is the base year (year 0), Thus the 
 former relates to the general case, the latter to a particular 
 case. Since the general includes the special, if the test is 
 fulfilled in general it is fulfilled in particular; the converse 
 is not necessarily true. But if the test is not fulfilled in the 
 particular case, it is not fulfilled in general; the converse of 
 this proposition is not necessarily true. In short, an afl&rma- 
 tive answer to the question of complete conformity carries 
 with it an affirmative answer to the question of partial 
 conformity; and a negative answer to the question of par- 
 tial conformity carries with it a negative answer to the 
 question of complete conformity. These two rules save 
 much labor in working out the figures in the table. 
 
 Our next task is to illustrate the eight tests by applying 
 them to a particular formula for Pi and the correlative 
 formula for Ti. We select for this illustration the pair of 
 
 formulae numbered (11) in the table, namely Pi = ^^ 
 
 2poQi 
 
 and Ti = SpoQi, and we seek to know how far this pair of 
 
 formulae conform to the eight tests. 
 
 Test 1. Proportionality as to prices. — We shall begin with 
 " the particular case " where one of the two years compared 
 is the base year. In concrete terms, this test means that, 
 if all prices for the year 1 are any given number of times 
 (k times) the prices for the base year 0, then the index num- 
 ber for the year 1 (in terms of the year 0) should be the 
 same number k. 
 
 The test is best expressed in algebraic language as follows : — 
 
 If ^=p;i=^=... =fc, 
 
 Po Po P 
 i.e. if pi = kpQ ; p\ = kp'o ; p'\ = kp"o • • •, fc being 
 
 the given constant price ratio, then also should
 
 410 THE PURCHASING POWER OF MONEY [APPEND. X 
 
 Po *' 
 
 that is (since Po = 1), Pi = k. 
 
 It is easy to apply this test to our given pair of formulae. 
 
 The formulae for year 1 are Pi = §^' ; Ti = SpoQi- 
 
 The formulae for year are Po = |^ ( = 1) ; To = ^poQo. 
 
 ^PoQo 
 
 It is evident that Px = ^^ = PiQ.^P^Q'^'h- 
 
 ^ (kpo)Qi-\-(kp'o)Q\-\- - _ k(poQi + p'oQ\-\- -") 
 SpoQi ^PoQi 
 
 SpoQi 
 
 Therefore test 1 is fulfilled for the particular case when 
 one of the years is the base year. 
 
 But, as we have noted, it does not follow that the test is 
 fulfilled in general. For " the general case " of any two 
 years the test may be thus stated : If the price of each good 
 for the year 1 is /c times the price of the same good for the 
 year 2, then the index number for the year 1 (in terms of 
 the year 0) should also be k times the index number for the 
 year 2 (in terms of the year 0). That this may be true, 
 the test requires, for the general case, that if 
 
 Pi-2j-£li- ... -k 
 -— , 77 — — «'> 
 
 P2 P2 P 2 
 
 i.e. if pi = kp2, p\ = kp'2, p"\ = kp"z etc., 
 
 then must -^ = k. 
 
 P2 
 
 This general test, however, will not be fulfilled, as may be 
 
 seen from the following : — 
 
 SpiQi k%PiQx 
 
 Pi ^ SpoQi ^ SpoQi _ 
 
 P2 SP2Q2 SP2Q2 
 
 2poQ2 2poQ2
 
 Sec. 6] APPENDIX TO CHAPTER X 411 
 
 In order that this last expression should reduce to k, it 
 is evident that l^E^i would have to be equal to ^^- But 
 
 this cannot be assumed to be always true. If this equality 
 should happen to hold true for any particular value of (say) 
 Q2, it would evidently be disturbed by the slightest deviation 
 from that value. If, for instance, Q2 should vary, the left 
 
 side, -£?^, of the supposed equality would be unaffected, but 
 
 the first term in the numerator and the first term in the 
 denominator of the right side would vary. Consequently the 
 
 right fraction -^^ would be affected, except when the ratio 
 
 of the first term, ^^", happened to be equal to :~^, in 
 P0Q2 ^PoQz 
 
 which case by a well-known principle of proportion (the 
 principle of "composition and division") the size of the 
 terms P2Q2 and P0Q2 would be immaterial. 
 
 The first test, therefore, is fulfilled for the particular case 
 where one of the two years compared is the base year, but is 
 not fulfilled in general. Therefore, following our convention, 
 we assign to formula 11 the number ^ as representing its 
 degree of conformity to test 2. 
 
 Test 2. Proportionality as to trade. This test, stated for 
 the general case, is: If the quantities of all goods sold in the 
 year 1 is fc times the quantities of the corresponding goods 
 sold in the year 2, the index number of trade for the year 
 1 (in terms of the year 0) should also be k times the index 
 number for the year 2 ( n terms of the year 0). 
 
 That is, if Ql = Qj^ = Ql!l= ... =h 
 
 Q2 Q'2 Q'\ 
 
 then should ~= k. 
 
 T. 
 
 We shall find that this test is fulfilled in the general case, 
 and therefore also in the particular case.
 
 412 THE PURCHASING POWER OF MONEY [Append. X 
 
 Evidently ?j = |2oQi ^ h%p,Q, ^ ^^ 
 
 which was to have been proved. Therefore test 2 is com- 
 pletely fulfilled, and the formula is therefore assigned the 
 full credit, " 1," in the table. 
 
 Test 3. Determinateness as to prices. This test is also 
 completely fulfilled. 
 
 If, in the formula for Pi, namely —^^ , some but not all 
 
 ^poQi 
 of the prices, as pi, or one of the quantities, as Qi, should 
 become zero, it is clear that the above expression would still 
 be determinate, and lie between zero and infinity. It will 
 merely happen that some of the numerous terms in the 
 numerator will vanish, but all the other terms will remain. 
 
 P 
 
 j Since the same reasoning applies to P2. it follows that ^ 
 
 must also be de'^erminate, being the quotient of two finite, 
 non-zero, and determinate numbers. Thus test 3 is com- 
 pletely fulfilled. 
 
 Test 4. Determinateness as to trade. The fourth test is 
 analogous to the third, and states that the trade index num- 
 ber must not be rendered indeterminate, zero, or infinity 
 simply because some price or prices should become zero. 
 
 The formula for Ti is always -~^ • Since, as neither the 
 
 -Pi 
 numerator nor the denominator of this fraction becomes 
 
 zero, infinity, or indeterminate by the vanishing of some but 
 not all of the p's or Q's, the quotient must Ukewise be non- 
 zero, finite, and determinate. Thus, test 4 is completely 
 fulfilled.^ 
 
 ^ It might seem that the simple tests of determinateness "would be 
 fulfilled by any formula whatever, but such is not the case. (If it 
 were, the total " score " given in the last column opposite test 4 
 would be 44 instead of 31.) Thus the simple geometrical average 
 (formula 7) will not conform to test 3 of determinateness as to 
 prices. The simple geometrical average for "n" commodities is 
 
 Pi =^21 . 2J^ .... Evidently if pi becomes 0, the value of the entire 
 
 ^ po p'o
 
 Sec. G] appendix to chapter x 413 
 
 Test 5. Withdrawal or entry as to prices. Suppose that 
 there are 100 specified commodities. If the general price 
 level of one year s k times that of another, and if any good, 
 the price of which in the one year is k times that in the 
 other, be withdrawn from the 100 commodities, leaving 99, 
 then the ratio of the price levels of the two years should 
 remain unchanged. 
 
 This is a difficult test to meet, and the formula under dis- 
 cussion meets it only partially, that is, when one of the two 
 years compared is the base year. 
 
 If J^^T^ = ^} where A; is a given ratio, 
 
 ^PoQi 
 
 and if also ^ = k, then we are 
 
 Po 
 
 to prove that J^ ri^ = k, where 
 2p oQ 1 
 
 of course ^v'lQ'r = v'lQ'i + v"iQ'\ + • •• 
 
 while SpiQi = viQi + p'lQ'i + v"iQ"i +• •• : 
 
 so that Sp'iQ'i = SpiQi — piQx. 
 
 Now we know that, 
 
 since ^ = fc, 
 
 then 2i^^ = /b.l 
 
 And, since J^^T^ = ^, -t follows by the principle of pro- 
 
 expression becomes 0. If, therefore, we should depend on the geo- 
 metric mean for ascertaining price levels, the temporary plethora of 
 any commodity, to the extent of making its price vanish for a single 
 moment, would cause the index number representing the entire price 
 level for that moment to fall to 0. A form of average which in an 
 extreme case is so absurd will approach absurdity before the ex- 
 treme is reached. Thus the geometrical average is unduly affected 
 by prices which are low, even if not actually zero.
 
 414 THE PURCHASING POWER OP MONEY [Append. X 
 portion (" composition and division ") that 
 
 SpoQi - PoQi 
 that is, J^ /a} — ^, which was to have been proved. 
 
 If the missing commodity is reentered, the ratio will 
 evidently be undisturbed, so the rule works both ways, i.e. 
 for entry as well as for withdrawal. Therefore, test five is 
 fulfilled for the particular case. 
 
 When, however, we consider the general case for price 
 ratios of two years neither of which is the base year, the test 
 will not be fulfilled. 
 
 That is, if ^ = k, 
 
 ^PoQ2 
 
 and if also — = k, 
 
 Pi 
 
 ^P\Q' 
 
 then ^^°^/ will not in general be equal to fc. 
 
 ^P 2V 2 
 
 Sp'oQ' 
 
 For, if this expression should happen to be equal to k in any 
 particular instance, a slight change in any base year price, 
 such as p'q, would disturb the equality, unless the variation 
 in p'o should affect the denominators of both numerator and 
 denominator of the last expression in the same proportion. 
 
 This would mean that the ratio J: fii} would be unaffected 
 
 by a change in p'o, which in turn would assume (by the prin- 
 ciple of " composition and division ") that 
 
 p'oQ'2 2p'oQ'2*
 
 Sec. 6] APPENDIX TO CHAPTER X 415 
 
 This is not necessarily true, as it is evidently easy to assume 
 values for (say) Q'l which would render it untrue. Thus, a 
 doubling of Q\ would double the left side but not the right. 
 Therefore test five is only partially met by our formula. 
 This is therefore to be credited only with ^ as its degree of 
 conformity to test 5. 
 
 Test 6. Withdrawal or entry as to trade. If the index 
 numbers for trade are in a given ratio, the inclusion or ex- 
 clusion of a given good, the quantities of which are in the 
 same ratio, ought not to disturb that ratio. This test is 
 completely fulfilled by our formula. 
 
 The test requires that if ^ = k, 
 and if Tl = ^=.k, 
 
 then should |2!o^i = fc. 
 
 This test is fulfilled; for from 
 
 it follows that ^oSl = fc^ 
 
 PoQ; 
 
 which combined with J^^T^ = ^> 
 
 2poQ2 
 
 by the principles of proportion (i.e. by "composition and 
 division ") gives ^PoQi-poQi ^ j^ 
 
 ^PoQ2 — P0Q2 
 
 That is, ¥^ = ^' 
 
 W0Q2 
 
 which was to have been proved. 
 
 Test 7. Changing the base. This test 7 is not fulfilled 
 by our formula even in the particular case. The particular 
 case means here the case of reversing the base, as between 
 (say) year 1 and year 0.
 
 416 THE PURCHASING POWER OF MONEY [Append. X 
 
 In order not to alter and thereby confuse the notation 
 we shall have to use the subscript 0, which indicated 
 the original base year, to indicate that same year, even 
 when, for the moment, it is not considered as the base 
 year; and likewise we shall use the subscript 1 to indicate 
 the year 1, even when it is, for the moment, taken as the 
 base year. 
 
 By the formula which we are testing, the price index ratio 
 
 for year 1 compared to year as the base is ~~^- By 
 analogy it is clear that the price index ratio for year 0, com- 
 pared with year 1 considered as the base, is -^^ • If these 
 
 two expressions are reciprocals of each other, then -r^ 
 
 ^PoQi 
 
 should be equal to ;~~' 
 ^PoQo 
 
 That this is not necessarily true is evident, since there is 
 no necessary relation between the Qo's and the Qi's. If the 
 equation should accidentally hold true for a particular set of 
 Qo's and Qi's, the change, even in the smallest degree, of a 
 single letter, say Qo or Qi, would evidently disturb the rela- 
 tion. Therefore the test is not fulfilled even for the par- 
 ticular case of reversing the base as between two years, and 
 the formula must therefore be assigned a "0" or complete 
 failure to conform to test 7. 
 
 Test 8. Changing units of measurement. If the unit for 
 indicating the price, say of coal, should be changed from 
 a ton to a pound, the index number ought not to be 
 affected thereby. We shall find that this test is met by 
 formula (11). 
 
 Evidently a change of unit, say from a ton to a pound, 
 applied to any particular goods (the prices of which are 
 Ph P'h P"h the corresponding quantities being Qi, Q'l, Q"i) 
 will magnify all the Q's 2000 times, but, on the other hand, 
 will reduce all the p's in the reciprocal ratio (tttW)- Con- 
 sequently, the products piQ\, p'xQ'i, p"\Q"\, will be unaffected.
 
 Sec. 6] APPENDIX TO CHAPTER X 417 
 
 Hence the sum of such products constituting the numerator 
 and denominator of the right side of the equation 
 
 Pi _ ^PoQi 
 
 Pz SP2Q2 
 
 will likewise be unaffected. Therefore the ratio of the index 
 
 p 
 numbers — ^ will be unaffected. Hence the test is completely 
 
 P2 
 
 fulfilled.* 
 
 ^ It might seem that every index number would conform to this 
 unit-shifting test. It is true of 40 formulae out of the 44. Yet the 
 index number which is perhaps the simplest of all, Bradstreet's, 
 
 Pi = ~^ , fails to conform. 
 
 It is evident that if there is a change in the unit of any one com- 
 modity, such as that whose prices are pi, and po, both the numerator 
 and denominator will be affected, but not in the same proportion, 
 except when it happens that 
 
 pi_ Spi 
 po Spo* 
 
 Consequently, the index number is dependent upon the nnitof 
 measurement. Such an index number is entirely arbitrary, and by 
 sufficient manipulation of the units of measurement could be made 
 to favor any particular commodity. The larger the unit of any 
 particular commodity employed, the higher the price for it which 
 enters into the formula, and the more that commodity tends to 
 affect the result. 
 
 Bradstreet uses 96 commodities in common use, all of which are 
 measured by the pound. The result is that silver, for instance, 
 dominates over iron, entering at several dollars a pound instead of 
 a few cents. If radium, which recently cost $8,000,000 an ounce, were 
 included, it would absolutely dominate the group, and we would 
 reach the absurd result that since radium has fallen to hundreds of 
 thousands instead of millions of dollars an ounce, the general price 
 level must have fallen several fold in spite of the general impression 
 of rising prices ! An index number of this kind is fitly called by 
 Walsh one of accidental or haphazard weighting. 
 
 2k
 
 418 THE PURCHASING POWER OF MONEY [Append. X 
 
 § 7. The 44 Formulce Compared 
 We have gone through the reasoning by which the con- 
 formity of one pair (Pi = ^^ ; Ti = SpoQi) out of the 
 
 44 pairs of index numbers of prices and trade, given in the 
 table, are tested and graded with respect to the eight tests. 
 The table contains for the remaining 43 formulae the results 
 of similar reasoning. This reasoning is here omitted to save 
 space. The mathematical reader who chooses can verify the 
 results as tabulated. He can also prove the relationship by 
 which it follows that the figure in any column for the odd 
 tests corresponds to that in the neighboring antithetical col- 
 umn for the even tests. In consequence of this relationship 
 the sum of any column for the odd tests equals the sum in 
 the antithetical column for the even tests. In fact, the table 
 is full of correspondences and relationships of many kinds. 
 
 The footings give us a means of comparing the merits of 
 the various index numbers. These footings are intended to 
 express, so far as may be, the fitness of the formulas to serve 
 as index numbers for price levels. Consequently the score 
 for test 6 should be omitted from the footing, as test 6 has 
 no value in regard to 'prices. (If it be desired to compare the 
 scores of the correlative index numbers for quantities or 
 trade, the score of test 6 will be included, but that of test 5 
 should then be omitted.) 
 
 Thus a perfect score would be seven. The highest score in 
 the table is 5^, the lowest, 2. 
 
 It would, of course, be absurd to compare the merits of 
 index numbers merely by their "score" in the table. This 
 score is more or less arbitrary, and it treats all seven tests as 
 equally important. Yet it affords at least some insight into 
 the comparative characteristics of the 44 formulae. It is 
 noteworthy that, in general, the simplest formulae have high 
 scores and the most compUcated have low scores. Thus 
 formulae 1 (Dutot), 7 (simple geometric), 9 (median), 11 and 
 12 (Scrope) have scores of 5 and 5^. The only others as
 
 
 ^(80t 
 
 (31) 
 
 " 
 
 TU./ 
 
 1 AC 
 
 
 
 
 i ■ 
 
 1 
 
 
 
 1 
 
 1 
 
 
 
 1 
 
 
 
 1 
 
 (1) 
 
 (0) 
 
 
 
 
 
 1 
 
 1 
 
 3 
 
 3
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 • 
 
 
 
 
 
 
 m 
 
 
 
 
 
 
 
 
 
 
 
 
 ( 
 
 I 
 
 \ 
 
 1 
 
 
 1 
 
 jss. 
 
 ^ 
 
 ■■5 
 
 f 
 
 ■^ 
 
 
 "■?■ 
 
 "'■ #• 
 
 .._. — ~. 1 
 
 
 ,..«_ — 
 
 ,-4 ...^ 
 
 ■",' 
 
 i 
 
 :J~- 1 
 
 , 1 , , 
 1 
 
 .1 1 s »' 
 
 L t 
 
 
 s 
 
 ■KSf 1 ... 
 
 m 
 
 m 
 
 
 jftl-«a'>" 
 
 ss 
 
 '■^ 
 
 
 '■^ 
 
 r^ 
 
 as 
 
 — ip 
 
 ■tISs 
 
 * 
 
 ■"*!■ ^ > ^£,--- •"■•<'::' - 
 
 — 
 
 
 --"-'" 
 
 
 ,^ 
 
 •niT)- 
 
 ..4^.. 
 
 -*— -, 
 
 
 ' 
 
 , 1 ., 
 
 ~ 
 
 .r , 1 , i'w, " 
 
 1 ; . 
 
 
 ) 
 
 1 
 
 „ , i „ I . 1 „ 
 
 1 T 
 
 . 
 
 B 
 
 
 
 
 
 
 
 » , > 
 
 « 
 
 1 
 
 II , I j « 
 
 
 
 
 
 
 
 
 , 1 1 , 
 
 » 
 
 ' 1 " ' ' i' ' ' 
 
 . . 
 
 1 ll 1 1 1 1 1 
 
 
 ■ 
 
 
 ,_„. 
 
 , 1 1 ,■ oil, 
 
 
 • 
 
 
 
 ° 
 
 i » , 1 » 1 1 1 ■ 1 1 
 
 1 
 
 " 
 
 
 
 » 
 
 101 
 
 (0) 
 
 
 m 111 
 
 
 ' 
 
 ^°_ 
 
 
 
 •i- — 
 
 Z^^i^::_^_,, 
 
 
 ~ 
 
 i~ 
 
 4^ 
 
 7l" 
 
 ' 1 ' 
 
 
 
 1 1 1 
 
 fJSi^'J^ ~~ — ■ ' " 
 
 
 
 
 4 
 
 1 1 1 
 
 
 
 
 
 
 J n 
 
 '^^^^^~f. 
 
 • 
 
 ( 
 
 » c 
 
 
 
 o
 
 Sec. 7] 
 
 APPENDIX TO CHAPTER X 
 
 419 
 
 high as 5 are "mixtures" of formulae 11 and 12. The simple 
 arithmetical (3) and simple harmonic (5) have a score of 4, 
 which is fairly high. The more comphcated forms which 
 have fairly high scores are in several cases "mixtures," 
 averages, or antitheses of simple formulae 11 and 12. 
 
 The above comparisons treat all the other seven tests as 
 of equal importance. But they are not of equal importance. 
 Since opinions might differ as to the exact relative impor- 
 tance of the various tests, we shall not attempt to "weight" 
 them. Nor will this be necessary in order to decide the 
 question of most importance to us, viz., which of the 44 
 index numbers meet the tests most completely. Tests 3 and 
 4 are probably of little practical importance as compared 
 with the remaining tests. Test 2, on the other hand, may be 
 accorded chief importance, for reasons given in section 5 of 
 this Appendix and in Chapter II. In order to select the 
 best index numbers of prices, therefore, let us first rule out 
 of the competition all the 18 formulae which have "0" for 
 test 2. We have left the following formulae classified into 
 two groups. 
 
 (Omitting test 6), score for formulae which do not com- 
 pletely fail on test 2, 
 
 Formula completely fulfilling 
 
 
 
 Test 2 
 
 Formula partially fulfilling iest z 
 
 Formulae 
 
 Score 
 
 Formulse 
 
 Score 
 
 2 
 
 4 
 
 12 
 
 5i 
 
 4 
 
 3 
 
 13 
 
 4 
 
 6 
 
 3 
 
 14 
 
 4 
 
 8 
 
 4 
 
 15 
 
 4i 
 
 10 
 
 H 
 
 16 
 
 ^l 
 
 11 
 
 5 
 
 17 
 
 5 
 
 28 
 
 4 
 
 18 
 
 H 
 
 30 
 
 3 
 
 20 
 
 4 
 
 34 
 
 3 
 
 21 
 
 5 
 
 38 
 
 3 
 
 22 
 
 4i 
 
 
 
 24 
 
 4 
 
 
 
 26 
 
 3i 
 
 
 
 32 
 
 2i 
 
 
 
 36 
 
 2i 
 
 
 
 42 
 
 2*
 
 420 
 
 THE PURCHASING POWER OF MONEY [Append. X 
 
 If, next, we rule out of the competition from among those 
 which completely meet test 2, all except those which have 
 scores of 4J or above, we have left only formulae num- 
 bers 10 and 11. Among the formulae which only partially 
 meet test 2 we may eliminate all which fail to exceed 4^ in 
 total score ; for, although those which reach 4^ tie formula 
 10, yet when all tests are counted as of equal importance, 
 they are inferior in not completely meeting the most impor- 
 tant test — test 2. Putting the matter in another way, we 
 may say that if test 2 should be weighted more heavily than 
 the other tests, the scores of those formulae half meeting that 
 test which now tie formulae wholly meeting that test would 
 fail to do so and would therefore drop out of competition 
 with formulae 10 and 11 in the first column. 
 
 Eliminating therefore from the second column all formulae 
 with scores of 4^ or less, we have as the only rivals of formulae 
 10 and 11, formulae 12, 17, and 21, having scores of 5|, 5, and 
 5 respectively. Our best formula, therefore, should be found 
 among numbers 10, 11, 12, 17, 21. We shall therefore exam- 
 ine with particular care these five surviving competitors. 
 
 These all conform to tests 3, 4, and 8. Comparing them 
 in other respects, we find : — 
 
 
 10 
 
 11 
 
 12 
 
 17 
 
 21 
 
 Test 1 
 
 Test 2 
 
 Test 5 
 
 Test 7 
 
 
 
 1 
 
 
 i 
 
 1 
 
 i 
 
 
 
 1 
 
 1 
 
 
 i 
 1 
 
 i 
 
 Total 
 
 U 
 
 2 
 
 2i 
 
 2 
 
 2 
 
 Tests 17 and 21 have scores identical in every instance, and 
 may therefore be said to be tied. 
 
 Comparing tests 11 with 17 (or 21), we see that 11 excels 
 in respect to the important test 2, and 17 in test 7. As test 
 2 is regarded as of more importance than test 7, we may
 
 Sec. 7] APPENDIX TO CHAPTER X 421 
 
 safely give the preference to formula 11 over 17 (or 21). 
 We therefore now strike out 17 and 21 from the competition. 
 
 We have left formulae 10, 11, 12; comparing 10 and 11, we 
 note that 10 excels in test 7, while 11 excels in tests 1 and 5. 
 If we maybe allowed here to exercise a comparative judgment, 
 we shall say that the superiority in the one test 7 is more than 
 offset by superiority in the two tests, 1 and 5. We therefore 
 eliminate formula 10. 
 
 We now have left only the two formulae, 11 and 12. There 
 is not much to choose between them. While 12 has the higher 
 score when all tests are counted as of equal importance, 11 
 excels in the most important test 2, and we are therefore in- 
 clined to give it the preference. 
 
 According to our judgment, therefore, test 11 emerges as 
 the winner in the score contest. It has also the advantage 
 of being among the very simplest formulae and of having as 
 its correlative formula for T the simplest of all formulae for T, 
 viz. Ti = :SpoQi. 
 
 In nonmathematical language, the pair of formulae 11 
 mean that the level of prices in any year is found by dividing 
 the total value of the quantities sold in that tjear by what that 
 value would have been at base prices, and that the trade index 
 in any year is simply the value of the quantities sold in that 
 year reckoned at base prices. 
 
 Applying formula 11 to the equation of exchange, we 
 
 have — 
 
 MV + M'V = ^PiQi (1) 
 
 = PiTi (2) 
 
 Kipt)^^*^' ''' 
 
 We wish now to emphasize once more the virtues of this 
 formula 11 in respect to test 2. The equation of exchange, 
 stated above, is intended to show how prices are affected by 
 changes in M, M', V, V or the Q's. It is evident from the 
 original form (1) of this equation that a proportional chane:e 
 in the M and M' (if the V's and Q's remain unchanged) will
 
 422 THE PURCHASING POWER OF MONET IAppend. X 
 
 affect all the pi's in exactly the same ratio, or else raise some 
 prices more and others enough less than this ratio to com- 
 pensate in the sense that the equation of exchange will be 
 preserved. In some sense, therefore, the general level of prices 
 varies exactly with M and M'. Form (3) enables us to ex- 
 press this proportionality by formulating the price level as 
 
 the fraction ^^M. xhig varies directly with the M's. 
 SpoQi 
 
 In precisely the same way we are enabled to state that a 
 
 uniform change in the two V's, or any change in the left side 
 
 of the equation as a whole, will affect prices in precisely the 
 
 same ratio (the QiS being assmned constant). We may also 
 
 say that a uniform change in the Qi's will affect Ti in exactly 
 
 the same ratio, and Pi in exactly the inverse ratio (assuming 
 
 the left side of the equation to be unchanged). In fact, if 
 
 we use formula 11 to express the average price ratio, we are 
 
 able to state in all cases (so long only as the Qi's change in 
 
 unison or not at all) that prices rise or fall "on the average" 
 
 directly as the left side of the equation, and inversely as the 
 
 Qi's. 
 
 As noted, these are the basic theorems for which the equa- 
 tion of exchange stands. We would naturally like to remove 
 the restriction as to the Qi's changing uniformly. We should 
 consider an index number perfect (so far as needed in the 
 equation of exchange) if we could assert of it the same 
 theorem of proportion as above, without the restriction as to 
 the Qi's changing uniformly, so that we might substitute an 
 average change in the Q's in place of a uniform change. No 
 such index is found in the table, and no such index seems 
 possible. Practically this conclusion does not greatly mat- 
 ter, for we are interested in prices far more than in quantities, 
 the latter being chiefly important as supplying weights for 
 the price indexes. As we have already noted, Edgewortb 
 has shown that considerable variation in weighting is ol 
 comparatively little practical importance. 
 
 The chief use of index numbers is to compare succesdvi^ 
 years, not years remotely distant from each other. We ar^
 
 Sec. 7] APPENDIX TO CHAPTER X 423 
 
 not so much interested in comparing the prices of 1909 and 
 1910 each with those of 1873 as we are in comparing them with 
 each other. In fact, the chief use of 1873 as a base year is to 
 enable us to compare any other two years with each other. 
 But only a few index numbers which afford a true comparison 
 between any year and another year as the base will give a 
 true comparison between any two years, each in terms of a 
 third year as the base. These few index numbers are those 
 which completely meet the base-shifting test 7.^ In the table 
 the only formulae which come up to this requirement are for- 
 mulae numbered 1, 2, 7, 8, 43, 44, to all of which there are 
 serious objections on other grounds. Formulae 1 and 2 are 
 very arbitrary, having "haphazard weighting"; formulae 43 
 and 44 have the lowest scores in the table ; formula 7 has no 
 system of weighting; and formula 8 becomes zero if a single 
 quantity, as Q, should disappear from a year's sales. 
 
 The question therefore arises, why should we, as has usually 
 been done, construct our index numbers with reference to a 
 fixed base in terms of which we indirectly compare two given 
 years? Why not make the comparison directly f The in- 
 direct comparison introduces an error in all cases except of 
 those formulae which conform to test 7. In these cases the 
 indirect comparison cannot, of course, give any better result 
 than the direct comparison, while in all other cases the direct 
 comparison is better. 
 
 It seems, therefore, advisable to compare each year with 
 the next, or, in other words, to make each year the base year 
 for the next. Such a procedure has been recommended by 
 Marshall, Edgeworth, and Flux.^ It largely meets the diffi- 
 
 ^ That this test is the most difficult one to meet is shown by the 
 fact that the total " score " as given in the last column opposite test 
 7 is the lowest in that column, being only 12 out of a possible 44; 
 the next most difficult test to meet is test 5 (or 6), opposite which 
 the total " score " is 13j. 
 
 The easiest test to meet is test 8, opposite which the total is 40 
 out of 44 ; the next easiest is test 3 (and 4) with 31 out of 44. 
 
 * " Modes of constructing Index Numbers,'! Quarterly Journal oj 
 Economics, August, 1907, pp. 613-631.
 
 424 THE PURCHASING POWER OF MONEY [Append. X 
 
 culty of non-uniform changes in the Q's, for any inequalities 
 for successive years are relatively small. 
 
 Such successive index numbers, each on the basis of 100 
 per cent for the previous year, will, if multiplied together, 
 give a chain of index numbers showing the fluctuations from 
 year to year, like any ordinary series, but much more suitable 
 for comparison of neighboring years. 
 
 Let us now reexamine the comparative merits of index 
 numbers on the supposition that they are to be used only for 
 successive years, that is, for comparison between each year 
 and the previous year as a base. In this case we do not need 
 to distinguish between a "partial" and a "complete" ful- 
 fillment of the tests. We may therefore now substitute " 1 " 
 for every "^." Omitting, as before, all formulae which fail 
 to meet test 2, we have the following results : — 
 
 Formula 
 
 Score 
 
 Formula 
 
 Score 
 
 2 
 
 4 
 
 20 
 
 5 
 
 4 
 
 3 
 
 21 
 
 7 
 
 6 
 
 3 
 
 22 
 
 6 
 
 8 
 
 4 
 
 24 
 
 5 
 
 10 
 
 4i 
 
 26 
 
 4 
 
 11 
 
 6 
 
 28 
 
 4 
 
 12 
 
 6 
 
 30 
 
 3 
 
 13 
 
 5 
 
 32 
 
 3 
 
 14 
 
 5 
 
 34 
 
 3 
 
 15 
 
 6 
 
 36 
 
 3 
 
 16 
 
 6 
 
 38 
 
 3 
 
 17 
 
 7 
 
 40 
 
 3 
 
 18 
 
 6 
 
 42 
 
 3 
 
 19 
 
 6 
 
 
 
 We note that formulae 11 and 12 have scores of 6 each, while 
 their average 15 (and 16) and their mixture 18 and also 22 
 have the same score, but that formulae 17 and 21, which are 
 mixtures of 11 and 12, have perfect scores, 7. Each of these 
 two formulae uses as weights the average of the weights used 
 in formulae 11 and 12. Theoretically, therefore, we find two 
 formulae which fit all tests perfectly so far as year-to-year 
 comparisons of prices are concerned.
 
 Sec. 8] APPENDIX TO CHAPTER X 425 
 
 Where, therefore, great accuracy is desired and there exist 
 abundant funds to provide for the laborious computations 
 necessary, we may recommend the use of formula 17 or 21, 
 This presupposes that statistics are available for the Q's, 
 which is not usually the case. 
 
 Thus far our conclusions therefore are (1) that theoretically 
 formula 11 is the best when each year is expressed in terms of 
 a common base; (2) that (also theoretically) formulae 17 and 
 21 are slightly superior when each year is expressed in terms 
 of the preceding year as base, and that these two meet all 
 tests for year-to-year comparisons. 
 
 § 8. Reasons for preferring the Median for Practical Purposes 
 
 Practically, however, there is little if any advantage in 17 
 and 21 over 11 (or 12, which in the case of year-to-year com- 
 parisons amounts to the same thing) because (1) weighting 
 is of little importance ; (2) the more perfect weighting con- 
 tained in formulae 17 and 21 will seldom differ materially 
 from that of 11 and 12, for any gain of precision would prob- 
 ably be less than the errors in measurement of the Q's, which 
 are never exactly known ; (3) the systems of 17 and 21 are 
 practically far more laborious. In the end we must be guided 
 largely by practical considerations except where the great 
 labor and expense of computation may be disregarded. If 
 in a practical spirit we examine the merits of the various 
 formulae, we shall, I believe, reject all formulae except 9 and 
 11, and come to the conclusion that the best index number is 
 the weighted median. It has no rival in ease of computation. 
 The score of the median in the table (formula 9) is high, 
 although it fails in test 2. Excepting this test it meets, 
 partially or wholly, every other test. It therefore possesses 
 some merit even on the theoretical side. 
 
 In passing, we may mention a feature of medians, although 
 I am disposed to regard it as a fault. Edgeworth empha- 
 sized the fact that price dispersion upward always or usually 
 exceeds the price dispersion downward. There is no limit to
 
 426 THE PURCHASING POWER OF MONEY [Append. X 
 
 the former, but the latter is limited by zero. Statistical tests 
 show clearly this asymmetry of dispersion.* From this fact 
 it has been argued that the best average should be one from 
 which large deviations above it count no more than small 
 deviations below it. This condition, whether good or ill, 
 is not met by arithmetical averages, but is met by the geo- 
 metric average and by the median ^ which, in fact, usu- 
 ally closely follows the geometric average. Edgeworth also 
 argues that the median is superior when the variabilities of 
 the various elements averaged are widely different.* 
 
 Edgeworth concludes that "in the present state of our 
 knowledge, and for the purposes on hand, the median is the 
 proper formula." * 
 
 As to methods of weighting, theoretical discussion with 
 reference to test 2 shows that the weighting should be made 
 on the basis of values sold in one or the other of the years 
 compared. 
 
 It is easy to show that a system of weighting the median 
 by given weights, that is, by counting each price ratio, not only 
 
 * See Edgeworth, "First Report on Monetary Standard," Report 
 of the British Association for the Advancement of Science, 1887, pp. 
 284-855. 
 
 ^ Edgeworth, ibid., pp. 284-286. From the standpoint, however, 
 of the relation of prices to the currency, a large upward variation 
 should count more than a small downward variation ; for it requires 
 more currency. In fact, as we have already seen, the arithmetical 
 average complained of is precisely the average needed to fit into the 
 aquation of exchange. See § 6 of Appendix to Chapter II and § 7 
 of this Appendix. As to the asymmetry of price dispersion, sea 
 Mitchell, Gold, Prices, and Wages under the Greenback Standard} 
 Berkeley (University of California Press), 1908, and reviews of same 
 by Edgeworth, Journal of the Royal Economic Society, December, 
 1908, pp. 578-582 ; and H. G. Brown, Yale Review, May, 1909, 
 pp. 99-101. 
 
 » Edgeworth, Report, etc., 1887, p. 291, and "On the Choice of 
 Means,'' Philosophical Magazine, September, 1887; see also Report 
 of the British Association for the Advancement of Science, 1889, pp. 
 156-161, and Journal of the Royal Statistical Society, June, 1888. 
 
 * Ibid., p. 191.
 
 Sec. 8] APPENDIX TO CHAPTER X 427 
 
 once but a certain number of times (that number being the 
 weight) will not affect the relative fulfillments of the tests as 
 met by the simple median 9, which is the only median in the 
 table. Edgeworth has shown that for all practical purposes 
 a very rough system of weighting will suffice.^ Whether the 
 weighting be according to the values PoQo, etc., or piQi, etc., 
 or poQi, etc., or piQo, etc., is usually of no practical importance 
 whatever. If, then, we subordinate theoretical to practical 
 considerations, the proper procedure would seem to be to 
 select certain constants consisting of simple integers, and as 
 near as may be to the values dealt with in the years consid- 
 ered. These weights need not be changed every year, but 
 should be changed when the values (piQi) change very greatly. 
 
 If it be desired to have a quantity or trade-index number 
 (Qi, or Ti) as well as a price-index number (Pi), we may like- 
 wise select as the form for Qi the median. In other words, 
 the indexes for p's and Q's are best selected independently of 
 each other. It is true we thereby abandon any absolute mu- 
 tual consistency between the two, but we are now speaking 
 of practical, not theoretical, considerations. 
 
 One of the great practical advantages of the median is its 
 use in conjunction with "quartiles" or "deciles" to portray 
 dispersion as well as averages. This method of showing dis- 
 persion about a mean is both easier to calculate, and capable 
 of more detail, if detail be desired, than the method of Karl 
 Pearson of the "Standard Deviation" about an arithmetical 
 mean. 
 
 The final practical conclusion, therefore, is that the weighted 
 median serves the purposes of a practical barometer of prices, 
 and also of quantities as well as, if not better than, formulae 
 theoretically superior. 
 
 In spite, however, of the peculiar simplicity and ease of 
 
 * See Report of the British Association for the Advancement of 
 Science, 1888, pp. 208-211. Edgeworth compares various means 
 for 21 articles in 1885 and 1873, one being that recommended by the 
 committee of which he was a member, and above referred to in the 
 text of Chapter X, § 5.
 
 428 THE PURCHASING POWER OF MONEY [Append. X 
 
 computation which characterizes the median, and in spite of 
 Edgeworth's strong indorsement, it remains still almost 
 totally unused, if not unknown. Wesley C. Mitchell ^ has 
 used the median for price indexes more extensively than any 
 one else. Professor Davis R. Dewey has used them for wages 
 in his special Census report on that subject. 
 
 § 9. Summary 
 
 The conclusions of this Appendix may be briefly stated as 
 follows : — 
 
 1. Any sum of products of two factors each, such as SpQ, 
 may be converted into any one of three forms : (1) PT, in 
 which P is an average of the ratios of the p's to some base 
 
 po's, and T is the quotient — w- ; (2) AQ, in which Q is an 
 average of the ratios of the Q's to some base Qo's, and A is the 
 quotient -^ ; (3) PQSpoQo- 
 
 2. Of the foregoing three formulae only the last is synmietri- 
 cal in the sense that the p's and Q's are treated alike. 
 
 3. P and T (or P and Q) are said to be correlative, and any 
 particular formula for either implies a particular correlative 
 formula for the other. 
 
 4. Two correlative formulae for P and Q are, in general, 
 quite unlike each other. If like formulae be constructed for 
 P and Q, the correlate of Q constitutes a new formula for P, 
 
 ^ Gold, Prices, and Wages under the Greenback Standard, Publica- 
 tions of the University of California. Mitchell's use of deciles, 
 however, is of small value, as he employs a common base, 1860, so 
 that his figures for each subsequent year give the dispersion of that 
 year relatively to 1860. There is practically no use in knowing the 
 dispersion of prices in 1909 or 1910 as compared with 1860, and this 
 knowledge throws no light on whether prices change uniformly or 
 disperse widely from 1909 to 1910. What is needed is a knowledge 
 of price dispersion from year to year, and this can readily be in- 
 dicated by drawing three radiating lines from 1909 to 1910, the 
 central one to show the movement of the median, and the other two 
 to show the movements of the two neighboring quartiles.
 
 Sec. 9] APPENDIX TO CHAPTER X 429 
 
 said to be antithetical to the original formula for P, and 
 vice versa. 
 
 5. There are an indefinite number of formulae for P, of 
 which 44 are given in the table ; and there are at least 8 
 important tests to which each formula may conform in one 
 of three degrees (1) wholly, or for the ratio of Pi to P2, each 
 being relative to a third year as a base ; (2) partially, or for 
 the ratio Pi to unity ; and (3) not at all. 
 
 6. The eight tests are of proportionality as to prices or 
 quantities (1 and 2) ; deter minateness as to prices or quan- 
 tities (3 and 4) ; withdrawal or entry as to prices and quanti- 
 ties (5 and 6) ; changing base as to prices and quantities (7) ; 
 and changing units as to prices and quantities (8) . 
 
 7. The tests arrange themselves in pairs, one of each pair 
 relating to the p's in the same manner as the other is related 
 to the Q's; but each test has significance both with respect 
 to the p's and the Q's. 
 
 8. The formulae arrange themselves in antithetical pairs. 
 
 9. Of any four neighboring compartments in the table, 
 relating to two correlative rows (tests) and two antithetical 
 columns (formulae), the diagonals will have the same "scores." 
 
 10. No known form of index number P conforms perfectly 
 to all the eight tests when a common base year is employed, 
 
 but several conform well, the best being formula No. 11, ^^^^^ ' 
 
 2poQi 
 
 11. But if we are content with year-to-year comparisons, 
 renouncing comparisons in terms of a third year, there are 
 two formulae which conform perfectly, viz. formulae 17 and 21. 
 
 12. Practically, however, formula 11 is superior to 17 or 
 21, and formula 9 (median) — when properly "weighted" — 
 is superior to 11. 
 
 13. For practical purposes, therefore, unless the expense and 
 labor of computation can be disregarded, the median (with 
 its two neighboring quartiles) is recommended, with a simple 
 system of weights (whole numbers) based on expenditures, 
 and changing from time to time for the sake of making better 
 year-to-year comparisons.
 
 APPENDIX TO CHAPTER XII 
 
 § 1 (to Chapter XII, § 1) 
 Professor Kemmerer's Calculations 
 
 Professor Kemmerer (Money and Prices, p. 99) estimates 
 the money in circulation (M) by deducting from the money 
 in the United States, as estimated by the Comptroller of the 
 Currency, two items, viz. the money in the United States 
 treasury and that in banks (reported and estimated). He 
 then estimates the velocity of circulation of money as 47 
 times a year, and assumes, in the absence of any data by which 
 to estimate its variations, that it remains constant. He 
 arrives at the figure 47 as follows : The amount of check 
 transactions he first estimates for 1896, at 143 billions (p. 111). 
 This estimate is based on figures taken from Kinley's investi- 
 gation, made through the Comptroller of the Currency in 
 1896. Referring to Kinley's estimate that check transactions 
 are at least three times money transactions, he takes one 
 third of 143 billions, or 47.7 billions, as the amount of money 
 transactions. Estimating the amount of money in circula- 
 tion at 1.025 billions for 1896, he divides 47.7 by 1.025 
 and obtains (p. 114) 47 times a year as the velocity of circu- 
 lation of money. This figure, as we shall see, is probably 
 nearly three times too large, the error arising from the fact that 
 Professor Kemmerer does not accept the opinion expressed 
 by Professor Kinley that his (Kinley's) estimate for the per- 
 centage of check circulation in 1896 was a "safe minimum," 
 but expressed the contrary opinion that it was rather a safe 
 maximum. We shall give reasons for believing that Kinley 
 was quite right in concluding that the estimate of check trans- 
 actions at three fourths of total transactions was a "safe 
 minimum." The calculations which we shall presently offer 
 prove nine tenths rather than three fourths to be the probable 
 figure. 
 
 Professor Kemmerer, as already indicated, estimates check 
 
 430
 
 Sec. 1] APPENDIX TO CHAPTER XII 431 
 
 transactions (what we have called M'V) at 143 billions in 
 1896. For other years than 1896, there being no corre- 
 sponding data, he estimates check transactions by assuming 
 that bank clearings are always 35 per cent thereof (p. 118). 
 He makes no attempt to estimate M' (bank deposits) and F' 
 (their velocity) separately. The volmne of trade (T) Pro- 
 fessor Kemmerer estimates relatively (i.e. he estimates what 
 we have called Q in the Appendix to Chapter X). This is 
 confessedly one of the roughest parts of all his estimates. 
 He seeks to get as many indicators as possible of the growth 
 of trade (p. 130), without much regard to their suitability. 
 His indicators are fifteen in number, viz. population, foreign 
 tonnage entered and cleared, exports and imports of mer- 
 chandise (values), revenues of Post Office Department, gross 
 earnings from operation of railroads in the United States, 
 freight carried by railroads, receipts of Western Union Tele- 
 graph Company, consumption of pig iron, bituminous coal, 
 wheat, corn, cotton, wool, wines and liquors, and market 
 value of reported sales on New York Stock Exchange. Rep- 
 resenting each of these sets of figures by index numbers, he 
 takes their simple average as the index number of trade for 
 each year in question. 
 
 Of course, as Professor Kemmerer well realized, many of 
 these figures are open to more or less serious objections. 
 Population is a poor index of trade when trade per capita is 
 changing. Values are inappropriate unless the prices are 
 supposed constant, which cannot be the case for exports and 
 imports, railroad earnings, or stocks, and can be only par- 
 tially the case for post office revenues and telegraph receipts. 
 
 Having thus computed for 1879-1908 the various elements 
 theoretically determining price levels (viz. MV+M'V and 
 T), Professor Kemmerer uses these to calculate an index 
 number of prices. The index number thus calculated from 
 the other magnitudes in the equation of exchange, he calls 
 the "relative circulation." He then compares the figures 
 for relative circulation (virtually from the formula P = 
 (MV -\- M'V) -i- T) with the actual statistics of price levels.
 
 432 THE PURCHASING POWER OF MONEY [Append. XII 
 
 These directly calculated index numbers of prices he takes 
 as an average of index numbers of wholesale prices (Com- 
 mon's figures and those of the Bureau of Labor, p. 137), 
 wages (those of reports of Bureau of Labor, p. 137), and of 
 the Industrial Commission), and prices of railroad stocks (In- 
 dustrial Commission and Wall Street Journal), weighting 
 them as follows : wages, 3 per cent ; stocks, 8 per cent ; 
 wholesale commodities, 89 per cent. 
 
 The two sets of figures — "relative circulation" and "gen- 
 eral prices" — presented visually by curves (p. 149), show 
 a general agreement. 
 
 § 2 (to Chapter XII, § 2) 
 
 Method of Calculating M 
 
 The estimates for M, or money in circulation in the United 
 States, are based on the reports of Comptroller of the Cur- 
 rency. The calculations are shown in the following table : — 
 
 Money in the United States, etc. (in Billions of Dollars) 
 
 (1) 
 
 (2) 
 
 (3) 
 
 (4) 
 
 (5) 
 
 (6) 
 
 (7) 
 
 (8) 
 
 
 ai 
 
 «il 
 
 CQ 
 
 2! 
 
 2 « S z 
 
 •^ [d K ^ 
 
 m 2 
 
 o 2 o 
 ca Q as 
 
 
 & 
 
 ^a 
 
 tJ 
 
 
 fifi^ScQ 
 
 p3 
 
 oS" 
 
 YSAB 
 
 
 se 
 
 Z » 
 
 2: a 
 
 a -. a 
 
 t. a 
 
 2B 
 
 ^ a 
 
 
 ^r. 
 
 i» H 
 
 f-5 
 
 IhS 
 
 o 5ft >- 
 
 w a 
 
 >-Za 
 
 
 u ^ 
 
 a K-"? 
 
 » 5 
 
 a o 
 
 ■^ w ° s 
 
 a «^^ 
 
 a ^ 2; 
 
 
 
 
 5- ^ 
 
 §1 
 
 w 2 z 3 
 
 t3WO§ 
 
 hi 
 
 
 1896 . . 
 
 1.80 
 
 1.74 
 
 .29 
 
 .53 
 
 8.4% 
 
 .58 
 
 .87 
 
 1897 . . 
 
 1.91 
 
 1.83 
 
 .27 
 
 .63 
 
 8.4% 
 
 .68 
 
 .88 
 
 1898 . . 
 
 2.07 
 
 1.94 
 
 .24 
 
 .69 
 
 7.7% 
 
 .74 
 
 .96 
 
 1899 . . 
 
 2.19 
 
 2.09 
 
 .29 
 
 .72 
 
 6.7% 
 
 .77 
 
 1.03 
 
 1900 . . 
 
 2.34 
 
 2.25 
 
 .28 
 
 .75 
 
 6.4% 
 
 .80 
 
 1.17 
 
 1901 . . 
 
 2.48 
 
 2.37 
 
 .31 
 
 .79 
 
 5.4% 
 
 .84 
 
 1.22 
 
 1902 . . 
 
 2.56 
 
 2.45 
 
 .31 
 
 .84 
 
 5.3% 
 
 .88 
 
 1.26 
 
 1903 . . 
 
 2.68 
 
 2.59 
 
 .32 
 
 .85 
 
 5.2% 
 
 .89 
 
 1.38 
 
 1904 . . 
 
 2.80 
 
 2.68 
 
 .28 
 
 .98 
 
 4.5% 
 
 1.03 
 
 1.37 
 
 1905 . . 
 
 2.88 
 
 2.77 
 
 .29 
 
 .99 
 
 3.9% 
 
 1.03 
 
 1.45 
 
 1906 . . 
 
 3.07 
 
 2.97 
 
 .33 
 
 1.01 
 
 3.4% 
 
 1.05 
 
 1.59 
 
 1907 . . 
 
 3.12 
 
 3.12 
 
 .34 
 
 1.11 
 
 4.2% 
 
 1.15 
 
 1.63 
 
 1908 . . 
 
 3.38 
 
 3.38 
 
 .34 
 
 1.36 
 
 3.8% 
 
 1.41 
 
 1.63 
 
 1909 . . 
 
 3.41 
 
 3.41 
 
 .30 
 
 1.44 
 
 2.8% 
 
 1.48 
 
 1.63
 
 Sec. 2] APPENDIX TO CHAPTER XII 433 
 
 Column (2) gives the money in the United States in the middle 
 of each calendar year according to the official estimates of the 
 director of the mint. In 1907 these official estimates were 
 corrected by subtracting an estimated error of $135,000,000 
 from the gold believed to be in the United States, this cor- 
 rection being made in view of the investigations of Maurice 
 L. Muhleman. The mint corrections were made, however, 
 only for the ends of calendar years. ^ In order to make the 
 corrections apply to the middle of a given calendar year, the 
 corrected figures for gold in the United States at the begin- 
 ning and end of it were averaged. The average thus obtained 
 was assumed to be the corrected figure for gold at the middle 
 of the year. This corrected figure was then compared with the 
 official figure for gold for the middle of the year and the differ- 
 ence assumed to be the correction for that date. This correc- 
 tion was then deducted from the figures for money in the 
 United States given in column (2) above. We thus obtain the 
 figures in column (3). Mr. Muhleman has made independent 
 corrections for the middles of the years 1896-1900 inclusive. 
 These are slightly smaller than those calculated from the mint 
 figures as given above, the differences being in successive 
 years, .05, .03, .00, .03, .05. Columns (4) and (5) of our table 
 give the money in the federal treasury and the money re- 
 ported in banks as stated in the annual reports of the Comp- 
 troller of the Currency. Column (6) gives the estimated per- 
 centage not reported. This estimate is found by assuming 
 that the unreported reserves bear the same ratio to there- 
 ported reserves as unreported deposits bear to reported de- 
 posits, the latter ratios being calculated from the table given 
 in the next section (§ 3) of this Appendix. 
 
 This estimated percentage being calculated and the correc- 
 tion found by it being added to the money in reporting banks, 
 (column 5), we get the total estimated money in banks, 
 (column 7). Column (8) is then found by subtracting from the 
 corrected money in the United States (as given in column 3), 
 
 ' See Report of the Director of the Mint, 1907, p. 87. 
 2f
 
 434 THE PURCHASING POWER OF MONEY [Append. XII 
 
 the sum of the money m treasury (column 4), and estimated 
 money in banks (column 7). These estimates of money in 
 nonreporting banks are of course subject to some error; but 
 even a 50 per cent error in the largest of them would not 
 affect the last column much more than 2 per cent. A more 
 important possible source of error is in column (2), which de- 
 pends upon hypothetical estimates of gold in the United 
 States. Mr. Muhleman writes me that in his opinion the 
 corrections made by the Mint Bureau are not adequate. 
 The corrections as made by that Bureau and here adopted 
 affect several of the figures in column (8) by as much as 10 
 per cent. The errors in these corrections would presumably 
 be much smaller than this. There are few other sources of 
 error and, taking all things into account, it seems likely that 
 the results are in general trustworthy — subject to a prob- 
 able error of perhaps 2 or 3 per cent. This is fair accuracy 
 as ordinary statistics go. 
 
 § 3 (to Chapter XII, § 2) 
 
 Method of Calculating M' 
 
 The calculations for obtaining M', or individual deposits 
 subject to check, are shown in the table on page 49. 
 
 The figures of column (2) are those of "Individual Depos- 
 its" taken from the annual reports of the Comptroller of the 
 Currency (see Report for 1909, pp. 64-66). For the years 
 1896-1899 correction is made for deposits of trust companies 
 and savings banks misclassified as individual deposits. Prior 
 to 1900 many banks included such deposits of bankers as 
 individual deposits. They should be deducted because such 
 deposits in one bank by other banks are not generally used 
 for commercial purchases, but for banking operations. These 
 deposits, to be deducted from column (2), are given in col- 
 umn (3). 
 
 The figures in cloumn (3) are estimates baaed on the fact 
 that the deposits of savings banks and trust companies in 
 national banks are (whenever comparison is possible, viz.
 
 Sec. 3] 
 
 APPENDIX TO CHAPTER XII 
 
 435 
 
 1900-1908) found to be approximately equal to the deposits 
 of state banks in national banks. As the state bank figures 
 are available for 1896-1899, they are taken in Ueu of the 
 missing trust and savings figures. Since the original edition 
 of this book was printed, consultation with the Comptroller 
 has convinced the writer that these corrections are too large 
 and that it would have been better to have omitted them 
 altogether. They are retained, however, in order not to 
 necessitate numerous changes in the plates. Fortunately, 
 as will be seen on page 492, the net error thus retained is 
 very small. 
 
 iNDivmuAL Deposits, Subject to Check (in Billions of Dollars) 
 
 (1) 
 
 (2)J 
 
 (3) 
 
 (4) 
 
 (5) 
 
 (6) 
 
 (7) 
 
 (8) 
 
 (9) 
 
 
 H 
 
 o 
 
 » OQ re 
 Q tH O M 
 
 «5 
 
 00 
 
 o 
 
 > 
 
 
 iO '-' 
 
 KM 
 
 00 
 
 KM 
 
 
 Q 
 
 B BS >■ l) 
 
 2; S 
 t> 9 
 
 < 
 
 OS 
 Ui o 
 
 
 n M 
 
 g^5 
 
 Yeab 
 
 < 
 g 
 > 
 
 a! o S 
 -< " Z z 
 J m •< S 
 O E- . . 
 
 '^ a. 
 
 bQ 
 
 < a 
 
 g 
 
 00 
 00 00 
 
 ooW 
 
 li 
 
 n •< 
 
 2q 00 
 
 Y« o 
 
 .-,0 w 
 
 
 X jO 
 
 
 a 
 2; 
 
 00 5! (B a! 
 
 SSopa 
 
 CO o 
 
 w2 
 
 
 o a 
 X J 
 WO 
 
 1 « J 
 S5S 
 
 s) 
 
 
 1896 . . . 
 
 4.95 
 
 .16 
 
 .40 
 
 1.91 
 
 .11 
 
 3.17 
 
 85 
 
 2.68 
 
 1897 . 
 
 
 5.10 
 
 .21 
 
 .41 
 
 1.94 
 
 .11 
 
 3.25 
 
 86 
 
 2.80 
 
 1898 . 
 
 
 5.69 
 
 .25 
 
 .42 
 
 2.07 
 
 .16 
 
 3.63 
 
 88 
 
 3.19 
 
 1899 . 
 
 
 6.77 
 
 .33 
 
 .44 
 
 2.23 
 
 .27 
 
 4.38 
 
 89 
 
 3.90 
 
 1900 . 
 
 
 7.24 
 
 
 .45 
 
 2.45 
 
 .18 
 
 5.06 
 
 87 
 
 4.40 
 
 1901 . 
 
 
 8.46 
 
 
 .46 
 
 2.60 
 
 .36 
 
 5.96 
 
 86 
 
 5.13 
 
 1902 . 
 
 
 9.10 
 
 
 .48 
 
 2.75 
 
 .36 
 
 6.47 
 
 84 
 
 5.43 
 
 1903 . 
 
 
 9.55 
 
 
 .50 
 
 2.93 
 
 .25 
 
 6.87 
 
 83 
 
 5.70 
 
 1904 . 
 
 
 10.00 
 
 
 .45 
 
 3.06 
 
 .23 
 
 7.16 
 
 81 
 
 5.80 
 
 1905 . 
 
 
 11.35 
 
 
 .44 
 
 3.26 
 
 .36 
 
 8.17 
 
 80 
 
 6.54 
 
 1906 . 
 
 
 12.22 
 
 
 .41 
 
 3.48 
 
 .40 
 
 8.75 
 
 78 
 
 6.84 
 
 1907 . 
 
 
 13.10 
 
 
 .55 
 
 3.69 
 
 .33 
 
 9.63 
 
 74 
 
 7.13 
 
 1908 . 
 
 
 12.78 
 
 
 .49 
 
 3.66 
 
 .29 
 
 9.30 
 
 71 
 
 6.60 
 
 1909 . 
 
 
 14.01 
 
 
 .39 
 
 3.91 
 
 .38 
 
 10.11 
 
 67 
 
 6.75 
 
 After deducting the correction of colunm (3), our next 
 step is to add the correction of column (4), the estimated 
 deposits unreported. 
 
 The figures for nonreporting banks for 1900 and 1902-1909
 
 436 THE PURCHASING POWER OF MONEY [Append. XII 
 
 are the official estimates of the Comptroller of the Currency. 
 (Those for 1900 and 1902 are entered in the Comptroller's 
 tables under the rubric "reporting capital only" instead of 
 "nonreporting," but I am assured by the Comptroller's 
 office that this is a distinction without a difference.) The 
 figure for 1901 is interpolated between those of 1900 and 1902. 
 The figure for 1896 is estimated by the aid of two assumptions. 
 The first assumption is that the unreported deposits in that 
 year should be larger relatively to all deposits than was the 
 case in 1903, as the table shows that the farther back we go 
 the larger is the percentage of missing deposits. This con- 
 sideration indicates that the correction exceeds .28. The 
 second assumption is that the correction should be less 
 absolutely than in later years ; because the total deposits were 
 then much less than later; and because the official figures 
 in column (4), viz. those for 1900 and 1902-1909 show, as we 
 proceed backward in time, that there is a shght tendency for 
 them to grow less in absolute amount. (The chief exception 
 is for 1909, when the special investigation of April 28 reached 
 an unusual degree of accuracy.) This consideration would 
 make the correction less than .50. Therefore, between .28 
 and .50 we select .40 as a rough mean. The error involved is 
 not likely to affect the final column more than 3 or 4 per 
 cent. The corrections for 1897-1899 are interpolated. 
 
 Column (5) gives a correction to be subtracted, viz. the 
 deposits in savings banks. These deposits, by the nature 
 of the case, are not used as a circulating medium, but are 
 nevertheless included in the official "individual deposits" 
 of column (2). The item for 1909 as here given includes, 
 besides the reported figures, an additional item of .20 (i.e. 
 $200,000,000), being the savings accounts of the state 
 banks of Illinois. The inclusion of this Illinois item is 
 simply in order to make the figures for 1909 comparable 
 with those of the preceding years in which the same item 
 had always been included (see Comptroller's Report, 1909, 
 pp. 43-44). 
 
 Column (6) contains another, though small, subtractive
 
 Sec. 3] APPENDIX TO CHAPTER XII 437 
 
 correction, viz. the "exchanges for clearing house." In 
 general, these exchanges represent checks which have been 
 deposited by the persons receiving them but which have not 
 yet reached the home bank and been charged against the per- 
 sons who drew them. Any one (except a sharper or a 
 blunderer) will, as soon as he has drawn a check, deduct the 
 amount of it (say $100) from his deposit balance and refrain 
 from drawing against it again. Such a person — say Smith 
 
 — regards the $100 as transferred to his drawee — say Jones 
 
 — and no more Smith's than money would be which he had 
 paid out. But it takes time before the bank on which Smith 
 draws knows of this transfer of Smith's deposits to Jones. 
 In the meantime the bank books still include this $100 among 
 Smith's deposits. The total figure for deposits is not dis- 
 turbed by the inclusion of the $100 in Smith's account pro- 
 vided it is not included in Jones's account also. But when 
 Jones deposits the check in his bank, this (Jones's) bank adds 
 $100 to Jones's account before Smith's bank can deduct it from 
 Smith's account. That is, the $100 is temporarily counted as 
 both Smith's and Jones's. If both sides of this transfer were 
 recorded at the same time, there would be no double counting. 
 But until the check reaches Smith's bank the only record of 
 the deduction which should be made from Smith's account is 
 in the ''exchanges for clearing house" which, accordingly, we 
 must deduct in our statistics. 
 
 These figures, however, have to be estimated. Only for 
 April 28, 1909, are they given for all banks, the figures being 
 those of the special Report of the Monetary Commission al- 
 ready referred to. Of this amount, four fifths are of national 
 banks ; and as national banks report annually their exchanges 
 against clearing houses, we assume that the total each year 
 is five fourths of that reported by the national banks (see 
 Comptroller's Report, 1908, pp. 514-522). The whole correc- 
 tion is so small that any error in this assumed ratio is quite 
 negligible in the final result. 
 
 Column (7) is derived by applying to column (2) the above 
 mentioned corrections, — deduction of items in column (3),
 
 438 THE PURCHASING POWER OF MONEY [Append. XII 
 
 addition of those of column (4), deduction of column (5), and 
 deduction of column (6). 
 
 But even yet we have not reached the desired item, — deposit 
 currency, or deposits subject to check. The net individual 
 deposits which we have estimated include, not only current 
 accounts, but deposits on certificate and other deposits which 
 are considered investments rather than media of exchange. 
 The first published attempt to give the true deposits subject to 
 check is that of the National Monetary Commission. In their 
 valuable special Report as of April 28, 1 909, constructed through 
 the Comptroller of the Currency, the checkable deposits are 
 given as 6.94 billions.^ This 6.94 is subject to an addition 
 for " nonreporting banks" and a deduction for "exchange 
 against clearing house." The unreported deposits of all 
 kinds are estimated for 1909 in the table at .39, of which, by 
 
 proportion, only — — of .39 or .19, is probably checkable. 
 
 The .38 exchanges against clearing houses must be assumed to 
 be almost wholly against deposits subject to check. The net 
 corrected figure is therefore 6.94 + .19 — .38 or 6.75 billions 
 as the checkable deposits in 1909. These constitute about 
 67 per cent of the "net individual deposits " of column (7). 
 
 This figure for checkable deposits in 1909 is found at the 
 bottom of column (9) in the table. As it is only 67 per cent 
 of the net individual deposits, and as it could not be assumed 
 that the same ratio obtained for other years, I was unwilling 
 to guess at the deposits subject to check for these other years 
 without further light. Accordingly I wrote to Mr. A. Piatt 
 Andrew, then Director of the Mint, and asked him whether, 
 in his capacity as advisor to the Monetary Commission, he 
 could not have a search made among the Comptroller's rec- 
 ords for 1896 and a few other years in order to obtain the 
 
 > See Senate Document, 225, 61st Congress, 2d Session, Special 
 Report from Banks of the United States, April 28, 1909, p. 261 ; also 
 Report of Comptroller of the Currency, 1909, p. 835. The figures are 
 exclusive of Hawaii, Porto Rico, and the Philippines, although the 
 8tun thus excluded is scarcely appreciable.
 
 Sec. 3] APPENDIX TO CHAPTER XII 439 
 
 corresponding ratio for such years. Through his kindness 
 and that of the Commission and Comptroller, in acceding to 
 my request, it has been made possible to work out the corre- 
 sponding ratio for 1896 as 85 per cent; for 1899 as 89 per cent; 
 and for 1906 as 78 per cent. 
 
 Mr. Andrew gives 4.97 billions as the total (uncorrected) 
 deposits of all banks as of July 14, 1896. This figure is 
 slightly more complete than what I had already used from the 
 Comptroller's Report (viz. 4.95), doubtless because, for this 
 particular inquiry, a larger number of banks were included 
 than had originally been used in the Comptroller's tables. 
 Mr. Andrew gives the checkable deposits as 2.59 billions. 
 This figure is subject to two corrections: one to account for 
 unreporting banks, and one to account for exchanges for clear- 
 ing house. We have estimated the deposits of nonreporting 
 banks at .40 ; and, since Mr. Andrew has discovered in such 
 banks .02 more total deposits (4.97) than the Comptroller 
 reported, we must assume that there are .02 less unreported 
 deposits in his figures than in the Comptroller's. This would 
 make the estimated unreported deposits for Andrew's figures 
 .38 instead of .40 which we assumed for the Comptroller's. 
 The part of this ascribable to the deposits subject to check 
 
 (2.59) is ^^ X .38 or .20. This is the first (and additive) 
 4.97 
 
 correction. The second (and subtractive) correction is the 
 
 exchanges for clearing house, viz. .11. The final corrected 
 
 figure is therefore 2.59 + .20 - .11 or 2.68. The ratio of 
 
 2 68 
 this to the "net deposits" is -^ or 85 per cent. 
 
 For 1899, Andrew's figures for total net deposits are 4.38 and 
 for checkable deposits 4.09. His figures for total deposits 
 (7.07) are .30 completer than those of the Comptroller em- 
 ployed in the first column of the above table, and thus reduce 
 the estimate for nonreporting banks apphcable to Andrew's 
 
 4 OQ M 
 
 figures from .44 to .14, of which -^ X .14 or .08 are ascnb- 
 * 7.07 
 
 able to the deposits subject to check. The correction con-
 
 440 THE PURCHASING POWER OF MONEY [Append. XII 
 
 sisting of exchanges for clearing house is .27. The figures 
 for checkable deposits are therefore 4.09 + .08 — .27 or 
 3.90, which is 89 per cent of the "net deposits" (4.38). 
 
 For 1906 Andrew's figures for total net deposits are 8.75 
 and for checkable deposits, 6.90. His figures for total 
 deposits (12.37) are less complete than those of the Comp- 
 troller, thus increasing the estimate for unreporting banks 
 
 apphcable to his figures from .41 to .61, of which X .61 
 
 or .34 are ascribable to the deposits subject to check. The 
 exchanges for clearing house were .40. The figures for check- 
 able deposits are therefore 6.90 + .34 — 40 or 6.84, which is 
 78 per cent of the "net deposits" 8.75) We thus have 
 figures for column (9) and column (8) for the years 1896, 
 1899, 1906, 1909. 
 
 If now, for intervening years, we interpolate evenly between 
 these percentage figures for the years 1896, 1899, 1906, 1909, 
 we shall have column (8) of the preceding table. 
 
 Column (9) may next be formed for the remaining years 
 by applying the percentages in column (8) to the net indi- 
 vidual deposits in column (7) . Thus the table is made com- 
 plete. 
 
 The results are of course subject to a probable error which, 
 however, is believed to be only some 2 or 3 per cent for 
 the years 1896, 1899, 1906, 1909, and perhaps double as 
 much for years midway in the intervals between these four 
 years. 
 
 It seems strange, since so much has been said of the relative 
 importance of check and money circulation, that no attempt 
 has previously been made to estimate or record the volume of 
 the currency which circulates by check. This currency and 
 its circulation are of many times the statistical importance of 
 money and its circalation. Our wonder is the greater when 
 we consider that " deposits subject to check" have been regu- 
 larly reported by individual banks to the Comptroller of 
 the Currency. The pubUshed figures began in the '60's to 
 omit this category and lump all "individual deposits" to-
 
 Sec. 4] APPENDIX TO CHAPTER XII 441 
 
 gether, and subsequent reports have simply followed the prec- 
 edent thus established. The present Comptroller states that 
 he intends, hereafter, to separate the item of deposits subject 
 to check ; so that we may hope from now on to have annual 
 returns of the checkable deposits. We shall then know each 
 year the magnitude of that item in our circulatory medium 
 which, as we shall see, does nine tenths of the exchange 
 work of the coimtry. 
 
 § 4 (to Chapter XII, § 3) 
 Method of Calculating M'V for 1896 and 1909 
 
 According to the Comptroller's Report for 1896, the total 
 sum (money and checks) deposited in all reporting banks on 
 the settling day nearest July 1, 1896, was 303 millions. Pro- 
 fessor Kemmerer's allowance for nonreporting banks (op. cit., 
 pp. 110-111) brings the figures up to 506 milhons. The pro- 
 portion of checks found in all deposits reported Avas 92.5 per 
 cent, which, if appUed to the estimated 506 millions of total 
 deposits, will give 468 millions as the total checks deposited 
 in one day. But July 1, being a first day of the month, 
 would show exceptionally large deposits. In order to de- 
 termine how much allowance to make for this fact, I have 
 obtained, through the kindness of Mr. Gilpin of the New 
 York clearing house, the figures for the New York clearings of 
 July 2, 1896. July 2 was selected because the checks depos- 
 ited in New York July 1 would appear in the clearing house 
 statistics of July 2. The clearings for July 2 amounted to 
 157 millions, while the daily average for 1896 was only 95 
 millions or 60 per cent as much. Thus, the excessive clear- 
 ings of July 2 have to be corrected by multiplying by .60 in 
 order to reach a true average for the year. It is perhaps fair 
 to assume that the deposits made on July 1 in New York 
 require substantially the same correction. If we could as- 
 sume that the abnormality of the day's deposits in the rest 
 of the country were exactly like that of New York, requiring 
 the same correction factor (.60), then this correction factoi
 
 442 THE PURCHASING POWER OP MONEY [Append. XII 
 
 would apply to the whole country. But this assumption we 
 cannot make. Doubtless .60 is too small an estimate of the 
 true multiplier for the whole country outside of New York. 
 The departure from the average was probably somewhat less 
 than in New York City. 
 
 That this is the case appears likely for various reasons. 
 In the first place New York is more sensitive to the varia- 
 tions in business activity than the country generally. Con- 
 sistently with this view, we find that the percentage fluctua- 
 tion in clearings from year to year is much greater in New 
 York than in the rest of the country. By comparing each 
 year with the next, we find this to be true of all except five of 
 the twenty-seven years from 1883 to 1909 ^ inclusive. 
 
 Again, the quarterly and semiannual dividends would cut a 
 larger figure in a financial center like New York than in other 
 places, in many of which few or no dividends are received. 
 
 Finally, in large cities like New York, checks are deposited 
 more systematically and promptly, so that a fuller proportion 
 of the first-of-the-month checks received on July 1 would be 
 deposited on that day than in a smaller community. In the 
 smaller community these checks straggle along to banks 
 through several days after being received, thus tending to 
 even up the daily flow and in particular to diminish the excess 
 on and about July 1. We conclude that .60 is a minimum 
 estimate for our multipHer for 1896. 
 
 Having obtained .60 as a minimum estimate, we next 
 proceed to ascertain a maximum estimate. We may be 
 reasonably sure that deposits outside of New York are so far 
 subject to the influence of quarterly dividends, first-of-the- 
 month payments, etc., that the volume of checks deposited 
 outside of New York must to some extent exceed the average 
 in 1896. We need to know to what extent we are safe in 
 assuming that this outside volume of checks deposited on the 
 day chosen exceeded the average. We can best reach such a 
 
 ' See Financial Review (the Annual of the Commercial and 
 Financial Chronicle), 1906, p. 26 and 1910, p. 33.
 
 Sec. 4] APPENDIX TO CHAPTER XII 443 
 
 safe estimate by means of some data on clearing houses in the 
 Finance Report for 1896 (p. 493, Comptroller's Report). 
 It is there shown that on July 1, or "the settling day nearest 
 July 1," 66 out of the 78 clearing houses of the country had 
 $228,000,000 of clearings. We are safe in assuming that the 
 country's total clearings on that day were larger than this, be- 
 cause the returns as given include only 66 out of the 78 clear- 
 ing houses of the country ; and that on the following day they 
 were larger still, ^ because it was then that occurred the bulk of 
 the heavy July 1 deposits of checks. If the $228,000,000 clear- 
 ings on July 1, 1896, were representative for each day of 
 1896, we could, simply by multipl3dng by the number of 
 setthng days of 1896, 305 days, find the total clearings of the 
 country. But the result of this multipUcation is 67.1 bil- 
 lions, whereas the actual clearings of the country for 1896 
 were only 51.2 billions. This is conclusive evidence that the 
 clearings on July 1, and presumably still more those of July 2, 
 exceeded the daily average and need to be reduced at least in 
 
 the ratio — — or .76. 
 67.1 
 
 Hence the true correction factor must he between .60 and 
 .76. Sphtting the difference we have .68 as an estimate which 
 cannot be far from the correct figures on either side ; espe- 
 cially as .60 and .76 are so very safe or extreme limits. Fig- 
 ures very near either of them are improbable. The 'probable 
 error is simply set at 5 or 6 per cent. 
 
 We turn now to similar calculations for 1909. At my 
 request Professor Weston of the University of Illinois, 
 through the kindness of Professor Kinley, has used sub- 
 stantially the same method for estimating the check circula- 
 
 1 Convincing proof that the clearings on July 2 exceeded those 
 on July 1 is afforded by the fact that whereas the New York state 
 clearings for July 1, 1896, were $140,000,000, as given in the Comp- 
 troller's Report for 1896 (p. 494), the New York City clearings 
 alone on July 2 were $157,000,000. 
 
 For New York City the clearings, as Mr. Gilpin of the New York 
 clearing house has informed me, were far larger on July 2, 1896, 
 than on July 1, the two figures being 157 and 138 millions respectively.
 
 444 THE PURCHASING POWER OF MONEY [Append. XII 
 
 tion of 1909 based on Kinley's investigation ' of that year for 
 March 16. Professor Weston estimates the total check de- 
 posits of March 16, 1909, at 1.02 billions. This is below the 
 daily average. A proof of this is found in the clearings of the 
 New York clearing house on March 17, which reflect the de- 
 posits made in New York banks on the previous day; these 
 were 268 millions, which was not representative of the year, 
 as the average daily clearings were much greater, being 342 
 millions, or 28 per cent greater than those of March 17. 
 1.28 is therefore the correction multiplier we would apply if 
 we could trust New York clearings to be a faithful barometer 
 for the whole country. But since, as we have seen, New 
 York is especially sensitive to speculative and other varia- 
 tions in banking operations, and as a part is usually more 
 variable than the whole, it is reasonable to assume that the 
 abnormality we find in New York of the deposits on March 
 16 exaggerates the abnormality of that day for the country 
 at large, and tiiat the correction multiplier should be less 
 than 1.28. In order to set a safe lower limit, we may see 
 what figure would result from the extreme assimaption that 
 outside of New York the day's deposits on March 16, 1909, 
 were exactly the same as the daily average for the year. 
 We can make a fairly good estimate of the resulting correc- 
 tion factor from the table on page 59. 
 
 This table is constructed from data taken from Kinley's 
 report to the Monetary Commission on Credit Instruments 
 (pp. 182, 186) together with the estimated corrections for the 
 whole country's check deposits made by Professor Weston. 
 
 The figure for deposits in New York City is given for March 
 16, 1909. Deducting these figures from those estimated by 
 Weston for the entire country, we have the deposits (786) 
 outside New York. But the daily average in New York has 
 been shown to be probably 28 per cent higher, or 306. These 
 figures, added to those for deposits outside New York (786), 
 
 ^ Kinley, The Use of Credit Instruments in Payments in the United 
 Slates, National Monetary Commission, 61st Congress, 2d Session, 
 Doc. No. 399, 1910.
 
 Sec. 4] 
 
 APPENDIX TO CHAPTER XII 
 
 445 
 
 give the daily average for the entire country, on the assump- 
 tion that only New York City was abnormal on the day se- 
 lected. The result (1092), compared with the actual deposits 
 on the day selected (1025), shows the correction factor on the 
 assumption that only New York was abnormal. This factor 
 is 1.07. This furnishes a lower limit for the correction factor 
 we are seeking. 
 
 Checks Deposited (in Millions) 
 
 (1) 
 
 March 16, 1909 
 
 Daily average if New York were alone 
 abnormal 
 
 Ratio average to actual = = 1.07 
 
 1025 
 
 (2) 
 
 New York 
 City 
 
 239 
 306 
 
 (3) 
 
 Outside 
 
 New York 
 
 City 
 
 786 
 786 
 
 (4) 
 
 Total 
 U.S. 
 
 1025 
 1092 
 
 Splitting the difference between our extreme Hmits, 1.07 
 and 1.28, we get, as our estimate of the correction factors, 
 1.17 in 1909 as compared with .68 for 1896. The range of 
 possible error on either side is about 10 for 1909 and 8 for 
 1896. As the limits are all very extreme, the probable error 
 must be much less — perhaps half as much. We may judge 
 that the correction factors, .68 and 1.17, are probably correct 
 within 5 or 6 per cent. 
 
 We conclude, then, that the 468 millions estimated as the 
 actual check deposits made on July 1, 1896, must be multi- 
 plied by .68 in order to obtain the estimated average daily 
 deposits in 1896. The result is 318 millions ; which, multi- 
 plied by the 305 (setthng days), gives 97.0 billions as our esti- 
 mate for the check transactions in the United States for the 
 year 1896. 
 
 Likewise, multiplying the estimated volume of actual 
 check transactions in the United States on March 16, 1909 
 (viz. 1025 millions) , by the correction factor, 1.17, we obtain
 
 446 THE PURCHASING POWER OF MONEY [Append. XII 
 
 1.20 billions as the estimated daily average check deposits 
 and transactions. Multiplying this by 303 (the number of 
 clearing days of the New York clearing house and presumably 
 the average number of banking days in the country), we 
 obtain 364 billions as our estimate of the check transactions 
 in the United States in 1909. 
 
 § 5 (to Chapter XII, § 3) 
 Method of Calculating M'V for 1897-1908 
 
 Although New York clearings constitute two thirds of all 
 clearings for the country, it cannot be imagined that the 
 check transactions in and about New York form two thirds 
 of the check transactions of the United States. We have 
 already seen that the reported check deposits in New York 
 on March 16, 1909, amounted to 239 millions. This figure, 
 being for New York, is probably nearly complete and indi- 
 cates, as we have seen, an estimated average for the daily 
 deposits in New York City in 1909 of 306 millions. This 
 gives 306 X 303 or 93 bilhons for New York City, for the 
 entire year. Our estimate for the entire country was 364 
 billions, leaving 271 billions outside of New York City. Let 
 us compare these estimated figures for checks deposited with 
 the figures for clearings. The New York clearings in 1909 
 amounted to 104 billions and those outside New York, to 
 62 billions. 
 
 The New York clearings (104) thus exceed the New York 
 check deposits (93), probably because the clearings on ac- 
 count of outside banks include clearings representing bank- 
 ing transactions as distinguished from commercial trans- 
 actions, since New York City is the chief central reserve 
 
 93 
 
 city. The New York City deposits were thus only — — ■ 
 
 or about 90 per cent of the New York clearings. Outside of 
 
 New York, on the other hand, the deposits far exceeded the 
 
 271 
 clearings, being in the ratio — - or 4.4. These ratios between
 
 Sec. 5] APPENDIX TO CHAPTER XII 447 
 
 check transactions and clearings, viz, .90 for New York and 
 4.4 for "outside," would indicate that the pubhshed figures 
 for clearings should be weighted in the ratio of 4.4 to .9 or 
 about 5 to 1. That is, on the basis of 1909 figures, five times 
 the outside clearings plus once the New York clearings should 
 be a good barometer of check transactions. 
 
 Of 1896, unfortunately, we lack the figures for New York 
 City deposits. We have, however, figures for the deposits 
 in New York state in both 1896 and ,1909 ; and a study of 
 these figures indicates that the ratio of weighting for 1896 
 should be something over 3 to 1. Not to put too fine a point 
 upon it, we shall use the weighting 5 to 1 for all the years. 
 The difference in the results between this system of 5 to 1 and 
 a system of 3 to 1, or any intermediate system, will be small, 
 but 5 to 1 is chosen because (1) the data for 1896 on which the 
 number 3 is based are less certain than those for 1909, and 
 (2) the New York clearings are not as good a representative 
 of New York deposits as the outside clearings are of outside 
 deposits ; the New York clearings being somewhat vitiated by 
 an element extraneous to New York and especially by the 
 banking transactions connected with adjustments of bank 
 reserves. We prefer, therefore, to give as much weight as 
 possible to the "outside" clearings. 
 
 Having obtained our "barometer" of check transactions, 
 viz. New York clearings plus five times outside clearings, we 
 merely need to multiply this by the proper ratio in order to 
 obtain the check transactions themselves. Absolute knowl- 
 edge of this ratio of check transactions to the barometer 
 exists only for 1896 and 1909, in which years we know 
 the check transactions as well as the barometer. These ra- 
 tios are .69 and .88. But we cannot err greatly in assuming 
 that the intermediate years have intermediate ratios, varying 
 regularly each year. The result is the following table : —
 
 448 THE PURCHASING POWER OF MONEY [Append. XH 
 Clearings as Barometer of Check Transactions 
 
 (1) 
 
 (2) 
 
 (3) 
 
 (4) 
 
 (5) 
 
 (6) M'V 
 
 (7)V' 
 
 Year 
 
 New York 
 Clearings 
 
 Outside 
 
 Clearings 
 
 Barometer 
 (2)-f-5X(3) 
 
 Ratio op 
 Check 
 Trans- 
 action TO 
 Barometer 
 
 Check 
 Trans- 
 actions 
 (4) X (5) 
 
 Velocity 
 op Circd. 
 
 OP De- 
 posits (V) 
 
 (6) -r- M' 
 
 1896 . 
 
 28.9 
 
 22.4 
 
 140.9 
 
 .69 
 
 97 
 
 36.2 
 
 1897 . 
 
 33.4 
 
 23.8 
 
 152.4 
 
 .70 
 
 106 
 
 37.9 
 
 1898 . 
 
 42.0 
 
 26.9 
 
 176.5 
 
 .72 
 
 127 
 
 39.8 
 
 1899 . 
 
 60.8 
 
 33.3 
 
 227.3 
 
 .73 
 
 166 
 
 42.6 
 
 1900 . 
 
 52.6 
 
 33.4 
 
 219.6 
 
 .75 
 
 165 
 
 37.5 
 
 1901 . 
 
 79.4 
 
 39.0 
 
 274.4 
 
 .76 
 
 208 
 
 40.6 
 
 1902 . 
 
 76.3 
 
 41.7 
 
 284.8 
 
 .78 
 
 222 
 
 40.9 
 
 1903 . 
 
 66.0 
 
 43.2 
 
 282.0 
 
 .79 
 
 223 
 
 39.1 
 
 1904 . 
 
 68.6 
 
 43.9 
 
 288.1 
 
 .81 
 
 233 
 
 40.2 
 
 1905 . 
 
 93.8 
 
 50.0 
 
 343.8 
 
 .82 
 
 282 
 
 43.1 
 
 1906 . 
 
 104.7 
 
 55.2 
 
 380.7 
 
 .84 
 
 320 
 
 46.8 
 
 1907 . 
 
 87.2 
 
 57.8 
 
 376.2 
 
 .85 
 
 320 
 
 44.9 
 
 1908 . 
 
 79.3 
 
 53.1 
 
 344.8 
 
 .87 
 
 300 
 
 45.5 
 
 1909 . 
 
 103.6 
 
 62.0 
 
 413.6 
 
 .88 
 
 364 
 
 53.9 
 
 As already indicated, only the first and last figures in column 
 (5) are independently calculated, the rest being interpolated. 
 The other figures in the table explain themselves. The last 
 column gives the very important magnitude which we have 
 called the velocity of circulation of bank deposits subject to 
 check, or the " activity " of checkable accounts. The probable 
 errors of the last column are believed to range between about 
 5 and 10 per cent. 
 
 § 6 (to Chapter XII, § 4) 
 
 General Practical Formula for Calculating V 
 I. An Approximate Formula 
 
 For the purpose of tracing the circulation of money, and 
 measuring it by bank records, we may classify the persons 
 who use money in purchase of goods into three groups : — 
 
 1. Commercial depositors, i.e. all engaged in business — 
 firms, companies, and others — who have bank deposits 
 mainly or wholly apart from personal accounts. 
 
 2. All other depositors, chiefly private persons.
 
 Sec. 6] APPENDIX TO CHAPTER XII 449 
 
 3. All who, like most wage earners, are not depositors at all. 
 
 These three classes we shall distinguish as "Commercial 
 depositors," "Other depositors," and " Nondepositors," 
 or C, 0, and N. The money in the possession of "Commer- 
 cial depositors" we shall call "till money," and the rest 
 "pocket money." 
 
 The three groups necessarily include all in the community 
 who circulate money. By circulating money is meant ex- 
 pending it in exchange, not for some other circulating medium, 
 as checks, but for goods. 
 
 The nature of these three groups of people must now occupy 
 our attention. In countries advanced in the art of banking, 
 "Commercial depositors" include practically all business 
 establishments, and little else; "Other depositors" include 
 most persons in the professional and salaried classes and pro- 
 prietors, and little else; while the class of " Nondepositors " 
 is almost coterminous with wage earners. 
 
 It is true that these characterizations of the three classes 
 are not quite complete. "Commercial depositors," for in- 
 stance, do not include some small business dealers, like street 
 vendors, for these usually have no bank accounts. But the 
 number of such is comparatively small in comparison with 
 the number of business men or corporations who do have ac- 
 counts, and, what is more to the point, the business they do is 
 still smaller. It follows that the money they handle is negli- 
 gible. In the United States, at least, excepting those rural 
 parts of the South and a few other places where the money 
 expenditures are very small, the custom of having bank 
 accounts is practically universal among business men, firms, 
 and corporations. 
 
 To keep a bank account is, in fact, a practical necessity of 
 business. Without such an account a business man practi- 
 cally deprives himself of three of the most essential aids in 
 modern business: the use of circulating credit; the use of 
 remittance by mail ; and the use of time credit. 
 
 Unless a dealer is obliged to pay "spot cash" or prefers 
 to do so — and such cases are both few in number and insignif* 
 2g
 
 450 THE PURCHASING POWER OF MONEY [Append. XII 
 
 icant in the amounts of money involved — he will almost in- 
 variably find it easier to make payment by check. More- 
 over, the very fact that most other business men use banking 
 facilities creates in his mind the desire to have an account 
 himself, both because he dislikes to appear "different," and 
 because, when others pay him by checks, he finds it necessary 
 to cash these checks, — a procedure which is always more 
 trouble than to deposit them. 
 
 Cash payments are especially inconvenient when business 
 is done at a distance. Remitting money by post, express, or 
 personal delivery is troublesome, risky, and expensive as 
 compared with posting a letter containing a check. Even 
 a post-office money order is a clumsy and expensive substi- 
 tute, and its use proclaims the user an insignificant financial 
 factor. 
 
 Again, a business man without a bank account cannot usu- 
 ally obtain time credit, either from dealers or from banks. 
 In the United States a bank likes to lend only to its own de- 
 positors. A business man who asks for a bank loan usually 
 meets with the request to open an account. If he should seek 
 a loan from another dealer, as for instance, his supply house, 
 the absence of a bank account would arouse suspicions as to 
 his business standing, and might lead to a refusal. 
 
 These facts, confirmed by observation and inquiry, have 
 led to the belief that practically all business transactions in 
 the United States, certainly over 99 per cent (measured, not 
 by their number, but by their aggregate size), make some use 
 of bank accounts. Even in localities where there are no banks, 
 traders usually like to have a bank account in the nearest 
 town, in order to facilitate their dealings as purchasers. 
 We conclude, therefore, that the category of "Commercial 
 depositors" coincides for all practical purposes with the cate- 
 gory of business establishments. 
 
 "Other depositors" include most proprietors, professional, 
 and salaried persons. Almost no wage earners are included, 
 and almost no business estabhshments or business men in a 
 business capacity. When a single individual conducts a busi-
 
 Sec. 6] APPENDIX TO CHAPTER XII 451 
 
 ness, he usually separates carefully his business self from 
 his personal self. John Smith, the individual, and the John 
 Smith Shop are distinct. The pocket money of the one and 
 the till money of the other are not often confused. Where 
 payments of money are made from one to the other, the trans- 
 action is regarded as of the same nature as the payments be- 
 tween the shop and any other person. Originally, and under 
 primitive conditions, it is of course true that no such distinc- 
 tion was observed, and even to-day the differentiation is 
 sometimes unmarked, e.g. in the case of hucksters, peddlers, 
 fruit-stand dealers, and small country shopkeepers. But, 
 as we have seen, these persons are not usually depositors 
 anyway. Moreover, their number is small; and since by the 
 nature of the case the money they handle is also small, their 
 classification is, for practical purposes, a matter of indifference. 
 It is true that occasional cases exist of ordinary business men 
 who have the exclusive ownership of a business and do not 
 take care to separate clearly their business and their personal 
 accounts. Yet we may, in such cases, perform the separation 
 in thought. When such a person withdraws money from his 
 till and puts it in his pocket, we may say his business self has 
 paid his personal self some dividends of the business. Like- 
 wise, his checks drawn are usually distinguishable as between 
 his business or his personal expenses, even though he him- 
 self fails to keep two separate bank accounts. But such cases 
 are rare and unimportant, because modern business of size is 
 usually conducted by partnerships and corporations, where a 
 strict separation of accounts is necessary to safeguard con- 
 flicting interests. 
 
 So much for the line of demarcation between "Other de- 
 positors" and "Commercial depositors." As to the hne 
 separating "Other depositors" and "Nondepositors," it 
 should be observed that, although "Other depositors" in- 
 clude most proprietors and professional and salaried persons, 
 yet some proprietors and professional men, especially in rural 
 communities, and some salaried persons, chiefly small clerks, 
 are "Nondepositors."
 
 452 THE PURCHASING POWER OF MO?>rEY [Append. XII 
 
 Finally, "Nondepositors" consist chiefly of those who are 
 classed in statistics as wage earners. While there are some 
 wage earners who are depositors,^ they are rare; and while 
 there are some "Nondepositors" who are not wage earners, 
 especially (as just indicated) the agricultural proprietors 
 (farmers) and small clerks, the amount of money circulated 
 by them is small in comparison with the total circulation. 
 While the line separating wages and salaries is not definitely 
 marked in theory, it is usually easily recognized in practice. 
 
 Children under, say, twelve years need not be included in 
 any of the three categories, as they are not handlers of money; 
 at least, not to a sufficient degree to have any appreciable in- 
 fluence on the total circulation. 
 
 We may now picture concretely the main currents of the 
 monetary flow, including the circulation of money in ex- 
 change for goods. Figure 18 illustrates the three principal 
 types. 
 
 The corners of the triangle, C, and N, represent the three 
 groups of "Commercial depositors," "Other depositors," 
 and "Nondepositors," and the 5's represent banks. The 
 arrows represent the flow of money from each of these four 
 categories to the others. Thus Bo represents the annual with- 
 drawals from banks by "Other depositors," Oc the spending 
 of this withdrawn money by "Other depositors" among 
 "Commercial depositors," and C,, the return of the money 
 from the "Commercial depositiors" to the banks. This 
 circuit (BoOcCi) of three links is very common, A second 
 type of circuit is represented by a chain of four arrows 
 (BoOnN.Ch). It is illustrated by private depositors draw- 
 ing money (Bo), and paying wages (On) to servants who in 
 turn spend the money (Nc) among tradesmen who finally 
 deposit it (C/,). A third type of circuit, also fourfold, is 
 represented by the arrows BcCnNcCh- It is illustrated by 
 commercial firms cashing their checks at banks (Be) for pay 
 
 1 The term "depositors," as here used, does not, of course, in- 
 clude savings bank depositors. A savings bank is not a true bank 
 of deposit, providing circulating credit.
 
 Sec. 6] 
 
 APPENDIX TO CHAPTER XH 
 
 453 
 
 rolls, with the cash so obtained paying wages (C„) to work- 
 men who spend it (Nc) among other tradesmen who redeposit 
 it in banks (C^). These three types are not the only ones, but 
 they are so much more important than any others that they 
 merit our undivided attention before a completer study is 
 undertaken. Figure 18 has been constructed for the purpose 
 of exhibiting them uncomphcated by other details. 
 
 Fig. 18. 
 
 It will be noted that not all of the flows described are ex- 
 amples of the circulation of money. As already indicated, 
 money may be said to circulate only when it passes in ex- 
 change for goods. Its entrance into and exit from banks is a 
 flow, but not a circulation against goods. In the diagram 
 the horizontal arrows represent such mere banking operations, 
 not true circulation. On the other hand, the arrows along the 
 sides of the triangle represent actual circulation. The dia- 
 gram shows four such arrows, representing the four chief 
 types of circulation: Oc payments of money from "Other
 
 454 THE PURCHASING POWER OF MONEY IAppend. XII 
 
 depositors" to "Commercial depositors" in the purchase of 
 goods; On payments from "Other depositors" to "Non- 
 depositors," as when a housewife pays wages; C„ payments 
 from "Commercial depositors" to "Nondepositors," as 
 when a firm pays wages; and Nc payments from "Non- 
 depositors" to "Commercial depositors," as when a wage 
 earner buys goods of a merchant. 
 
 These four types of circulation of money occur in the three 
 circuits already described, being sandwiched between the flows 
 from and to the banks. The first, Oc, is contained within 
 the circuit BoOcC^, and, since no "Nondepositors" inter- 
 vene, represents money changing hands once between its with- 
 drawal from bank and its re-deposit there. The remaining 
 types {On, Cn, and Nc) are contained within the two other 
 circuits {BjOnNcC^ and BcCnNcCf,), and, owing to the fact 
 that "Nondepositors" intervene, represent money circulat- 
 ing twice between withdrawal and re-deposit. 
 
 In short, one of the three circuits {BoOjC^) shows money 
 circulating once out of bank. Both the others pass through 
 N, and show money circulating twice out of bank. The 
 diagram, then, represents all circulating money as springing 
 from and returning to the banks; all of it as circulating at 
 least once in the interim; and that portion handled by "Non- 
 depositors" as circulating once in addition. Therefore, the 
 total circulation exceeds the total flow from and to banks 
 by the amount flowing through "Nondepositors." In other 
 words, the total circulation in the diagram is simply the sum 
 of the annual money flowing from and to banks and the 
 money handled by "Nondepositors." The quotient of this 
 sum divided by the amount of money in circulation will give 
 approximately the velocity of circulation of money. 
 
 II. The Complete Formula 
 
 We have, however, still to consider the correction to be 
 made for the less important forms of monetary circulation 
 excluded from Figure 18.
 
 Sec. 6] APPENDIX TO CHAPTER XII 455 
 
 In order to estimate the degree of accuracy of the first 
 approximation just made for the circulation of money, we 
 need to compare this approximation with a complete formula 
 framed to include all possible transfers of money against 
 goods.' There are nine possible kinds of transfers, three 
 being respectively within each one of the three groups C, 0, 
 and N, and six being between each pair of these three, in either 
 direction. 
 
 The exchanges possible within a class are (1) those between 
 one "Commercial depositor " and another "Commercial 
 depositor"; (2) those between one "Other depositor" and 
 another; and (3) those between one "Nondepositor " and 
 another. The transfers possible between classes are (4 
 and 5) those between "Commercial depositors" and "Other 
 depositors " in either direction ; (6 and 7) those between 
 " Other depositors " and " Nondepositors " in either direction; 
 and (8 and 9) those between "Nondepositors" and "Com- 
 mercial depositors" in either direction. Thus there are 
 three intraclass kinds and six interclass kinds of transfers of 
 money against goods. 
 
 Figure 19 gives a complete picture of all these nine flows 
 of money in exchange for goods; that is, of the entire "cir- 
 culation of money." The nine flows are represented in the 
 diagram by the nine arrows about the triangle, six being along 
 the three sides of the triangle and representing interclass 
 circulation, and three (c, o, and n) at the corners to represent 
 intraclass circulation. The remaining six arrows on the hori- 
 zontal lines represent, of course, mere banking operations. 
 The total circulation or monetary flow (F) in exchange for 
 
 ^ That is, all transfers within the community considered. If it 
 is desired to include as part of a community's circulation the sums 
 exported or imported in foreign trade, these may most conveniently 
 be added at the end. But even if they be included, they will be of 
 trifling significance, partly because foreign trade is usually very 
 small compared with domestic, and partly because money is so little 
 used in foreign trade, especially if we exclude bullion from the 
 category of money.
 
 456 THE PURCHASING POWER OF MONEY [Append. XH 
 
 goods is, therefore, the sum of the magnitudes represented 
 by these nine arrows, viz. 
 
 F = Oc-\-Co^-Nc^-Cn + On + No + c + o-\-n. 
 
 (1) 
 
 This is an exact formula for the circulation of money. We 
 shall now compare it with the inexact first approximation, 
 
 Qi 
 
 '3 
 
 a 
 
 Fig. 19. 
 
 namely, "money deposited plus expenditures of 'Nondeposi- 
 tors. '" This comparison will express the error of the first 
 approximation, and will suggest a method of transforming the 
 exact formula (1) into a shape more suitable for statistical 
 application. First, we need to express algebraically the 
 first approximation. This may easily be done by inspect- 
 ing Figure 19. The total money deposited is 0^ + 06 + 
 Nj, while the total expenditure of " Nondepositors " is 
 Nc + No. The sum of these two expressions we shall call ¥'. 
 It is: — 
 
 /^' = C, + 0,+Ar, + iV, + iV„ (2)
 
 Sec. 6] APPENDIX TO CHAPTER XII 457 
 
 which is, therefore, the algebraic expression for the first ap- 
 proximation. 
 
 To obtain the difference, F — F', between the exact and the 
 approximate formula, we subtract (2) from (1), canceling Ne 
 and No and placing the negative terms first. We thus obtain 
 for a remainder (/•) the following : — 
 
 r=/r_/r'= -c,-0,-N,+Oc-h Co+Cn-{-On-\-c+o-\-n. (3) 
 
 That the value oi F — F' is small may be seen clearly by 
 transforming (3) . We shall transform it by means of another 
 equation (4) given below. In order to derive this new equa- 
 tion (4), we shall need to make a digression. This new equa- 
 tion is merely a special application of the general principle 
 that the net outflow (i.e. outflow minus inflow) from the con- 
 tents of any reservoir must equal the net decrease in its con- 
 tents during the same time, or (algebraically expressed) that 
 the net outflow (positive or negative) plus the net increase 
 in contents (negative or positive) must be zero. We m_ay 
 apply this principle to any reservoir or store of money, but 
 shall here find it most helpful to apply it to the reservoir of 
 money contained among the "Commercial depositors" and 
 "Nondepositors" taken together as one grmip. Let us desig- 
 nate the combination of these two as the "CN group." The 
 total outflow indicated in the diagram from this "CN group" 
 is evidently C,, + C<, + A^j, + No, and the total inflow Be + 
 Oc -\- Bn -\- On- Hence, the net outflow, so far as the diagram 
 shows us, is : — 
 
 C,-hCo + N, + No-Bc-Oc-Br,-On. 
 
 This, plus the net outflow not shown in the diagram, is the 
 true net outflow. Since the diagram was constructed to show 
 only flows against goods (monetary circulation), and flows to 
 or from banks, we have still to take account of money flow- 
 ing in the community in exchange for something else than 
 goods, and that flowing without any exchange at all, as well 
 as any net outflow outside of the community. 
 
 We have thus to take account of three undiagramed flows.
 
 458 THE PURCHASING POWER OF MONEY [Append. XII 
 
 The first is the net outflow of money from the '^CN group " to 
 the " group," which, though in exchange, is not in exchange 
 for goods. This means simply cashed checks, for, according 
 to the classification we are here using, "goods" are taken to 
 include anything exchangeable, not either money or checks. 
 Our first correction is, therefore, the net outflow of money from 
 the ^^CN group" for cashing checks, i.e. the difference be- 
 tween the checks cashed by the '^CN group" for the "0 
 group " and those cashed in the opposite direction. 
 
 It will be understood that we have nothing to do here with 
 the cashing of checks at banks, for this is included in the dia- 
 gram {Bo, Bn, and B^. Moreover, we have nothing to do 
 here with cashing of checks within the "CAT group," as when 
 a storekeeper cashes a check presented by a "Nondepositor." 
 We have only to do with the net outflow for cashed checks 
 from CN to 0. This net outflow (which may be positive, 
 negative, or zero) we shall designate by the letter a, to stand 
 for "accommodation" checks. 
 
 For the second correction, we have to designate the net out- 
 flow of money given away by the "CN group" in gifts, taxes, 
 thefts, etc., for which no speciflc goods are received in return. 
 This net outflow may be designated by g. 
 
 We have, thirdly and lastly, the net outflow of money with 
 respect to the "CN group" outside of the community, i.e. the 
 net amount of money which is lost to the country by export, 
 fire, shipwreck, melting, etc., in excess of that imported, 
 minted, etc. This net outflow may be designated by e, to 
 stand for "external" outflow. Adding the net undiagramed 
 outflow (a -{- g -{■ e) to the net diagramed outflow, we have, 
 for the total net outflow, 
 
 C, + Co + N, + No- Bc-Oc- Bn-On + a + g-\-e. 
 
 Now, on the reservoir principle already explained, the alge- 
 braic sum of this net outflow from the "CN group" and the 
 net increase of the money in that group must be zero. That 
 is, representing this net increase by i, we have 
 
 0=C, + Co + N,-{-N,-B-O,-Bn-0n-{-a-{-g-{-e-{-i. (4)
 
 Sec. 6] APPENDIX TO CHAPTER XII 459 
 
 We now place this new equation (4) under the old equation (3), 
 giving the value of r = F — F' in the following manner : — 
 
 r = - (Cb) -Ob- {Nb) + (Oc) + Co+Cn+ iOn)]+c + o+n 
 
 0= (Cb) + Co+{Nb) + No-Bc-{Oc)-Bn ~{On) + a + g + e + i. 
 
 Adding and canceling the terms of (3) and (4) indicated in 
 parentheses, and rearranging the remaining terms, we have 
 
 r = F-F'= (Co-\-Cn- B,)-\- (Co + No - Ob) + {c + o 
 + n) + (a-\-g + e)-\-i-Bn. (3)' 
 
 The letters are grouped in parentheses forming six terms, 
 arranged, as far as can be judged, in the order of descending 
 importance. 
 
 By using the expression just obtained for r, the complete 
 formula (1) for the circulation of money may now be put in a 
 form suitable for statistical application. Since r = F — F', 
 then F = F' -\- r. Substituting for F' and r the expression 
 already given in equations (2) and (3)', we have, as a trans- 
 formation of (1), 
 F = F' -\-r 
 
 =-{Cb + Ob-^Nb) + {Nc-VNo) 
 
 + (a + Cn-5,) + (C<, + Ar„-0,) + (c + o + n) + (o + g 
 + e) + ^• - 5„ (1)' 
 
 = (1) all money deposited 
 
 + (2) money expenditures of " Nondepositors " 
 
 + (3) Cs money expenditures from tills {i.e. money expendi- 
 tures in excess of money withdrawn from bank) 
 
 + (4) O's money receipts pocketed {i.e. money receipts in 
 excess of money deposited in bank) 
 
 -|- (5) intraclass monetary circulation 
 
 + (6) CN'^ undiagramed net outflow of money 
 
 -f (7) CN'b net increase of money on hand 
 
 — (8) iV's withdrawals of money from bank. 
 
 This is a complete and universal formula for the circu- 
 lation of money in any community. Its first two terms
 
 460 THE PURCHASING POWER OF MONEY [Append. XII 
 
 constitute the first approximation, and the other six 
 terms constitute r, which may be called the "remainder 
 term." 
 
 The first and second terms are by far the most important. 
 The last three terms — sixth, seventh and eighth — are 
 doubtless quite negligible under all circumstances actually 
 met with, I am also reasonably confident that, in the United 
 States, the 3d, 4th, and 5th terms amount to less than 10 per 
 cent of the total and probably less than 5 per cent. There- 
 fore, the complete omission of all except the first two terms 
 would still give us a fairly good figure for the total F; for 
 any one familiar with the inaccuracies of statistics knows 
 that 5 or 10 per cent is a small error, especially for a 
 magnitude which has hitherto eluded any attempt at meas- 
 urement. 
 
 We may, therefore, distinguish three successive stages in our 
 approximations. The first approximation comprises only 
 the first two terms, viz. money deposited plus expenditures 
 of " Nondepositors " ; the second includes, in addition, terms 
 (3), (4), and (5), viz. till-paid money expenditures of C, pock- 
 eted money receipts of 0, and intraclass circulation; while 
 the third is rendered absolutely complete by including terms 
 (6), (7), and (8), none of which has practical importance. 
 The complete formula is presented in the hope of arousing 
 discussion and investigation which will disclose in particular 
 to what extent it may be applied in countries where data 
 exist for the first two terms, viz. money deposited and expend- 
 itures of " Nondepositors." The former is to a large extent 
 a matter of daily record in most civilized countries, and the 
 latter consists chiefly of wages, a magnitude which has for 
 long been a favorite subject for statistical estimate. 
 
 § 7 (to Chapter XII, § 4) 
 Application of Formula to Calculation of V for 1896 and 1909 
 
 We shall now exemplify the use of our formula by means of 
 actual figures for the United States. The Report of the
 
 Sec. 7] APPENDIX TO CHAPTER XII 461 
 
 Comptroller of the Currency for 1896, already referred to, 
 and the special report of the National Monetary Commission 
 for 1909, give a basis for estimating the first term (Cs + O* + 
 Nb), the annual money deposited in banks in those years. 
 Both reports were made under the direction of Professor 
 David Kinley of the University of Illinois. We shall consider 
 first the figures for 1896. The total money deposited in 
 banks on the settling day nearest July 1, 1896, was 7.4 per cent 
 of the total deposits of all kinds. This total for all reporting 
 banks was 303 millions, of which 7.4 per cent would make 
 $22,400,000. It was made up of over $16,200,000 from 3474 
 national banks, and the remainder from 2056 other banks. 
 There were, all together, according to the Comptroller's Re- 
 port, about 13,000 banks in the country at that time. On the 
 basis of these figures, the Comptroller attempts to estimate 
 the (retail) deposits of all kinds for all these 13,000 banks, 
 assuming that the average deposit was the same as for the 
 country banks replying. This average was $2375 for 
 banks in places of 12,000 inhabitants or less. Applying 
 this average to the unreporting banks, we would increase 
 the retail deposits (which were $26,500,000) by an addi- 
 tional $17,800,000. 
 
 If we assume the same ratio of increase for the total money 
 deposits, the sum of 22.4 millions would be increased by 15.0 
 millions, making a total of 37.4 millions, as the amount of 
 money deposited in banks on the settling day nearest July 1, 
 1896. This figure represents at least a rough approximation 
 to the inflow of cash into, and, therefore, also the outflow of 
 cash from, the banks of the country. Multiplying by 305 
 settling days for the year, we obtain 11.4 ])illions as the 
 total annual amounts deposited. The figures, being for the 
 settling day nearest the first of July, are probably above 
 the daily average for the year. Thus 11.4 is an upper limit 
 rather than an estimate. Later we shall also set a lower 
 limit. 
 
 The preceding figures relate to the year 1896. Similar 
 calculations for 1909 have been made by Professor David
 
 462 THE PURCHASING POWER OF MONEY [Append. XII 
 
 Kinley ^ with the assistance of Professor Weston. The re- 
 sulting figure for money deposited in 1909 is 19.1 billions. ^ 
 
 But if it is necessary to adjust the figures for deposits of 
 checks in 1896 and 1909 because the days selected are excep- 
 tional (see § 4 of this Appendix) , it is also necessary to 
 adjust the figures for the deposits of money. On July 1, 1896, 
 many June bills must have been paid by cash as well as by 
 check and on March 16, 1909, the middle of a month, there 
 must have been slackness of settlements by cash as well as 
 by check. Consequently, like the total deposits of checks, 
 the total deposits of money made on July 1, 1896, were in all 
 probability above the daily average for 1896, and on March 
 16, 1909, they were below the daily average for 1909. In 
 other words, without adjustment for the abnormality of the 
 days selected, the figure expressing monetary circulation for 
 1896 would be too large, and that for 1909, too small. That 
 is, without such adjustment our calculations merely set an 
 upper limit in 1896 and a lower limit in 1909. 
 
 But we may easily set the opposite limits. We may be 
 reasonably sure that deviations from the average are less 
 for money deposits than for check deposits. It cannot be 
 expected that daily money deposits fluctuate as greatly as 
 
 ' See "Note on Professor Fisher's Formula for Estimated Velocity 
 of Circulation of Money." Publications American Statistical Asso- 
 ciation, March, 1910. The calculations are based on data taken from 
 Professor Kinley's valuable monograph on " Credit Instruments," 
 61st Congress, 2d Session, Doc. No. 399 in Reports of National 
 Monetary Commission. 
 
 2 Professor Kinley gives 18.3. The difference is due to the fact 
 that Professor Kinley, while estimating the daily deposits as 62.9 
 millions, calls this in round numbers 60 millions. It seems prefer- 
 able to use the estimate as it stands and make any allowances for 
 errors at the end rather than the beginning. Professor Kinley also 
 takes 305 settling days for the year, this being the number used by 
 Professor Kem merer for 1896. But Mr. Gilpin of the New York 
 clearing house tells me that the clearing house business days, though 
 305 in 1896, were 303 in 1909. I have therefore used 303 as the 
 number of settling days in 1909. The product 62.9 millions, times 
 303, is 19.1 biUions.
 
 Sec. 7] APPENDIX TO CHAPTER XII 463 
 
 daily check deposits. Practically all check payments are in- 
 fluenced by the periodicity in receipts of checks by the de- 
 positors (as of their salary, interest, or dividend checks) , or by 
 the periodicity of credit extended to them (as of the trades- 
 men who render them monthly bills) . While the fluctuations 
 to which money payments are subject are more or less similar, 
 they are much less in extent for two reasons : First, the pay- 
 ment or credit cycles which influence the fluctuations of 
 money deposits are usually shorter than those which influence 
 the fluctuations of check deposits ; the wage earner usually 
 gets his money weekly as against the salaried man who re- 
 ceives his check monthly, or the stockholder who receives 
 his dividends quarterly. Secondly, unlike check payments, 
 many, if not most, money payments have no payment or credit 
 cycle. There is no credit cycle in what are called "cash" 
 payments, for they imply that no credit is given. The receipts 
 at "cash stores," the smaller receipts at all stores, the receipts 
 of tramway, railway, and steamship oflices, the receipts at 
 theaters and many miscellaneous establishments are almost 
 wholly on a cash basis and result in daily and fairly steady 
 money deposits made by these establishments. These are 
 facts of every-day experience and are confirmed by inquiry of 
 bankers, who state that their money deposits are far steadier 
 day by day than their check deposits. Confirmatory and 
 conclusive evidence is also obtainable from Kinley's investi- 
 gation in the Comptroller's Report for 1896 (p. 95). If check 
 and money deposits were to fluctuate in perfect sympathy 
 with each other, the percentage of the total which consists of 
 checks would remain constant. But if, as we shall endeavor 
 to show, the excess or abnormality of check deposits on July 1 
 is greater than the excess or abnormality of money deposits 
 on that date, then we ought to find that the percentage of 
 check deposits is greater on July 1 than usual. The figures 
 of the Comptroller's Report indicate that this is the case. 
 They show that the percentage of checks received (unfortu- 
 nately not quite synonjonous with "deposits") was on 
 September 17, 1890, 91.0 per cent and on July 1 of the same
 
 464 THE PURCHASING POWER OF MONEY [Append. Xil 
 
 year, 92.5 per cent, or 1^ per cent higher. Again, com- 
 paring July 1, 1896, with the nearest available date for another 
 season of the year, namely, September 15, 1892, we find the 
 figures to be as follows: for September 15, 1892, check re- 
 ceipts, 90.6 per cent; for July 1, 1896, check deposits, 92.5 
 per cent, or 1.9 per cent higher. The excess would have been 
 still greater if both the figures were for receipts instead of one 
 of them being for deposits; for, as the Comptroller says, the 
 inclusion of other receipts than deposits tends to exaggerate 
 the percentage of checks. That July 1 has a far larger pro- 
 portion of checks than June 30 is indicated by the figures for 
 retail deposits for June 30, 1894, and July 1, 1896, the former 
 being 58.5 per cent and the latter 67.6 per cent, or 9.1 per 
 cent higher. We should be cautious, however, in drawing any 
 quantitative conclusion from this difference, since the investi- 
 gations for 1894 and 1896 were conducted somewhat differ- 
 ently. But the difference, as we find it, harmonizes with all 
 the facts at hand. Similar confirmation may be drawn from 
 the absence of any contrast between the figures for June 30 
 and September 17, 1881, as compared with the" sharp contrast 
 already noted between July 1 and September 17, 1890. The 
 credit receipts in 1881 on June 30 and September 17 were 
 91.77 per cent and 91.85 per cent, respectively, which figures 
 are substantially equal, while, as above noted, for July 1 and 
 September 17, 1890, we find a difference of 1|- per cent. 
 
 We feel, therefore, safe in concluding that check deposits 
 are subject to greater fluctuations or abnormalities than 
 money deposits. Consequently the deposits of money on 
 July 1, 1896, while they may have exceeded the daily aver- 
 age, were probably not so far above the daily average as 
 were the deposits of checks; also on March 16, 1909, the 
 deposits of money were probably not so far below the 
 average daily deposits of money as were the deposits of 
 checks. 
 
 Now, if this were not true, — if the money deposits fluctu- 
 ated exactly parallel with check deposits, — we should need to 
 assume the same correction-factors for money as for checks,
 
 Sec. 7] 
 
 APPENDIX TO CHAPTER XII 
 
 465 
 
 viz. .68 in 1896 and 1.17 in 1909, with the results given in 
 column (1) of the following table: — 
 
 
 
 Estimated Money Deposits of Yeab 
 
 (1) 
 
 (2) 
 
 Monet De- 
 posited ON Day 
 Selected 
 (In Millions) 
 
 (3) 
 
 Assuming Day 
 
 AN Average One 
 
 (In Billions) 
 
 (4) 
 Assuming Cor- 
 rection Factors 
 equal to those 
 FOB Check 
 Deposits 
 
 (5) 
 
 Mean between 
 
 Two Preceding 
 
 Columns 
 
 1896 . . 
 1909 . . 
 
 37.4 
 62.9 
 
 11.4 
 19.1 
 
 7.8 
 
 22.3 
 
 9.6 
 20.7 
 
 We see that the true value of the money deposited in banks 
 in 1896 must in all probability lie between 7.8 and 11.4 bilUons, 
 and in 1909, between 19.1 and 22.3 billions. If, in each case, 
 we split the difference, the estimates become for 1896, 9.6, 
 and for 1909, 20.7. The truth cannot be far from these 
 figures, for there are only narrow hmits on either side. The 
 probable error, judged roughly from the calculated limits and 
 from the character of the estimates of these limits, is placed 
 at about 1 billion in each case. It will be noted, of course, 
 that this error is larger proportionally in 1896 than in 1909. 
 
 We have now estimated the first term (total deposits) of the 
 formula for the total circulation of money. 
 
 The next term (Nc+Ng) is the expenditure of the "Non- 
 depositors" made to other classes. This is practically the 
 expenditure of wage earners. The Census gives the average 
 wages in manufacturing industries as $430. Mr. William C. 
 Hunt of the Census Bureau, in an unofficial memorandum 
 which he has kindly allowed me to see, has estimated that the 
 laborers in the United States number about 18,400,000. Let 
 us assume, as a reasonable approximation, that their average 
 wages are the same as the average in manufacturing industries, 
 namely, $430. We first apply this to the 8.5 millions of people 
 which Mr. Hunt estimates are engaged in manufacturing and 
 mechanical pursuits and trade and transportation. These 
 2h
 
 466 THE PURCHASING POWER OP MONEY [Append. XII 
 
 persons, therefore, receive about 3.7 billions of dollars in 
 wages. 
 
 The remaining classes of laborers are domestic servants and 
 agricultural laborers. These, however, receive board and 
 lodging as part pay. Since food and rent form about 60 per- 
 cent of workingmen's budgets, we may assume that the actual 
 money paid to domestic and agricultural workers is only about 
 40 per cent of that paid to manufacturing laborers, i.e. about 
 $170. Mr. Hunt estimates the number of domestic and agri- 
 cultural laborers at 9.9 millions. Hence the total money 
 they handle in a year is probably about 1.7 billions. This, 
 added to the previous 3.7 bilhons, gives 5.4 billions as the to- 
 tal money paid in wages in the United States All these 
 figures relate to the year 1900, while the figures for our first 
 term relate to 1896. In the interim both the number of 
 laborers and their wages doubtless increased somewhat and 
 we must, therefore, make a correction for each. We shall as- 
 sume that the number of laborers increased in the same ratio 
 as population, and that population increased between 1896 
 and 1900 at the same rate per annum as between 1890 and 
 1900. This would reduce the 5.4 bilhons to 5.0 billions. 
 If, instead of population, we use the number of employees in 
 manufacturing and mechanical pursuits as given by the 
 Bureau of Labor,^ the result is lower, viz. 4.6. The truth prob- 
 ably lies between, since agricultural labor, for which we 
 have no statistics, has probably not increased as fast as 
 manufacturing labor, and, therefore, even if labor as a whole 
 increased in the same ratio as population, the relative in- 
 crease of manufacturing labor, as compared with agricultural 
 labor, would mean a greater payment of money wages. We 
 may select 4.8 billions as close to the truth. As to the rate of 
 wages, the index numbers of the Bureau of Labor ^ for 1896 
 and 1900 are 99.5 and 104.1 respectively. On this account, 
 therefore, we should still further reduce our estimate of money 
 
 1 Bulletin of the Bureau oj Labor, No. 77, July, 1908, p. 7. 
 » Ibid., p. 7.
 
 Sec. 7] APPENDIX TO CHAPTER XII 467 
 
 wages paid in 1896, — in the ratio of 104.1 to 99.5 or from 
 4.8 billions to 4.6 billions. Furthermore, a small fraction 
 of these laborers are prosperous enough to have bank ac- 
 counts, and the expenditures of these should not be included 
 among the expenditures of "Nondepositors." About 4^ bil- 
 lions is probably as close to the truth as we can expect to get. 
 
 But we must now add to this an allowance for " Nondeposi- 
 tors " other than wage earners. Some of the 2.1 milUon clerks 
 and 8.6 miUion proprietors and professional men in Mr. 
 Hunt's estimates, though not laborers, are nevertheless 
 "Nondepositors." As to the clerks, it is said by business 
 men that most clerks who receive over $100 a month, and 
 some who receive less, have bank accounts. Probably, the 
 great bulk of the 2 millions of persons estimated as clerks 
 are far below $100 a month, and many are doubtless included 
 who, like office boys, have less than what are ordinarily 
 called wages. To make a guess sure to be large enough, let us 
 say that three-fourths of the clerks have no bank account and 
 average $60 a month. Even then the total cash-paid clerk hire 
 would scarcely exceed a billion. 
 
 Among the proprietors and professional men, the only 
 group we need to consider is agricultural proprietors (5.7 
 millions). The remainder consists of classes among which 
 bank accounts are practically universal. Of these agricul- 
 tural proprietors, those who have no bank accounts are doubt- 
 less smaller ones, living in districts where little money changes 
 hands. Their number could certainly not exceed four mil- 
 lions, which would be over two thirds of the whole. The prob- 
 lem is, What cash do these farmers pay to depositors, com- 
 mercial and other ? Practically, this means, What do they 
 pay to country storekeepers ? Their payments to laborers or 
 other farmers are payments to other " Nondepositors " and do 
 not concern us here. For rent, food, or such farm supplies 
 as they can raise themselves, they pay little or nothing. 
 Thus, the hay crop of the nation is said to exceed in value the 
 wheat crop; but so little hay is marketed that it is seldom 
 quoted or thought of as a market commodity. Even the
 
 468 THE PURCHASING POWER OF MONEY [Append. XII 
 
 trade of these farmers with the storekeeper is conducted 
 largely by barter or book credit. Their expenditures in actual 
 money may be conjectured to average less than S250 a year 
 for each farmer, making less than a billion dollars at most 
 (even if the number of such farmers be counted at 4 
 millions). 
 
 It seems safe to say, then, after allowing a billion for clerks 
 and a billion for farmers, that the total expenditures of 
 " Nondepositors " cannot exceed 4^ + 1+1 = Q^ billions. 
 
 On the other hand, it can scarcely be less than 5 billions. 
 To reduce it to this figure would require us practically to ig- 
 nore the existence of " Nondepositors " other than wage 
 earners, or to assume a large error in the estimate of wages. 
 
 We conclude that for 1896 the second term lies somewhere 
 between 5 and 6^ billions. Placing it midway, we obtain ap- 
 proximately 5.7 billions with a possible error of .7 or. 8. Sim- 
 ilar calculations for 1909 show 13.1 billions for the second 
 term with a possible error of 1.0. To quote from Professor 
 Kinley's article already referred to : ^ — 
 
 " The second term of the formula is the money payments of 
 * Nondepositors,' made up principally, as Professor Fisher 
 thinks, of the wages of working people. The following table 
 shows an estimate of the increase from 1900 to 1909 in certain 
 pursuits on the basis of the percentage of increase from 1890 
 to 1900 and on census and railroad returns since 1900. As 
 far as possible salaried officers are eliminated. 
 
 Increase Estimate 
 
 1890 1900 Per 1909 
 Cent 
 
 Agricultural pursuits . 8,565,926 10,381,765 21.2 12,362,605 
 Domestic and personal 
 
 service .... 4,220,812 5,580,657 32.2 7,377,628 
 
 Total 19,740,233 
 
 Trade and transporta- 
 tion ..... 1,977,491 2,617,479 35.2 4,275,913 
 Manufacturing and 
 
 mechanism . . . 4,251,613 5,208,406 6,935,113 
 
 Total 11,211,026 
 
 * Publications of the American Statistical Association, March, 1910,
 
 Sec. 7] APPENDIX TO CHAPTER XII 469 
 
 "A rough calculation based on the figures of Census BuU 
 letin No. 93 gives us about $550 as the average yearly wages 
 of people in manufacturing. If we should include mechani- 
 cal pursuits, probably the average should be raised a little. 
 Very likely $600 would be more nearly correct for this class. 
 
 "Again the Report of the Interstate Commerce Commission 
 for 1907 gives figures from which it appears that the average 
 yearly wage is about $640. It is more difficult to get a ground 
 for making an estimate of the money wages of those engaged 
 in agricultural and domestic pursuits. Doubtless it is more 
 than, at first thought, might be believed. The money wages 
 of domestic servants at present probably will average not less 
 than $250 a year. Agricultural laborers are certainly receiv- 
 ing a good deal more than formerly, and $300 or $350 probably 
 will not be too large a sum to assign to these. Accordingly, we 
 may recapitulate as follows : — 
 
 Trade and transportation 4.3 millions at $640 $2,752 millions 
 
 Manufacturing and me- 
 chanical pursuits . 6.9 millions at $550 $3,790 millions 
 
 Agricultural pursuits . . 12.4 millions at $300 $3,720 millions 
 
 Domestic and personal ser- 
 vice 7.4 millions at $250 $1,850 millions 
 
 Clerks, etc., having no 
 
 bank account $1,000 millions 
 
 Total $13,112 miUions 
 
 "This gives us the second term of the formula." 
 We have now estimated the first two terms (constituting 
 together what has been called the first approximation) for 
 both 1896 and 1909. 
 
 To this first approximation must be added the remainder, 
 r, consisting of the many terms already explained, most of 
 which are not known with exactness, but all of which are 
 known to be small. The term "small" is always relative, 
 and in this case a term is small for 1896 which is small com- 
 pared to 16 bilhons. For instance, 160 millions is a mere 
 trifle, being only 1 per cent of 16 bilhons, while 16 millions is 
 only one tenth of 1 per cent. For purposes of comparison 
 we do not need exact statistics for the various terms of which
 
 470 THE PURCHASING POWER OF MONEY [Append. XII 
 
 r is composed. All we need to know is that r is small and 
 that it varies approximately as the rest of circulation varies. 
 Under these circumstances a large mistake in estimating it 
 will make a small error in comparisons. Only in case r were 
 at once large and variable relatively to the other terms could 
 a mistake in its estimation greatly affect the comparisons. 
 Our attempt to estimate r has been made, not so much for 
 the purpose of obtaining its absolute value, as to set for it 
 wide and safe limits. 
 
 The magnitude r consists of all the five terms of our for- 
 mula beyond the second. We shall take these up in order. 
 
 The third term of the formula is (Co -\- Cn — Be). This 
 represents the till-paid commercial expenditures, or the excess 
 of the money paid out by "Commercial depositors" over the 
 money withdrawn by them from banks. Personal inquiry 
 shows that the great bulk of the money withdrawn by "Com- 
 mercial depositors" from the banks is drawn for the purpose 
 of paying wages ; also that the great bulk of the actual money 
 expended by "Commercial depositors" is expended for wages. 
 In other words, €„ is very small compared with Cn, and the 
 sum of the two is nearly the same as Be. Hence the difference 
 {Co-hCn — Be), or till-paid expenses, is nearly zero. Till- 
 paid expenses, being mostly wages and, as all observation 
 shows, only a small part of total wages {4:^ billions) — cer- 
 tainly not over one tenth — can be set down as less than half 
 a billion in 1896 and less than a billion in 1909. 
 
 The fourth term (C^ -\- No — Oj,) is O's money receipts 
 which are pocketed instead of being deposited. Now O's 
 money receipts, Cq-^No, are small in the first place, for 0, 
 being depositors, usually receive their dividends, interest, 
 and salaries by check. The chief exception is found in the 
 rents and the professional fees paid by workingmen to land- 
 lords, physicians, etc., payments which constitute most of No. 
 But these rents and fees paid by workingmen to private indi- 
 viduals are only a part of total rents and fees of workingmen, 
 and the total rents and fees themselves are known by statistics 
 of workingmen's budgets to be only about 20 per cent of
 
 Sec. 7] APPENDIX TO CHAPTER XII 471 
 
 wages. From this and other clews, we may safely set half a 
 billion as an upper limit for the fourth term in 1896. Pro- 
 fessor Kinley places .8 billion as the upper limit in 1909. 
 
 The fifth term {c-\- o-{-n) is the circulation within each 
 of the three groups. Obviously only in trifling cases does 
 money circulate between one "Commercial depositor" and 
 another, between two "Other depositors," or between two 
 "Nondepositors." Half a billion is put as an extreme upper 
 limit for the total for 1896 and .8 by Professor Kinley for 1909. 
 This would mean that about one dollar out of every thirty-five 
 expended is passed on to other persons who are within the class 
 to which the expender belongs. In fact, the universal testi- 
 mony of such few representatives of c, o, and n as I have been 
 able to interrogate personally is that the true ratio is less than 
 this. 
 
 The remaining three terms are even more insignificant. In 
 the normal state of equiUbrium for the "CN group" it is evi- 
 dent that the sixth and seventh terms would both be sub- 
 stantially zero. The eighth term, withdrawals from banks 
 by people who have no bank accounts, represents very excep- 
 tional conditions, such as where workmen cash checks at 
 banks. Workmen seldom have checks to cash and, when 
 they have, usually cash them in stores or saloons. 
 
 We shall summarize the estimates for each of the eight 
 terms in the following table. Each term is placed midway 
 between upper and lower limits estimated as safe, and the 
 possible variation in either direction is indicated after a " ± ". 
 Thus, $300,000,000 ± $300,000,000 means simply that, though 
 $300,000,000 is assigned as the estimate, the true value 
 may be more or less by an amount not exceeding S300,- 
 000,000, in other words, that the truth lies between $600,000,- 
 000 and zero. Instead of half billions we have used in the 
 table $600,000,000 as being more easily divisible by two. 
 The results for both years are given in the following table, in 
 which generous estimates are given for the "probable error" 
 in each case. In fact most of these "probable" errors are 
 improbably large.
 
 472 THE PURCHASING POWER OF MONEY [Append. XII 
 
 1896 
 
 1909 
 
 1. Money deposited (Cs + Ob 
 
 + N) 
 
 2. Expenditure of " Nonde- 
 
 positors" {Nc + A'',,) • . 
 
 3. C's expenditure, till paid . 
 
 {Co + C„- Be) . . . . 
 
 4. O's receipts, pocketed 
 
 (Co +No-Oh) . . . . 
 
 5. Intraclass circulation ( c + 
 
 + n) 
 
 6. Net undiagramed outflow 
 
 from CN (a + g + e) 
 
 7. Net increase of money of 
 
 CN (i) 
 
 8. Money withdrawn from 
 
 banks by "Nondeposi- 
 tors" ( - Bn) . . . . 
 
 9.6 ± 1.5 
 
 5.7 ± .7 
 0.3 ± .3 
 0.3 ± .3 
 0.3 ± .3 
 0.0 ± .1 
 0.0 ± .1 
 
 -0.001 ±.001 
 
 20.7 ± 1.5 
 
 13.1 ± 1.0 
 
 0.5 ± .5 
 
 0.4 ± .4 
 
 0.4 ± .4 
 
 0.0 ± .2 
 
 0.0 ± .2 
 
 -0.001 ±.001 
 
 16.2 ± 2 
 
 35.1 ± 2 
 
 The first two terms (F') constitute the great bulk of the 
 total. The remaining six terms (r) make up less than a billion 
 more for either year. The total reaches about 16 billions as 
 the estimated circulation of money in the United States in 
 1896. This estimate is subject to error, but not as much as 
 the total of the possible errors of individual terms, which is 
 over 3 billions. Even if each of the possible errors indicated 
 were as likely as not to occur, the chance that in all eight 
 cases they should all simultaneously occur in the same direc- 
 tion is (i) ^, or one chance in 256. We may, therefore, "trust 
 to luck" that the errors will, to some extent, offset each other. 
 In fact, the chance of the error reaching the sum of those of 
 the first three terms, or 3 billions, is less than a half. The 
 "probable error" can therefore be placed with some confi- 
 dence as less than 2 billions. 
 
 Dividing the figures we have obtained for the total circula- 
 tion of money by the figures for the amount of money in cir- 
 culation, we obtain figures for the velocity of circulation. 
 These are 18.6 in 1896 and 21.5 in 1909, which show remark- 
 ably little change. 
 
 Reverting now to the remark with which we began the dis-
 
 Sec. 7] APPENDIX TO CHAPTER XII 473 
 
 cussion of money velocity, namely, that it circulates but sel- 
 dom outside of banks, let us picture our statistical results in 
 the light of this fact. 
 
 Evidently, if all money circulated once only, then the bank 
 record for 1896, showing about 9^ billions annually flowing 
 into and out of the banks, would also exactly indicate the 
 volume of the intervening work done. This would then be 
 9;^- bilhons. But the true figure is, as we have shown, prob- 
 ably about 16 billions, and consequently we infer that some 
 of the 9t^- billions emanating from banks changes hands more 
 than once before it returns. 
 
 Next let us suppose that all of the 91 bilhons circulate once, 
 except the part passing through the hands of "Nondeposi- 
 tors" (6 bilhons), and that the latter circulates twice. Then 
 3| billions circulate once only. Under this assumption we 
 can account for 3^ + 2X6= 15] billions of exchange work. 
 But we have found in fact 16 bilhons. The difference of about 
 half a billion is chiefly due to the existence of some money 
 which circulates more than twice outside of banks. 
 
 The entire 16 bilhons may be roughly accounted for by 
 dividing the 9| billions flowing from banks into three streams ; 
 Sj bilhons circulating once and once only ; 5^ billions, twice 
 and twice only ; and ^ billion, three times. This makes 85- 
 + 2X5I+ 3X1= 16 billions. Of the three parts, the 
 first (31 billions) is mainly the spending money drawn by 
 "Other depositors," the second (5^ billions) is money with- 
 drawn from bank for wages and other payments to "Non- 
 depositors," and the third (| billion) is the small amount not 
 otherwise accounted for. This is only a rough scheme of divi- 
 sion. A very small part circulates oftener than three times.^ 
 
 1 It may avoid some confusion to remind the reader that we are 
 dealing with sums of money expended for goods, not with individual 
 coins. Many coins remain "in circulation" a long time without 
 returning to bank, because used "in change." But money used in 
 change enters as a subtractive term in monetary expenditures. 
 When $10 are given for an S8 purchase, and $2 are received back 
 in change, $12 have changed hands, but only $8 of monetary cir- 
 culation against goods have been effected.
 
 474 THE PURCHASING POWER OF MONEY [Append. XIJ 
 
 Similarly, for 1909, of the 21 billions flowing into and out 
 of the banks, the 13 billions passing through the hands of 
 " Nondepositors " must have circulated twice or more and 
 thus have accounted for 26 billions or more of the total circu- 
 lation (35 billions), leaving 21 — 13, or 8, to have circulated only 
 once. This would account for 26 + 8 or 34 billions. The 
 entire 35 billions may be accounted for by supposing the 21 
 billions flowing from banks to be divided into the following 
 three streams : — 
 
 8 billions circulating once, making 8 billions, 
 12 billions circulating twice, making 24 bilUons, 
 1 billion circulating three times, making 3 billions. 
 
 The whole 21 billions, bank outflow, perform 35 billions of 
 circulation before returning to bank. 
 
 The first two terms of the formula for the monetary circu- 
 lation evidently give 15 1 billions out of our estimated total 
 of 16 billions for 1896, and 34 out of 35 for 1909 ; showing 
 that the remainder, unless it has been greatly underestimated, 
 is relatively small. The significance of this fact is that the 
 terms most difficult to estimate statistically are least impor- 
 tant. Of the two terms constituting the "first approxima- 
 tion," the first and most important is susceptible of the most 
 accurate determination of all, while the second is made up 
 chiefly of wages, which also are susceptible of statistical 
 determination, or seem destined to become so. 
 
 In fact, if we should, as a statistical makeshift for the first 
 approximation, merely add the amount of money annually with- 
 drawn from bank to the annual money wages, we should, as to 
 the year 1896, account for 9y + ^2 or 14 out of 16 billions, leav- 
 ing only 2 billions to be otherwise accounted for. In other 
 words, this makeshift — the part most adapted to statistical 
 measurement — accounts for about 88 per cent of the total 
 circulation, leaving only 12 per cent for the part which can 
 only be determined within wide limits. For 1909, deposits 
 plus wages make up about 32 billions out of 35, or over 90
 
 Sec. 7] APPENDIX TO CHAPTER XII 475 
 
 per cent. A still simpler makeshift is to add the deposits 
 to the total wages without attempting to ascertain the part 
 which is paid in money. This makeshift might be justified 
 on the ground that total wages are more exactly ascertain- 
 able than the part paid in money, and that presumably the 
 money part will maintain a fairly constant ratio to the 
 total wages from year to year. The two parts here indi- 
 cated may be distinguished as the measurable part (com- 
 prising the first term of our formula (1)' and most of the 
 second term), and the conjectural part, comprising the re- 
 mainder of the second term and the other six terms. Even 
 if the allowance for the conjectural part should prove to 
 be but half the truth, the measurable part would still con- 
 stitute the great bulk of the total. The measurable part 
 would therefore still be a safe practical index, or barometer 
 of changes in the volume of circulation. Any excess of varia- 
 tion in the conjectural part, as compared with the measurable 
 part, would, when spread over the whole, produce a disturb- 
 ance only one fourth as great. It is reasonable to suppose 
 that the conjectural and measurable parts will ordinarily vary 
 together. If the measurable part varies 10 per cent, it is natu- 
 ral to suppose that the conjectural part, and therefore also the 
 total of both, will vary likewise. But suppose this assump- 
 tion erroneous and that, while the measurable part varies 10 
 per cent, the conjectural part really varies 14 per cent or 6 per 
 cent. The difference between these and 10 per cent, i.e. 4 
 per cent, representing a supposed excess or deficiency of vari- 
 ation of the conjectural part, would produce a difference of 
 only 1 per cent in the total ! That is, the total, instead of 
 varying 10 per cent, would vary 11 per cent or 9 per cent. 
 Evidently, therefore, any unknown variation in the conjec- 
 tural part can cause only a trifling variation in the result. 
 In other words, the measurable part will always be a good 
 index of the total — a reliable barometer of circulation. If 
 we divide this by the quantity of money in circulation, we 
 obtain a figure indicating the relative velocity of circulation 
 of money from year to year. We conclude, therefore, that
 
 476 THE PURCHASING POWER OF MONEY [Append. XII 
 
 money deposits plus wages, divided by money in circulation, 
 will always afford a good barometer of the velocity of 
 circulation. 
 
 It is not always the absolute value of any magnitude we 
 find most useful, but its relative value under different con- 
 ditions. We may compare the relative length of two ships by 
 measuring their water lines, although this method omits the 
 overhang at either end. Such a comparison will apply roughly 
 to any two vessels, and with great exactness to two ships of 
 the same build. Similarly, our proposed barometer will af- 
 ford rough comparisons for any two coimtries using banking 
 facilities in comparable degrees, and will afford fairly exact 
 comparisons for two successive years in the same country. 
 
 The proper statistical procedure would, therefore, seem to be 
 to provide for the conjectural part by an estimated percent- 
 age correction, to be applied to the measurable part as a con- 
 stant factor. Different correction factors will presumably 
 apply in different countries, as, let us say, 10 per cent in the 
 United States, 20 per cent in England, 30 per cent in France, 
 etc. The chief value of such conjectural corrections would be 
 to enable us to compare roughly the circulations and velocities 
 of different countries. For comparisons in the same country 
 at different times it would be almost immaterial what per- 
 centage correction were adopted or whether none at all were 
 employed. 
 
 By means of the method which has been explained, it is be- 
 lieved that some interesting and valuable results can in the 
 future be obtained, if statisticians in various lands will obtain 
 (1) the total money deposited each year in banks (except by 
 other banks), or, what is normally the same thing, the total 
 money withdrawn from banks (except by other banks) ; (2) 
 the total wages expended, or, what is practically the same 
 thing, the total wages received; (3) if desired, a conjectural 
 percentage addition to allow for the remaining and less known 
 part of our formula ; (4) the total money in circulation. The 
 sum each year of (1) and (2) corrected by (3) and divided by 
 (4) will be a very accurate barometer of the velocity rela-
 
 Sec. 8] APPENDIX TO CHAPTER XII 477 
 
 tively considered, as well as a fair approximation to its abso- 
 lute value. The omission of (3) will not invalidate the re- 
 sults for purposes of relative comparison. 
 
 The importance of such accurate determinations can 
 scarcely be overestimated, as the remarks on the subject by 
 Jevons, Landry, and others have shown. When we know sta- 
 tistically the velocity of circulation of money, we are in a 
 position to study inductively the "quantity theory" of money, 
 and to discover the significance of that velocity in reference 
 to crises, accumulation of wealth, density of population, 
 rapid transit, and communication, as well as many other con- 
 ditions. In fact a new realm in monetary statistics is laid 
 open. 
 
 § 8 (to Chapter XII, § 4) 
 
 Interpolating Values of V for 1897-1908 
 
 To interpolate values for V we split the difference between 
 two extreme hypotheses : the one of extreme steadiness ; the 
 other of extreme variability. 
 
 The first of these hypotheses is that V changes in a steady 
 progression from its value of 18.6 in 1896 to its value of 21.5 
 in 1909. This would imply a perfectly steady growth with 
 time, with no temporary fluctuations. But it seems unlikely 
 that the velocity of circulation of money should not fluctuate 
 somewhat from year to year. We have seen that, theoreti- 
 cally, there is a tendency under normal conditions for money 
 expenditures (MV) to keep pace with check expenditures 
 (M'V). If this correspondence were perfect, we should have 
 the ratio of ilf F to M'V, if not constant, at least changing in 
 a perfectly even manner with time. Now this ratio for 
 1896 is 16.7 per cent and in 1909, 9.6 per cent. If we were to 
 assume a perfectly steady change in this ratio during the in- 
 tervening 13 years, the resulting value for V would have to 
 vary considerably. This assumption is our second hypothesis 
 of extreme variability. The following table shows the re- 
 sults of the two extreme hypotheses. It will be seen that 
 in general there is no great difference between them.
 
 478 THE PURCHASING POWER OF MONEY [Append. XII 
 
 
 (1). 
 
 (2) 
 
 Htpothbsis of 
 ExTBEME Varia- 
 
 (3) 
 
 Tbar 
 
 Htpothesib op 
 Extreme Steadi- 
 ness 
 
 bility 
 V 
 
 VARYDJa AS 
 NEEDED TO PRE- 
 SERVE EVENLY 
 
 CHANGING Ratio 
 or MV TO AI'V 
 
 Mean op two 
 I'rbcedino 
 
 1896 
 
 18.6 
 
 18.6 
 
 18.6 
 
 1897 
 
 18.8 
 
 19.4 
 
 19.1 
 
 1898 
 
 19.0 
 
 20.6 
 
 19.8 
 
 1899 
 
 19.3 
 
 24.4 
 
 21.9 
 
 1900 
 
 19.5 
 
 20.4 
 
 20.0 
 
 1901 
 
 19.7 
 
 23.9 
 
 21.8 
 
 1902 
 
 19.9 
 
 23.6 
 
 21.8 
 
 1903 
 
 20.2 
 
 20.9 
 
 20.6 
 
 1904 
 
 20.4 
 
 20.9 
 
 20.7 
 
 1905 
 
 20.6 
 
 23.0 
 
 21.8 
 
 1906 
 
 20.8 
 
 22.5 
 
 21.7 
 
 1907 
 
 21.1 
 
 21.0 
 
 21.1 
 
 1908 
 
 21.3 
 
 18.6 
 
 20.0 
 
 1909 
 
 21.5 
 
 21.4 
 
 21.5 
 
 A supplementary calculation reveals the interesting fact 
 that the " hypothesis of extreme variability" would make 
 money velocity fluctuate approximately with deposit velocity. 
 Splitting the difference between the two extreme hypotheses, 
 — that of extreme steadiness and that of extreme variability, 
 — we have what would seem to be an approximately correct 
 estimate of actual velocity. It is probably correct in most 
 cases for the first two digits. We cannot assume even for 
 1896 and 1909 that the third digit, that beyond the decimal, 
 is correct, much less can we assume this to be true for the inter- 
 vening years. But it is sometimes advisable to carry out the 
 calculations to one digit beyond " the last significant figure." 
 
 § 9 (to Chapter XII, § 5) 
 
 Method of Calculating T 
 
 The table in the text is taken from the final column of the 
 following more complete table : —
 
 Sec. 9J 
 
 APPENDIX TO CHAPTER XII 
 
 479 
 
 H 
 
 O 
 
 -< 
 
 a 
 
 b 
 O 
 
 H 
 P 
 
 O 
 > 
 
 o 
 
 n 
 a 
 
 1 
 
 o 
 
 (11) 
 
 Absolute 
 Trade (T) 
 
 
 05aiOcciO'-HtjHioTt<ooo(N.-iOi 
 oco<ot>i>'-ioco(Mt^a>.-iooo5 
 
 (M(N(N(M(NCOCOCOCOC«3CO'*cCCO 
 
 (10) 
 Relative 
 
 Trade 
 
 Weighted 
 
 average 
 
 2x(5)+lx(9) 
 
 TO 
 
 .-Hf0f-l«0t>^00OOI>T}<OG0>O 
 OOOiOOOCNi-iCOWTtiiOOTj^iO 
 
 (9) 
 
 (8) Re- 
 duced to 
 Calendar 
 Years 
 
 CO 00 O CO O lO lO O CO .-H lO Tj< rt< 1 
 t^ t^ 00 Oi 05 O "-I (N (N ■* lO lO »0 1 
 
 1 
 
 g 
 
 -So 
 
 g 
 Q 
 
 (8) 
 
 Weighted 
 
 average 
 
 of two 
 
 preceding 
 
 2x(6)+lx(7) 
 
 CO 
 
 (M-^COOt^OOOOCOOOOSO 
 t^t>000001O'-iMMC0iOC0Tti«0 
 
 I— li-tl-Hi-4i— ll— Ii-ItHi-H 
 
 (7) 
 
 P. 0. 
 
 Letters 
 Carried 
 
 1 CO00(N00iO(M^»O^00t^(M(N 
 
 1— 1 1— 1 1— 1 1— 1 1— ( i-H I— 1 
 
 (6) 
 
 R. R. 
 
 tons 
 Carried 
 
 t^OSrHOOt^OOOiOt^-^—KNlN 
 «> t^ 05 05 O O I-H CO (M TjH <£> t> lO 1 
 
 % 
 
 m 
 
 >< 
 
 % 
 a 
 z 
 
 ■< 
 
 o 
 
 o 
 
 o 
 g 
 
 s 
 
 B 
 
 (5) 
 
 Weighted Average 
 
 of Three Preceding 
 
 20x(2)+3x(3) + lx(4) 
 
 ^ 
 M 
 
 <lOOOS(M'-H050iOi005CC(N»OC^ 
 0000'-i,-t(N(NCONTl<iOO'<l<iO 
 
 (4) 
 
 Sales of 
 Stocks 
 
 »0t^C0<O00O05»-it^C0'*cCit^lO 
 
 iot>'-Ht^cocooo;ooocoooo505'-i 
 
 1— ll— It— l(Ni— It— li— (C^C^i— li— IC^ 
 
 (3) 
 
 Exports 
 
 and 
 Imports 
 
 cot^coO'-ir^(N'-<'-ia)'^t^oio 
 
 t>-00050000000'-i'-i'-i(N 
 
 (2) 
 
 Internal 
 Commerce 
 
 a>coi-ii-irHioai05ioCT>(Nt^ooeo 
 
 OOO— It-It-KMt-iCOIN-^iOCOtJhiO 
 
 (I) 
 Year 
 
 
 
 ?Or>OOOiO^(NCOTj<U5COt^OOOi 
 OOiOJOiOOOOOOOOOO 
 00000000O5O5O5O5O>O5O>O5aiO5 
 I— li-Hl-H»Hl— l»-tl-li— (i-Hi— (tHi— IrHrH
 
 480 THE PURCHASING POWER OF MONEY [Append. XII 
 
 This table is constructed as follows : — 
 
 Column (2) is constructed for 1900-1909 from monthly 
 figures on Internal Commerce pubUshed in the Monthly 
 Su7nmary of Commerce and Finance of the United States. 
 By taking the monthly figures it was possible to obtain re- 
 sults for calendar years. This column is an average of sepa- 
 rate indices for the following articles for which records were 
 available. The original figures give the quantities of each 
 article brought into the principal cities of the United States. 
 These quantities were each multiplied by an assumed price 
 which remained as a constant multipUer for every year. The 
 products were then added together and the figures thus ob- 
 tained taken to represent the total trade in these commodi- 
 ties, and to be a barometer of the relative internal commerce 
 in the United States. 
 
 The articles referred to, and the dates for which data 
 were used (as well as the price factors employed as explained 
 below) are as follows : — 
 
 Articles 
 
 Price 
 
 Dates 
 
 Cotton 
 
 $45.00 bale 
 
 Jan., 
 
 1900-1909 
 
 Rice 
 
 5.00 sack 
 
 Aug. 
 
 , 1900-1909 
 
 Fruit 
 
 1000.00 car 
 
 Feb., 
 
 1900-1909 
 
 Lumber (Shipments 
 
 
 
 
 from South and 
 
 
 
 
 Southwest) 
 
 .02 ft. 
 
 Feb., 
 
 1900-1909 
 
 Boots and Shoes . 
 
 80.00 case 
 
 Mar. 
 
 , 1900-1909 
 
 Anthracite Coal . 
 
 4.74 ton 
 
 Jan., 
 
 1900-1909 
 
 Bituminous Coal . 
 
 2.74 ton 
 
 Jan., 
 
 1900-1909 
 
 Pig iron, coke, and 
 
 
 
 
 anthracite . . 
 
 19.40 gross ton 
 
 July, 
 
 1902-1909 
 
 Petroleum (Ship- 
 
 
 
 
 ments by water 
 
 
 
 
 from Texas) . . 
 
 1.80 bbl. 
 
 Nov. 
 
 , 1901-1909 
 
 Cattle (Receipts at 
 
 
 
 
 five cities) . . 
 
 55.00 head 
 
 Jan., 
 
 1900-Dec., 1903 
 
 Cattle (Receipts at 
 
 
 
 
 seven cities) . . 
 
 55.00 head 
 
 Jan., 
 
 1900-1909 
 
 Hogs (Receipts at 
 
 
 
 
 five cities) . . 
 
 18.00 head 
 
 Jan., 
 
 1900-Dec., 1903
 
 Sec. 9] 
 
 APPENDIX TO CHAPTER XII 
 
 481 
 
 Articles 
 
 Pbiob 
 
 Dates 
 
 Hogs (Receipts at 
 
 seven cities) . 
 Sheep (Receipts at 
 
 five cities) 
 Sheep (Receipts at 
 
 seven cities) . . 
 Wheat (Receipts at 
 
 eleven cities) 
 Wheat (Receipts at 
 
 twelve cities) 
 Wheat (Receipts at 
 
 fourteen cities) . 
 Wheat (Receipts at 
 
 fourteen cities) . 
 Wheat (Receipts at 
 
 fifteen cities) 
 Corn (Receipts at 
 
 twelve cities) 
 Corn (Receipts at 
 
 fourteen cities) . 
 Corn (Receipts at 
 
 thirteen cities) . 
 Corn (Receipts at 
 
 fifteen cities) 
 Oats (Receipts at 
 
 twelve cities) 
 Oats (Receipts at 
 
 fourteen cities) . 
 Oats (Receipts at 
 
 fifteen cities) 
 Barley (Receipts at 
 
 nine cities) . . 
 Barley (Receipts at 
 
 ten cities) . . 
 Barley (Receipts at 
 
 eleven cities) 
 Barley (Receipts at 
 
 twelve cities) 
 Barley (Receipts at 
 
 thirteen cities) . 
 Barley (Receipts at 
 
 fourteen cities) , 
 Rye (Receipts at 
 
 eleven cities) 
 Rye (Receipts at 
 
 twelve cities) 
 Rye (Receipts at 
 
 thirteen cities) . 
 Rye (Receipts at 
 
 fourteen cities) . 
 
 $18.00 head 
 
 4.00 head 
 
 4.00 head 
 
 1.00 bu. 
 
 1.00 bu. 
 
 1.00 bu. 
 
 1.00 bu. 
 
 1.00 bu. 
 
 .75 bu. 
 
 .75 bu. 
 
 .75 bu. 
 
 .75 bu. 
 
 .53 bu. 
 
 .53 bu. 
 
 .53 bu. 
 
 .70 bu. 
 
 .70 bu. 
 
 .70 bu. 
 
 .70 bu. 
 
 .70 bu. 
 
 .70 bu. 
 
 .80 bu. 
 
 .80 bu. 
 
 .80 bu. 
 
 .80 bu. 
 
 Jan., 1900-1909 
 Jan., 1900-Dee., 1903 
 Jan., 1900-1909 
 June, 1903 
 
 Apr., 1903-Dec., 1903 
 May, 1904-1909 
 May, 1904-1909 
 Apr., 1903-1909 
 Apr., 1903-Dec., 1903 
 Jan., 1904-1909 
 Feb., 1906-Feb., 1907 
 Apr., 1903-1909 
 Apr., 1903-Dec., 1903 
 Feb., 1906-Feb., 1907 
 Apr., 1903-1909 
 June, 1903-Aug., 1908 
 Apr., 1903-May, 1908 
 Sept., 1903- June, 1908 
 Feb., 1906-Sept., 1908 
 Feb., 1904-1909 
 Apr., 1903-1909 
 Apr., 1903-June, 1906 
 Jan., 1905^Aug., 1908 
 Apr., 1904-1909 
 Apr., 1903-1909 
 
 2i
 
 482 THE PURCHASING POWER OF MONEY [Append. XII 
 
 Articles 
 
 PaicB 
 
 Dateb 
 
 Flaxseed (Receipts 
 
 
 
 
 at four cities) 
 
 $1.50 bu. 
 
 Feb. 
 
 , 1905-1909 
 
 Flaxseed (Receipts 
 
 
 
 
 at five cities) 
 
 1.50 bu. 
 
 Jan., 
 
 1904-1909 
 
 Flaxseed (Receipts 
 
 
 
 
 at six cities) . . 
 
 1.50 bu. 
 
 Jan., 
 
 1904-1909 
 
 Flour (Receipts at 
 
 
 
 
 ten cities) , . . 
 
 4.80 bbl. 
 
 Apr. 
 
 1903-1909 
 
 Flour (Receipts at 
 
 
 
 
 eleven cities) 
 
 4.80 bbl. 
 
 Jan., 
 
 1904-1909 
 
 Flour (Receipts at 
 
 
 
 
 twelve cities) 
 
 4.80 bbl. 
 
 Mar. 
 
 , 1904-1909 
 
 Flour (Receipts at 
 
 
 
 
 thirteen cities) . 
 
 4.80 bbl. 
 
 Apr., 
 
 1903-1909 
 
 Petroleum (Ship- 
 
 
 
 
 ments by Pipe- 
 
 
 
 
 lines — Reg. De- 
 
 
 
 
 liveries. App. 
 
 
 
 
 Field .... 
 
 1.80 bbl. 
 
 Jan., 
 
 1901-1909 
 
 These articles are representative for the trade of the 
 country and may well serve as a barometer of that trade. 
 Yet the amount of trade, actually consisting of the sales of 
 these articles in the few cities concerned, constitutes of 
 course only a very small part (probably less than one tenth 
 of 1 per cent) of the total trade of the country. 
 
 The actual figures first obtained were all divided by two 
 before being entered in column (2) in order to bring them 
 down to a scale more comparable with the figures of column 
 (3). Since not all of the commodities were quoted in all 
 the years, the table had to be "pieced out" for the defective 
 years by the principles of proportion as already exemplified. 
 As the statistics of the Monthly Summary go back only to 
 1900, the table had to be "pieced" back to 1896. This was 
 done by using data from the statistical abstract of the United 
 States and the abstract of the United States Census for 1900. 
 The only figures obtainable for important articles in internal 
 trade were those for grain, received during calendar years at 
 fifteen principal primary markets, and for the estimated 
 national consumption during fiscal years of the following
 
 Sec. 9] APPENDIX TO CHAPTER XII 483 
 
 articles, chiefly, or largely, of domestic production: cotton, 
 wool, bituminous coal, pig iron, iron and steel railroad bars, 
 and "distilled spirits, wines, and malt liquors." 
 
 The fiscal year figures were taken from 1896 to 1901 inclu- 
 sive and reduced to calendar years on the assumption, for 
 instance, that the true figure for the calendar year 1896 is the 
 average of those for the two fiscal years ending June 30, 1896, 
 and June 30, 1897. In this way we get hypothetical calen- 
 dar year figures for 1896 to 1900. These figures and those for 
 grains, which were already for calendar years, were then 
 reduced by a factor so that each was made to be 111 for 1900, 
 the number for that year found by the calculations involv- 
 ing the articles in the series, 1900-1909. The figures thus 
 found were then averaged with weights selected to correspond 
 with the estimates of their respective importance as judged 
 from the estimates of their national consumption values and 
 from the fact that some of them are indicators of large re- 
 lated businesses. The weights chosen were : for grains 
 (including wheat, wheat flour, corn, rye, oats, barley, malt, 
 and pease > 20 ; for bituminous coal, iron and steel, liquors, 
 and cotton, 5 each ; and for pig iron and wool, 1 each. 
 
 The data for 1896-1899 are far inferior to those for 1900- 
 1909 taken from the Monthly Summary, and this for three 
 reasons : (1) because they are so few in number ; (2) be- 
 cause all except the grains are for fiscal years and the hypo- 
 thetical correction to calendar years is subject to error; 
 and (3) because all except the grains are very rough estimates 
 of consumption, not based on shipments or receipts, but based 
 on estimated production, corrected for exports and imports, 
 which three elements are all subject to error. 
 
 We should not be surprised, therefore, to find larger errors 
 in the resulting figures for 1896-1899 than for 1900-1909. 
 In fact, we shall see that such is probably the case. 
 
 For carrying out the laborious operations involved in 
 ascertaining the index numbers from 1900 to 1908, I am in- 
 
 * See Statistical Abstract of United States, 1908, p. 523.
 
 484 THE PURCHASING POWER OF MONEY [Append. XII 
 
 debted to one of my undergraduate students, Mr. Robert N. 
 Griswold, and for bringing them down to 1909, to one of my 
 graduate students, Mr, W. Y. Smiley. 
 
 Column (3) is also based on laborious calculations which 
 were performed by Mr. Griswold. The materials were also 
 taken from the Monthly Summary of Finance and Commerce 
 and covered 23 staple articles of import and 25 for export. 
 The quantities of each were multiplied by a uniform price, and 
 the sum of the resulting figures for imports and exports was 
 taken. The articles of imports (with the price multipliers 
 used) were : — 
 
 Imports of the United States 1896-1909 
 (Bulletin of Bureau of Commerce and Statistics) 
 
 Cocoa . 
 
 
 .13 lb. 
 
 Raw silk . . . .04 lb. 
 
 Tea . . 
 
 
 .16 lb. 
 
 Hides and skins 
 
 Coffee . 
 
 
 .07 lb. 
 
 (other than fur 
 
 Sugar 
 
 
 .02 lb. 
 
 skins) 11 lb. 
 
 Lemons 
 
 
 .04 lb. 
 
 Raw wool . . . .13 lb. 
 
 Bananas 
 
 
 1.60 bunch 
 
 India rubber ... .78 lb. 
 
 Cheese . 
 
 
 .17 lb. 
 
 Boards and sawed 
 
 Distilled spirits 
 
 
 lumber . . . 18.00 M. ft. 
 
 (imported) . 
 
 5.00 gal. 
 
 Coal (anthracite & 
 
 Sparkling wines 
 
 
 bituminous) . 2.60 per t. 
 
 (Champagne) 
 
 29.00 doz. qts. 
 
 Tin 28 1b. 
 
 Leaf tobacco . 
 
 1.00 lb. 
 
 Copper (pigs, bar, 
 
 Cotton . 
 
 
 ingots, old, un- 
 
 (mfg. cloth) 
 
 .09 sq. yd. 
 
 manufactured) .17 lb. 
 
 Linens (mfg. flax 
 
 
 Pig iron . . . 23.00 per t. 
 
 hemp, or ramie ] 
 
 .50 sq. yd. 
 
 Sodium nitrate 38.00 per t. 
 
 Woolen dress 
 
 
 
 goods 
 
 • 
 
 .21 sq. yd. 
 
 
 The articles of exports were : — 
 
 Exports of the United States 1896-1909 
 (Bulletin of Bureau of Commerce and Statistics) 
 
 Wheat .... 1.00 bu. 
 Flour .... 4.80 bu. 
 Tobacco leaf . .10 lb. 
 Sawed lumber . 23.00 M. ft. 
 Wood pulp . . .015 lb. 
 
 Linseed oil (cake) .014 lb. 
 Refined illuminating 
 
 oil 07 gal. 
 
 Cottonseed oil . .40 gal. 
 Coal .... 3.70 ton 
 
 Copper 17 1b. 
 
 Steel rails . . 31.60 ton 
 Sheet steel . . .0135 ton 
 
 Cattle . . . 
 
 55.00 head 
 
 Hams . . . 
 
 .11 lb. 
 
 Salt pork . . 
 
 .09 lb. 
 
 Fresh beef 
 
 .10 lb. 
 
 Canned beef . 
 
 .11 lb. 
 
 Bacon 
 
 .11 lb. 
 
 Lard . . . 
 
 .11 lb. 
 
 Butter . . . 
 
 .21 lb. 
 
 Sole leather 
 
 .21 lb. 
 
 Boots and shoes 
 
 2.75 pr. 
 
 Raw cotton 
 
 .48 bale 
 
 Cotton cloth . 
 
 .09 yd. 
 
 Corn . . . 
 
 .60 bu.
 
 Sec. 9] APPENDIX TO CHAPTER XII 485 
 
 The statistics of exports and imports are probably fifty 
 times as full as those of internal commerce and therefore 
 (on the principle that probable errors vary inversely as the 
 square root of the fullness of returns) some seven times as accu- 
 rate. But, on the other hand, exports and imports represent 
 less than 1 per cent as much trade as the internal commerce 
 of the United States, and, by the principles already explained 
 in previous chapters, should count in the equation of exchange 
 only at half its value, one of the parties in the exchange being 
 a foreigner. In spite, however, of the diminutive character 
 of external commerce, it is to some extent an index of internal 
 commerce; since a vast amount of internal business is a pre- 
 liminary to exports and a sequel to imports, while perhaps a 
 still larger amount is in other ways indirectly related to such 
 commerce. By balancing these and other considerations, the 
 relative weights to be assigned to the external and internal 
 trade were selected as given in column (5). 
 
 Column (4) gives the sales of stocks according to the 
 ordinary figures as given, for instance, in the Financial Review. 
 These figures are, of course, not for values, but for amounts. 
 
 Column (6) gives the figures for tons of freight carried by 
 railroads according to Poor's Railroad Manual for fiscal years. 
 
 Column (7) gives the figures for pieces of first-class mail 
 matter carried in fiscal years. These figures were kindly 
 supplied by the Post Office Department. They are lacking 
 for 1896. 
 
 We have still to describe the method employed for combin- 
 ing columns (2), (3), (4), (6), (7). 
 
 The first three are regarded as constituting a group by 
 themselves, representing direct indices of trade : and the last 
 two are regarded as constituting another group of indirect 
 indices. 
 
 The direct indices are combined by weighting the internal 
 commerce, twenty, the exports and imports, three, and sales 
 of stocks, one. These weights are, of course, merely matters 
 of opinion, but, as is well known, wide differences in systems of 
 weighting make only slight differences in the final averages.
 
 486 THE PURCHASING POWER OF MONEY [Append. XII 
 
 In this way, column (5) is found. 
 
 As to the relative weights to be given to the railroad and 
 post office statistics, the former were weighted as two and the 
 latter as one. Railway tonnage represents almost every con- 
 ceivable commodity in commerce and comes far closer to 
 actual trade than post office letters. 
 
 After railroad and post ofl&ce indexes are thus combined, 
 the transition from fiscal to calendar years is made on the 
 assumption that the figures for a calendar year are the mean 
 of the figures for the fiscal years ending June 30 of that year 
 and June 30 of the next year. 
 
 In this way column (9) is obtained. 
 
 From columns (5) and (9) column (10) is obtained by 
 weighting (5) two, and (9) one. 
 
 Finally, column (11) is found by magnifying the figure of 
 column (10) in the ratio fff in order to make the figure for 
 the base year, 1909, equal to 399 billions of dollars, — the total 
 value of the left side of the equation (MV + M'V). 
 
 The probable errors in the values of T which have been 
 calculated are believed to be some 5 to 10 per cent for the 
 years 1900-1909 and 10 to 15 per cent for the years 1896-1900. 
 
 § 10 (to Chapter XII, § 5) 
 
 Method of Calculating P 
 
 The table in the text for index numbers of prices is taken 
 from the last column of the table on page 487. 
 
 Column (2) gives the index numbers of the United States 
 Labor Bureau (No. 81, March, 1909, p. 204). 
 
 I am under obligations to the Commissioner of Labor, Mr. 
 Neill, for his courtesy in supplying me with the figure for 1909 
 in advance of publication. 
 
 Column (3) is taken from the Bulletin of the Bureau of 
 Labor, July, 1908, p. 7. 
 
 Column (4) is from "The Prices of American Stocks, 1890- 
 1909," by Wesley C. Mitchell, Journal of Political Economy^
 
 Sec. 10] 
 
 APPENDIX TO CHAPTER XII 
 
 487 
 
 May, 1910. These figures are doubtless the best yet avail- 
 able in this difl&cult subject. 
 
 Index Numbers of Prices 
 
 (1) 
 
 Year 
 
 (2) 
 
 Wholesale, 
 
 258 
 Commodities 
 
 (3) 
 Waoes 
 
 (4) 
 
 FORTT 
 
 (5) 
 Weighted 
 Average 
 
 (6) 
 Column (5) 
 reduced to 
 
 PER Hour 
 
 Stocks 
 
 30x(2)+lx(3)+3x(4) 
 
 Basis of 100 in 
 
 
 34 
 
 1909 
 
 1896. . . 
 
 90 
 
 100 
 
 77 
 
 89 
 
 63.3 
 
 1897. . . 
 
 90 
 
 100 
 
 84 
 
 90 
 
 63.7 
 
 1898. . . 
 
 93 
 
 100 
 
 94 
 
 93 
 
 66.2 
 
 1899. . . 
 
 102 
 
 102 
 
 128 
 
 104 
 
 73.8 
 
 1900. . . 
 
 111 
 
 105 
 
 134 
 
 113 
 
 80.2 
 
 1901 . . . 
 
 109 
 
 108 
 
 211 
 
 118 
 
 83.7 
 
 1902. . . 
 
 113 
 
 112 
 
 250 
 
 125 
 
 88.7 
 
 1903 . . . 
 
 114 
 
 116 
 
 201 
 
 122 
 
 86.5 
 
 1904. . . 
 
 113 
 
 117 
 
 192 
 
 120 
 
 85.1 
 
 1905. . . 
 
 116 
 
 119 
 
 250 
 
 128 
 
 90.8 
 
 1906. . . 
 
 123 
 
 124 
 
 267 
 
 136 
 
 96.5 
 
 1907. . . 
 
 130 
 
 129 
 
 204 
 
 137 
 
 97.2 
 
 1908. . . 
 
 123 
 
 — 
 
 201 
 
 130 
 
 92.2 
 
 1909. . . 
 
 127 
 
 — 
 
 277 
 
 141 
 
 100.0 
 
 The general index number in column (5) is a weighted aver- 
 age of the figures in the three preceding columns, the weights 
 being essentially the same as those used by Professor Kem- 
 merer and for the same reasons.^ For ease in computation the 
 weights are taken in integers, viz. 30 for column (2), 1 for 
 column (3) and 3 for column (4). This calculation brings the 
 table down through 1907. As column (3) is defective for 
 1908-1909, these years and 1907 are worked out as averages 
 of columns (2) and (4), the weights being the same as already 
 mentioned. The result is two series of figures, one for all three 
 columns ending in 1907, and the other for two columns begin- 
 ning in 1907. As in this case it happens that both series have 
 the same figure (137) for 1907, no corrections need be made in 
 1908 and 1909. The probable errors in the figures for P may 
 be placed as about 5 to 10 per cent. 
 
 1 See Money and Credit Instruments, New York (Holt), 1909, 
 p. 139.
 
 488 THE PURCHASING POWER OF MONEY [Append. XII 
 
 §11 (to Chapter XII, §7) 
 Mutual Adjustments of Calculated Values of M, M', V, V, P, T 
 
 There are various methods of calculating the best adjust- 
 ments, involving the theory of least squares. But the prob- 
 lem may be greatly simplified by dividing the process into a 
 few separate steps. First, we ascertain the best adjustments of 
 the calculated values of each side of the equation of exchange 
 considered as a whole. We shall need to exercise judgment in 
 deciding the relative errancy of the two sides, but the total 
 adjustments are so small that differences in judgment could 
 not make much difference in the results. 
 
 After a careful weighing of all the evidence, it is believed 
 that the errors in the right side (PT) are liable to be about 
 double those in the left (MV -\-M'V'). Accordingly, the 
 discrepancy between the two sides is corrected by changing 
 PT twice as much as MV + M'V ; that is, by applying to 
 PT a correction equal to two thirds of the total discrepancy, 
 and by applying the remaining one third to MV -\- M'V, 
 the two corrections being, of course, opposite and such as to 
 bring the two sides into agreement. Thus, for 1899, the total 
 discrepancy is 5 per cent, of which we assign about a third, 
 say 2 per cent, to MV -\- M'V, and the remaining 3 per 
 cent to PT. That is, we propose to increase the calculated 
 figures for ilf F + M'V by 2 per cent and decrease those of PT 
 by 3 per cent. The result will bring them nearly into agree- 
 ment at 185 biUions. Sometimes the results will not exactly 
 agree, as this method of adding and subtracting percentage 
 corrections is only approximately correct ; but any remaining 
 sUght discrepancies are readily adjusted by slight empirical 
 changes in the factors. The result is shown in the Figure 20, 
 which gives MV -\- M'V and PT (reduced by dividing by 
 1.11) as originally calculated, and a mean (dotted) curve 
 which is the revised estimate of both MV + M'V and PT. 
 
 The corrections which are thus made in MV -\- M'V and 
 PT, by which they are brought into mutual agreement, are
 
 Sec. 11] 
 
 APPENDIX TO CHAPTER XII 
 
 489 
 
 small; but the corrections necessary in the individual factors, 
 M, F, M', V, P, T, are smaller still. We assume, for simphc- 
 ity, that the percentage corrections to be made in M and M' 
 are equal to each other and also that the corrections to be 
 made in V and V are equal to each other. This is a reason- 
 able assumption ; but even if some other assumption were 
 made, the final results would be scarcely changed. 
 
 
 ::t:::::::::::::: 
 
 fffH 
 
 -X+i: 
 
 1: 
 
 
 
 
 
 ^Ililll'IIHillll 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 800 x ± 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 coo - 4= , s 
 
 
 
 
 -- 
 
 
 
 
 - 
 
 
 
 
 
 :: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 -,,'----,,%■■----- 
 
 
 UT~lf 
 
 
 ^ 
 
 
 
 
 
 
 M-'---'-'"W-- 
 
 ay EK II • 
 
 ..'- 
 
 [tl::z 
 
 -- 
 
 J 
 
 
 
 ::.::: X-,;. 
 
 
 
 
 
 
 
 
 
 
 
 
 |K 1' 
 
 • _. 5. 
 
 5: 
 
 ^ ■' : n 
 
 E . ' I _ 
 
 
 S(> i|^y 4iR Ht rrf 'rn 
 
 ~r ' 
 
 1 
 
 
 
 - - 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ±±:::::: 
 
 -- --- _-_^| ^. 
 
 
 
 
 
 
 
 -.:..::; :;::±::;; 
 
 I89G IS.S7 1893 I8S 
 
 « ISOO 1901 1902 IS 
 
 03 1304 
 
 I903 1 
 
 90 
 
 6 190 
 
 7 ISO 
 
 8 1909 
 
 
 Fig. 20. 
 
 A correction of 1 per cent simultaneously in M and M' 
 will produce a correction of 1 per cent in AIV -{- M'V. 
 Likewise a correction of 1 per cent simultaneously in V and 
 V will produce a correction of 1 per cent in MV -\- M'V. 
 We may then regard the correction of MV -\- M'V as 
 practically consisting of two parts : one, the correction of M 
 and M' ; and the other, the correction of V and V. As the 
 Af' s are more accurately ascertained than the F's, theip correc- 
 tion should be smaller. Thus, for 1897, the total correction 
 assigned to MV -\-M'V' is 3 per cent, of which we assign 
 1 per cent to M and M', and the remaining 2 per cent to V
 
 490 THE PURCHASING POWER OF MONEY [Append. XII 
 
 and v. That is, we increase the calculated values of M and 
 M' by 1 per cent and those of V and V by 2 per cent, 
 thus effecting (approximately) the desired increase of 3 per 
 cent in MV -{-M'V. In like manner the total correction 
 assigned to PT is distributed over P and T, assigning the 
 major part to T. By thus distributing the corrections over 
 (1) M and M\ (2) V and V, (3) P, and (4) T, we find that 
 only very slight individual corrections are needed, the maxi- 
 mum being only 5 per cent and the vast majority (50 out of 
 56 cases) not exceeding 2 per cent. In fact, a decided major- 
 ity (35 out of 56 cases) are within 1 per cent. It is really 
 astonishing to think that a correction of only 2 per cent or 
 less is usually required in our calculated values of M, M', F, 
 F', P, T, in order to make them conform perfectly to the 
 equation of exchange. In fact, 2 per cent is less than what 
 might naturally be considered the probable error in most of 
 the figures as calculated. This fact justifies confidence in the 
 general correctness of our results. 
 
 Having thus corrected, by mutual adjustment, all the 
 factors in the equation of exchange, we are left with a figure 
 for P which is not 100 per cent for any one year. As we 
 prefer to call 1909 the unit year, the figures for P are 
 adjusted on that basis and the figures for T accordingly. 
 This change disturbs the system of corrections as measured 
 relatively to the original figures. It reduces to zero the cor- 
 rection of P for 1909. In general, it makes smaller the cor- 
 rections for P and T for years near 1909 and makes corre- 
 spondingly larger those for years remote from 1909. But, 
 even so, the corrections never exceed 10 per cent for T nor 6 
 per cent for P. As the entire scheme of corrections thus out- 
 lined is a matter of judgment and each figure was frankly "doc- 
 tored " on its own individual merits in view of all the circum- 
 stances in the case, it seems inadvisable to burden these pages 
 by any fuller statement of the voluminous details of the pro- 
 cess. The results as shown in Figures 13, 14, 15, and 16, 
 already given in the text, speak for themselves.
 
 Sec. 12] 
 
 APPENDIX TO CHAPTER XII 
 
 491 
 
 § 12 (to Chapter XII, § 17) 
 
 Credit and Cash Transactions. Comparison with Kinley's Esti- 
 mates 
 
 These figures agree surprisingly well with what might be 
 expected from a rougher calculation from Kinley's investiga- 
 tions. For July 1, 1896, he found that money deposits con- 
 stituted 7.4 per cent of all deposits and, on March 16, 1909, 5.9 
 per cent. Both of these figures are too low to represent the 
 percentage of money transactions, for the reason that money 
 often circulates more than once before being deposited, 
 whereas checks in general circulate but once. The figure for 
 1896, especially, is too low, because of the excessive amounts 
 of checks deposited on July 1. In fact, it was largely be- 
 cause the 1896 figures had been criticized in this respect that 
 Kinley made the 1909 investigation. He did not, of course, 
 take the figures of deposits as indicating exactly the ratios of 
 check and money transactions. He recognized the fact that 
 these would give too low a ratio for money and too high a ratio 
 for checks. He expressed the belief that a safe minimum for 
 check transactions in 1896 was 75 per cent ^ and in 1909, 88 
 per cent, implying that 25 per cent and 12 per cent were safe 
 maxima for monetary circulation. Professor Kinley's pur- 
 pose seems to be to establish safe maxima rather than to at- 
 tempt exact estimates. Tabulating Kinley's figures, we have 
 for money transactions expressed in percentage of all trans- 
 actions : — 
 
 (1) 
 
 (2) 
 
 (3) 
 
 (4) 
 
 (5) 
 
 Year 
 
 1896 .... 
 1909 .... 
 
 Maximum 
 (Kinley's 
 estimate) 
 
 25 
 12 
 
 Minimum (as 
 
 indicated by 
 
 deposits) 
 
 7.4 
 
 5.9 
 
 Mean of two 
 preceding 
 
 16i 
 9 
 
 Present 
 estimate 
 
 14 
 9 
 
 ^ His original estimate for a safe minimimi was 80 per cent. But 
 in the Journal of Political Economy, Vol. V, p. 172, and in "Money,'' 
 p. 44, and pp. 108, 14, he takes 75 per cent as safer.
 
 492 THE PURCHASING POWER OP MONEY [Append. XII 
 
 According to this table, if we take the percentage of money 
 in bank deposits as a lower limit of the percentage of money 
 transactions, and if we take Kinley's estimates as a safe upper 
 limit, and if we split the difference between these two limits, 
 we shall reach almost ^ the same results as already reached by 
 the more exact calculations in this book, which results are 
 given, for comparison, in the last column. Thus the results of 
 this book strikingly confirm those of Professor Kinley. They 
 also agree remarkably well with the prevailing impression 
 among business men that about 90 per cent of trade is now 
 performed by means of checks. 
 
 ADDENDUM FOR SECOND EDITION 
 
 The figures in this second edition have been brought down 
 to date by adding data for 1910, 1911, and 1912 to the tables 
 on pages 304 and 317 and inserting a new diagram between 
 pages 306 and 307. (For full explanations as to these figures 
 see page xxiii of this book and " ' The Equation of Exchange,' 
 1896-1910," American Economic Review, June, 1911 ; " ' The 
 Equation of Exchange ' for 1911 and Forecast," ibid., June, 
 1912 ; and " ' The Equation of Exchange ' for 1912 and Fore- 
 cast," ibid., June, 1913.) 
 
 Professor Wesley Clair Mitchell has kindly shown me the 
 sheets of his forthcoming book (University of California 
 Press) on Business Cycles, in which he has reestimated the 
 deposits subject to check (M') by somewhat different methods 
 and with the aid of some data not available when the present 
 book was written. 
 
 If I were rewriting this book, I should adopt Professor 
 Mitchell's more perfect methods and results. But to do so 
 now would involve a disturbance of a large number of plates 
 for the sake of a very small net change in final results. I 
 
 1 If we take Kinley's original " safe minimum " for cheeks of 80 
 per cent, and consequently the " safe maximum " for cash as 20 per 
 cent, we shall obtain in the above table 14 per cent, instead of the 
 figure I62, which would make the last two columns agree absolutely.
 
 ADDENDUM FOR SECOND EDITION 
 
 493 
 
 content myself, therefore, by here giving a table of Professor 
 Mitchell's figures, including columns showing how much mine 
 are larger or smaller. 
 
 Professor Mitchell's Estimates of Deposits Subject to 
 Check and the I']xtent to which the Present Writer's 
 exceed or pall short of said estimates. 
 
 
 
 F.'s Excess (o 
 
 R Deficiency) 
 
 
 A/TTTT'TTirT r *Q T?ir^TTT TH 
 
 
 
 
 iVXli LfUCjljLi 9 IXCjciV LilO 
 
 Unadjusted 
 
 Adjusted 
 
 1896 
 
 2.69 
 
 -.01 
 
 + .02 
 
 1897 
 
 2.75 
 
 + .05 
 
 + .11 
 
 1898 
 
 3.20 
 
 -.01 
 
 + .02 
 
 1899 
 
 3.87 
 
 + .03 
 
 + .01 
 
 1900 
 
 4.21 
 
 + .19 
 
 + .23 
 
 1901 
 
 4.96 
 
 + .17 
 
 + .17 
 
 1902 
 
 5.37 
 
 + .06 
 
 + .03 
 
 1903 
 
 5.54 
 
 + .16 
 
 + .19 
 
 1904 
 
 5.85 
 
 -.05 
 
 -.08 
 
 1905 
 
 6.56 
 
 -.02 
 
 -.02 
 
 1906 
 
 6.86 
 
 -.02 
 
 -.05 
 
 1907 
 
 7.11 
 
 + .02 
 
 + .02 
 
 1908 
 
 6.52 
 
 + .08 
 
 + .05 
 
 1909 
 
 6.81 
 
 -.06 
 
 -.13 
 
 1910 
 
 7.71 
 
 -.47 
 
 -.48 
 
 1911 
 
 8.24 
 
 -.46 
 
 -.46
 
 APPENDIX TO THE SECOND EDITION, ON 
 "STANDARDIZING THE DOLLAR" 
 
 The plan for stabilizing the price level (and therefore the 
 purchasing power of money) sketched in Chapter XIII 
 (pages 340-346) in relation to the gold exchange standard has 
 been more fully and more popularly explained since this 
 book was written. (See, e.g., Report of International Con- 
 gress Chambers of Commerce, September 26, 1912 ; Inde- 
 pendent, January 2, 1913 ; New York Times, December 22, 
 1912 ; British Economic Journal, December, 1912, The 
 most complete statement is that in The Quarterly Journal 
 of Economics, February, 1913.) 
 
 The writer also hopes soon to publish a book devoted to 
 this particular subject. 
 
 The following is an extract from an address in Boston 
 before the American Economic Association, December, 1912, 
 printed in the American Economic Review Supplement, 
 March, 1913 : — 
 
 Briefly stated, the plan is to introduce the multiple stand- 
 ard, in which the unit is a "composite ton" or "composite 
 package" of many staple commodities, not of course by us- 
 ing such a package in any physical way but by employing 
 instead its gold bullion equivalent. In essence it would 
 simply vary the weight of gold in the dollar or rather behind 
 the dollar. The aim is to compensate for losses in the 
 purchasing power of each grain of gold by adding the neces- 
 sary number of grains of gold to the dollar. 
 
 Both on the basis of theory and of facts, 'we may accept as 
 sound the principle that the lighter the gold dollar the less 
 its purchasing power and the more magnified the scale of 
 prices ; and that the heavier the dollar the greater its pur- 
 chasing power and the more contracted the scale of prices. 
 Evidently if we can find some way to increase the weight of 
 
 494
 
 APPENDIX TO THE SECOND EDITION 495 
 
 the dollar just fast enough to compensate for the loss in the 
 purchasing power of each grain of gold, we shall have a fully 
 "compensated dollar," that is, a dollar which has constantly- 
 restored to it any purchasing power it may lose by gold 
 depreciation. 
 
 We now have a dollar of fixed weight (25.8 grains), but 
 varying purchasing power. Under the plan proposed, we 
 should have a dollar of fixed purchasing power, but varying 
 weight. 
 
 But how is it possible to have a dollar of varying weight 
 without the annoyance of a constant recoinage of gold coin ? 
 Moreover, if this can be done, how can we know at any time 
 what weight the dollar ought to have without leaving this 
 to the tender mercies of some political official ? Here are 
 two very vital questions. 
 
 As a preparation for answering these two questions, it 
 will be a little easier to explain the principle of the proposal 
 if for a moment we assume that there are no actual gold 
 coins in circulation, but only gold certificates. This sup- 
 position is, in fact, not very far from the truth in the United 
 States ; for, outside of California, there is very little actual 
 gold coin in circulation. We have instead nearly a billion 
 dollars of gold certificates in circulation, representing gold 
 in the Treasury of the United States. We are supposing 
 for the moment that gold circulates in no other way. Under 
 these circumstances it is evident that the ultimate gold 
 dollar is out of sight in the Treasury of the United States 
 in bars of gold bullion. Every 25.8 grains of this gold bul- 
 lion is a virtual dollar behind a dollar of gold certificates 
 outstanding. A gold bar (of standard bullion) weighing 
 25,800 grains virtually contains 1000 gold dollars. 
 
 The gold miner takes such bars of standard gold to the 
 mint and deposits them without waiting for their coinage, 
 receiving gold certificates in return, one dollar of gold cer- 
 tificates for each 25.8 grains of standard gold which he de- 
 posits. On the other hand, holders of gold certificates may 
 at any time receive gold bullion in return, when they desire
 
 496 THE PURCHASING POWER OF MONEY 
 
 this for export, or for use in the arts of jewelry, dentistry, 
 gilding, etc., receiving 25.8 grains of gold for each dollar of 
 gold certificates. Thus the government on demand gives 
 or takes money at the rate of 25.8 grains of bullion per 
 dollar ; the virtual, though invisible, dollar being this 25.8 
 grains of gold bullion, nine-tenths fine. 
 
 The proposal here made is to change the weight of the 
 dollar as an offset to changes in value. If there are no gold 
 coins, it is very easy to do this. For example, if there should 
 be a decrease of 1 per cent in the value, that is, purchasing 
 power of gold, then the weight of gold bullion which consti- 
 tutes the virtual dollar would be declared 1 per cent greater, 
 becoming 26.058 instead of 25.8. If there should be an 
 increase in the purchasing power of gold, the weight of the 
 virtual dollar would be reduced accordingly. Whenever the 
 gold miner took gold to the mint, he would receive a gold 
 certificate not necessarily at the rate of one dollar for each 
 25.8 grains of standard gold, but for a larger or smaller 
 amount as the case might be, the amount always being that 
 amount which would possess the same purchasing power. 
 Similarly the holder of gold certificates who wishes them 
 redeemed in bullion for export or for the arts, would not 
 always get exactly 25.8 grains for each dollar of certificates, 
 but a larger or smaller sum, as the case might be. Thus the 
 government would be receiving gold from the miner and giv- 
 ing it out to the jeweler just as at present, but in varying 
 weights per dollar, instead of at the arbitrarily fixed weight 
 of 25.8 grains. The weight of gold per dollar in which, at 
 any particular time, gold certificates were redeemable would 
 constitute the virtual and only gold dollar. Under these 
 circumstances it is clear that it would be entirely feasible 
 to change up and down the weight of the gold dollar (that 
 is, the amount of gold bullion interconvertible with a dollar 
 of gold certificates), and without any recoinage or other 
 interference with the outward appearance of the currency in 
 our pockets. 
 
 We should familiarize ourselves with another way of stat-
 
 APPENDIX TO THE SECOND EDITION 497 
 
 ing all this. Instead of saying that the government receives 
 gold bullion at the mint and uses this for redeeming gold 
 certificates, we may, if we prefer, say that the government 
 buys and sells gold. It buys gold from the miner, paying 
 for it in gold certificates ; it sells gold to the jeweler, who 
 redeems these certificates. At present, the price at which 
 gold is bought and sold by the government is $18.60 an 
 ounce (for standard gold nine-tenths fine). This is easily 
 figured out from the weight of the gold dollar ; for 25.8 
 grains of gold being our present dollar, each ounce (or 480 
 grains) of gold bullion contains 480/25.8 or 18.60 virtual 
 dollars. To say, then, that we now have a fixed weight in 
 our gold dollar, 25.8 grains, is the same thing as to say that 
 we have a fixed government price for gold, $18.60 per ounce. 
 To raise the weight of the gold dollar 1 per cent, or from 
 25.8 grains to 26.058 grains, is the same thing as to lower 
 the government price of gold from $18.60 to $18.42 per 
 ounce. 
 
 We come now to the second question : How would it be 
 possible to know the proper adjustments to be made in the 
 weight of the virtual dollar — the gold bullion interconver- 
 tible with each dollar of gold certificates — without putting 
 a dangerous power of discretion in the hands of government 
 officials? In other words, how can the adjustment in the 
 weight of the virtual dollar be made automatic? The 
 answer is : By means of statistics called "index numbers of 
 prices." Such statistics are to-day published by the London 
 Economist, the United States Bureau of Labor, the Canadian 
 Department of Labour, and several commercial agencies, such 
 as Bradstreet. The index number of the Bureau of Labor 
 is based on the wholesale prices of 257 commodities, and 
 shows from year to year the extent to which prices on the 
 whole advance or fall, — the average movement of all the 
 257 prices. 
 
 There are various systems of index numbers, but they 
 practically all agree remarkably well with each other. When 
 once a system of index numbers is decided upon, their numer-
 
 498 THE PURCHASING POWER OF MONEY 
 
 ical calculation becomes a purely clerical matter. A sta- 
 tistical bureau (as for instance the present Bureau of Labor 
 or an international statistical office) would compile and 
 publish these statistics periodically and the actual prices on 
 which they were based. If at any time the official index 
 number showed that the price level had risen 1 per cent above 
 par, this would be the signal for an increase of 1 per cent in 
 the virtual dollar. 
 
 The plan, then, is : first, to provide for the calculation of 
 an official index number of prices ; second, to adjust corre- 
 spondingly the official weight of the virtual dollar at which 
 the government shall issue gold certificates to miners or 
 redeem them for jewelers, in other words, to adjust the official 
 prices of gold at which the government stands ready to buy 
 or sell at the option of the public. 
 
 This, then, is the plan in brief — a plan virtually to mark 
 up or down the weight of the dollar (that is, to mark down or 
 up the price of gold bullion) in exact proportion to the devia- 
 tions above or below par of the index number of prices. 
 
 A few additional details essential to the working of the 
 plan may now be briefly mentioned. You are still waiting 
 to see how actual gold coin could be used in such a system. 
 To be continually recoining the gold in circulation would, 
 of course, be quite impracticable. But this would be un- 
 necessary. Existing gold coin would remain unchanged at 
 25.8 grains per dollar, and new gold coins would be given 
 the same weight. Gold coins would simply become what 
 silver dollars now are, token coins. Or, better, they would 
 be, like the gold certificates, mere warehouse receipts, or, as 
 it were, "brass checks" for gold bullion on deposit in the 
 Treasury. Otherwise expressed, gold coins would be merely 
 gold certificates printed on gold instead of on paper. They 
 would be used exactly as gold certificates are used — namely, 
 issuable to the gold miner in return for his bullion, and 
 redeemable for those who wished bullion for export or in 
 the arts. 
 
 The excess of bullion over the weight of the coined dollar
 
 APPENDIX TO THE SECOND EDITION 499 
 
 itself would be analogous to what has generally been called 
 " seigniorage" ; so that in a sense, the plan may be described 
 as a plan to restore the ancient custom of seigniorage on 
 gold coin. Thus, if the virtual dollar were at any time 
 35.8 grains, the excess of ten grains above the weight of the 
 coin dollar, 25.8 grains, would be "seigniorage." The gold 
 miner, in return for every 35.8 grains of standard gold bul- 
 lion taken to the mint, would receive, at his option, a gold 
 certificate on paper, or a gold certificate on gold (that is, a 
 dollar gold coin) — the latter containing, just as at present, 
 25.8 grains. Any holder of gold coin, old or new, and any 
 holder of gold certificates could receive from the govern- 
 ment gold bullion at the official rate declared from time to 
 time. He would thus be receiving a larger quantity of gold 
 bullion than the amount of bullion in the gold dollar. The 
 gold coin would then, like all our other coins, be worth more 
 as coin than as bullion, and its value would be determined 
 just as the value of a gold certificate or any other paper 
 money is to-day determined, by the ultimate bullion with 
 which it would be interconvertible, this bullion being of 
 greater weight than the weight of the dollar itself. 
 
 The only real complication which would be introduced 
 by allowing gold coin to remain at its present weight and 
 fineness would be to limit the operation of the system when 
 prices tended to fall below the par or starting point at which 
 the system began. The weight of the virtual gold dollar 
 could never be reduced below the weight of the coin dollar ; 
 for, if this were done, the seigniorage would become a minus 
 quantity and all the gold coin would be immediately melted 
 into bullion, being worth more melted than coined. One 
 proviso, therefore, in the system would be that the weight 
 of the virtual dollar should never be less than 25.8 grains 
 and that therefore the government price of gold should never 
 be more than $18.60 per ounce. Perhaps, in view of the 
 present dissatisfaction with high prices, many people would 
 not object to this limitation which permits prices to fall 
 below the present level, but does not permit them to rise
 
 500 THE PURCHASING POWER OF MONEY 
 
 further. Yet it is a poor rule that will not work both ways. 
 Consequently, while I personally look forward to an upward 
 tendency of prices in the future, the possibility of a downward 
 movement should be provided for. For this purpose, gold 
 coin could, if desired, be recalled at the outset and recoined 
 in lighter weight, just as the Philippine peso was recalled 
 and reduced in weight when the recent rise in the price of 
 silver threatened to lead to melting the silver pesos. But 
 I do not advocate crossing the bridge until we come to it. 
 It would be sufficient to provide in advance for crossing it in 
 case we should ever come to it. This could be done in one 
 of two ways. It could be provided that, if ever the price 
 level should, in the future, sink more than, say 10 per cent 
 below the original par or price level from which the system 
 started, all gold coins should then be withdrawn from cir- 
 culation and gold certificates employed instead. In this way 
 we should be rid of any complication from the use of gold 
 coin, and would be at liberty forever after to adjust the 
 weight of the virtual dollar downward as well as upward. 
 Or, if preferred, it could be arranged that when prices should 
 sink more than the suggested limit of 10 per cent below the 
 original level, we should then recoin and reduce our gold 
 coins. This would merely mean that the gold on which we 
 print our gold certificates would be reduced in weight. It 
 would not, of course, reduce the value of the gold coin any 
 more than the reduction in the weight of the Philippine peso 
 which was made for a similar contingency — or, to take an 
 example nearer home, the reduction of 10 per cent in the 
 weight of our subsidiary silver coins half a century ago — 
 had any tendency to reduce the value of these coins. 
 
 If the latter plan were chosen, the amount of reduction 
 in the gold coin should be enough to provide a comfortable 
 margin for any similar emergencies in the future. Any 
 subsequent recoinages would thus be deferred a long time 
 and similar provision for them could be made. Personally 
 I should prefer the former method, eliminating gold coins 
 altogether.
 
 APPENDIX TO THE SECOND EDITION 501 
 
 Another essential detail is a proviso to avoid speculation in 
 gold disastrous to the government. This would be accom- 
 plished by means of a slight government charge, say 1 per 
 cent, for minting. This charge, which existed in former 
 days, is called brassage. It would mean that the price at 
 any particular date at which the government bought gold 
 would be slightly less than the price at which it sold it. 
 Without such a margin to protect the government, it is 
 evident that when the government raised its price, say from 
 $18 to $18.10 an ounce, speculators might, in anticipation 
 of this rise, buy all the gold in the government vaults at 
 $18 in order to sell it back to the government immediately 
 after the change in price, at $18.10, thus profiting ten cents 
 per ounce at the expense of the government. 
 
 Similarly, a fall in price, say from $18.10 to $18 per ounce, 
 would encourage the opposite form of speculation. Holders 
 of bullion would then rush it to the government to sell it 
 at the present rate of $18.10, and immediately after the 
 change in price, buy it back at $18, thus profiting again 
 ten cents per ounce at the expense of the government. If, 
 however, the government were protected by a brassage charge 
 of 1 per cent and if it were provided that no single shift in 
 the government pair of prices, whether they were both moved 
 up or both moved down, should exceed the "brassage" or 
 margin between them, it is clear that no such speculation 
 could occur, for there would be a greater loss from the pay- 
 ments of brassage to the government than any speculative 
 gain possible from the change in price. 
 
 Other details relate to the provisions for establishing and 
 maintaining a gold reserve at the outset where no such 
 reserve existed in the first place. In the United States we 
 could utilize the 50,000,000 ounces of gold already in the 
 Treasury for the very purpose of redeeming the $900,000,000 
 of gold certificates outstanding. 
 
 We have standardized every other unit in commerce 
 except the most important and universal unit of all, the unit 
 of purchasing power. What business man would consent
 
 502 THE PURCHASING POWER OF MONEY 
 
 for a moment to make a contract in terms of yards of cloth 
 or tons of coal, and leave the size of the yard or the ton to 
 chance ? Once the yard was the girth of a man. In order 
 to make it constant, we have standardized it. We have 
 standardized even our new miits of electricity, the ohm, the 
 kilowatt, the ampere, and the volt. But the dollar is still 
 left to the chances of gold mining. At first we could not 
 standardize units of electricity because we had no adequate 
 instruments for measuring those elusive magnitudes. But 
 as soon as such measuring devices were invented, these units 
 were standardized. We have hitherto had a similar excuse 
 for not standardizing the dollar as a unit of purchasing 
 power, and so a standard for deferred payments; we had 
 no instrument for measuring it or device for putting the 
 results in practice. With the development of index numbers, 
 however, and the device of adjusting the seigniorage accord- 
 ing to those index numbers, we now have at hand all the 
 materials for scientifically standardizing the dollar and for 
 realizing the long-coveted ideal of a "multiple standard" 
 of value. In this way it is within the power of society, when 
 it chooses, to create a standard monetary yardstick, a 
 stable dollar.
 
 INDEX 
 
 Aldrich Report on Wholesale Pricea, 
 
 cited, 259, 260, 399. 
 Aldrich-Vreeland bill of 1908, 146 n. 
 American colonies, paper money in 
 
 the, 256-258. 
 Arrays, use of, in calculating 
 
 quantities, prices, and averages, 
 
 355-362, 367-368. 
 Arts, influence on quantity of money 
 
 of consumption of gold in the, 103. 
 Assets of bank, must be adequate to 
 
 meet liabilities, 38-39 ; form must 
 
 be such as to meet liabilities 
 
 promptly, 42-47. 
 Assignats, experience of French Rev- 
 
 olurionists with, 252-253. 
 Atkinson, F. J., on "Silver Prices in 
 
 India." 243. 
 Aupetit, Albert, cited, 157, 234, 237, 
 
 240. 
 Australia, rise of prices due to gold 
 
 discoveries in (1851-1852), 241- 
 
 242. 
 Austria, adoption of gold standard 
 
 by (1892), 243; experience of, 
 
 with paper money, 255-256 ; 
 
 monetary system of, referred to, 
 
 341-342, 344. 
 Averages, discussion and explanation 
 
 of, 23-24, 198-203, 349-352. 
 
 Bank checks. See Checks. 
 
 Bank deposit circulation, before and 
 during crises, 267-270. <See De- 
 posit currency. 
 
 Bank deposits. See Deposits. 
 
 "Bank gold," 115 n.'. 
 
 Banking laws, relative increase in de- 
 posits partly due to recent, 315. 
 
 Bank notes, 38-39 ; circulation of, 
 before, during, and after crises, 
 267-270. 
 
 Barter, the exchange of goods against 
 goods, 13. 
 
 Base, selection of a, in constructing 
 index numbers, 203. 
 
 Benefits of wealth, meaning of, 6 ; 
 future benefits are those referred 
 to, 6. 
 
 Bills of exchange, comparative ad- 
 justability of prices of, 186. 
 
 Bimetallism, mechanical operation 
 of, 115 ff. ; two requisites of com- 
 plete : free and unlimited coinage 
 of both metals at a fixed ratio, 
 and the unlimited legal tender of 
 each metal at that ratio, 117; 
 illustrations of workings of, by 
 the case of France and the Latin 
 Monetary Union, 132-135 ; the 
 claim that prices would be 
 steadied by, 324-325 ; shown to 
 be an indifferent remedy for vari- 
 ations in price level, 325-326 ; 
 possibility of the system breaking 
 down, 326 ; possible disruption of 
 prices by overvaluation of one 
 metal a risk to be feared, 327 ; 
 limits for ratios within which bi- 
 metallism is possible, 378. 
 
 Bland-Alli.son Act of 1878, 142. 
 
 Bolles, Albert S., cited, 257. 
 
 Bonds, prices of, among least ad- 
 justable, 186-187 ; effect of non- 
 adjustability of, shown in super- 
 sensitiveness of stocks, 190-192. 
 
 Book credit, velocity of circulation 
 increased by, 81-83 ; effect of, on 
 equation of exchange, 370-371, 
 491^92. 
 
 Boom periods leading to crises, 58- 
 67. 
 
 Bortkiewicz, L. von, cited, 32. 
 
 Brace, Harrison H., Gold Production 
 and Future Prices by, cited, 80, 
 241, 249. 
 
 Brown, Harry G., cited, 37 n., 65, 
 212 n.», 269, 426. 
 
 503
 
 504 
 
 INDEX 
 
 Bullion, influence on quantity of 
 money of melting coin into, 96-99. 
 Business barometers, 322, 478. 
 
 California, rise of prices due to gold 
 discoveries in, 241-242. 
 
 Capital, defined as a stock of goods 
 existing at an instant of time, 7 ; 
 influence of accumulation of, on 
 volume of trade, 76. 
 
 "Charging," velocity of circulation 
 increased by, 81-83 ; influence of 
 habit of, on volume of deposits, 
 88-89. 
 
 Checks, bank, function of, 33-35. 
 
 Checks, effect of use of, on velocity 
 of circulation, 83 ; increase in, 
 caused by increase in trade, 165 ; 
 statistics of payments by (1909), 
 305-306 ; statistics of total ex- 
 change work performed by (1896, 
 1909), 317-318; constitute nine 
 tenths of the country's transac- 
 tions, 318 ; method of calculating 
 deposits subject to, 434-441. 
 
 Checking accounts, statistics of 
 amounts of, from 1896-1909, 281- 
 282, 491-492. 
 
 Check transactions and money trans- 
 actions, statistical statement of 
 relative importance of, 317-318. 
 
 Chili, adoption of gold standard by 
 (1895), 243. 
 
 China, rise of prices in (1874-1893), 
 243-244. 
 
 Circulating credit, or bank deposit 
 currency, 33 S. See Deposits. 
 
 Circulating media, classification of, 
 in United States, 12-13. See 
 Currency. 
 
 Circulation, statistics of money in 
 circulation from 1896-1909, 280- 
 281. See Velocity of circulation. 
 
 Circulation of bank notes and bank 
 deposits before and at times of 
 crises, 267-270. 
 
 Circulation of money, signifies the 
 aggregate amount of its transfers 
 against goods, 13 ; general practi- 
 cal formula for calculating, 448- 
 460 ; application of formula to 
 calculation of circulation during 
 1896-1909, 460 ff. 
 
 Clark, J. B., cited, 221. 
 
 Coefficient of correlation, application 
 of, 294-296. 
 
 Coin-transfer concept of velocity, 353. 
 
 Commerce, foreign compared with 
 internal, 305-306, 484-486. 
 
 Committee of British Association for 
 Advancement of Science, report 
 of on index numbers, 228-229. 
 
 Commodities, defined, 2 ; com- 
 parative adjustability of prices of, 
 186-187 ; changes in quantities 
 of, corresponding to changes in 
 prices, 194-195 ; types of, con- 
 trasted, 382-384. 
 
 Conant, Charies A., cited, 132, 140, 
 223. 
 
 Confederate States, value of gold and 
 index numbers of prices in the, 
 263-265. 
 
 Continental paper money, 257-258. 
 
 Contracts, restriction of free move- 
 ment of prices because of, 185, 
 189 ; nonadjustability of prices 
 varies with length of, 189 ; meas- 
 urement of appreciation or depre- 
 ciation of loan contracts, by use 
 of index numbers, 208-225. 
 
 Costa Rica, adoption of gold stand- 
 ard by (1896), 243. 
 
 Cost of living, rise in, concluded to 
 be merely a part of general move- 
 ment of prices, 316. 
 
 Credit, circulating, or bank deposit 
 currency, 33 ff. 
 
 Credit cycle, history of a, 58-72 ; 
 table of statistics illustrating cul- 
 mination of a, 271-273 ; lessening 
 of fluctuations by tabular stand- 
 ard of value plan of regulating 
 price level, 335. 
 
 "Crime of 73," the, 141. 
 
 Crises, the culmination of an up- 
 ward price movement, 65 ; be- 
 lated adjustment of rate of 
 interest as a factor in, 66 ; corre- 
 spondence between circulation, 
 private deposits, and, 265-270 ; 
 conditions preceding, 266 ; a 
 crisis defined as an arrest of the 
 rise of prices, 266 ; international 
 character of, 266-270. 
 
 Currency, or circulating media, de- 
 fined as any type of property right 
 which serves as a means of ex-
 
 INDEX 
 
 505 
 
 change, 10 ; two chief classes : 
 money and bank deposits subject 
 to check, 10 ; bank deposits, 33 ff. 
 See Deposits. 
 
 D 
 
 Darwin, Leonard, Bimetallism by, 
 cited, 127. 
 
 D'Avencl, Vicomte, estimates by, 
 cited, 234, 237. 
 
 Deferred payments, use of index 
 numbers for measuring apprecia- 
 tion or depreciation of, 208-225. 
 
 De Launay, The World's Gold by, 
 cited, 98. 
 
 Del Mar, History of the Precious 
 Metals by, cited, 237, 239. 
 
 Demand, difference between effects 
 of an increased, for an individual 
 commodity and of an increased 
 general demand for goods, 180. 
 
 Demonetization of silver, lowering 
 of prices in gold-standard countries 
 by, 242-245. 
 
 Density of population, effects of in- 
 creased, on velocity of circulation 
 and on volume of trade, 164-166, 
 315. 
 
 Deposits, bank (deposit currency), 
 influence of, on equation of ex- 
 change and hence on purchasing 
 power, 33 ff. ; quantitative rela- 
 tion of, to money in a given com- 
 munity, 51-52, 151 ; expansion 
 of, during periods of rising prices, 
 58-60, 273 ; contraction of, in 
 period of falling prices, 67-70 ; 
 velocity of circulation of, increases 
 with density of population, 87 ; 
 dependence of, on quantity of 
 money, 162 ; effects of change in 
 ratio between quantity of money 
 and, 162-163 ; increase in, will 
 have no appreciable effect on 
 velocities of circulation and 
 volume of trade, but will raise 
 prices slightly, 163-164 ; effects 
 on prices of changes in (with 
 special attention to crises and 
 depressions), 265 ff. ; statistics of 
 amounts of, from 1896-1909, 281- 
 285 ; proved to have tripled, and 
 velocity of circulation of, to have 
 increased 50 per cent in fourteen 
 
 years, 304-305 ; statistics of 
 amount per capita and velocity 
 of circulation (1909), 305; growth 
 of, shown to be a large factor in 
 raising prices, 307-311 ; chief 
 causes of increase in, 315 ; velocity 
 of circulation of, chiefly due to 
 concentration of population, 315; 
 description of method of calculat- 
 ing, 434-441. 
 
 Depression, causes of period of, 58— 
 67, 71-72. See Crises. 
 
 Dewey, Davis Rich, cited, 258 ; use 
 of the median for wages by, 428. 
 
 Dispersion of prices, 184 ff. ; caused 
 by previous contract, legal re- 
 strictions, and custom, 185-189 ; 
 by nonvariation of articles related 
 to the money metal, 189-190 ; 
 by variation of individual prices 
 under influence of law of supply 
 and demand, 190-194. 
 
 Drobisch, M. W., cited, 396. 
 
 Dunbar, Theory and History of Bank- 
 ing by, cited, 35. 
 
 E 
 
 Economics, defined as the science of 
 wealth, 1. 
 
 Ecuador, adoption of gold standard 
 by (1899), 243. 
 
 Edgeworth, F. Y., cited, 25 n.", 167, 
 199, 218, 220, 325, 328, 334, 392, 
 396, 397. 423, 426, 427. 
 
 Egypt, adoption of gold standard by 
 (1885), 243. 
 
 England, statistics of price move- 
 ments in, 238-240 ; account of 
 experience of, with paper money, 
 238-239, 253-255; dates of fi- 
 nancial crises in, 267. 
 
 England, Minnie Throop, statistics 
 by, cited, 174, 273. 
 
 Equation of exchange, defined as 
 the equation between a stream 
 of transferred rights in goods and 
 an equivalent stream of trans- 
 ferred money or money substi- 
 tutes, 7 ; is a statement in mathe- 
 matical form of the total trans- 
 actions effected in a certain period 
 in a given connmunity, 15-16 ; the 
 money side and the goods side, 
 16-17 ; the magnitude called
 
 506 
 
 INDEX 
 
 velocity of circulation or rapid- 
 ity of turnover, 17 ; arithmetical 
 illustration of, 17-21 ; mechani- 
 cal illustration of, 21-24 ; alge- 
 braic statement of, 24-28, 364, 
 368 ; influence of bank deposit 
 currency on, 33 ff. ; application 
 of, to bank deposits or circulating 
 credit, 48^9 ; disturbance of, 
 during periods of transition, 55 
 ff. ; implies no causal sequence, 
 149-150 ; statistical verification 
 of, 276-318 ; construction of 
 index numbers required by, 198 
 S. (see Index numbers) ; benefits 
 €o business men of a fuller knowl- 
 edge of, 322-323; effect of time 
 credit on, 370-371 ; modification 
 of, required by international 
 trade, 372-375. 
 
 Essars, Pierre des, cited, 63, 87, 269, 
 270. 
 
 Evelyn, Sir G. S., early attempt to 
 construct series of index numbers 
 by, 208 n. t 
 
 Exchange, defined as consisting of 
 two mutual and voluntary trans- 
 fers of wealth, 3. »See Equation 
 of exchange. 
 
 Exchangeability, quality of, which 
 makes a commodity money, 9 ; 
 differing degrees of, found in real 
 estate, mortgages on real estate, 
 corporation securities, govern- 
 ment bonds, bills of exchange, 
 sight drafts, and checks, 9-10. 
 
 Exchanges, classification of, into ex- 
 change of goods against goods 
 (barter), of money against money 
 (changing money), and of money 
 against goods (purchase and sale), 
 13. 
 
 Expectation, results of, on prices, 
 262-263. 
 
 Failures, causes leading to commer- 
 cial, 64-67. 
 
 Fairchild, F. R., article by, cited, 193. 
 
 Falkner, Roland P., index numbers 
 of, 229. 
 
 Farm lands, value of, affected by 
 changes in rate of interest, 193. 
 
 Fetter, Frank, cited, 221. 
 
 Fiars prices, Scotch, 334. 
 
 Fiduciary money, definition of, 11. 
 
 Fisher, Irving, The Nature of Capi- 
 tal and Income by, cited, 1, 44, 
 214; The Rate of Interest by, 
 cited, 56, 57, 58, 65, 70, 210, 214, 
 216, 224, 266 ; papers and articles 
 by, 25 n.2. 115, 174, 190, 210, 211, 
 244. 384. 
 
 Fleetwood, Bishop William, work by, 
 cited, 208 n. 
 
 Flow or stream of goods, distinction 
 between stock or fund of goods 
 and, 7 ; three classes of economic 
 flows, besides income, 7. 
 
 Flux, A. W., cited, 423. 
 
 Food, rise of wholesale prices of, 
 compared with general change in 
 prices, 316. 
 
 Forecasts, economic, 321-322. 
 
 Foreign trade, influence of, on quan- 
 tity of money, 90-96 ; volume of, 
 contrasted with internal, 305- 
 306, 484-486. 
 
 Forest land, sensitiveness of value of, 
 to changes in rate of interest, 193. 
 
 Foxwell, H. S., cited, 218. 
 
 France, experience with bimetallism 
 in, 132-135 ; experiences of, with 
 paper-money schemes, 252-253 ; 
 dates of financial crises in, 267. 
 
 Freedom of trade, effect of, on 
 volume of trade and price level, 
 77-78. See Tariff. 
 
 Geographical influence on volume of 
 trade, 75. 
 
 "George Smith's money," 47. 
 
 Germany, adoption of gold standard 
 by (1871-1873), 242-243. 
 
 Giffen, Robert, cited, 206, 392. 
 
 Gold, the best example of a money 
 commodity, 2 ; comparative non- 
 adjustability of prices of articles 
 made of, 187, 189-190 ; statistics 
 of increase in annual production 
 of, 235-236 ; continued increase 
 in prices predicted, due to in- 
 crease in production of, 248-249 ; 
 increasing output of, 249 ; statis- 
 tical comparison of greenbacks 
 and, 259 ; difficulties of finding 
 substitute for, as a medium, 323- 
 324; various proposed substi-
 
 INDEX 
 
 507 
 
 tutes : bimetallism, polymetal- 
 lism, convertible paper currency, 
 tabular standard of value, com- 
 bination of gold-exchange stand- 
 ard and tabular standard, etc., 
 324-348 ; variabilities of pro- 
 duction of silver and, 326 n. 
 
 Gold bullion and gold coin, equal 
 values of, 97-99. 
 
 Gold coin, the only primary money 
 in the United States, 13. 
 
 Gold-exchange standard, system of 
 partial redeemability known as, 
 131-132, 337 ff. ; in British India, 
 138-140; in the Philippines, 
 Mexico, and Panama, 140. 
 
 Gold mining, chief cause of increase 
 of money, 315. 
 
 Gold standard, general adoption of, 
 and resultant fall of prices (1873- 
 1896), 242-243. 
 
 Goodbody, Robert, article by, cited, 
 188. 
 
 Goods, definition of the term, 6. 
 
 Greenbacks, issuance of, in United 
 States, 141 ; a useless anomaly, 
 145 ; depreciation of, 258-260 ; 
 comparison of prices in gold and 
 in (1861-1879), 259; explanation 
 of value of, found in expectation 
 of redemption, 261. 
 
 Gresham's Law, that cheap money 
 will drive out dear money, 112 flf. 
 
 Griswold, Robert N., calculations by, 
 484. 
 
 H 
 
 Hadley, A. T., Economics by, cited, 
 
 25 n.2. 
 Hardy, S. M., paper by, mentioned, 
 
 277 n.2. 
 Hazard, Thomas, Account Book of, 
 
 quoted, 256-257. 
 Hertzka, joint-metallism scheme of, 
 
 328. 
 Hickernell, W. F., table by, 146, 147. 
 Hildebrand, work by, cited, 161. 
 Holt, Byron W., cited, 186. 
 Hunt, William C., estimates by, 
 
 465-467. 
 
 Income, definition of, as flow of 
 benefits from stock of goods 
 (capital), 7. 
 2k 
 
 Index number, use of an, to stand 
 for prices taken collectively (P), 
 184 ; to stand for volume of trade 
 (T), 195-196. 
 
 Index numbers, a necessity owing 
 to dispersion of prices, 184-196 ; 
 comparison of, as to form, 198 fif. ; 
 simple or unweighted averages, 
 198-199 ; weighted averages, 199- 
 203 ; methods of constructing, 
 200-202; selection of the base, 
 203 ; the successive base or chain 
 system, 203-204 ; selection of 
 prices, 204 ff. ; use of, to measure 
 capital and to measure income, 
 205 ; to measure six subclassifi- 
 cations, 205-206 ; use of, to serve 
 as basis of loan contracts, or 
 standard of deferred payments, 
 208 ff. ; report of committee of 
 British Association for Advance- 
 ment of Science, 228-229; ad- 
 vantages of the median over 
 other forms of, 230-231 ; index 
 numbers of prices from 1896- 
 1909, 290-293, 486-487 ; of vol- 
 ume of trade from 1896-1909, 
 290, 478 ff. ; use of, in tabular 
 standard of value plan for con- 
 trolling price level, 332-337 ; each 
 form of index number for prices 
 demonstrated to imply a correl- 
 ative form of index number for 
 quantities, 385-391 ; eight tests for 
 a good index number, 400-417. 
 
 India, experience of, with the limp- 
 ing standard, 138-140 ; adoption 
 of gold standard by (1893), 243; 
 resultant rise of prices in, 243-244. 
 
 Inflation, rate of interest raised by, 
 57-58. 
 
 Insolvency in banking, 43. 
 
 Insufficiency of cash, condition of, 
 at banks, 43-45. 
 
 Interest. See Rate of interest. 
 
 International trade, modification of 
 equation of exchange required by, 
 90-96, 372-375. 
 
 Invention, as a disturbing force to the 
 financial equilibrium, 70 ; in- 
 fluence of, on volume of trade and 
 price level, 77. 
 
 Irredeemable paper money, effects of, 
 on prices, 238-239, 250 £F. Se4 
 Paper money.
 
 508 
 
 INDEX 
 
 Italy, the case of an overissue of paper 
 money in, 114. 
 
 Jacob, William, cited, 237. 
 
 Japan, adoption of gold standard by 
 (1897), 243; resultant rise of 
 prices in, 243-244. 
 
 Jevons, W. S., cited, 8, 9, 12, 80, 88, 
 186, 195, 237 n., 241, 249, 254, 
 332, 335, 397; quoted on diffi- 
 culties of determining velocity of 
 circulation of money, 286 ; claim 
 of, that a bimetallic standard 
 would tend to steady prices, 325. 
 
 Johnson, J. F., Money and Currency 
 by, cited, 136, 251, 333. 
 
 Joint-metallisms, schemes of, 328. 
 
 Juglar, Clement, cited, 65 n.^, 266, 
 267, 269, 270. 
 
 Kemmerer, E. W., works by, cited, 
 14 n., 25 n.2, 4.'S, 139, 140, 213, 
 226, 279, 282, 331, 487; pioneer 
 work of, in testing statistically 
 the quantity theory, 276-278, 
 430-432. 
 
 Kinley, Money by, cited, 60, 87, 212 ; 
 Credit Instruments, 226, 444, 462 ; 
 original statistical work of, 282- 
 283, 461-462, 491-492. 
 
 Knapp, G. F., cited, 32. 
 
 Knowledge of technique of produc- 
 tion, influence on volume of trade, 
 76. 
 
 L 
 
 Labor, influence of division of, on 
 
 volume of trade, 75. 
 Labor standard of purchasing power 
 
 of money, proposed, 222. 
 Labor unions, inability of, to affect 
 
 general price level, 179-180. 
 Lake, A. C, pamphlet by, cited, 
 
 347 n. 
 Landry, Adolphe, cited, 84, 85. 
 Latin Monetary Union, the, 134-135. 
 Lauck, cited, 269. 
 Laughlin, work by, cited, 14 n., 50 n., 
 
 140, 242 n.2 ; quoted, 104 n., 165 n. 
 Launay, L. de, cited, 248. 
 Law, John, paper-money scheme of, 
 
 252. 
 
 Legal tender, what constitutes, 8. 
 
 Leslie, Clifife, cited, 236. 
 
 "Limit of tolerance" of mints, 114— 
 115. 
 
 "Limping" standard, monetary sys- 
 tem called, 127 ; the gold-ex- 
 change standard a kind of, 131— 
 132 ; experience of British India 
 with, 138-140; in the United 
 States, 140-148; Walras's gold 
 standard with a "silver regulator" 
 a variant of, 328-329. 
 
 Loan contracts, measurement of ap- 
 preciation or depreciation of, by 
 index numbers, 208 ff. See Con- 
 tracts. 
 
 Logan, Walter S., article by, cited, 
 188. 
 
 Loss, influence on quantity of money 
 of consumption of gold by, 103. 
 
 Lowe, Joser,h, suggestion of use of 
 index number or tabular stand- 
 ard of value by, 208 n., 332. 
 
 M 
 
 Macleod, H. D., History of Economics 
 by, cited, 112. 
 
 Magee, J. D., figures of, on world's 
 production of gold and silver, 
 235 n., 241. 
 
 Mandats, French paper money, suc- 
 cessors to the assignats, 253. 
 
 Marginal cost of production, ex- 
 planation of, 99-101. 
 
 Marshall, Alfred, Principles of Eco- 
 nomics by, quoted, 71-72 ; system 
 called symmetallism suggested by, 
 328; cited, 423. 
 
 Massachusetts, paper money in 
 colonial, 256. 
 
 Median, advantages of, over other 
 forms of index numbers, 230-231, 
 425-428. 
 
 Menger, work by, cited, 5. 
 
 Merriam, Lucius S., cited, 221. 
 
 Mexico, adoption of gold standard 
 by (1905), 243. 
 
 MUl, J. S., cited, 25 n.^, 31, 102, 
 200. 
 
 Mining land, value of, as affected 
 by changes in rate of interest, 
 193. 
 
 Minting and melting, influence of, 
 on quantity of money, 96-99.
 
 INDEX 
 
 509 
 
 Mitchell, W. C, works by, cited, 141, 
 200, 268, 259, 260, 265, 426, 486 ; 
 use of the median for price in- 
 dexes, 428. 
 
 Money, definition of, aa any com- 
 modity generally acceptable in 
 exchange, 2, 8 ; three meanings of: 
 in the sense of wealth, in the sense 
 of property, and in the sense of 
 written evidence of property 
 right (bank-notes, checks, stock 
 certificates, etc.), 5; "circula- 
 tion" of, consists of a stream of 
 transferred money or money sub- 
 stitutes, 7 ; use of gold dust and 
 gold nuggets, tobacco, wampum, 
 shells, etc., for, 8-9 ; quality of 
 exchangeability which makes, 9- 
 10 ; distinction between bank de- 
 posits subject to check and bank 
 notes, 11 ; money rights are what 
 a payee accepts without question, 
 by legal-tender laws or well- 
 established custom, 1 1 ; primary 
 and fiduciary money, 11-12; 
 circulation of, siginfies the ag- 
 gregate amount of its transfers 
 against goods, 13 ; the purchas- 
 ing power of, is indicated by the 
 quantities of other goods which 
 a given quantity of money will 
 buy, 13-14 ; bank notes, 38-39, 
 47 ; Gresham's Law, that cheap 
 money will drive out dear money, 
 112 ff. ; comparison of stocks of, 
 in Europe, and price levels, 237- 
 238 ; statistics of money in cir- 
 culation from 1896-1909, 280- 
 281, 430-434; shown to have 
 nearly doubled in fourteen years, 
 304-305 ; statistics of actual cir- 
 culation of, 305-306 ; statistical 
 statement of check and cash trans- 
 actions, 317-318, 491-492; sub- 
 stitutes for, unlike other sub- 
 stitutes, 376-377. See also Quan- 
 tity of money. 
 
 Money changing, the exchange of 
 money against money, 13. 
 
 Money famines, causes of, 67-69. 
 
 Morawetz, Victor, cited, 45. 
 
 Mortgage notes, prices of, among 
 least adjustable, 186-187. 
 
 Muhleman, Maurice L., calculations 
 of, 245, 433-434. 
 
 Mulhall, Dictionary of Statistics, cited, 
 240. 
 
 N 
 
 National Bank notes. United States, 
 145-146. 
 
 Netherlands, adoption of gold stand- 
 ard by (1875-1876), 243. 
 
 Newcomb, Simon, Principles of 
 Political Economy by, 25 n.'. 
 
 Nicholson, J. S., cited, 206, 392. 
 
 Nitti, cited, 199. 
 
 Nogaro, Bertrand, cited, 32, 127. 
 
 Norton, J. Pease, cited, 59 ; index 
 numbers of, 230. 
 
 O 
 
 Oresme, Nicolas, 112. 
 Orient, regarded aa the " sink of 
 silver," 236, 247. 
 
 Pair of prices device, 343-344. 
 
 Palgrave, Dictionary of Political 
 Economy by, cited, 8. 
 
 Panics and their causes, 64-66. 
 
 Paper money, slight influence on 
 prices of the English irredeem- 
 able (1801-1820), 238-240; usual 
 effects of redeemable and of irre- 
 deemable, on prices, 250 ff. ; pre- 
 carious value of, 251-252 ; ex- 
 periences of various countries with, 
 252 ff. ; John Law's scheme, 252 ; 
 account of England's experience 
 with, 253-255 ; in Austria, 255- 
 256 ; American Continental, 257— 
 258 ; experience of United States 
 with, 258-203 ; Confederate, 263- 
 265 ; redeemable, suggested as a 
 price-steadying plan, 331-332. 
 
 Pareto, work by, cited, 70. 
 
 Pars, readjustment of gold, undei 
 author's proposed plan for reg- 
 ulating price level, 341->342, 
 344-345. 
 
 Pearson, Karl, the "correlation co- 
 efficient" of, 294. 
 
 Persons, Professor, cited, 278-279, 
 294. 
 
 Person-turnover concept of velocity, 
 353, 362-363. 
 
 Peru, adoption of gold standard by 
 (1897), 243.
 
 510 
 
 INDEX 
 
 Philippines, buying and selling ex- 
 change in the, 337, 338. 
 
 Polyinctallism, proposed scheme for 
 steadying monetary standard, 
 327-328. 
 
 Population, increased density of, 
 quickens flow of money and 
 checks, 164-165 ; changes in 
 volume of trade and velocity of 
 circulation caused by changes in 
 density of, 165-166 ; concentra- 
 tion of, the chief cause of increase 
 of velocity of circulation, 315. 
 
 Porter, Morgan, calculations by, 326 
 n. 
 
 Price, L. L., Money and its Relation 
 to Prices by, cited, 235, 237, 241. 
 
 Price level, dependent on three sets 
 of causes : quantity of money in 
 circulation, "efficiency" or ve- 
 locity of circulation, and volume 
 of trade, 14 ; the quantity theory, 
 that prices vary in direct propor- 
 tion to quantity of money, 14, 
 157-159, 296-297 ; varies directly 
 as the quantity of money in cir- 
 culation, directly as the velocity 
 of circulation, inversely as the 
 volume of trade done by it, 29 ; 
 effect on, of doubling the denomi- 
 nations of all money, 29-30 ; of 
 debasing the currency, 30 ; of 
 doubling the coinage, 30-31 ; 
 effects of rising and of falling, on 
 rate of interest, 56 ff. ; history 
 of a period of rising, leading to a 
 crisis, 58-67 ; the corresponding 
 downward course of, 67-70 ; out- 
 side influences which tend to 
 lower : geographical differences 
 in natural resources, division of 
 labor, improved productive tech- 
 nique, and accumulation of capi- 
 tal, 74-76 ; lowering of, by 
 changes in human wants, 76-77 ; 
 lowering of, by increased trans- 
 portation facilities, relative free- 
 dom of trade, development of 
 eflBcient monetary and banking 
 systems, and business confidence, 
 77-79 ; increase of, by book 
 credit, 81-83 ; raising of, by den- 
 sity of population and increased 
 transportation facilities, 88 ; regu- 
 lation of, by international and 
 
 interlocal trade, 90-96 ; workings 
 of a protective tariff in regard to, 
 93-95, 312-314; restatement of 
 truth that the normal effect of 
 an increase in the quantity of 
 money is an exactly proportional 
 increase in the, 157-159 ; slight 
 effect of changes in volume of 
 trade on, 166-169; held not to 
 be an independent cause of 
 changes in any of the other mag- 
 nitudes in equation of exchange, 
 169 ff. ; normally the one abso- 
 lutely passive element in the 
 equation of exchange, 172 ; em- 
 phasis laid on distinction between 
 individual prices relative to each 
 other and the price level, 175 ; not 
 determined by individual prices, 
 175-180 ; inability of trusts or 
 labor combinations to affect, 179- 
 180 ; increased general demand 
 for goods results in a lower, 180 ; 
 effect of dispersion of prices, 184— 
 197 ; general trend upward of, 
 234 ; influence on, of discovery 
 of America and increase in pro- 
 duction of gold and silver, 235- 
 236 ; comparison of metallic 
 stocks in Europe at various dates 
 and, 237-238 ; summary of move- 
 ments of, during nineteenth cen- 
 tury, 240-242 ; rapid rise of, from 
 1789-1809, 240-241 ; fall of, to 
 two fifths, between 1809-1849, 
 241 ; rise of by one third to one 
 half, in 1849-1873, 241-242; 
 lowering of, from 1873 to 1896, 
 242 ; effect on, of general adop- 
 tion of gold standard, 242-243; 
 effect on silver countries of adop- 
 tion of gold standard in other 
 countries, 243-245 ; rise in, from 
 1896 to present, 245-246; con- 
 tinued rise in, predicted, due to 
 increase in gold production, 248- 
 249 ; effects on, of changes in 
 deposit currency, 265 ff. ; con- 
 clusion that expansion of deposit 
 currency raises, rather than that 
 rise of prices creates deposit cur- 
 rency, 273 ; statistics of, as shown 
 by index numbers of general 
 prices from 1896-1909, 291-292; 
 importance of appreciating exist-
 
 INDEX 
 
 511 
 
 ence of a law of direct proportion 
 between quantity of money and, 
 296-297 ; shown to have risen by 
 two thirds, in fourteen years 
 (1896-1909), 304-305; summing- 
 up concerning rise of and causes, 
 from 1896-1909, 307; discussion 
 and analysis of the separate fac- 
 tors concerned in rise of, 307-311 ; 
 conclusion as to importance of 
 increase of money as a factor in 
 price-raising, 311 ; full effect of 
 quantity of money on, not felt 
 on account of overflow to foreign 
 countries, 311-312; question as 
 to whether price level is control- 
 lable, 319 ff. ; proposed methods 
 of maintaining a stable level : by 
 bimetallism, 324-327; by poly- 
 metallism, 327-328; by sym- 
 metallism, joint metallism, and 
 other purely academic schemes, 
 328-329 ; by inconvertible paper 
 money, 329 ; by a var3dng seign- 
 iorage charge, 330-331 ; by 
 convertible paper currency, re- 
 deemable on demand, 331-332; 
 by a tabular standard of value 
 plan, 332-337 ; by gold-exchange 
 standard combined with tabular 
 standard, 337-346 ; changes in 
 individual prices demonstrated 
 not to affect, necessarily, 382- 
 384. 
 
 Prices, individual : method of ob- 
 taining a price, 3 ; dispersion of, 
 184 ff. ; index numbers of, 184, 
 486-487 ; nonadjustment of some, 
 causes greater ratio of change in 
 others, 185 ff. ; of contracts, cus- 
 tom, and legal restrictions, 185, 
 187-189 ; classification of goods 
 according to adjustability of 
 prices, 186-187 ; narrow range 
 of variation in, of articles made 
 of money metal, 189-190 ; factors 
 working through law of supply 
 and demand which affect, 192- 
 194 ; effect on, of changes in rate 
 of interest, 193 ; impossibility of 
 a uniform change in, 194-195 ; 
 changes in quantities of commodi- 
 ties with changes in, 194-195. 
 
 Primary money vs. fiduciary money, 
 11-12. 
 
 Production, influence of knowledge 
 of technique of, on volume of 
 trade, 76. 
 
 Property, or property right, defined 
 as the right to enjoy the services 
 or benefits of wealth, 4 ; distinc- 
 tion between wealth and, 4 ; 
 units for the measurement of, 
 4-5 ; distinction between property 
 rights and the certificates of those 
 rights, 5. 
 
 Purchase and sale, the exchange of 
 money against goods, 13. 
 
 Purchasing power of money, as re- 
 lated to the equation of exchange, 
 8 ff. ; is indicated by the quan- 
 tities of other goods which a given 
 quantity of money will buy, 13- 
 14 ; influence of deposit currency 
 on, 33 ff. ; disturbance of, during 
 transition periods, 55-73 ; vari- 
 ous indirect influences on, — 
 conditions of production and 
 consumption, individual habits, 
 foreign trade, melting and mining, 
 etc., 74 ff. ; influence of monetary 
 systems, 112-148; influence of 
 quantity of money, 149 ff. ; index 
 numbers of, 184-233 ; problem 
 of making more stable, 319-348. 
 See Price level. 
 
 Q 
 
 Quantities of commodities, changes 
 in, corresponding to changes in 
 prices, 194-195, 382-384. 
 
 Quantity of money, relation of prices 
 to, 14, 157-159, 296-297 (see 
 Quantity theory) ; deposit cur- 
 rency normally proportioned to, 
 49-53 ; increase in, a cause of 
 disturbance to financial equilib- 
 rium, 70; causes outside the 
 equation of exchange that affect, 
 90 ff. ; influence of foreign trade, 
 90-96 ; influence of melting and 
 minting, 96-99 ; influences operat- 
 ing through the production and 
 consumption of money metals, 
 99-104 ; influence of monetary 
 systems, 112 ff. ; doubling of, 
 will double deposits, will not 
 affect velocity of circulation, but 
 will increase prices in proportion
 
 512 
 
 INDEX 
 
 to its own increase, 151-159 ; the 
 law of direct proportion between 
 quantity of money and price 
 level, 157-159, 296-297; ratio 
 between deposits and, 162 ; effect 
 on, of changes in velocities of cir- 
 culation, 164-165 ; effects on, of 
 changes in volume of trade, 165 ; 
 proof of importance of, as a price- 
 raising factor, 307-311 ; full effect 
 of increase in, not felt in United 
 States because of overflow abroad, 
 311-312; causes working toward 
 increase of, 315. 
 
 Quantity theory of money, that prices 
 vary proportionately to money, 
 14, 157-159, 296-297; causes 
 leading to contesting of this 
 theory, 14-15 ; the equation of 
 exchange, 15-31 (see Equation of 
 exchange) ; three illustrations of, 
 29-31 ; dependent on the fact 
 that money has no power to 
 satisfy human wants except a 
 power to purchase things which 
 do have such power, 32 ; in causal 
 sense, 151 ff. ; does not hold 
 strictly true during transition 
 periods, 159-162. 
 
 Quarries, effect on value of, of 
 changes in rate of interest, 193. 
 
 R 
 
 Railways, influence of, on velocity of 
 circulation, 88. 
 
 Rate of interest, determination of, 
 in banking, 45 ; effects of rising 
 and falling prices on, 56-58, 266 
 n.i ; the outstripping of, by prices 
 in period of rising prices, 59-60, 
 271-273 ; commercial crises due 
 to belated adjustment of, 66, 71- 
 72 ; tardiness of lowering of, in 
 period of falling prices, 68 ; effect 
 of changes in, on individual prices, 
 193 ; adjustment of, not sufficient 
 to compensate for fluctuations in 
 value of money, 223, 232-233. 
 
 Real estate, scope of, as a class of 
 wealth, 1-2 ; comparative ad- 
 justability of price of rented, 186 ; 
 prices of leased, among the least 
 adjustable, 186 ; value of, affected 
 by changes in rate of interest, 
 
 193 ; small part taken by, in total 
 business transactions of United 
 States, 226. 
 
 Receipts and disbursements, effect 
 on velocity of circulation of in- 
 creased frequency of, 83-85 ; 
 effect of regularity of, 85-86. 
 
 Reserves, banking, 45 ff . ; legal regu- 
 lation of, 46 ; effect of rising 
 prices on, 64-65 ; ratio which 
 exists between quantity of money, 
 amount of deposits, and, 162. 
 
 Retail prices, data concerning com- 
 parative importance and adjust- 
 ability of, 226-227. 
 
 Rhode Island, paper money in 
 colonial, 256-257. 
 
 Ricardo, theory of equation of ex- 
 change launched by, 25 n.* ; 
 cited, 31 n., 44, 188, 250, 343. 
 
 Robertson, J. Barr, articles by, cited, 
 244 n. 2, 245. 
 
 Ross, Edward A., cited, 221. 
 
 "Runs on banks," caused by period 
 of rising prices, 65. 
 
 Russia, adoption of gold standard by 
 (1897), 243. 
 
 Sakata, translation by, 243 n. *. 
 
 Salaries, relative adjustability of, 
 regarded as one of class of prices, 
 187. 
 
 Sauerbeck, statistics by, cited, 238- 
 240, 242. 
 
 Scandinavian monetary union, adop- 
 tion of gold standard by, 243. 
 
 Schwab, J. C, Confederate States oj 
 America by, quoted, 263-265. 
 
 Scott, Money a7id Banking by, quoted, 
 15 n. 
 
 Scrope, G. P., use of index number 
 to indicate standard of value sug- 
 gested by, 208 n., 332. 
 
 Seager, Introduction to Economics by, 
 cited, 144 n. 
 
 Seasonal changes, effects of, on ve- 
 locity of circulation, quantity of 
 money and deposits, 72, 161. 
 
 Sea-water gold, 249. 
 
 Sedgwick, H., cited, 200. 
 
 Seigniorage, charge for changing bul- 
 lion into coin, 98 ; regulation of 
 supply of metallic money by a 
 varying, proposed, 330-331.
 
 INDEX 
 
 513 
 
 Shaler, N. S., quoted, 324. 
 
 Shaw, W. A., History of the Currency 
 by, cited, 133, 134, 136. 
 
 Sherman Act of 1890, 142-143. 
 
 Short crops, as a disturbing force to 
 the financial equilibrium, 70. 
 
 Siberia, effect of introduction of gold 
 from, 241. 
 
 Silver, statistics of increase in annual 
 production of, 235-236 ; variabili- 
 ties of production of gold and, 
 326 n. ; danger from overvalua- 
 tion of, in case bimetallism were 
 a standard, 327. 
 
 Silver certificates in United States, 
 143-145. 
 
 Silver countries, effect on, of adop- 
 tion of gold standard by other 
 countries, 243-245. 
 
 Simple averages, 198-199. 
 
 Smiley, W. Y., mentioned, 484. 
 
 Smith, J. Allen, cited, 335. 
 
 Soetbeer, Adolf, figures of, on world's 
 production of gold and silver, 
 235 n., 237. 
 
 Sprague, O. M. W., editor Dunbar's 
 Theory and History of Banking, 
 35 ; cited, 269 n. ». 
 
 Stock of goods, distinction between 
 flow of goods and, 7. 
 
 Stocks, adjustability of prices of, 187 ; 
 supersensitiveness of, to monetary 
 fluctuations, 190-192 ; trans- 
 actions in listed securities con- 
 stitute eight per cent of country's 
 business, 226. 
 
 Stokes, joint-metallism scheme of, 
 328. 
 
 Substitutes, prices of, move in sym- 
 pathy with prices of articles 
 themselves, 189-190 ; substitutes 
 for money unlike other substi- 
 tutes, 376-377. 
 
 Sumner, W. G., cited, 8, 9, 255, 256. 
 
 Supply and demand, factors working 
 through principle of, which affect 
 individual prices, 192-194. 
 
 Symmetalism, system called, 328. 
 
 Tabular standard of value plan for 
 controlling price level, 332-337 ; 
 main objections to, 335-337 ; com- 
 bination of plan with the gold-ex- 
 
 change standard, suggested, 338- 
 346. 
 
 Tariff, effects of, on purchasing 
 power of money, 93-95 ; tem- 
 porary effect of a protective, to 
 raise price level of protected 
 country, 312; afterward ceases 
 to affect price level, except for its 
 interfering effect, 312-313; con- 
 sideration of tariffs of 1897 and 
 1909, 313-314. 
 
 Technical knowledge, influence of, on 
 volume of trade and price level, 76. 
 
 Telegraph, velocity of circulation in- 
 creased by the, 88. 
 
 Tests for index numbers, 400-417. 
 
 Thom, De Courcy W., cited, 266, 
 267, 268. 
 
 Thrift, influence of, on velocity of cir- 
 culation, 79-81. 
 
 Timber land, effect on value of, of 
 changes in rate of interest, 193. 
 
 Time, the element of, and relation 
 of wealth, property, and benefits 
 to, 6-7. 
 
 Time of turnover, concept of, 354, 
 363. 
 
 Tithe averages in England, 333. 
 
 Tokens, forms of fiduciary money 
 called, 12. 
 
 Trade, defined as a flow of transfers, 
 7 ; influence of foreign, on quan- 
 tity of money, 90-96 ; volumes of 
 foreign and domestic compared, 
 305-306, 484-486. See Volume 
 of trade. 
 
 Transfer of wealth, defined as a 
 change of its ownership, 3. 
 
 Transition periods, temporary effects 
 of, on equation of exchange, 55 
 ff. ; characterized by rising or by 
 falling prices, 56 ; effect of, on 
 equation of exchange, 159-162. 
 See Crises. 
 
 Transportation facilities, effect of, 
 on volume of trade, 77 ; relation 
 between velocity of circulation 
 and, 88, 166. 
 
 Trusts, inability of, to affect the 
 general price level, 179-180. 
 
 Turnover, rapidity of, 17 ; rates of 
 individual, dependent on volume 
 of expenditure, 167 ; statistics of, 
 at Yale University, 37^-382. Set 
 Velocity of circulation.
 
 514 
 
 INDEX 
 
 U 
 
 United States, sketch of monetary 
 system of, 140 ff. ; issuance of 
 greenbacks, 141 ; complicated 
 and objectionable features of 
 monetary system, 143 ff. ; ex- 
 perience of, with paper money, 
 258-263 ; dates of financial crises 
 in, 267. 
 
 Unweighted averages, 198-199, 349- 
 352. 
 
 Uses of wealth, to be distinguished 
 from utility of wealth, 6. 
 
 Utility standard of purchasing power 
 of money, 220-222. 
 
 Value, the magnitude called, and 
 its determination, 3 ; is the price 
 of any item of wealth multiplied 
 by its quantity, 3-4. 
 
 Velocity of circulation, dependence 
 of price level on, 14 ff. ; definition 
 of, 17, 352 ff. ; causes outside the 
 equation of exchange which affect, 
 79-89 ; increase of, by habit of 
 "charging," or book credit, 81- 
 83 ; increase of, by use of checks 
 rather than money, 83 ; increase 
 of, by increased frequency of re- 
 ceipts and disbursements, 83-85 ; 
 effect of regularity of receipts and 
 disbursements, 85-86 ; increased 
 by density of population, 87, 315 ; 
 affected by extent and speed of 
 transportation, 88 ; proved to be 
 unaffected by quantity of money 
 or of deposits, 151-154 ; changes 
 in velocities affect prices but not 
 quantity of money or volume of 
 trade, 164-165 ; effects on, of 
 increase in volume of trade, 165- 
 168 ; before, during, and after 
 crises, 270 ; statistics relative to 
 that of bank deposits from 1896- 
 1909, 282-285 ; statistics of circu- 
 lation of money from 1896-1909, 
 285-290 ; velocity of circulation 
 of money proved to have in- 
 creased only 10 per cent in thirteen 
 years, 304-305 ; of money shown 
 to be twenty-one times a year, 
 (1909), 305-306; of deposit 
 
 currency shown to be fifty-three 
 times a year (1909), 305; of 
 money shown to be a negligible 
 factor in raising prices, 307-311 ; 
 of deposits a large factor in raising 
 prices, 307-311; discussion of 
 concept of, 352—354 ; coin-trans- 
 fer and person-turnover concepts 
 of, 353, 362-363 ; time of turn- 
 over concept, 354, 363 ; method 
 of calculating velocity of circula- 
 tion of deposits, 441-446. 
 
 Venezuela, adoption of gold standard 
 by (1896), 243. 
 
 Volume of trade, dependence of price 
 level on, 14, 18-21, 24 ff. ; causes 
 outside the equation of exchange 
 which affect: geographical dif- 
 ferences, division of labor, extent 
 and variety of human wants, etc., 
 74-79 ; proved to be independent 
 of quantity of money (except in 
 transition periods), 155-156; in- 
 crease in, increases money in 
 circulation, 165 ; effects of, on 
 velocity of circulation, 165-168 ; 
 statistics of, from 1896-1909, 290- 
 291, 304-306; method of calcu- 
 lating (1896-1909), 478 ff. ; in- 
 dex numbers of, 479. 
 
 W 
 
 Wages, effect of frequency of pay- 
 ment of, on velocity of circula- 
 tion, 83-85 ; relative adjustability 
 of, considered as prices, 186-187 ; 
 obtaining a true index number 
 for, 207-208; amount to three 
 per cent of total business transac- 
 tions in United States, 226. 
 
 Walker, Francis A., works by, cited, 
 8, 11, 251, 265, 333. 
 
 Walras, scheme of a gold standard 
 with a silver regulator suggested 
 by, 328-329. 
 
 Walsh, C. M., cited, 199, 208 n., 
 223, 225, 393, 394, 396, 397, 
 398. 
 
 Wealth, defined as material objects 
 owned by human beings, 1 ; two 
 essential attributes of, materiality 
 and appropriation, 1 ; classifica- 
 tion of, under three heads, real 
 estate, commodities, and human
 
 INDEX 
 
 515 
 
 beings, 1-2 ; possibDity of measur- 
 ing, in physical units, 2-3 ; trans- 
 fer, exchange, price and value of, 
 defined, 3—4 ; ownership of, or 
 property, 4; meaning of "bene- 
 fits of wealth," 6. 
 
 Weighted averages, 199-203, 349- 
 352. 
 
 Wells, David A., referred to, 176. 
 
 White, Andrew D., Paper Money 
 Inflation in France by, cited, 
 252. 
 
 White, Horace, Money and Banking 
 by, cited, 47. 
 
 Wicksell, Knut, article by, cited, 59, 
 
 60. 
 Workmen, relative adjustability of 
 
 price of servicea of, 186-187. 
 
 Yale University, statistics of rapidity 
 of individual turnover at, 167, 
 379-382. 
 
 Z 
 
 Zizek, Frans, work by, cited, 349. 
 Zuckerkandl, cited, 14 n. 
 
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