PR 2 2 194§' 
 
 University of California 
 College of Agriculture 
 Agricultural Experiment Station 
 Berkeley, California 
 
 A STATISTICi:^, iU^ALYSIS OF THE DOIaESTIC DEiAM) FOR LEJONS, 1921-1941 
 
 by 
 
 G« M» Kuznets and Lavvrence R. Klein 
 
 June, 1943 
 
 Giannini Foundation of Agricultural Economics 
 Mimeographed Report I<fo» 84 
 
 UNIVERSITY OF CALIFORNIA 
 
 UBRARY 
 
 COLLEGE OF AGRICULTURE 
 DAVIS 
 
TABLE OF CONTENTS 
 
 Page 
 
 Introduction ....... • 1 
 
 Statistical considerations 4 
 
 Demand for summer lemons 11 
 
 Demand for winter lemons ...... 34 
 
 Allocation of shipments «•• 47 
 
 Summary 55 
 
 Appendix A. Series used in the study 57 
 
 Appendix B. Price and quantity residuals and tests 
 
 of randomness 83 
 
 Appendix C. Net regression charts 88 
 
 Appendix D» Auxiliary tables 101 
 
 Appendix E» The use of mean monthly maximum temperatures 
 
 in the summer lemon regression analysis 107 
 
... . . VJ.^i;^,;.j: 
 
 i'.-fe.t^.l' '■'■■f:'- -''i 'W-')S- . . • . v.-^. 
 
 1^ .i* 
 
 ♦^1 xj;. 
 
ii 
 
 LIST OF TABLES 
 
 Page 
 
 Table 1. Weekly average consiomption of lemons by native-white 
 nonrelief families classified by income and region, 
 selected cities, May-August, 1936 12 
 
 Table 2* Summer lemons: Basic series used in the demand analysis, 
 
 1922-1941 15 
 
 Table Summer lemons: Regression coefficients and auxiliary 
 
 constants, 1922-1941 16 
 
 Table 4» Sumraer lemons: Coefficients of separate determination . « • • • 20 
 
 Table 5. Summer lemons; Cadculated coefficients of price flexibility 
 
 and demand elasticity, 1922-1941 23 
 
 Table 6. Simmer lemons: Regression coefficients and auxiliary constants 
 
 for additional equations, 1922-1941 . 32 
 
 Table 7. Tfinter lemons; Basic series used in the demand analysis, 
 
 1921-22 to 1940-41 38 
 
 Table 8, Winter lemons: Regression coefficients and auxiliary constants 
 
 1921-22 to 1940-41 (1936-37 excluded) 39 
 
 Table 9. Ti'inter lemons: Calculated coefficients of price flexibility'' 
 
 and demand elasticitj^, 1921-22 to 1940-41 (1936-37 excluded). . 42 
 
 Table 10. Winter lemons: Coefficients of separate determination 44 
 
 Table 11. Allocation of Ho vember -April and May-October lemon shipments 
 to maximize f .o.b. returns for an undetermined and for a 
 fixed volume of annual shipments, 1921-22 to 1940-41 49 
 
 Table 12, Shipments of summer and winter lemons maximizing value on tree 
 and minimizing average annual f .o.b. price for fixed value 
 on tree • ••• 54 
 
 Table 13. Seasonal average f.o.b, prices of California lemons, 1921-22 
 
 to 1940-41 58 
 
 Table 14. Estimates of correlation betvreen California Fruit Grovrers 
 
 Exchange and industry weighted average prices under various 
 assumptions ......••..••«•....•••••••• ^ 
 
 Table 15. Comparison of f.o.b. prices of lemons excluding and including 
 
 exports, 1935-36 to 1940-41 62 
 
 Table 16. Average sizes of lemons shipped by the California Fruit Growers 
 Exchange and proportion of shipments graded Sunkist, 
 1930-31 to 1940-41 63 
 
 Table 17. YiTinter lemons: Domestic shipments, per-capita domestic ship- 
 ments. United States supply, and per-capita supply, 1921-22 
 to 1940-41 65 
 
I 
 
iii 
 
 Page 
 
 Table 18, Smnmer lemons: Domestic shipments. United States supply, 
 
 and per-capita United States supply, 1922 to 1941 67 
 
 Table 19, Industry shipments of winter and summer lemons for fresh 
 
 consumption, 1921-22 to 1940-41 69 
 
 Table 20. YiTinter lemons: California Fruit Grovrers Exchange domestic 
 
 shipments and outside domestic shipments, 1921-22 to 1940-41. . 71 
 
 Table 21. Summer lemons: California Fruit Growers Exchange domestic 
 
 shipments and outside supply, 1922-1941 ..... 72 
 
 Table 22. Indexes of total and per capita nonagri cultural income pay- 
 ments in the United States, 1921-22 to 1940-41 74 
 
 Table 23. Indexes of v/inter and summer temperatures, 1921-22 to 1940-41 • . 77 
 
 Table 24. Population weights employed in the construction of indexes 
 
 of summer and virinter temperatures 79 
 
 Table 25. Index of the incidence of influenza, 1921-22 to 1940-41 82 
 
 Table 26. Summer lemons: Price and quantity residuals 84 
 
 Table 27. Summer lemons: Tests of randomness of residuals ........ 85 
 
 Table 28, Winter lemons: Price and quantity residuals 86 
 
 Table 29, TiTinter lemons: Tests of randomness of residuals 87 
 
 Table 30. Tfinter lemons: The effect of adjusting domestic shipments in 
 1936-37 on the net regression coefficients and on the co- 
 efficients of multiple correlation ........ ...... 102 
 
 Table 31, Summer lemons: Inter correlations of the series employed in 
 
 the regression analyses 103 
 
 Table 32, Summer lemons: Reciprocal correlation matrices 104 
 
 Table 33, TJinter lemons: Intercorrelations of the series employed in 
 
 the regression analyses 105 
 
 Table 34, ViTinter lemons: Reciprocal correlation matrices ......... 106 
 
 Table 35. Mean maximum temperatures in 22 cities, May-September, 
 
 1922 to 1941 109 
 
 Table 36, Average rail and boat unloads of lemons in May, June, July, 
 
 August, and September in 22 cities, 1931 to 1938 , , 110 
 
 Table 37, Summer lemons: Regression coefficients and auxiliary constants 
 obtained v/hen mean maximum temperature in 22 cities is used 
 as the temperature variable ........... Ill 
 
 Table 38, Suiiiner lemons: Correlation matrix and its inverse obtained vrhen 
 mean maximum temperature in 22 cities is used as the temperature 
 variable ........... 112 
 
 1 
 
I 
 
LIST OF FIGURES 
 
 Page 
 
 Fig. 1. California f.o.b. price and donestio shipments of (A) winter 
 
 and (B) summer lemons, 1921-22 to 1940-41 3 
 
 Fig. 2, Domestic shipments of (A) winter and (B) summer lemons and 
 
 shipments maximizing f.o.b. returns, 1921-22 to 1940-41 .... 50 
 
 Fig. 3. Summer lemons: Net regressions of price on (a) United States 
 supply, (B) index of nonagricultural income payments, and 
 (C) index of temperature. Arithmetic form ....... ... 89 
 
 Fig. 4. Summer lemons: Net regressions of United States supply on 
 (a) price, (B) index of nonagricultural income payments, 
 and (C) index of temperature, 1922-1941. Arithmetic form ... 90 
 
 Fig; 5. Summer lemons: Net regressions of price on (a) per capita 
 
 United States supply, (B) index of per capita nonagricultural 
 
 income payments, and (c) index of temperature. Arithmetic 
 
 form 91 
 
 Fig. 6. Summer lemons: Net regressions of per capita United States 
 
 supply on (a) price, (B) index of per capita nonagricultural 
 
 income payments, and (c) index of temperature. Arithmetic 
 
 form 92 
 
 Fig. 7. Summer lemons: Net regressions of price on (A) United States 
 supply, (b) index of nonagricultural income payments, and 
 (C) index of temperature, 1922-1941. Logarithmic form .... 93 
 
 Fig. 8. Summer lemons: Net regressions of United States supply on 
 (a) price, (B) index of nonagricultural income payments, 
 and (C) index of temperature. Logarithmic form ........ 94 
 
 Fig. 9. ITinter lemons: Net regressions of price on (A) domestic ship- 
 ments, (B) index of nonagricultural income payments, (C) 
 index of temperature, and (d) time* 1921-22 to 1940-41. 
 Arithmetic fom 95 
 
 Fig. 10. Tlinter lemons: Net regressions of domestic shipments on 
 
 (a) price, (B) index of nonagricultural income pajmients, 
 (C) index of temperature, and (D) time, 1921-22 to 1940-41. 
 Arithmetic form 93 
 
 Fig. 11. Winter lemons: Net regressions of price on (a) per capita 
 
 domestic shipments, (b) index of per capita nonagricultural 
 
 income payments, (c) index of temperature, and (D) time. 
 
 Arithmetic form 97 
 
 Fig. 12, TJinter lemons: Net regressions of per capita domestic shipments 
 on (a) price, (B) index of per capita nonagricultural income 
 payments, (c) index of temperature, and (d) time, 1921-22 
 to 1940-41, Arithmetic form 98 
 
• • « 
 
Page 
 
 Fig, 13» Winter lemons: Net regressions of price on (A) domestic ship- 
 ments, (B) index of nonagricultural income payments, 
 (C) index of temperature, and (d) time, 1921-22 to 1940-41. 
 Logarithmic form ...••*...• 99 
 
 Fig. 14. Winter lemons: Het regressions of domestic shipments on 
 (a) price, (B) index of nonagricultural income payments, 
 (B) index of temperature, and (c) time, 1921-22 to 1940-41 
 Logarithmic fox*m .•...•.*••.••... • 100 
 
• » ♦ » » 
 
 , i. ! » 
 
A STATISTICAL ANALYSIS OF THE DOMESTIC DEMAND FOR LEMONS, 1921-1941 
 G» M« Kuznets ^ and Lawrence R» Klein 
 
 Introduction 
 
 This report presents some of the results of a study of the lemon industry 
 now in progress at the Giannini Foundation of Agricultural Economics of the Univer- 
 sity of California, Specifically, this paper describes a statistical analysis of 
 
 3/ 
 
 the demand relations facing handlers of California lemons. 
 
 The period under review is the twenty-year period 1921 to 1941. The geo- 
 graphic market for the purposes of this study is the continental United States. 
 During the last half of the period, that is, since 1932, practically all of the 
 lemons marketed in the United States were produced in California. This, however, 
 is not true of the first part of the period. In some of the earlier years imports 
 constituted a significant fraction of our total lemon supply. 
 
 California lemons are marketed in' the United States throughout the year. 
 The marketing year is generally taJcen to be the twelve-month period, November 1 to 
 October 31. Numerous references in the trade literature point to the notion that 
 the demand for lemons marketed during the winter months is affected by the prevalence 
 of colds and influenza, \Yhile the demand during the summer months is greatly 
 responsive to weather conditions. It would thus appear that greater homogeneity 
 would be attained by a separate consideration of the demand situation prevailing 
 during the winter and summer months. For this reason separate analyses are 
 
 y Instructor in Agricultural Economics, Junior Agricultural Economist in the 
 Experiment Station, and Junior Agricultural Economist on the Giannini Foundation. 
 
 y Research Assistant on the Giannini Foundation, June to September, 1942. 
 
 y A "handler" is defined by the California Agricultural Prorate Act as "any 
 person receiving agricultural commodities from the producer for the purpose of 
 marketing the same." Statutes of California, 1933. Chapter 754. 
 
Hp I 
 
 1..:. \, ,. • •• ^ ' ■• 
 
 " 'jo ai 
 
 TO' 
 
 \ 1' 
 
 'it 
 
presented in this paper for lemons shipped during the six months November through 
 
 April (winter lemons) and for those shipped in May through October (summer lemons) 
 
 of each marketing year. 
 
 The time sequence of seasonal average f«o*b« prices and domestic shipments 
 
 of lemons is portrayed for the months November through April in panel A, and for 
 
 4/ 
 
 May through October in panel B of figure !• It vdll be observed that both ship- 
 ment series exhibit a marked upward trend. Accompanying the upjvard trend in ship- 
 ments is a price trend vrhioh exhibits, at least for winter lemons^ an obvious 
 discontinuity roughly near the middle of the twenty-year period. For both winter 
 and summer lemons the price trend is up^vard for the nine years 1922 through 1930. 
 For the remaining eleven years the trend in the f .o^b. prices of v/inter lemons is 
 horissontal, while the trend of the prices of summer lemons is declining. The 
 tendency for the differential between f .o.b, prices of winter and summer lemons to 
 diminish is evident. Attention should also be drawn to the marked season-to-season 
 fluctuations in the separate price series. The expected inverse relation between 
 the year-to-year movements of prices and shipments is discernible for both winter 
 and summer lemons, but exceptions to this tendency may be noted. 
 
 Such is the course that prices and shipments have taken during the period 
 under consideration. YJhat are the factors that have fashioned this sequence? 
 How much and in what manner have these factors influenced the two time series? 
 These are the questions considered in this paper. 
 
 4/ 
 
 These series 6a*e given in appendix A. The price series consist of the 
 average prices, f.o.b, packing house, of lemons marketed by the California Fruit 
 Growers Exchange. 
 
,4 rfoae '}o 
 
 ■ ; • ■» ■ » 
 
2.50 ! ■■■J 1 . , . , ■ , _ _ ■ i ■ i ■ ■ 
 
 1S21-22 1923-24 1925-26 1927-28 1929-30 1931-32 1933-34 1935-36 1937-38 1939-40 
 
 Fig. 1. — California f.o.b. price and doniestic shipnents of (A) winter and (B) suramer lemons, 1921-22 to 1940-41. 
 The equations of the least sqviares price trend lines are (1) p^, = 3.7022 + 0.1283 t-j^ (origin at 1925-26), 
 (2) p;; = 3.0027 - 0.0066 tg (origin at 1935-36), (3) p^ = 4.5433 + 0.1230 (origin at 1926), 
 (4) p" = 3.7627 - .1255 tp (origin at 1936). (Data from tables 13, 17, and 18, appendix A.) 
 
■:.v.:,.>>. «7tir«c. .rwf i.-^i -safiKasi, j-swoiw' -f^-T^'S '/SsfS:' 
 
 '51 
 
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 1- 
 
4. 
 
 Statistical Considerations 
 
 Formally, the observations of price and quantity recorded in the raarket may 
 be viewed as the simultaneous solutions of the equations, 
 
 ^'t (P* ^t* a!^, a^) » 0 ' 
 
 , „ ^ t = 1, 2, M 
 
 6t (P» <1J \» \» \) =0 
 
 where p is price, q is quantity, f^ is the demand schedule at time t, is the 
 supply schedule, and b^ are the parameters of the ixio schedules. It is probably 
 psychologically more defensible and logically more convenient to viev/ the market 
 observations as the simultaneous solutions of the above equations in a stochastic 
 model, after a random component has been added to eachj that is, as the solutions of 
 
 tt tt 0.^,0 V, 
 
 t II „ i/ = x,t;,.».,i^ 
 
 St (p» ^t' \* \* ^t^ " ° 
 
 where s and s. are random variables, 
 t t 
 
 If one of the tv/o cxarves f^ or g^ remained fixed while the other shifted, 
 the price-quantity scatter would trace out the stable curve. This situation, it 
 has been argued, is approximated for some cominodities, such as agricultural 
 staples. — Clearly, however, this condition is not met by our data. It is 
 reasonable to assume that the supply curve for lemons has not remained fixed, but 
 has shifted in response to varying crop conditions and to changes in other factors. 
 But it cannot be assumed that the demand schedule has remained fixed. The demand 
 for lemons is presumed to be affected by weather conditions during the summer months 
 and by the prevalence of colds and influenza during the vd.nter. These are abruptly 
 changing factors \7hioh should induce erratic shifts of the demand curve from one 
 period to another. 
 
 — ■ Schultz, H. The theory and measurement of demand. The University of 
 Chicago Press. Chicago, 1938. p. 136. 
 
" '^h e. 
 
 7 
 
 I 
 
With both schedules shifting, the parameters of the theoretical demand 
 schedule could still be estimated if (1) the form of the demand curve, (2) the 
 complete set of shift variables, and (3) the distribution functions of the random 
 components were known. Not all of these items of information, however, are equally 
 important for the determination of statistical demand functions. It is argued here 
 that useful demand equations can b© secured even if nothing is loiovm concerning the 
 form of the demand function and the distribution functions of the rsindom components. 
 
 Let us suppose that we are able to catalogue and measure the important factors 
 
 which cause the demand to shift, and that these factors are, on the uriaole, distinct 
 
 from those that affect supply. Let us then choose some function and some method of 
 
 fit — being guided in this primarily by considerations of simplicity and convenience 
 
 but taking care not to gainsay whatever information is supplied by economic theory 
 
 and our acquaintance with the commodity and its markets. Finally, let us suppose 
 
 this 
 
 that with these shift variables and/function we have secured an excellent fit (the 
 measure of goodness of fit being consistent with our assumptions concerning the 
 random components). The resulting equation is not the market demand schedule of 
 the theoretical economist, but it is something more than just an estimation equation 
 for predicting price and quantity. It is clearly an equation pertaining to the 
 demand side of the market. Such equations, it is felt, should give us an insight 
 into the demand relations prevailing in the market. 
 
 The foregoing argument constitutes in a sense the rationale of this study. 
 The remainder of this section is devoted to a more detailed consideration of the 
 procedure v/e have follovred, 
 
 1, Shift Variables ,— Among the shift variables we have employed are 
 indexes measuring the level of temperatin-es prevailing in the important metropolitan 
 districts of this country, income payments used as a measure of consumer purchasing 
 power, and "time," There is little doubt that the temperature variables measure 
 factors which act on the demand side of the market. The most obvious influence of 
 temperature on supply is through the effect on crop conditions, but the geographical 
 
t * -■ ( 
 
 : •: • r: :•: :.: n-j :t;:i-.i;.v-.' -,,; •;:!• - ; ■ . .■ • 
 
 ^ n» Tjioaalo ai J- J. 
 
 ©•Mi f? . ■ 
 
6. 
 
 coverage of the temperature variable excludes this poeolbility. "Time" should be 
 
 adequate for "explaining" shifts in demand due to widespread advertising campaigns 
 
 and gradual changes in consumption habits. Income payments, in so far as they 
 
 represent consumer purchasing power, are a demand factorj but the role played by 
 
 this variable is equivocal because this index could be used as a measure of general 
 
 business conditions and thus be simultaneously (although with a smaller weight) a 
 
 supply factor. These variables considered as a group, however, are seen to be 
 
 important on the demand rather than the supply side of the market, 
 
 2» Form of Equations .— In this study, price or quantity was expressed as 
 
 a linear function of the shift variables or of their logarithms. By this it vms 
 
 implicitly assumed that the shifts of the demand schedule are parallel. At a time 
 
 t the net relation betv/een price and quantity is p «» aq + d^ or log p = a 'log q + d^, 
 
 where and d^ are the shift parameters of the demand schedule. It is evident 
 
 that d^ is a weighted average of the values of the shift variables at time t,and that 
 f 
 
 d^ is a similar average of their logarithms — the weights in both oases consisting 
 of the coefficients of the shift variables. 
 
 The conventional character of this procedure must be emphasized. There is a 
 temptation to a'ttaeh too much significance to the specific form of the net relations, 
 especially if the fit of the total equation is good. However, other functions 
 describing markedly different net relations might fit the data equally well and 
 possibly better than the functions selected by the investigator. It is chiefly 
 because of the uncertainty concerning the form of the net relations that tviTO 
 different, yet a priori equally admissible functions, vrere fitted. But it is not 
 intended that this choice imply that the true relations lie somewhere betv/een the 
 net relations described by the two functions. 
 
 3. Method of Fit .— • If the statistical results of this paper are to be 
 looked upon merely as estimation equations, then the following model may be adopted. 
 
era. 
 
 » - 
 
 .Jb'+ 'p« '•""q 'ei -^^'sJ-^V 
 
 :rtt. . \i: ■• 
 
 ••1^.' 
 
 1 : ri 
 
 '■" 'eicff <" 
 
 9d -ft- 
 
(i = 1, 2, N) 
 
 "i " * °2i^2 + + Osi^s 
 
 where the X^'s are the N observations of the dependent variable, m^i^ = E(X^) is the 
 expectation of X^, the e^^'s are independent random variables with standard errors 
 (T^ =Cr(unknown), — ' the Oj^'s are known numbers, and the a^'s are iinknown para- 
 meters. This specification makes possible the calculation of the best unbiased 
 
 linear estimate of the dependent variable and of the unbiased estimate of its 
 7/ 
 
 standard error. — ' Similarly, the unbiased estimate of the standard error of the 
 coefficients of the above linear estimate (net regression coefficients) may also 
 be calculated,. 
 
 4.. Tests of Significance . — In the course of the investigation questions 
 usually arise concerning the satisf actoriness of the equation as a whole and con- 
 cerning the significance of the coefficients of the equation. Criteria either in 
 terms of the standard error of the regression function or in terms of the standard 
 error of the regression coefficients may be formulated by the investigator to answer 
 such questions.. For oxtimple, the equation may be deemed satisfactory if the ratio 
 of the standard error of the equation to the estimated value is less than some 
 nvmiber k.. Or a given independent variable may be eliminated if the ratio of its 
 coefficient to the standard error is less than a certain fixed value. The advantage 
 of such "absolute" criteria is that they do not involve knowledge of the distribution 
 function of the residuals e^^. Such tests, however, are in the main unsatisfactory 
 
 6/ ^ 
 
 — ^ More generally, (7^ = B^p' where B^^'s are knovm numbers.. Throughout we 
 
 assme that » 1 (i =1, 2, ,.»,,N). 
 
 Unbiased in the sense that the mathematical expectation of the estimate is 
 equal to the true value and"best"in the sense that of all unbiased linear estimates 
 it has the smallest standard error. A detailed derivation of the estimate and of 
 its standard error is given in: David, F..H.. and J. Neyman. Extension of the 
 Markoff theorem on least squares.., Statistical Research Memoirs 2:105-116. 1938. 
 
■ . I * 
 
 ai*i lo 1' ■,, ••-11^ '^P Cits i> ; osij x - : ■ - 
 
 ffpas ri.'.riif. sa-?/' f?- 1 Pn^- ^."v!--'J'F'-5"'>^-'*' ''*c%^ •' • 
 
 r;- 
 
 e i 9ii 
 
8. 
 
 because of their extreme arbitrariness and because, vrLthout knov/ledge of the distri- 
 bution functions* only very weak probability statements can be made. 
 
 The assumption that the residuals follow the normal law removes the arbitrari- 
 ness inherent in the use of "absolute" criteria in multiple regression. However, 
 such an assumption as to the distribution of the residuals may be considered arbi- 
 trary in that there are many other equally admissible assimptions about the pro- 
 bability function of the residuals. It may be desirable to consider the hypothesis 
 most frequently tested in this paper, namely, that one of the parameters, say ag, 
 is zero in some detail so that the nature of the test may be properly appreciated. 
 
 Let U be the set of hypotheses ascribing to aj^, ag,Cr any real values 
 
 with the restriction that J"> 0, and let u be a subset of U consisting of hypotheses 
 specifying = 0 but ascribing to the other parameters a]^, a^^^* CT any real 
 
 values (Cr>0). According to the Neyman-Pearson principle of likelihood the 
 test of the hypothesis ag * 0 should be based on the value of the ratio 
 
 L Pu / Pu 
 
 or a constantly increasing or decreasing function of L , where p^ is the maximum 
 of the joint probability function of (Xj_, X2, Xjj) relative to hypotheses con- 
 
 tained in u, and p^ a similar maximum probability relative to hypotheses contained 
 in U. A low value of L implies that the set of observations (Xi, Xjj) is much 
 
 more probable on the basis of some hypothesis included in (U-u) than on the basis 
 of the hypothesis tested and would thus lead to a rejection of the latter. 
 
 Direct calculations lead to the following expression for L , for the hypo- 
 
 thesis tested a =0: 
 s 
 
 T M 2 n/2 
 
 where r is the partial correlation Qoefficient« It is somewhat more convenient 
 xs « 
 
 8 / 
 
 — I Neyman, J, and .E. S. Pearson. On the use and interpretation of certain test 
 criteria for purposes of statistical inference. Part I. Biometrika 20A: 175-240. 
 1928, 
 
'Mcf bna aawf ^ one 
 
9. 
 
 to use the following constantly decreasing function of L , 
 
 (iJ-s) ( L-2A - 1) 
 
 (iJ-s) 
 
 1-r 
 
 xs. 
 
 It will be recognized that L ^ is the ratio of the net regression coefficient of X 
 
 on s to the unbiased estimate of its standard error. The distribution of this ratio 
 
 for the case a^ = 0 is knora, -i/ and thus the probability of rejecting a true 
 
 hypothesis may be reduced to any desired level. 
 
 It has been shown that a common best critical region for all admissible 
 
 10/ 
 
 alternatives e;:ists if the hypotheses in (U-u) specify a > 0 or a < 0. ^ This 
 
 s 
 
 region is defined by the inequality L j_ for a^ > 0 or by the inequality 
 
 L^_^- t^ for ag<0. In these inequalities t^ is obtained from tables of the 
 integral of the Student-Fisher t distribution for (ll-s) degrees of freedom and for 
 (probability of rejecting a true hypothesis) based on one tail of the distribution. A 
 test based on the best critical region is to be preferred to other tests because 
 for any set level of significance, its power (the probability of rejecting the 
 hypothesis v/hen it is v/rong) is not less than the power of any other test determined 
 at the same level of significance. 
 
 The use of "standard errors" in connection with time-series data is 
 frequently criticized by economists and statisticians. Aside from the question of 
 the formal satisfaction by the data of the specific assumptions underlying the 
 coEEiionly used tests, much of the strength of the criticism is derived from a general 
 feeling concerning the lack of roalism in the basic specifications. The notion of 
 a random sample when applied to describe a configuration of prices or quantities 
 over time appears to be highly inappropriate, not only because the price or quantity 
 
 9/ 
 
 — ' Fisher, R, A. Appli 
 
 1925. 
 
 Application of "Student's" distribution, Metron 5:90-104. 
 
 10/ 
 
 — Kolodziejczyk, S. On an important class of statistical hj'-potheses. Bio- 
 metrika 27:161-190. 1935, 
 
■'uJ&il'-i.iitih. 
 
 tv:~ Is. 
 
 9.?t,f')L<:<; f-<^* ^^-t^^f^^Wwrf ■'• ' * I 9jf o ;r aj^if >■ , vo-- | 
 
10. 
 
 observations may be shoim to be serially related, but because the sequence of 
 prices or quantities appears to be unique. When separated from a consideration of 
 the specific conditions which must be met by the data in each problem, such atti- 
 tudes become an expression of the convictions of the investigator and are difficult 
 to evaluate objectively. 
 
 The randomness of residuals with regard to time is a condition of importance 
 in the application of classical regression methods to time -series data. The formal 
 satisfaction of this condition in a given problem can be tested, at least approxi- 
 mately, and such tests have been carried out ia this paper. The normality of 
 residuals, however, was not actually tested since there were too few observations 
 on which to base such a test. 
 
flf 
 
 ■■■ ' ■ ■■■■■■ ■ . ,:';i'}vi^r](!(/k .pJ-jJft'ir V-h 
 
Hi 
 
 Demand for Summer Lemons 
 
 The shift variables considered explicitly in the analysis of demand for 
 
 lemons during the summer months were consumer income, index of temperatures, time, 
 
 and volume of production. Of these only the first two variables proved to be 
 
 statistically significant, but there are indications that such trend factors as 
 
 growth of population during the period under review, advertising, etc., did exert 
 
 an influence on the demand for susfimer lemons in this country. 
 
 Consumer Income . In table 1 is given the average weekly consumption of 
 lemons by income class obtained in some of the regional samples of the 1935-36 
 Consumer Purchases Study, It is seen that in these samples the relation be- 
 tv/een family income and consumption of lemons is positive and that f,or the 
 range of income considered, the relation is approximately linear, ly It would 
 have been of interest to combine such budget data with time series "market" 
 data on prices and quantities as suggested recently by Marsohak.-^V In this 
 manner additional Information provided by the budget data could be utilized, 
 Hovrever, while this approach may be suitable in a study of demand for goods" at 
 the retail level, it is not well adapted to analyses of demand at other stages 
 of the marketing process. The existence, at a given time, of a relation between 
 consumer income and lemon consumption is, therefore, used here only to suggest 
 that consumer income may be an important factor affecting demand for lemons. 
 
 For a description of the particular income index employed (index of nonagri- 
 cultural income payments) and a discussion of its limitations, the reader is 
 referred to appendix A, Here it should be pointed out that both prices and 
 income are used throughout this study in current dollars — no attempt has 
 been made to deflate these series. It is largely a matter of individual prefer- 
 ence as to whether demand is to be defined in money or in real (deflated) 
 prices. It may be deemed desirable to eliminate from prices changes assoc- 
 iated with the movement of the general price level and to consider the effect 
 on demand for a specific commodity of changes in real rather than money incomes. 
 However, the crude adjustments commonly employed for this purpose are of ques- 
 tionable validity; their use may actually distort the relations which the 
 analysis seeks to describe. 
 
 Weather » The effect of weather on the demand for summer lemons has long 
 been observed by the trade. Since the principal use of lemons during the 
 
 A similar relation is fovind in the September-November data for regions cited 
 in table 1 and in the village and farm samples tabulated by the Bureau of Home Econ- 
 omics, See; United States Bureau of Home Economics, Family food consumption and 
 dietary levels. Farm series, Misc, Pub, 405, Urban and village series. Misc. 
 Pub. 452, Washington, D.C., 1941, 
 
 IH/ Marschak, J, Money illusion and demand analysis, Reviev; of Economic Stat- - 
 istics 25;40-48. February, 1943, 
 
 i^/ V/orking, E, J, Indications of changes in the demand for agricultural pro- 
 ducts. Jour, Farm Econ, 14:239-256, 1932, 
 
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 [it^Ui.p^):)l-^.^:t^:^.'ri'^'.^ r . ;;-v' ^^i;;.:;i•.-V>c;^■ 
 -0<i:^,:V-<,:i.m^,«^s^;r*O^}y|^^^;^^^ . f vX^Vf .ti^^ S^-V -i 
 
 :>■■•■■ 
 
TABLE 1 
 
 Weekly Average Consumption of Lemons by Native-White Nonrelief 
 Families Classified by Income and Region, Selected Cities, 
 May-August, 1936 
 
 
 Average weekly family consumption of lemons 
 
 
 Income 
 class 
 
 New York 
 City and 
 Chicago 
 
 New England 
 and East 
 Central 
 
 Southeast 
 
 West Central 
 and Rocky- 
 Mountain 
 
 Pacific 
 North- 
 west 
 
 Dollars 
 
 Dozens 
 
 
 500- 999 
 
 .07 
 
 .06 
 
 ,28 
 
 ,08 
 
 
 ,08 
 
 1,000-1,499 
 
 .12 
 
 .13 
 
 .45 
 
 .15 
 
 
 .14 
 
 1,500-1,599 
 
 .11 
 
 .17 
 
 .53 
 
 .21 
 
 
 .14 
 
 2,000-2,999 
 
 .21 
 
 .20 
 
 .64 
 
 .25 
 
 
 .26 
 
 3,000-3,999 
 
 .27 
 
 .38 
 
 .78 
 
 .33 
 
 
 .37 
 
 4,000-4,999 
 
 .21 
 
 .41 
 
 .94 
 
 .47 
 
 
 .39 
 
 Source of data: 
 
 United States Bureau of Labor Statistics. Study of consumer 
 purchases. Family expenditures in selected cities, 1935-36, 
 Volume 11: Food. Bulletin No. 648, Govt. Print. Off. T/fashington, 
 D. C. 1940. 
 
■ ; 'T - ^5" 'jr* '>"^ vc V X :*•♦■*'; « .I'a * *i ■ 
 
 .0 
 
13. 
 
 summer months is in cooling beverages, weather conditions affecting consump- 
 tion of cold drinks may also be expected to affect the demand for lemons* 
 
 It is unlikely that temperature is the only weather factor affecting the 
 summer demand for lemons. Other factors such as relative humidity, amount of 
 precipitation, wind velocity, hours of sunshine, etc., may be required to 
 measure properly the effect of weather. Furthermore, each of these variables 
 is in itself complex, and various characteristics of their temporal distribu- 
 tion would have to be examined to determine the most appropriate measure or 
 combination of measures to be employed, YJith the few observations at our dis- 
 posal, it was obviously unwise to attempt a comprehensive coverage of these 
 factors. In the analyses to be described, w© have used the average, for a 
 number of cities, of daily positive departures of maximum temperatures from an 
 arbitrary reference point to represent the vreather variable. A mention of th^ 
 reasons leading to the choice of this measure will be found in appendix A.iS' 
 
 Trend Factors . Under the rubric "trend factors" are included demand influ- 
 ences whose aggregate effect is to change the demand for lemons slowly and 
 smoothly. During the twenty years under consideration the population of the 
 continental United States increased by some 25 millions of persons} extensive 
 advertising of lemons was carried on yearly^ new outlets and better marketing 
 facilities were developed. It is reasonable to assume that in the aggregate 
 such factors have increased the demand for lemons slowly and smoothly. Because 
 of the difficulty of measuring the separate net effects, of such variables, 
 only their aggregate contribution can be considered.!^ 
 
 It is usual in statistical demand studies based on time series data to 
 account for the influence of trend factors by the introduction of a "time" 
 variable. This practice has been followed in the present study. In the cor- 
 relation of time series the variable "time" has also a more formalistio duty 
 to perform, namely to randomize residuals. It is, of course, highly desirable 
 that the contribution of "time" be minor relative to the contribution of the 
 other more explicit independent variables; otherwise a large part of the 
 variance of the dependent variable is allocated to factors not properly identi- 
 fied. 
 
 Vol ume of Domestic Production , The variables we have considered thus far 
 are factors which might reasonably be expected to affect the consumer demand 
 for lemons. The statistical analyses reported in this paper, however, are 
 oriented not toward consumer demand, but toward the derived demand, at the 
 f.o.b. level, facing handlers of lemons. Hence, factors unrelated to consumer 
 demand, but directly affecting the derived demand must also be considered. 
 Such factors are certainly more difficult to measure than those already dis- 
 cussed. While it was not possible to undertake a thorough study of these 
 variables, some attempts have been made to test their influence. 
 
 Another temperature index is described in appendix E. 
 
 15/ 
 
 The influence of the population factor was partly eliminated in some of the 
 regression equations described below by the use of per-oapita data. Such an adjust- 
 ment, however, obviously ignores the effect of changes in the age distribution of 
 the population. 
 
£3;'' 
 
 ^riW ;-v><^cf! =ly&tfc r^i^jii '^4ndV'-7 ' 
 
 ,^.,;rr- 'i./v ■.■ t:■^ ;,i.v.:' Ki;;- ,. X;^...:^ :•: .• 
 
14 
 
 Knowledge (expectations) by dealers of the volume of lemons available for 
 disposal as fresh fruit may exert a net influence on the level of f»o»b» prices. 
 In years of unusually large crops a given level of shipments may result in 
 prices substantially lower than those called forth in years of short crops 
 (factors affecting consumer demand remaining constant) by an identical level 
 of shipments. A widespread expectation of an unusually large crop may create 
 an unwillingness on the part of dealers to buy extensively in the present market 
 because of the anticipation of a fall in prices. On the other hand, a wide- 
 spread knowledge among dealers of the shortness of the crop may induce a will- 
 ingness to pay "scarcity" prices even though the supply of lemons in the whole- 
 sale markets may be ample. A striking illustration of the operation of this 
 mechanism is described in the next section. 
 
 The measurement of the influence of this variable is complicated by the fact 
 that since 1924 marketing agreements containing provisions for limitation of 
 shipments have been in effect in the lemon industry. Because of the presence 
 of control over volume of shipments, it is possible that a greater expression 
 of this factor is to be found in years characterized by short crops than in 
 years of large crops. However, until 1941 marketing agreements were not in- 
 dustry-vri.de. Fiirthermore, in years of large crops, grower pressure to increase 
 shipments regardless of demand conditions may be expected. Y^hatever the reasons, 
 the fact is that, for the period under review, the year-to-year fluctuations in 
 
 quantity shipped. 16/ A large crop, then, has meant more often than not large 
 shipments and hence anticipated Icvi prices. 
 
 Volume of Im p orts . Mention has already been made of the fact that during the 
 first half of tho period under review large quantities of lemons were imported 
 into this country. This source of supply, obviously, cannot be left out of 
 consideration in a demand study, even though the problems created by imports 
 are nov/ only of historical interest. Little is known concerning the substitute 
 ability relations between imported and domestic lemons; hence not much can be 
 said concerning the expected direction and degree of influence of the import 
 variable. The statistical analysis may throw some light on the above-mentioned 
 relationships. 
 
 The series used in the analysis of demand for summer lemons are given in 
 table 2, A linear form expressing f.o.b. prices as a function of total United States 
 supply of lemons, nonagri cultural income payments, and the temperature index was 
 found to fit the data rather closely (see equation Is, table 3). An examination of 
 the scattering of residuals about the various net regression lines, shown in figure 
 3, appendix C, did not reveal marked departures from linearity, ll/ 
 
 The correlation between first differences in industry annual shipments and 
 first differences in annual production is .55. 
 
 11/ The charts given in appendix C v/ere constructed by drawing a trace of the 
 regression surface in a plane with the dependent variable measured on the vertical 
 axis and each of the independent variables measured on the horizontal axis. The 
 points represent the residuals (see table 26, appendix B) as calculated from the re^ 
 gression equation, plotted as deviations from the net regression line corresponding 
 to the values of the independent variable at which they were calculated. 
 
 production were 
 
 fluctuations in 
 
At 
 
 i ■ 
 
 ■^5-'" , . ■ "' •.- . ex.: . . < — t-r:— 
 
 - I'- r. , ■ •■; '-f -, , . '• 'r • .. .. . -• ■. 
 
 •v"Ui^' •'^r t ■ ■ ♦•.■•i;;';.:»ofl ;.v .;i 
 
 . - • ■• .- 
 
 ' ■' ■ ■ - 3 but 
 
TABLE 2 
 
 Summer Lemons: Basic Series Used in the Demand Analysis, 1922-1941 
 
 
 
 
 i'er capita 
 
 
 
 
 
 Index of 
 
 - — 
 
 rer capita 
 
 
 
 Year 
 
 F .o.b. 
 
 United 
 
 United 
 
 Domestic 
 
 Imports 
 
 C.F.G.E. 
 
 Outside 
 
 nonagri- 
 
 nonagri- 
 
 index of 
 
 May- 
 
 price 
 
 States 
 
 States 
 
 shipments 
 
 for con- 
 
 domestic 
 
 supply 
 
 cultural 
 
 cultural 
 
 tempera- 
 
 October 
 
 
 supply 
 
 supply 
 
 
 sumption 
 
 shipments 
 
 
 income * 
 
 i ncome 
 
 tures "if 
 
 
 1 
 
 2 
 
 0 
 Xp 
 
 2d 
 
 Xqt 
 
 Xqo 
 cc 
 
 
 X-, 
 3 
 
 0 
 X, 
 
 o 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 c 
 D 
 
 c 
 
 o 
 
 n 
 1 
 
 Q 
 
 0 
 
 Q 
 
 y 
 
 T A 
 
 
 dollars 
 
 10,000 
 
 pounds 
 
 10,000 
 
 10,000 
 
 T A AAA 
 
 10 ,000 
 
 10,000 
 
 per cent 
 
 per cent 
 
 per cent 
 
 
 per box 
 
 boxes 
 
 
 boxes 
 
 boxes 
 
 boxes 
 
 boxes 
 
 
 
 
 1922 
 
 4.48 
 
 328 
 
 2.27 
 
 235 
 
 93 
 
 201 
 
 127 
 
 88 
 
 88 
 
 100 
 
 1923 
 
 5.23 
 
 312 
 
 2.13 
 
 202 
 
 110 
 
 193 
 
 119 
 
 100 
 
 97 
 
 92 
 
 1924 
 
 2.74 
 
 369 
 
 2.48 
 
 322 
 
 47 
 
 276 
 
 93 
 
 101 
 
 96 
 
 80 
 
 1925 
 
 4.93 
 
 399 
 
 2.64 
 
 289 
 
 110 
 
 267 
 
 132 
 
 110 
 
 103 
 
 120 
 
 1926 
 
 3.23 
 
 403 
 
 2.63 
 
 328 
 
 74 
 
 300 
 
 103 
 
 113 
 
 103 
 
 88 
 
 1927 
 
 4.88 
 
 351 
 
 2.26 
 
 289 
 
 62 
 
 259 
 
 92 
 
 116 
 
 104 
 
 75 
 
 1928 
 
 4.86 
 
 350 
 
 2.22 
 
 303 
 
 47 
 
 281 
 
 69 
 
 119 
 
 104 
 
 89 
 
 1929 
 
 5.36 
 
 355 
 
 2.22 
 
 322 
 
 33 
 
 292 
 
 63 
 
 123 
 
 106 
 
 105 
 
 1930 
 
 5.18 
 
 388 
 
 2.40 
 
 333 
 
 55 
 
 308 
 
 80 
 
 111 
 
 94 
 
 138 
 
 1931 
 
 4.50 
 
 399 
 
 2.44 
 
 381 
 
 18 
 
 348 
 
 51 
 
 96 
 
 81 
 
 150 
 
 1932 
 
 4.41 
 
 312 
 
 1.90 
 
 307 
 
 5 
 
 283 
 
 29 
 
 74 
 
 62 
 
 110 
 
 1933 
 
 3.60 
 
 354 
 
 2.14 
 
 347 
 
 7 
 
 311 
 
 43 
 
 71 
 
 59 
 
 136 
 
 1934 
 
 3.85 
 
 406 
 
 2.44 
 
 404 
 
 2 
 
 368 
 
 38 
 
 81 
 
 67 
 
 142 
 
 J. 
 
 
 A'l fi 
 HI. D 
 
 
 •x J. U 
 
 
 
 36 
 
 87 
 
 71 
 
 106 
 
 
 
 431 
 
 2.56 
 
 4? 7 
 
 A 
 
 408 
 
 23 
 
 104 
 
 85 
 
 151 
 
 1937 
 
 4.86 
 
 387 
 
 2.28 
 
 384 
 
 3 
 
 369 
 
 18 
 
 108 
 
 87 
 
 127 
 
 1938 
 
 2,87 
 
 435 
 
 2.55 
 
 435 
 
 
 414 
 
 21 
 
 99 
 
 79 
 
 115 
 
 1939 
 
 3.17 
 
 470 
 
 2.73 
 
 470 
 
 
 445 
 
 25 
 
 107 
 
 65 
 
 140 
 
 1940 
 
 3.04 
 
 461 
 
 2.66 
 
 461 
 
 
 422 
 
 39 
 
 114 
 
 90 
 
 106 
 
 1941 
 
 3.19 
 
 550 
 
 3.14 
 
 550 
 
 
 507 
 
 43 
 
 135 
 
 105 
 
 145 
 
 X 
 
 4.114 
 
 393.8 
 
 2.429 
 
 360.2 
 
 33,4 
 
 331.6 
 
 62.2 
 
 102.9 
 
 88.3 
 
 115.8 
 
 
 0.860 
 
 56.5' 0.264 
 
 82.5 
 
 37.9 
 
 79.7 
 
 36*4 
 
 16.0 
 
 11.4 
 
 23.6 
 
 * 1935-39 = 100. 
 t 1922 = 100. 
 
 Sources of data: Col. 1: Table 13. Cols, 8 and 9: Table 22. 
 
 Cols. 2, 3, 4, and 5: Table 18. Col. 10: Table 23. 
 
 Cols. 6 and 7: Table 21, 
 
.1 c 
 
 (1 
 
 |; 
 
TABLE 3 
 
 Summer Lemons: Regression Coefficients and Auxiliary Constants, 1922-1941 
 (Figures in parentheses are standard errors) 
 
 
 
 Net reeression coefficients * 
 
 Adjusted 
 coefficient 
 01 multiple 
 correlation 
 
 Elasticity 
 
 1 1 
 
 Flexibility 
 
 01 price 
 
 f t 
 
 Equation 
 
 Dependent 
 variable 
 
 (x) 
 
 Constant 
 term 
 
 c 
 
 F»o»b. price! 
 
 ^1 
 
 Ui.ited j 
 States j 
 supply 
 
 Nonagri- 
 cultural 
 income 
 
 ^3 
 
 Index of 
 tempera- 
 tures 
 
 ^4 
 
 Is 
 2s 
 
 ^1 
 
 ^2 
 
 4 ,o4o2 
 185.6147 
 
 -41.2473 
 (4.4092) 
 
 (0.0022) 
 
 (0.0067) 
 
 2.1239 
 (0.2387) 
 
 (0.0047) 
 
 1.3774 
 
 (0.1607) 
 
 0.9050 
 0.9569 
 
 -0.4309 
 
 -1.9620 
 
 
 (x) 
 
 c 
 
 X 
 
 1 
 
 Fer capita 
 United 
 State s 
 supply 
 
 ^2 
 
 Per capita 
 nonagri cul- 
 tural in- 
 come 
 
 x° 
 ^3 
 
 ^4 
 
 R 
 
 
 
 3s 
 4s 
 
 ^1 
 
 4.8712 
 
 (C.0250) 
 
 
 
 -3.6617 
 
 { 0 .3^90^ 
 
 0.0565 
 
 f 0 .0075^ 
 
 0 .0146 
 (0.0016) 
 
 0.0272 
 ( G fcC'046 ) 
 
 ( 0 .0073 
 (0.0010) 
 
 0.9089 
 0.9401 
 
 -0.3888 
 
 -2.1615 
 
 
 ^(x) 
 
 C 
 
 Log x^ 
 
 Log Xg 
 
 Log X3 
 
 
 R 
 
 
 f 
 
 5s 
 
 Log 
 
 3.5555 
 
 
 -2.0854 
 (0.2385) 
 
 1.0356 
 (0.1747) 
 
 0.0074 
 (0.013) 
 
 0.8922 
 
 
 -2.0854 
 
 6s 
 
 ^Og Xg 
 
 1.6757 
 
 -0.3965 
 (0.0454) 
 
 
 0.4865 
 (0.0613) 
 
 0.0036 
 (0.0004) 
 
 u.you^ j — u.o^joa 
 
 
 (Footnotes on next pagej a. 
 
Table 3 continued: 
 
 * "^2. ~ average f ,o.b. price in dollars per box. 
 
 Xg = United States supply of lemons in units of 10,000 boxes. 
 
 x° = Per capita United States supply of lemons in pounds, 
 
 Xj = Index of nonagricultural income payments, 1935-39 = 100. 
 
 x° = Per capita index of nonagricultural income -ayments in oer cent. 
 3 
 
 x^ = Index of daily maximum temperature departures from 80° in 39 metropolitan districts, May through October. 
 At the centroid. 
 In natural logarithms. 
 
 -3 
 
18, 
 
 A linear equation expressing the United States supply of summer lemons as a 
 function of the f,o,b, prices, nonagrioultural income, and the index of summer temp- 
 eratures (see equation 2s, table 3) was found to give an excellent fit to the data. 
 With supply as the dependent variable, the adjusted multiple correlation coefficient 
 is 0«9569 v/hi«h is markedly higher than the corresponding coeffif>ient of 0.9050 
 with price a« the dependent variable* The scatters of supply residuals about the 
 vajfiouB net regression lines are shown in the panels of figure 4,- appendix C. It 
 is evident from these charts that the use of curved net regressions would not mark- 
 edly improve the fit of the equation. 
 
 The results of tests of randomness of residuals derived from the two equations 
 are found in table 27, appendix B. Neither the magnitudes of the lagged correlatiq;i 
 coefficients nor the probabilities derived from the Wallis-Moore test force the 
 rejection of the hypothesis that the residuals constitute a random series. 
 
 In both equations Is and 2s as, in fact, in all of the regression equations 
 discussed in this paper — the signs of the net regression coefficients agree with 
 the direction of influence expected on a priori grovinds. Nonagrioultural income 
 pajipients and the temperature index are related directly to both the f «f>»b, prices 
 and the United States supply of summer lemons, while the two latter variables are 
 related inversely* The inverse net price-supply relationship is, of course, in 
 agreement with the demand relationship discussed in theoretical economics. The 
 direct variation of both prices and quantities with income and temperature is also 
 entirely reasonable. An increase in purchasing pov/er should express itself either 
 in higher prices of lemons, if the quantity of lemons purchased remains constant, 
 or in larger quantities of lemons purchased if the price remains constant. A 
 similar relation is evident for the seasonal demand factor, temperature. 
 
 Of some interest is the determination of the relative contribution of the 
 several independent variables. In almost all statistical demand studies the two 
 variables of prim© importance are price and quantity} the investigator usually 
 
J '^^rva^^'k^ rl'^--i^t. sf^m^ B^S^vJ . ■ ., j^.. , ja ...rji 
 
 t--'"' ■• ■■• rift* i-i>-;. ;/.v; , vlciri ti: sjc^ . ' 
 
 ..„]?;. v;;; '• ^ ■■ • "..cv vi;; ;u -:v; -w;; o';-- ^i^jj:'.? :: •^ ■; rarr a;/ • 
 
 ■■ ■" ' •' ••■ ■ — ■. * — • -.W i;/-: exv, r,.^. .-'V-':' al 
 
 ■■ '■•■v;.;; •■ . •: ■,'iJ,;i-.; :;rvi/ / "ii-;./;, 
 
 ■x-'. -i-., -.r'l.: \- .i'liai i- Or:. 5^10 : . ; .;■ :. : '■ .' , ;• rr:-;v;' ■ ■ "c •-. . . 
 
 . ,-::':-r-ui'y'y --iiT'i-; - A:: 'r l-..-. • , ; a' J.- ;-: — •; -;- 
 
 ?v;: .i;z<«t^-";^ ••.w.-:>;^.j,rii rJ o .;;;vi-:-.J : i.:. , ^ ■;■;::) v ■ '. :■ • ■ . 
 
Id, 
 
 expects a significant part of the variation in price to be associated vdth the 
 
 variation in the amount sold, and inversely. The supply-price relationship is 
 
 also the most strategic from the point of view of policy, fcr these are ordinarily 
 
 the only two variables in the formulation which are capable of being controlled. 
 
 Of interest is also the contribution of the temperature factor to price and supply 
 
 variance, since this non-eoonomio seasonal factor has been given great prominence 
 
 in the discussions of the demand for siimmer lemons found in trade publications* 
 
 The net regression coefficients in the two equations cited above cannot be 
 
 taken as they stand to measure the contribution of the independent variables in 
 
 "accounting" for the price or supply variance. In fact, the problem of measuring 
 
 the relative importance of independent variables may not have a unique solution; 
 
 certainly, none of the measures at present available can be deemed satisfactory. 
 
 Of the several measures of relative importance commonly employed, the coefficient of 
 
 separate determination, d. . ■ iff . . r^ j, is, probably, the least ambiguous because of 
 
 m 2 
 
 its additive property^ d^j = R^, where is the multiple correlation coefficient. 
 The ambiguity introduced by the occasional appearance of negative values of d^^ can 
 be removed by a minor adjustment which does not disturb the additive property of 
 this coefficient. 
 
 18/ 
 
 The first two rows of table 4 give the coefficients of separate determination 
 for equations Is and Zsi It will be observed that either f .o.b, price or the quan- 
 tity of summer lemons accounts for the major part of the variance of the dependent 
 variable. This is particularly evident in equation 16 in which approximately 73 
 per cent of the variance of f.o.b* prices is allocated to the United States supply > 
 9 per cent to nonagrioultural income, and only 2 per cent to the temperature variable. 
 
 18/ o i di . , , V 
 
 — ' The adjustment is of the form d, » d. . ^"^^T < (ijjtj)* 
 
 ij I 10 
 
 131 
 
J^'a'ilii ibtfb'rVi iikilfi;^/ 
 
 li" It. ii-'' -■■''■'sXiiir -j/w ■ ■ ■ _ 
 
20. 
 
 TABLE 4 
 
 Summer Lemons: Coefficients of Separate Determination 
 
 Equation 
 
 U6 peii 0.011 u 
 variable 
 
 F.o.b, 
 
 price 
 
 United 
 States 
 supply 
 
 Per capita 
 United 
 States 
 supply 
 
 Index of 
 nonaf,r i- 
 cul bural 
 inc ome 
 
 Per capita 
 nonagri- 
 cul tural 
 income 
 
 inaex oi 
 tempera- 
 tures 
 
 
 
 ^1 
 
 ^2 
 
 -I 
 
 ^3 
 
 0 
 
 X 
 
 3 
 
 ^4 
 
 
 
 Per cent 
 
 
 Is 
 
 ^1 
 
 
 73.4 
 
 
 9.4 
 
 
 2,0 
 
 2e 
 
 ^2 
 
 35.9 
 
 
 
 27,3 
 
 
 29,7 
 
 3s 
 
 ^1 
 
 
 
 58.8 
 
 
 24.7 
 
 1,9 
 
 4s 
 
 x° 
 2 
 
 41,1 
 
 
 
 
 26,5 
 
 22,6 
 
 58 
 
 Log 
 
 
 75.6 
 
 
 6,8 
 
 
 0,4 
 
 6s 
 
 LOG 
 
 35.7 
 
 
 
 24,7 
 
 
 31,6 
 
 Source 
 
 of data: 
 
 
 
 
 
 
 
 
 Based on equations 
 
 Is through 6s given 
 
 in table 
 
 3, Coefficients based 
 
 on equations Is and 3s adjusted to remove negative signs. 
 
 I 
 i 
 
7, ■'.'•rr;, -in 
 
 .•.xrna i 
 
21. 
 
 The variance of quantity is partitioned more evenly among the independent variables 
 in equation 2s j the allocations to f»o»b« price, income, and temperature variables 
 are respectively 36 per cent, 27 per cent, and 30 per cent. Not much confidence 
 can be felt in the reversal of the relative importsince of the income and tempera- 
 ture factors in the two equations, for such results are not obtained when other 
 
 19/ 
 
 measures of relative importance are employed. — ' 
 
 In view of the great prominence given weather factors in trade descriptions 
 
 of the behavior of prices of summer lemons, it is somewhat surprising to find that 
 
 the foregoing rough measures assign relatively little importance to the temperature 
 . 20/ 
 
 variable. — < However, it is doubtful whether the total effect on demand for 
 lemons of changes in weather conditions has been or could be ascertained by means 
 of the temperature index we have employed. As was stated previously, temperature 
 is not the only condition of relevance; furthermore, only one measure of the temper- 
 ature variable was used. On the other hand, the possibility that the effect of 
 
 weather has been given undue emphasis in trade discussions of interseasonal varia- 
 
 ^. ^ , . , 21/ 
 
 tion or lemon prioee and shipments cannot be ruled out of consideration. — ' 
 
 The values of the coefficient of flexibility of price calculated from equa- 
 tion Is at the centroid and of the coefficient of elasticiiy of demand calculated 
 
 22/ 
 
 from equation 2s, similarly at the centroid, are given in table 3. — • Demand for 
 19/ 
 
 The squares of the pertinent partial correlation coefficients are: 
 
 r?o = 0.8454, r^, = 0.7350, r^ „ = 0,6910, = 0.8319, and r^ 
 
 12.34 13.24 14.23 23.14 24.13 
 
 0.8212, 
 
 Y\rith regard to goodness of fit of the equations, temperature is an important 
 variable, for its omission results in a marked reduction of fit. For example, with 
 temperature omitted the adjusted coefficient of multiple correlation (price depen- 
 dent) is only 0.6699 — a considerable reduction from its former value of 0,9050, 
 
 21/ 
 
 __/ The statistical results pertain to interseasonal behavior of prices and 
 quantities; temperature may v/ell be the major factor affecting the intraseasonal 
 variation of prices and shipments. 
 
 22/ cp = 3- " p ^2 and H = ^""2 % = b^, ""l , where the 
 
 ^ ^^2 ^ ^ % 21 ^ 
 
 x's are means and b^^ is the net regression coefficient (i denoting the dependent 
 
 (Continued on next page) 
 
... • . .•.r-n^-.U' . . 
 
 -. TV: 
 
22« 
 
 (Footnote 22/ continued) 
 
 variable). For significance tests in connection with f and rj. see: Girshick, M»A« 
 The application of the theory of linear hypotheses to the coefficient of elasticity 
 of demand. Jour. Amer, Stat. Assn. 37:233-237. 1942, 
 
 summer lemons at the f.o.b. level, based on these equations and measured at the 
 
 centroid, is seen to be inelastic. Since in the linear formulation the values of 
 
 flexibility and elasticity change from point to point on the regression hyperplane, 
 
 it is of interest to consider the magnitudes of the coefficients of flexibility and 
 
 23 / 
 
 elasticity in each of the years included in the analysis. — As can be seen from 
 
 the enclosed tabulation (table 5), the absolute values of the seasonal coefficients 
 
 of flexibility are all greater than 1 and correspondingly the absolute values of 
 
 the seasonal coefficients of elasticity are all less than 1. While the reciprocals 
 
 of the coefficients of flexibility do not agree exactly with the values of the 
 
 elasticity coefficients, differences are to be expected from the very nature of the 
 
 two estimation equations. It will be noted further that there is a trend in the 
 
 calculated values of . This trend is due to the upward trend in supply, for it 
 
 is the property of negatively sloped linear demand laws that flexibility increases 
 
 24 / 
 
 with an increase in quantity. — ' Obviously, the trend in the calculated values 
 of 1^ is opposite to that for (|3 • ' 
 
 The findings with regard to coefficients of elasticity and flexibility accord 
 with a priori expectations concerning the nature of the demand for lemons. Lemons 
 are used in various drinks, in cooking and baking, for flavoring and seasoning, 
 as garnish, as salad dressing, and as hair rinse. In all but a few uses lemons are 
 
 23/ 
 
 The values of ^ and for year t were calculated from the expressions 
 
 <f =» b,o and h = b„, ^"^^ where x' is the estimated f.o.b, price 
 
 1 t l** I ''t '^^ 
 
 it 
 
 Y ^ X' 
 
 It 2t » 
 
 for the year t calculated from equations Is and x is the estimated supply calcu- 
 
 lated from equation 2s ^ 
 
 It is possible, however, v/ith a multidimensional linear equation that <^ is 
 not a monotonically increasing function of quantity. 
 
X bst. 
 
TABLE 5 
 
 Summer Lemons: Calculated Coefficients of Price Flexibiliby and 
 Demand Elasticity, 1922-1941 
 
 Year 
 Hay-October 
 
 Price 
 flexibility 
 
 Demand 
 elasticity 
 
 \x 
 
 Per capita formulation 
 
 Price 
 
 1 xexi D 1 -11 uy 
 
 Demand 
 e last ic ity 
 
 K 
 
 
 1 
 
 2 
 
 
 A 
 •± 
 
 1922 
 
 -1.4668 
 
 -0.5678 
 
 -1,9558 
 
 -0.4611 
 
 1923 
 
 -1.2803 
 
 -0,6981 
 
 -1,5444 
 
 -0,5635 
 
 1924 
 
 -2.1408 
 
 -0.2845 
 
 -2.6788 
 
 -0,2418 
 
 1925 
 
 -1.8397 
 
 -0.5335 
 
 -2.2533 
 
 -0,4544 
 
 1926 
 
 -2.2974 
 
 -0.3221 
 
 -2.7914 
 
 -0.2808 
 
 1927 
 
 -1.6245 
 
 -0.6027 
 
 -1.8349 
 
 -0.5114 
 
 1928 
 
 -1.4414 
 
 -0,5561 
 
 -1.6129 
 
 -0,4871 
 
 1929 
 
 -1.3222 
 
 -0,5969 
 
 -1.4542 
 
 -0,5302 
 
 1930 
 
 -1.5228 
 
 -0,5371 
 
 -1.7097 
 
 -0.4892 
 
 1931 
 
 -1.7522 
 
 -0.4521 
 
 -1.9465 
 
 -0.4165 
 
 1932 
 
 -1.4719 
 
 -0.5823 
 
 -1.5776 
 
 -0.5244 
 
 1933 
 
 -1.7772 
 
 -0.3957 
 
 -1.9300 
 
 -0.3656 
 
 1934 
 
 -2.2918 
 
 -0,4026 
 
 -2.4957 
 
 -0.3728 
 
 1935 
 
 -3.1826 
 
 -0,3713 
 
 -3.3884 
 
 -0,3427 
 
 1936 
 
 -2.0098 
 
 -0.4342 
 
 -2.1304 
 
 -0.4059 
 
 1937 
 
 -1.6527 
 
 -0,5147 
 
 -1.7073 
 
 -0,4808 
 
 1938 
 
 -2.8976 
 
 -0,2716 
 
 -2.9927 
 
 -0.2563 
 
 1939 
 
 -2.8169 
 
 -0.2753 
 
 -2.8725 
 
 -0.2626 
 
 1940 
 
 -3.1942 
 
 -0.2797 
 
 -3.1420 
 
 -0.2653 
 
 1941 
 
 -3.5595 
 
 -0.2435 
 
 -3.5378 
 
 -0.2362 
 
 Source of data: 
 
 Calculated from equations Is, 2s, 3s, and 4s respectively for 
 the values of the independent variables which prevailed in the 
 various years. 
 

 
 1 
 
 
 i ^, - 
 
 
 
 
 
 ; ■ . ' • 
 
 
 
 . . : : 
 
 
 
 
 
 
 
 p " " 7" • 
 
 ■ ■ ' ' ' i 
 
 . ■■ ' 
 
 
 
 
 f 
 r 
 
 
 •■■ . ' 
 
 * 
 
 ; 
 
 
 : .. .. . 
 
 
 
 
 
 •i 
 
 
 
 : 
 
 • 
 
 
 
 
 ' ■ ' 
 
 
 
 
 
 
 
 '! . ' .". ■ • *■ " ' 
 
 
 
 
 • 
 
 i 
 
 
 
 
 
 V • . ■ . 
 
 
 
 i 
 
 
 ■ ■ . . i 
 
 i 
 
 
 
 I 
 
 \.. i 
 
 
 
 
 
 : -.-•.Trsr'.-.-;;rr.7r-.— vjr.iiii ;-- 
 
24. 
 
 an important ingredient but at the same time a minor element of the cost of the 
 total product.. This vrould lead one to expect that consumption of lemons is not 
 highly responsive to changes in their prices, that is, that the demajid for lemons is 
 inelastic. 
 
 The use of equations Is and 2s for estimation purposes should be accompanied 
 
 by some measure of the uncertainty of the estimate. The unbiased estimates of the 
 
 2&/ 
 
 variance of the best linear unbiased estimate of and Xg are given herewith,. — 
 
 2 2 2 2 
 
 M = 0.0070 + 0,0153 z + 0.0115 z + 0.0124 z. - 0.0162 zoZ, - 
 /^f-|_ 2 3 4 ^ 
 
 -0.0179 ZgZ^ + 0.0113 ZgZ^ 
 
 and 
 
 2 
 f. 
 
 2 
 
 /J^ " = 14.18 + 14.39 2^ + 14.62 + 14.43 z" - 3.36 z^z, + 
 
 2 
 
 '3 
 
 2 
 ^4 
 
 '1''3 
 
 +0.335 z,z^ + 3.72 z z, 
 14 3 4 
 
 where the z^'s are the "noxTnalized" values of the independent variables for which 
 
 t 
 
 x-^ or is estimated. The statistical uncertainty accompanying the estimate x is 
 
 t f 
 
 then expressed in the form of the confidence interval x - j^f^h $ ^ * ^ac/^i" 
 
 where t^ is the Student-Fisher t at the level of significance r)C»and 1 - oC is 
 
 2 
 
 the confidence coefficient. The expressions for yt>t^ will not be stated explicitly 
 for the other estimation equations to be considered in this section. However, 
 
 / 2 
 
 = ^D: Ifi.lJPl ivhere IR| is the determinant of the matrix of inter- 
 
 ' H (N-n)|Rii|2 
 
 correlations between the n variables, jR^ij is the minor of in iRj , |d! is the 
 determinant of the matrix 
 
 D 
 
 -1 
 
 ^2 
 
 ^3 • 
 
 
 ^n 
 
 
 1 
 
 ''23 • 
 
 . » 
 
 *"2n 
 
 H 
 
 ^23 
 
 1 
 
 . .. 
 
 ^Zn 
 
 
 '^2n 
 
 '^3n - 
 
 . • 
 
 1 
 
 1 — . 2 
 
 and z. = i_ (x^ - x^^). The formula for used here is equivalent to the expres- 
 
 ^ 0\ / ^1 
 
 sioa derived in: David, F. N.. and J» Neyman. Extension of the Markoff theorem on 
 
 least squares. Statistical Research Memoirs 2:105-116. 1938. 
 
-. : / ;:.y; 
 
 r..V^-'Cf!i**.l?C'; a-Si.iln.'IV'. • 5; 
 
 : si. . 
 
 L ^ 
 
25*- 
 
 sufficient information is given in this paper to enable the calculation of the 
 
 standard error of the regression equation for any of the estimation equations given 
 
 , 2 2 
 
 in tables 3 and 8, Attention should also be drawn to the fact that ( + S^), 
 
 each i 
 v/here S. is the unbiased estimate of the variance of/x^, is the appropriate variance 
 
 26 / 
 
 for determining the confidence limits of the future observation. — i 
 
 An attempt was made to introduce a measure of the factor discussed in 
 previous pages under the rubric "volume of production." First differences in 
 annual production of lemons and first differences in California Fruit Growers Ex- 
 change lemon picks and the Exchange May 1 storage were not found to be related to 
 either price or quantity residuals secured from equations Is and 2s respectively. 
 These measures, then, if introduced as additional independent variables in the 
 
 equations vrould not reduce significantly the "unexplained" variance of the dependent 
 
 27 / • 
 variable. — ■ Hovrever, first differences in Exchange May-October lemon picks 
 
 appeared to be related to price and quantity residuals. It is difficult to see why 
 
 first differences in picks alone should bear a significant net relation to prices 
 
 or shipments, since May 1 storage has been an important constituent of the supply of 
 
 lemons available for shipments during the summer months. Because complete data on 
 
 — ^ See Eisenhart, C. The interpretation of certain regression methods and their 
 use in biological and industrial research. Annals of Math. Stat. 10:162-186. 1939. 
 Also, Ezekiel, Mordecai, Methods of correlation analysis. Second edition. Chapter 
 19, John YiTiley & Sons, Inc., New York, 1941. 
 
 "^iJ Let j be the additional independent variable under consideration and i the 
 dependent variable. Then 
 
 where r . is the correlation between residuals and the additional variable, Rj is 
 the coefficient of multiple correlation between j and the other variables including 
 i, N is the nvmiber of observations, and n the number of constants in the regression 
 equation. The magnitude of t may be deduced from this expression knowing Tgj and 
 assigning some plausible value to R.. 
 
— •■■ .•c'-". : - - , • ,\- -.i>- . .... 
 
 mI.TTV -- ..^ tof: y -^^ ^, 
 
26. 
 
 lemon piftks foSr the pdi^iod under review were not available at the time these cal- 
 culations vrere made, further consideration of this factor was not attempted, 
 
 An attempt was also made to account for the influence of the trend factors by- 
 introducing "time" as a separate variable in the estimation equations. In the 
 equations given below, is f,o,bo price, Xg United States supply of summer lemons, 
 Xg index of nonagricultural income payments, x^ the index of summer temperatures, 
 and Xg "time" measured in units of six months from an origin midway between 1931 
 and 1932, The figxires in parentheses are standard errors of the net regression 
 coefficients. It is seen that the added variable does not have a significant in- 
 fluence. With f,o,b, price as the dependent variable, the standard error of the 
 coefficient of Xg is greater than the coefficient. In the other equation^ the 
 
 ratio of the coefficient of x to its standard error (t = 1,586) falls short of 
 
 5 
 
 the value of t corresponding to the 5 per cent level for 15 degrees of freedom 
 
 x' = 4,5214 - 0.0210 x„ + 0,0450 x^ + 0,0279 x. + 0.0032 x^ 
 
 (0,0030) (0,0072) (0,0050) (0,0129) 
 
 t 
 
 X = 206,4872 - 36,3209 x. + 1,9942 x, + 1,1373 x^ + 0,7911 x^ 
 
 2 13 4 5 
 
 (5,2356) (0.2424) (0.2157) (0.4988) 
 
 As vj-ill be indicated in some detail below, "time" was found to be an 
 important factor in the analysis of the data on winter lemons. The question 
 naturally arises as to v/hy trend factors fail to play a role in the analysis of 
 the demand for lemons during the summer months. Should it be concluded that the 
 factors which "time" is presumed to represent did not affect the demand for summer 
 lemons during the period under consideration? 
 
 28/ 
 
 — ' The scatter diagrams of residuals against first differences in picks were 
 based on only eighteen observations. 
 
7. . 
 
27. 
 
 A partial answer to this question is found in the happenstance that the index 
 
 of temperatures exhibits an upward trend during the period under review. This trend 
 
 may have, to some extent, played the part of the catoh-all "time" variable, A 
 
 further circumstance to be considered in this connection is that the quantity 
 
 variable used in the summer equations consisted of domestic shipments of lemons 
 
 plus imports for consumption; whereas in the winter equations the quantity variable 
 
 consisted only of domestic shipments. The use of United States supply, rather than 
 
 domestic shipments, as the quantity variable makes the trend factors less important, 
 
 because the trend in imports in the period under consideration runs exactly counter 
 
 29/ 
 
 to the strong upward trend in domestic shipments, ' The results secured when 
 domestic shipments of summer lemons are employed together with "time" constitute an 
 empirical confirmation of this point. These equations, both vdth price and with 
 domestic shipments (x^^) as the dependent variables, are given below. The figures 
 in parentheses are standard errors, 
 
 x' = 5.492 - 0,0209 x , + 0,0320 x^ + 0,0247 x. + 0,0691 x^ 
 
 I 2d 3 4 o 
 
 (0,0030) (0,0062) (0.0049) (0,0207) 
 
 x' = 253.95 - 36,3242 x, + 1.3769 x„ + 0.9857 x. + 3.9632 x^. 
 2d J. o t o 
 
 (5.2951) (0.2451) (0,2182) (0.5045) 
 "Time" (x^.) is novr significant in both equations and the adjusted multiple correla- 
 tion coefficients, 0.8969 for price dependent and 0.9813 with domestic shipments 
 as the dependent variable, are of about the same magnitude as those previously 
 secured. Thus it is questionable whether economic meaning should bo road into the 
 failure of "time" to contribute significantly to the fit of the sumr.ier equations. 
 
 29/ 
 
 The following equations represent the linear trend in domestic shipments of 
 summer lemons and United States supply of sxammer lemons, respectively. Both quan- 
 tity series are in units of 10,000 boxes, 
 
 x' = 360.23 + 6.5921 t (Domestic shipments) 
 2d 
 
 x' = 393.80 + 3.6865 t (United States supply) 
 2 
 
 i. 
 
its (r- 
 
 
28. 
 
 It appears rather that the explanation lies in the charaoteristics of the variables 
 used. . 
 
 The reality of the upward trend of summer temperatures is of no particular 
 relevance to the problem of eliminating the effect of trend factors. It is of 
 primary importance, however, in connection with the proper measurement of the 
 effect of the temperature factor, ■ A detailed study of the methods employed in the 
 construction of the temperature index failed to reveal how the trend in the index 
 could be an artifact of the procedure employed in its construction. Nevertheless, 
 
 the possibility that it is an artifact cannot be completely ruled out of considera- 
 
 30/ 
 
 tion. — ' Thus the question of the separate contributions of the smooth and 
 erratic components of the temperature index must be considered. The case for 
 temperature as a significant factor affecting demand of lemons during the summer 
 months would be strengthened if it could be shown that each component of the temp- 
 erature index makes a significant contribution. 
 
 The answer to this question is already given indirectly by the equations just 
 cited, for in those equations both the temperature index and "time" are statistically 
 significant. More direct evidence is obtained by separating the smooth and erratic 
 components of the temperature variable and introducing each into the regression 
 equation in conjunction with other variables previously employed. The smooth 
 component of the temperature index was defined by the least squares equation 
 
 x' = 115,75 + 1,2402 x^ where x^ represents "time," and the erratic component by 
 4 5 5 
 
 the algebraic residuals of the temperature observations from this trend line 
 t 31/ 
 
 (x^ - x^),'~^n the regression equations given below, x^ is f.o.b.. price of summer 
 lemons, Xp is the United States supply of summer lemons, x is the index of 
 
 In this connection see appendix E in which a different temperature index 
 is used as an independent variable. 
 
 ^ k parabolic regression of tompcrature on time r.-ould have probably described 
 the smooth component of the temperature index more fully, Hov;ever, the linear trend 
 is an excellent approximation to the smooth component of the index. 
 
as 
 
 ..7 Tti C 
 
 3i 
 
29. 
 
 nonagricultural income payments, Xr- = — i (x - 115.75) is the adjusted linear 
 
 "^ 5 1.2402 4 ^ 
 
 component of the temperature index and z its erratic component. A comparison of 
 the coefficients of Xg and z with their standard errors (given in parentheses) 
 reveals that both coefficients are significant. 
 
 x^ = - 0,0209 Xg + 0.0451 x^ + 0,0374 Xg + 0.0278 z j 
 (0,0030) (0,0073) (0.0131) (0,0050) I 
 
 t 
 
 X = C„ - 36.3057 X, + 2.0012 x_ + 2,2011 Xc + 1.1358 z 
 
 2 2 1 3 5 
 
 (5.2945) (0,2455) (0.3687) (0.2190) 
 
 It is likely that groi/rbh of population is a major trend influence; hence by 
 using per-oapita data the effect of at least this trend factor may to some extent 
 be given implicit consideration. Two new variables, per-capita United States supply 
 of summer lemons and per-capita nonagricultural income, were used, replacing United 
 States supply and nonagricultural income, respectively. The net regression co- 
 efficients and other pertinent statistics for the analysis of the per-capita data 
 are given in the third and fourth row of table 3 (equations 3s and 4s). The net 
 regression lines and scatters of residuals derived from these equations are shown 
 in the various panels of figures 5 and 6. TThere comparison is possible the results 
 are seen to be remarkably similar to those secured in the original analysis. The 
 adjusted coefficients- of multiple correlation differ but slightly from those pre- 
 viously secured. The estimates of flexibility and elasticity at the centroid are 
 consistent with the values derived from equations Is and 2s. The sajiie statement 
 applies to the annual flexibility and elasticities shown in columns 3 and 4 of 
 table 5, The use of per-capita income has apparently given income greater relative 
 importance in equation 3s than it had in equation Is (see table 4). The significance 
 of such a difference, hovrever, is difficult to establish* 
 
 The per-capita formulation also allows us to test the hypothesis that the 
 population factor is the only trend factor of significance in connection with summer 
 
30. 
 
 lemons* If this hypothesis were true, a trend factor, such as the trend component 
 of the temperature variable, would fail to exert a significant influence in the per- 
 oapita formulation. The introduction of the trend and erratic components of the 
 temperature variable (x^) into the per-capita estimation equations replacing x^ 
 leads to the following equations (in normalized form): 
 
 I 
 
 1 
 
 z = -1.0647 z° + 0.9059 z° + 0.3650 z^. + 0.6122 z 
 
 2 3 5 
 
 (0.1464) (0,1426) (0.1461) (0.1070) 
 
 and 
 
 0 o 
 Zg = -0,7318 z^ + 0.8025 + 0.4206 z^ + 0.4985 z 
 
 . ^,.^..„ . v..^ 
 
 (0.1006) (0.0930) (0.0949) (0*0921) 
 where = (x.^ - x^)/(r^, Zg is the trend component, and z the erratic component of 
 the temperature variable. The figiores in parentheses are standard errors. Since 
 for 15 degrees of freedom t at the 5 per cent level is 2,131, it is seen that the 
 coefficient of z_ in both equations is statistically significant. This result 
 suggests that growth of population is not the only trend factor that may have 
 shifted the demand for summer lemons upward during the period under reviev/. 
 
 Thus far all of the equations were based on a formulation in which the 
 dependent variable was treated as a linear function of the independent variables. 
 A linear form in the logarithms of the variables has also been frequently employed 
 in statistical demand studies, mainly, one supposes, beoause it leads to constant 
 coefficients of elasticity and flexibility. The net regression coefficients and 
 auxiliary constants secured when the logarithmic form was fitted to the data are 
 given in the last two rows of table 3. Expressed on the arithmetic scale, equations 
 5s and 6s are as follows i 
 
 359.3 
 
 -2.0854 1.0356 0.0074 x^ 
 
 "3 
 
 Cg = 4.739 x^ 
 
 -0.3965 0.4685 0,0036 X4 
 
 (5s) 
 (6s) 
 
oris- s-?JrT{-^' ■ ('..« h.Ti"?cJ to rrri-ir-.r-'-oic'-rii' r"*'T nXr'.Trar''i 
 
 s/ut -iaiaiLj 4i0Oi3 :.• i. e -ijjc iayvai ,<■•■, ■.■rH') ••x.s*^j ci t. _ , .;ra 'to 
 
 w-w-'ivea •?xQ{jny .boi-xsu a'c-jf' •ij'ii»r!v-i> 0-ti*&<.jt/ ^nrBm ^tija^vw;-. -ao'i . ^ii •.v«^'i-x 
 
 ;0 
 
31. 
 
 The logarithmic form fits the data about as well as the linear form (see the 
 adjusted multiple correlation coefficients in table 3), The demand for summer 
 lemons at the f,o»b« level is again shown to be inelastic* This is apparent from 
 the values of the coefficients of price flexibility and demand elasticity shown for 
 these equations in table 3, It will be noted that the values of these coefficients, 
 differ but little from the values of price flexibility and demand elasticity at the 
 oentroid, derived from the previous equations. 
 
 To test the possibility that trend factors may have a measurable influence 
 
 in the logarithmic form, "time" was introduced linearly as an independent variable. 
 
 The results secured were very similar to those obtained when "time" was introduced 
 
 in equations Is and 2s. The ratios of the net regression coefficients of "time" to 
 
 their standard errors in both equations of the logarithmic form fell short of the 
 
 32/ 
 
 t's corresponding to -tiie 5 per cent level for 15 degrees of freedom. — ' It thus 
 appears that also in the logarithmic form trend factors are of little significance, 
 once the effects attributable to the other independent variables are eliminated. 
 
 Tv/o other sets of regression equations require a brief comment,. In the first 
 set» imports of lemons are treated as a separate variable; in the second, the supply 
 series is broken dovm into the quantity of lemons marketed by the California Fruit 
 Growers Exchange, and the quantity sold by other marketing agencies. The shipment 
 data used in these formulations are cited in table 2, 
 
 The equations, vJhen domestic shipments of summer lemons and imports for 
 consumption during the months May through October are used as separate variables 
 (see equations 7s and 8s of table 6), show little improvement over the original 
 formulations. The values of the adjusted multiple correlation coefficients are of 
 
 I'irith the logarithm of f.o.b. price as the dependent variable, the ratio of 
 the net regression coefficient to its standard error was less than 1. In the other 
 equation, the t-ratio vms 1.653. The t-ratio corresponding to the 5 per cent level 
 for 15 degrees of freedom is 2.131. 
 
•. . • ... ■■'.. -■■i-. ' : ■ ■ ■ ■■ . : ■■ . • ■ • 
 
 •• ■ a.!-'i>'.fcj. i-j.'.j- .. • -,. . .yiisj. '. ^.'■'.v- ii/^' i.^ 
 
 •i-.— vr.- .*-<srA" V ■ .v^i «. ■.t-.'-.v^wu .■--r.-^'- 
 
 l.-'WjAl.JaVr J-nIJ-/,. ■ ., v ., "V - .■ •itfwfii'^^v oL^ift^t. f^x\f'--'^ 
 
TABLE 6 
 
 r Lemons: Regression Coefficients and Auxiliary Constants for Additional Equations, 1922-1941 
 
 (Figures in parentheses are standard errors ) 
 
 
 
 
 Net repression coefficients * 
 
 
 Adjusted 
 
 
 
 Equation 
 
 variable 
 
 1 
 
 Constant 
 term 
 
 F.o.b. price 
 
 Domestic 
 shipments 
 
 Imports for 
 consumption 
 
 N onagri - 
 cultural 
 income 
 
 Index of 
 temper- 
 atures 
 
 coefficient 
 of multiple 
 correlation 
 
 Elastic- 
 ity of 
 demand 
 
 Flexi- 
 bility 
 of price 
 
 
 (x) 
 
 c 
 
 ^1 
 
 2d 
 
 x„. 
 
 2i 
 
 x^ 
 3 
 
 
 R 
 
 a ^ 
 
 r t 
 
 7s 
 
 ^1 
 
 4.0437 
 
 
 -0.0196 
 ^0 .002o; 
 
 -0.0172 
 
 \ u •uufiy } 
 
 0.0423 
 
 \ U .UU 1 ^ J 
 
 0.0289 
 (0.0048) 
 
 0.9022 
 
 
 -1,5076 
 
 8s 
 
 ^2d 
 
 185.1003 
 
 -40.5952 
 [ 5 .3425; 
 
 
 -1.0280 
 
 2.1283 
 
 1.3611 
 
 (0.2011) 
 
 0.9788 
 
 -0.4636 
 
 
 
 
 
 
 Exchange 
 
 
 
 
 
 
 
 
 
 
 
 domestic 
 
 Outside 
 
 
 
 
 
 
 
 ^(x) 
 
 c 
 
 ^1 
 
 shipments 
 
 X 
 
 2e 
 
 shipments 
 ^2o 
 
 X 
 
 3 
 
 ^4 
 
 R 
 
 ^e 
 
 ' e 
 
 9s 
 
 
 1 
 
 4.1525 
 
 
 -0.0201 
 (0.0024) 
 
 -0.0188 
 (0.0046) 
 
 0.0435 
 (0.0072) 
 
 0.0287 
 to. 0050) 
 
 0.8996 
 
 
 -1.6205 
 
 10s 
 
 ^2e 
 
 188.3385 
 
 -40.8252 
 (4.9562) 
 
 
 -1.0308 
 
 ! (0.1385) 
 
 2.1274 
 (0.2466) 
 
 1.3523 
 
 (0.2004) 
 
 0.9772 
 
 1 -0.5065 
 
 
 * X = Seasonal average f.o.b. price in dollars per box. 
 
 X = Domestic shipments of lemons in units of 10,000 boxes. 
 2d 
 
 ^2i ~ Imports of lemons for consumption in units of 10,000 boxes. 
 
 Xgg = Domestic shipments of lemons by the California Fruit Growers Exchange in units of 10,000 boxes. 
 
 XgQ = Domestic shipments of lemons outside California Fruit Growers Exchange plus imports for consumption, in 
 units of 10,000 boxes. 
 
 X = Index of nonagricultural income payments, 1935-39 = 100. 
 3 
 
 x^ = Index of daily maximum temperature departures from 80° in 39 metropolitan districts. May through October, 
 At the centroid. 
 
' r ~:..- — , 
 
 1 
 
 
 
 
 
 
 
 
 ..... -.^^2;^ 
 
 
 
 ■ 
 
 
 
 
 
 
 
 
 ... .^1 I 
 
 I 
 
 
 
 
 
 
 i. 
 
 
 :.' 
 1 
 
 
 
 
 
 ■ 1 
 
 *• * - K - - ; ^ - 
 
 3 ^ 3 
 
 ■r' ■ -.-.ilio^'iJ^^:..- . 
 
 1 
 
 ■ X .. ; ;. ... ; J. , V 
 
33. 
 
 about the same magnitude as those previously secured, and the residuals in the two 
 
 different price equations (equations Is and 7s) agree precisely in sign and closely 
 33/ 
 
 in magnitude, — i The coefficients of domestio shipments and imports for consumption 
 agree closely in magnitude. The difference between them in relation to the magni- 
 tudes of their standard errors is so small as to obviate the necessity of testing 
 its significance. Thus, for the period May through October, domestic shipments and 
 imports of lemons for consmnption are not distinguishable in their contributions 
 toward the estimation of f ,o,b, prices. 
 
 The second formulation attempts to test a similar hypothesis with regard to 
 lemons marketed by shippers other than the California Fruit Growers Exchange, The 
 multiple regression equations relating to this formulation are given in the last 
 two rows of table 6 (equation 9s and 10s), In these equations, domestio shipments 
 
 of lemons by the California Fruit Growers Exchange (x„ ) and shipments of lemons 
 
 2e 
 
 for fresh consumption by other marketing agencies plus imports for consumption (x„ ) 
 
 u* O 
 
 replace the United States supply of stmmer lemons as the quantity variable. Since 
 the difference between the coefficients of Exchange domestio shipments and outside 
 shipments is small and not significant (see equation 9s), the hypothesis that lemons 
 marketed by the California Fruit Growers Exchange and other lemons si ipped for fresh 
 consumption during the summer months are statistically differentiable components of 
 the total United States supply of lemons must be rejected. 
 
 The correlation betiireen price residuals of equations Is and 7s is ,98« 
 
 According to the "special theory of related demands" (see: Schultz, H, 
 Theory and measurement of demand, 569-604p, University of Chicago Press, 1938), 
 the negative sign of the coefficient X2o indicates that lemons marketed by the 
 Exchange and lemons marketed by other shippers are competing. The equality of the 
 coefficients suggests that lemons marketed by the two groups of shippers are per- 
 fectly competing. The other conditions on the parameters of the linear demand 
 function discussed by Schultz cannot be tested because of lack of data on prices 
 received by shippers outside the Exchange, 
 
34. 
 
 Demand for YiTinter Lemons 
 
 Regression equations in which price of winter lemons was expressed as a 
 linear function of doraeatic shipments of lemons, consumer income, and time were 
 found to give a poor fit to the data. Equally unsatisfactory were the equations in 
 which the logarithm of price was expressed as a linear function of the logarithms 
 of shipments, income, and time. A study of the residuals derived from these equa- 
 tions revealed that the fit could not be improved by any reasonable modification 
 of the form of the net regression functions. Apparently oystematic factors, in 
 addition to those considered above, have affected the demand for lemons during the 
 winter months* 
 
 References to the prevalence of colds and influenza as a variable in account- 
 ing for the up-vmrd shift of demand for winter lemons are not infrequently found in 
 citrus trade publications* Hot lemonade is probably one of the common home remedies 
 for colds, a use of lemons which has received extensive mention in the advertising 
 campaigns of the California Fruit Gro^rers Exchange. Accordingly, it appeared 
 worth while to introduce a measure of this factor into the regression equations. 
 Since statistics on the incidence of colds are not available, only an index of the 
 incidence of influenza could be constructed (see table 25, appendix /). This index 
 was introduced linearly into the regression equations, and also some non-linear 
 transformations of this variable to both algebraic and transcendental functions 
 were used. It appeared, however, that no reasonable function of this index v;ould 
 be statistically significant. 
 
 First differences in annual production of lemons and first differences in 
 Exchange lemon picks and Exchange November 1 storage were considered as possible 
 independent variables, but their contribution did not prove significant. Other 
 variables used in the regression equations, along v/ith price and supply, were 
 storage rates of lemons and various combinations of data pertaining to storage, 
 picks, and shipments during the winter months. However, these variables also proved 
 
■ : ■' ■'•'r-'f'v-'y'k'S:'!:?!'' .(.'i.f.:l''.r.'- OT t>5' 
 '^'/;v, ^ • ■ : . ■ ■ ■ ■ ■ 
 
 -.■j'i'ti/Oo?).« ".'Ti oiJM 
 
 f .. ■■- ♦i'l- 
 
 *, ■<}.-?v-».-- 
 
 C'5i ■ S! f ■ 
 
 .'9 1 -Ift 
 
35. 
 
 to be of little significance in the analysis* These unsatisfactory results may be 
 due to the fact that the unit of time employed is too long a period in which to con- 
 sider relations among picks, average storage rates, and shipments because of too 
 extensive double counting. In a long enough period, the same lemon may be counted 
 in picks, storage, and shipments as it passes through each of these stages on the 
 vra.y to final consumption. 
 
 The failure of the influenza index to improve the fit of the regression equa- 
 tions may be due to poor reporting of influenza case rates, but the possibility must 
 be considered that even adequate data on incidence of influenza may not provide a 
 
 measure v/hich would prove to be statistically significant. Apparently the attack 
 
 35/ 
 
 rate of influenza is not related to that of common colds. Thus, v^hile the 
 incidence rate of influenza may itself be related to consumption of lemons, because 
 of the relatively small frequencies involved the net effect of this factor may 
 not be statistically measurable. 
 
 In searching about for a variable v/hich could take the place of an index 
 of incidence of colds, it occurred to the wTiters that severity of winter climate 
 may be related to incidence of colds and consequently to consumption of lemons 
 during the winter months. Some evidence may be cited in support of this conjecture, 
 particularly with reference to temperature. To test this conjecture statis- 
 tically, an index of average temperatures for the months December, January, and 
 
 35/ 
 
 Frost, Tf. H. and M. Gover. Incidence and time distribution of common colds 
 in several groups kept under continuous observation. Pub. Health Rep. 47:1815. 
 September 2, 1932. These virriters found no relation betvireen incidence of colds and 
 influenza in the groups \inder observation. 
 
 36/ 
 
 Gover, M., L. J. Reed, and S. D. Collins. Time distribution of common colds 
 and its relation to corresponding weather conditions. Pub. Health Rep. 49:811-824. 
 July 13, 1934. In this study deviations of the weekly incidence of respiratory 
 attack during an eighteen-month period among students in various universities in 
 the United States vrere correlated with deviations of v/eather conditions from mean 
 or normal. A weak but consistent inverse relation vms observed betiveen weekly de- 
 partures from the norm of the respiratory attack rate and deviations from mean 
 temperature. Other vj-eather conditions such as hours of sunshine, wind velocity, 
 precipitation, etc., did not show a consistent association with incidence rate of 
 colds. 
 
 i 
 
tit ti&CSJ^.O 
 
 i-.^Vj6 J... 
 
36, 
 
 February was constructed and introduced as an added variable into the regression 
 equations. This variable proved to bo statistically significant. 
 
 Before going on to the discussion of the regression equations, a point of 
 procedure must be emphasized. The period considered is that beginning with the 
 season 1921-22 and ending with the season 1940-41, but one season is omitted, 
 namely 1936-37, This omission requires somewhat extensive discussion, for v;ith 
 only twenty observations at our disposal, the rejection of one season represents 
 a loss of 5 per cent of the total information* 
 
 In January 1937 severe frosts occurred in southern California causing pre- 
 sumably extensive damage to the lemon crop. Successive forecasts of the 1936-37 
 lemon crop by the California Cooperative Crop Reporting Service provide a quantita- 
 tive expression of current judgment concerning the extensiveness of the damage. 
 The forecast of the crop as of January 1, 1937, just prior to the freeze, was 
 8,316,000 boxes. The forecast as of February 1, just after the freeze, was about 
 
 2,500,000 boxes less, namely 5,832,000 boxes. The forecasts of the volume of crop 
 
 37/ 
 
 on March 1 and April 1 were of about the same magnitude aa on February 1. V/ith 
 the prospects of an extremely short crop facing the trade, the movement of lemons 
 was brisk and the prices received, relative to the quantity moved, were quite 
 high, In point of fact, however, the frost damage to the lemon crop vra.s not as 
 extensive as was believed. The final production figures for 1936-37 were 7,579,000 
 boxes or almost 2,000,000 boxes above the February, March, and April forecasts. ^ 
 
 37 / 
 
 — i California Cooperative Crop Reporting Service. California Citrus Fruit 
 Report as of January 1, 1937; February 1, 1937; March 1, 1937; April 1, 1937. 
 Sacramento, California. (Mimeo.) 
 
 38/ 
 
 See: California Fruit Growers Exchange. Annual report of the general 
 manager for the year ended October 31, 1937. 
 
 39/ 
 
 California Cooperative Crop Reporting Service. California citrus crops 
 production and utilization estimates, 1909-10 to 1937-38. Sacramento, California, 
 September 15, 1939. 
 
 1 
 
'u 
 
 •iv »8i. 
 
 ii* fan 
 
37. 
 
 It is believed that this combination of factors ^ms unique in the twenty-year period 
 under review. 
 
 As an alternative to omitting 1936-37, the domestic shipment figure for 
 that season v;as reduced to the level of expectations based on the just quoted fore- 
 casts of the lemon crop by the California Crop Reporting Service, The use of the 
 adjusted shipment figure gave results almost identical with those secured when the 
 season was omitted. Because of the some¥/hat arbitrary character of the adjustment. 
 
 stants corresponding to six equations, each based on nineteen observations. The 
 
 series used are given in table 7, The equations are of the same form as those 
 
 4-1 / 
 
 calculated for summer lemons, — i It will be noted that the adjusted multiple cor- 
 relation coefficients are of about the same magnitude as those secured for analogous 
 summer regression equations; that the linear form, per-capita formulation, and the 
 logarithmic form fit the data equally ^toII; that the estimation equations with 
 shipments as the dependent variable fit the data better than the regression equation 
 with f,o,b, price as the dependent variable; that all of the net regression co- 
 efficients are apparently significant; and that the demand for winter lemons 
 
 — The net regression coefficients and auxiliary constants v/hen all of the 
 observations v/ere used and v/hen the 1936-37 shipment observation was adjusted are 
 given in table 30, appendix D, 
 
 It should be pointed out that in calculating per-capita domestic shipments 
 and per-capita nonagricultural income, population figures as of July 1 were employed. 
 In this analysis it would have been formally more correct to have used population 
 figures adjusted to January 1 of each year. In view of the fallibility of the 
 annual population estimates, especially of the estimates of farm population, such 
 an adjustment v>ras not deemed v;orth v/hile. Later calculations indicated that the 
 use of population figures interpolated to January 1 of each year would have had the 
 following effects on the two per-capita series 9 per-capita doraestio shipment 
 figures would each have changed by 0.01 and 5 values of the index of per-capita 
 nonagricultural income v/ould have each ohai:ged by 1 point. Such changes could have 
 but an entirely negligible effect on the magnitudes of the various statistical con- 
 stants calculated in the winter lemon analysis • 
 
 however, it was deemed preferable to omit the season. 
 
 In table 8 are given the net regression coefficients and auxiliary o 
 
 on- 
 
 40/ 
 
'ia at-, 
 
TABLE 7 
 
 ■winter Lemons: Basic Series Used in the Demand Analysis, 1921-22 to 1940-41 
 
 ! - ■■ 
 
 
 
 
 j 
 
 
 TnHpv of 
 
 P p y CA-D 1 1 a 
 
 
 Year 
 
 F.o.b. 
 
 Domestic 
 
 Per capita 
 
 C.F>G.E. 
 
 Outside 
 
 nonagri- 
 
 nonagri- 
 
 Index of 
 
 November- 
 
 price 
 
 shipments 
 
 domestic 
 
 domestic 
 
 domestic 
 
 cultural 
 
 cultural 
 
 tempera- 
 
 April 
 
 
 shipments 
 
 shipments 
 
 shipment" 
 
 income * 
 
 income 
 
 tures f" 
 
 
 "^1 
 
 ^2 
 
 ^2 
 
 ^2e 
 
 ^2o 
 
 ^3 
 
 x° 
 
 ■ ' 
 
 -^4 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 
 dollars 
 
 1.000 
 
 pounds 
 
 1.000 
 
 1,000 
 
 per cent 
 
 per cent 
 
 per cent 
 
 
 
 boxes 
 
 
 boxes 
 
 boxes 
 
 
 
 
 1921-22 
 
 3.48 
 
 1,641 
 
 1.14 
 
 1,423 
 
 218 
 
 71 
 
 71 
 
 81 
 
 1922-23 
 
 4.20 
 
 1,308 
 
 0.89 
 
 1,226 
 
 82 
 
 83 
 
 81 
 
 78 
 
 1923-24 
 
 2.38 
 
 1,911 
 
 1.28 
 
 1,754 
 
 157 
 
 92 
 
 88 
 
 85 
 
 1924-25 
 
 3,87 
 
 1,648 
 
 1.09 
 
 1,491 
 
 157 
 
 93 
 
 87 
 
 82 
 
 1925-26 
 
 3.33 
 
 1,750 
 
 1 ,14 
 
 1,623 
 
 127 
 
 100 
 
 91 
 
 80 
 
 1926-27 
 
 2.73 
 
 1,954 
 
 1.26 
 
 1,570 
 
 384 
 
 102 
 
 91 
 
 82 
 
 1927-28 
 
 4.81 
 
 1,517 
 
 0.96 
 
 1,393 
 
 124 
 
 102 
 
 89 
 
 84 
 
 1928-29 
 
 3.58 
 
 2,146 
 
 1.34 
 
 1,881 
 
 265 
 
 106 
 
 91 
 
 81 
 
 1929-30 
 
 4.94 
 
 1, 558 
 
 0.96 
 
 1,410 
 
 148 
 
 105 
 
 89 
 
 86 
 
 1930-31 
 
 3.09 
 
 2,008 
 
 1,23 
 
 1,713 
 
 295 
 
 91 
 
 76 
 
 87 
 
 1931-32 
 
 2.49 
 
 1,984 
 
 1.21 
 
 1,615 
 
 369 
 
 75 
 
 63 
 
 100 
 
 1932-33 
 
 3.09 
 
 1,761 
 
 1,07 
 
 1,556 
 
 205 
 
 61 
 
 51 
 
 91 
 
 ±yo»^— o*± 
 
 
 
 1 .25 
 
 1,820 
 
 253 
 
 69 
 
 57 
 
 76 
 
 1934-35 
 
 2.18 
 
 2,609 
 
 1.56 
 
 2,077 
 
 532 
 
 74 
 
 61 
 
 79 
 
 1935-36 
 
 3.72 
 
 2,339 
 
 1.39 
 
 2,174 
 
 165 
 
 82 
 
 67 
 
 67 
 
 1936-37 
 
 3.79 
 
 2,559 
 
 1.30 
 
 2,393 
 
 166 
 
 93 
 
 75 
 
 90 
 
 1937-38 
 
 3.50 
 
 2,283 
 
 1,34 
 
 2,078 
 
 205 
 
 88 
 
 70 
 
 84 
 
 1938-39 
 
 2.56 
 
 2,491 
 
 1.45 
 
 2,143 
 
 348 
 
 90 
 
 71 
 
 87 
 
 1939-40 
 
 2.99 
 
 2,746 
 
 1.58 
 
 2,345 
 
 401 
 
 97 
 
 76 
 
 77 
 
 1940-41 
 
 2.42 
 
 3.013 
 
 1.72 
 
 2.459 
 
 554 
 
 109 
 
 85 
 
 83 
 
 « f 
 
 3.293 
 
 2,038.9 
 
 1.256 
 
 1,776.4 
 
 262.6 
 
 88,9 
 
 76.6 
 
 82.6 
 
 tr ^ 
 
 0.762 
 
 440.0 
 
 0.216 
 
 341.2 
 
 132.8 
 
 13.6 
 
 12,4 
 
 6.5 
 
 * 1925-1929 = 100. 
 f 1931-32 = 100. 
 
 Excluding 1936-37. 
 Sources of data: Col. 1: Table 13. 
 
 Cols, 2 and 3: Table 17, 
 Cols. 4 and 5: Table 20, 
 
 Cols. 6 and 7: Table 22, 
 Col, 8: Table 23. 
 
'» . , • ■ 
 
 
 
 
 
 
 
 
 
 
 
 • 
 
 
 
 
 
 V.'i ; 
 
 i 
 
 
 
 
 
 
 
 T - 
 
 ■ .1 i 
 
 
 
 
 
 * 
 
 
 
 is 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 ..'.\ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 • • - 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ' 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 • 
 
 
 
 
 
 
 - i 
 
 
 
 
 
 
 ■ r 
 
 ' 1 
 
 
 
 
 ! 
 
 
 ,■■.-*■■• 1 
 
 1 
 
 ... .. - ( 
 
 
 
 
 
 . 1 
 
 -JS-i. G''i.-X--- 
 
 
 
 
 
 
 
 
ThBLE 8 
 
 Winter Lemons: Regression Coefficients and Auxiliary Constants 
 1921-22 to 1940-41 (1936-37 excluded) 
 (Figures in parentheses are standard errors) 
 
 1 
 
 Equation 
 
 
 Net regression coefficients * 
 
 1 1 
 
 -Adjusted ! 
 
 Flexibility 
 
 r 
 
 Dependent 
 variable 
 
 ^x) 
 
 Constant 
 term 
 
 c 
 
 F.o .b. 
 
 price 
 
 Domestic 
 shi pments 
 
 ^Jonagri- 
 cultural 
 income 
 
 x^ 
 
 J 
 
 Ir>dpx of 
 
 temper- 
 atures 
 
 Time 
 ^5 
 
 of multiple 
 correlation 
 
 R 
 
 of demand 
 
 Iw 
 
 2vv 
 
 ^1 
 
 ^2 
 
 10.9472 
 3,690.0778 
 
 -294.9264 
 (37.9659) 
 
 -0.0028 
 (0.0004) 
 
 0.0225 
 (0.0059) 
 
 7.3125 
 (1.9295) 
 
 -0.0484 
 (0.0124) 
 
 -15.9275 
 
 (4.0358) 
 
 0.0636 
 (0.0132) 
 
 24.8053 
 (2.3908) 
 
 0.9022 
 0.9697 
 
 -0.4764 
 
 -1.7044 
 
 
 ^(x) 
 
 c 
 
 "l 
 
 Far capita 
 
 domestic 
 
 shipments 
 
 yj 
 
 ^2 
 
 Per capita 
 nonagri- 
 cultural 
 income 
 
 0 
 
 ^3 
 
 ^4 
 
 X 
 
 5 
 
 R 
 
 'L r 
 
 T t 
 
 3w 
 
 4w 
 
 X 
 
 1 
 
 ^0 
 
 10.9687 
 
 2.2768 
 
 1 . 
 
 -0.1825 
 
 (0.0232) 
 
 -4.4674 
 (C.5679) 
 
 0.0245 
 (Q.0071) 
 
 0.0050 
 (0.0014) 
 
 -0.0474 
 (0.C124) 
 
 -0.0096 
 (0.0025) 
 
 0.0479 
 (0.0113) 
 
 0.0115 
 10.0016) 
 
 0.9021 
 0.9514 
 
 -0 .4786 
 
 -1.7038 
 
 
 
 1 
 
 i I 
 
 
 
 Log x^ 
 
 Log Xg 
 
 Log X, 
 1 ^ 
 
 Log 
 
 
 R 
 
 
 i 
 
 5w 
 
 Log x-j^ 
 
 5.4798 
 
 
 -1.5816 
 (0.2191) 
 
 (0.4510 
 (0.1544) 
 
 ! 
 
 -1.1632 1 0.0169 
 (0.3182)j(C.0040) 
 
 0.8698 
 
 
 -1,5816 
 
 6w 
 
 Log Xg 
 
 3.2845 
 
 -0.4984 
 
 ' (0.0590) 
 
 
 0.2556 
 (0.0872) 
 
 -0.6412 1 0.0117 
 (0.1816)i(0.0013) 
 
 0.9623 
 
 -0.4984 
 
 
 (Footnotes on next page) 
 

 
 
 • : - 
 
 ■ - * ■ , . * 
 
 
 
 
 - : ■ : 
 
 
 
 
 .... V..''..i.- 
 
 Z.'. 5 
 
 
 
 i 
 
 I 5'- 
 .1 - 
 
 
 ■ > 
 
 
 
 
 ;■ " ■ ■ ' : 
 
 , .:.7. 
 
 
 
 
 f " " 
 j 
 
 * 
 i 
 
 :l i 
 
 
 ■ 
 
 
 
 
 
 - 
 
 
 ■■■ ■ 
 
 
 
 
 
 
 .. .... 
 
 » - ■ 
 
 
 
 
 
 
 f. 
 
 - ■■ . • f 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
(Table 8 continued) 
 
 * = Seasonal average f.o.b. prices in dollars per box. 
 
 = Domestic shipments of California and Arizona lemons in units of 1,000 boxes. 
 x° = P.r capita domestic shipments of California and Arizona lemons in pounds. 
 Xj = Index of nonagri cultural income payments, 1924-25 to 1928-29 = 100. 
 x° = Per capita index of nonagricultural income payments in per cent. 
 
 x^ = Index Of mean temperatures in December, January, and February in 32 metropolitan districts, 1931-32 = 100. 
 
 x^ = Time in units of half-years, origin half-way between 1930-31 and 1931-32, 
 ■f At the centroid. 
 ^ In natural logarithms. 
 
 O 
 
41. 
 
 measured at the centroid is consistently inelastic in all formulations. Attention 
 is also drawn to the annual values of price flexibility and demand elasticity based 
 on equations Iv;, 2w, 3w, and 4w (see table 9). For tliree of the nineteen seasons 
 under consideration — namely, 1922-23, 1927-28, and 1929-30 ~ the values of the 
 coefficient of price flexibility indicate that the demand for winter lemons v/as 
 elastic. Otherwise, the remaining entries confirm the presumption that an inelastic 
 demand for winter lemons faced handlers of lemons during the period under review. 
 
 The net regression lines and scatters of residuals derived from the equations 
 cited in table 8 are shown in the various panels of figures 9, 10, 11, 12, 13, and 
 14, appendix C. In no case is it apparent that a modification of the form of net 
 regressions vrould result in a significant Lmprovement of fit. The results of the 
 tests of randomness of residuals are summarized in table 29, appendix B. It is 
 evident that the hypothesis of randomness of residuals with respect to time cannot 
 be rejected on the basis of these tests. 
 
 An examination of the scatters of residuals about the net regression of 
 price and of shipments on temperature (see panel C of figs. 9 to 14, appendix C) 
 might lead to the conclusion that the temperature variable would not contribute 
 significantly, were it not for the close fit of the observations for 1931-32 and 
 1935-36, To test this suggestion, the seasons 1931-32 and 1935-36 were omitted 
 and two equations, one with f.o.b, price and the other with per-capita shipments as 
 the dependent variable, vrere fitted to the remaining seventeen observations, 
 
 42/ 
 
 —J The lanbiased estimates of the variance of the best linear xuibiased estimates 
 jf XI and X2 (equations Iw and 2w) are, 
 
 /^\^ = 0.0060 + 0.0243z^ + 0,0064z| + 0.0065z^ + 0,0233Zg - O.OOSSzgZg + 
 
 +O.OO62Z2Z4 - O.O409Z2Z5 + O.OOOSZgZ^ + 0.0093ZgZ5 - 0»D048z4Z5 
 
 ^■oA z 2 2 ? 2 
 
 M, ^ = 642,74 + 836. 74z^ + 688,13Z2 684.43z^ + 761.76Zg - 37O.I2Z1Z3 + 
 
 2 
 
 +347.73zj^z^ + 627.9IZ1Z5 + Z^,bdz^z^ - 149.24z2Zg + 184.91z^Z5, 
 where z. = J_ (x. - x. ). 
 
!>■;*■■ 
 
TABLE 9 
 
 T/inter Lemons: Calculated Coefficients of Price Flexibility and 
 Demand Elasticity, 1921-22 to 1940-41. (1936-37 excluded) 
 
 
 
 
 Per capita formulation 
 
 Year 
 November— 
 April 
 
 Price 
 flexibility 
 
 Demand 
 elasticity 
 
 Price 
 flexibility 
 T 
 
 Demand 
 elasticity 
 
 M 
 
 1921-22 
 
 -1.5619 
 
 -0.7220 
 
 -1.7760 
 
 -0.637C 
 
 ) 
 
 1922-23 
 
 -0.3276 
 
 -0,8684 
 
 -0.8900 
 
 -0.7922 
 
 ■ 
 
 1923-24 
 
 -1.9620 
 
 -0.3627 
 
 -2.1491 
 
 -0,336'- 
 
 r 
 
 1924-25 
 
 -1.2260 
 
 -0.7132 
 
 -1.3079 
 
 -0.663J 
 
 > 
 
 1925-26 
 
 -1.2675 
 
 -0.5190 
 
 -1.3444 
 
 -0.49 5E 
 
 
 1926-27 
 
 -1.6230 
 
 -0.3831 
 
 -1.7303 
 
 -0.372] 
 
 L 
 
 1927-28 
 
 -0.9183 
 
 -0.9415 
 
 -0.9435 
 
 -0.9205 
 
 ) 
 
 1928-29 
 
 -1.8584 
 
 -0.5292 
 
 -1.9095 
 
 -0.527] 
 
 L 
 
 1929-30 
 
 -0.9204 
 
 -0.9359 
 
 -0.9238 
 
 -0.942' 
 
 
 1930-31 
 
 -1.7353 
 
 -0.4481 
 
 -1.7352 
 
 -0.453£ 
 
 i 
 
 1931-32 
 
 -2.2855 
 
 -0.3791 
 
 -2.2358 
 
 -0.383J 
 
 5 
 
 1932-33 
 
 -1.4905 
 
 -0.4926 
 
 -1.4611 
 
 -0.500J 
 
 
 1933-34 
 
 -1.6654 
 
 -0.4360 
 
 -1.6325 
 
 -0.448; 
 
 5 
 
 1934-35 
 
 -3.5114 
 
 -0.2568 
 
 -3.3389 
 
 -0,264' 
 
 7 
 
 1935-36 
 
 -1.7513 
 
 -0.4671 
 
 -1.6976 
 
 -0.488^ 
 
 I 
 
 ± C tj U— ij 1 
 
 
 
 
 
 
 1937-38 
 
 -1.8502 
 
 -0.4516 
 
 -1.7916 
 
 -0.481( 
 
 
 1938-39 
 
 -2.4053 
 
 -0.2927 
 
 -2,2904 
 
 -0.311 
 
 7 
 
 1939-40 
 
 -2.6908 
 
 -0.3251 
 
 -2.4013 
 
 -0,348 
 
 3 
 
 1940-41 
 
 - 3.6239 
 
 -0.2442 
 
 -3.2754 
 
 -0.263 
 
 1 
 
 Z 
 
 Source of 
 
 data : 
 
 
 
 
 
 Calculated from equations Iw, 2vir, ,3w, and 4w respectively for the 
 values of the independent variables which prevailed in the various years. 
 
43. 
 
 The two equations (in standard form) ai'e given below (the figures in paren- 
 theses are standard errors of the |S* - coefficients). The adjusted coefficients of 
 multiple correlation are fairly high, 0.8902 for the first equation and 0.9494 for 
 the second equation. The t-ratio for the coefficient p is 1.979. Since the set 
 of admissible alternatives specifies negative values of ^ we need to consider 
 only one tail of the t-distribution. For 12 degrees freedom t Qg is 1.782 and 
 thus the null hypothesis can be rejected. The t-ratio for the coefficient 
 is 2,455. These results tend to strengthen the presumption that the temperature 
 factor is a significant variable affecting the demand for lemons during the winter 
 
 months. ' 
 t 
 
 z = -l,3023z„ + 0,4029z - 0.2412z. + 0.7415z, 
 
 1 2345 
 
 (0.1844) (0.1282) (0.1219) (0.1960) 
 
 I 
 
 z' = -0.6189Z, + 0,2794z„ - 0,l939z. + 0.6177z<, 
 
 2 i o 4 5 
 
 (0.0876) (0.0879) (0.0790) (0.0907) 
 
 I 
 
 The coefficients of separate detennination for all of the regression equa- 
 tions summarized in table 8 are given in table 10. It will be noted that the con- 
 tribution of winter temperatures to the variance of the dependent variable is 
 of about the same magnitude as that of income in all of the formulations thus far 
 considered. Each of these variables contributes less than 10 per cent to the 
 variance of the dependent variable. Vfith price as the dependent variable, the 
 contribution of the trend factors is somewhat larger, betv/een 15 and 20 per cent, 
 but still considerably smaller than the contribution of the quantity variable. 
 Hovrever, in the equations with domestic shipments as the dependent variable, the 
 trend factors are seen to "account" for a large proportion of the variance of the 
 dependent variable. Thus in equation 2'w, 55 per cent of the variance of the 
 dependent variable is allocated to the trend factors and only 33 per cent of the 
 variance to the price factor. It is for this reason that the per-capita formulation 
 is of particular significance in the winter analysis, for obviously it is necessary 
 
44. 
 
 TABLE 10 
 
 Tlinter Lemons: Coefficients of Separate Determination 
 
 Eqvation 
 
 Dependent 
 variable 
 
 F.o.b, 
 
 price 
 
 Domestic 
 shipments 
 
 Per capita 
 
 domestic 
 
 shipments 
 
 Index of 
 nonagri- 
 oultural 
 income 
 
 Per capita 
 nonagri- 
 oultural 
 income 
 
 Inde: 
 temps 
 
 IC 
 
 jr- 
 
 3 S 
 
 Time 
 
 
 
 ^1 
 
 ^2 
 
 
 ^3 
 
 0 
 
 ^3 
 
 ^4 
 
 
 ^5 
 
 
 
 Per cent 
 
 
 
 
 Iw 
 
 ^1 
 
 
 56,4 
 
 
 5,2 
 
 
 4.{ 
 
 i 
 
 19.3 
 
 2w 
 
 X 
 
 2 
 
 33.0 
 
 
 
 3,0 
 
 
 4.] 
 
 L 
 
 55,3 
 
 3w 
 
 \ 
 
 
 
 55,6 
 
 
 8,4 
 
 5. J 
 
 ) 
 
 16,3 
 
 4w 
 
 2 
 
 41,5 
 
 
 
 
 4,4- 
 
 5,^ 
 
 t 
 
 41,3 
 
 5w 
 
 Log Xj^ 
 
 
 56.7 
 
 
 3,8 
 
 
 5,4 
 
 t 
 
 18,0 
 
 6w 
 
 Log Xg 
 
 35,3 
 
 
 
 2,1- 
 
 
 3.£ 
 
 
 53,1 
 
 Source of data: 
 
 Based on equations Iw through 6w given in table 8, Coefficients based 
 on equations Iw, 3w, 4w, and 5w adjusted to remove negative signs. 
 
 1 
 

 
 
 
 
 
 1 '( ■ 
 
 
 
 
 
 
 
 
 
 -A 
 
 V ., .. 
 .-. • 
 
 • 
 
 
 
 
 
 
 .v - • 
 
 
 
 •Sv^-'- ■■ ■■ 
 
 
 tf ■ 
 
 
 
 
 
 
 
 
 
 
45. 
 
 to account more explicitly for the multitude of influences that are represented by- 
 time. However, the introduction of the population factor»while reducing the con- 
 tribution of "time" still leaves it of considerable importance. Thus in equation 
 4w, roughly 41 per' cent of the shipment variance is allocated to the trend factors. 
 The major importance of the time variable in the shipment equations is an undesirable 
 feature of these equations and one which should induce considerable caution in their 
 use. 
 
 In all of the equations thus far considered, the quantity variable was re- 
 presented by dOTiestio shipments of lemons during the months November through April 
 of each year. In the summer analysis imports were shown to be a homogeneous part 
 of the total supply of lemons during the months May through October. Such, appar- 
 ently, is not the case during the winter months. The use of United States supply of 
 lemons during the winter months — that is, of domestic shipments plus imports — 
 as the quantity variable reduces the adjusted multiple correlation coefficient from 
 0,9022 to 0.5144 with price as the dependent variable and from 0.9697 to 0,8666 
 with United States supply as the dependent variable. It is not satisfactory, either , 
 to include imports separately as an independent variable, for then imports add little 
 to the fit of either the price or the shipment equations. This analysis has found 
 no empirical grounds for including imports explicitly or implicitly in the equations 
 for vdnter lemons. 
 
 The lack of relevsinoe of the import variable during the v/inter months is 
 difficult to explain, especially in viev/ of the fact that the relative magnitudes 
 of imports for consumption during the two seaccns were quite similar. It is possi ble 
 that lemons imported during the viinter months were intended primrily for consumption 
 during the summer months. The fact that heavy imports of lemons have usually 
 occurred in Februaiy, March, and April lends some support to this conjecture. 
 
 43/ 
 
 Hovrever, domestic shipments of lemons also exhibit practically the same 
 pattern. For the ten-year period 1921-22 through 1930-31, imports of lemons for con- 
 sumption during the months November, December, and January constituted 19.4 per cent 
 of the California Fruit Grovrers Exchange movement of lemons into fresh consumption. 
 For the months February, March, and April this proportion rose only to 21,3 per cent. 
 
; ■!■ 
 
 ■4 f ni 
 
 Tg-^f^8. 
 
 •I ^v»-^ 
 
 4 
 
 *0' 
 
 V'?f t •■. 
 
46. 
 
 It is also possible that due to sudden and large shifts of demand induced by \ireather 
 factors, the product differentiation whioh obtains during the winter is much weakened 
 during the summer months. While the fifst possibility appears, off-hand, to be more 
 plausible than the second, neither has direct evidence which could be cited in its 
 support. 
 
 As was the case in the analysis of data on summer lemons, the replacement of 
 
 domestic shipments by two quantity variables, one consisting of domestic shipments 
 
 by the California Fruit Growers Exchange and the other of domestic shipments by 
 
 other marketing agencies, leads to the conclusion that such a breakdovm of the 
 
 quantity variable has little effect. Below is given the price equation in which 
 
 Exchange domestic shipments (x„ ) and domestic shipments of shippers outside of the 
 
 Exchange (x„ ) are used ae two independent variables. The other variables in the 
 
 equation are f,o,b, prices (xj^), index of nonagricultural income (xg), index of 
 
 temperatures in December, January, and February (x^), and "time" (xg). The figures 
 
 in parentheses are standard errors of the partial regression coefficients. While 
 
 the adjusted multiple correlation coefficient is somewhat lower for this equation 
 
 than for equation Iw (0,8502 as against 0,9032), the coefficients of the two quantity 
 
 series are almost identical in magnitude, 
 f 
 
 x^ = 3,2926 - 0.0028X2^ - 0.0027x2q + 0,0226x2 - 0,0492x_^ + 0,0642X5 
 (0,0006) (0,0010) (0,0062) (0,0155) (0,015l) 
 
'■ '•. 
 
 "ill' 08^0 -oiT:*^ ■ '33*7 -Bvi 
 
 f.r. 'r 
 
 "J-- 
 
 c;. 
 
Allocation of Shipments 
 
 In this section we shall confine ourselves to a brief consideration of two 
 types of allocation of shipments over time. In the first class are included allo- 
 cations designed to maximize returns to the industry; the second is comprised of 
 allocations designed to maximize shipnents or minimize prices for fixed "net" 
 returns to the industry. 
 
 The basic interval of time for which most marketing decisions are made in 
 the lemon industry is much shorter than the six-month period on which the analyses 
 described in the preceding section were based, Hovraver, if the results of these 
 analyses are to be at all useful in connection with the problem of allocation, a 
 time interval shorter than six months cannot be employed. Thus the allocation of 
 shipments that v/ill be considered is that betvTeen the two periods November through 
 April and May through October of each marketing year. The discussion to follow is 
 pertinent to decisions concerning shipments for other time intervals only in so far 
 as such decisions affect the total quantity shipped during each of the two six- 
 month periods, 
 
 ViTe shall begin by determining the allocation required to maximize f ,o,b. 
 returns. In this simplified case all costs to growers are disregarded. Further- 
 more, neither returns from diversion of lemons to processing nor the long-run 
 effects of the allocation are considered. Subsequently we shall take into account 
 some of the costs and the additional revenue from processed fruit received by the 
 grovrers. The long-run effects of the allocations discussed in this section, however 
 cannot be determined on the basis of the information at present available. 
 
 For a given marketing year let the price-quantity relation in each of the 
 two subperiods be, 
 
 I 
 
 xi - a + a^xg 
 yj^ = b + b2y2 
 
 where X], is the f,o,b, price per box and Xg domestic shipments for the six-month 
 
... ... . ■'•.■<: ::•>;■■ ■' ■ ■ 
 
 ,:..U-v. .... 
 
 - . Mr •■■ 
 

 48. 
 
 period November through April, and where yj^ and yg denote respectively f.o 
 
 •b. prices 
 
 and domestic shipments for the period May through October. The f»o»b« returns for 
 
 a given year are given by: 
 
 
 2 2 
 
 R - axg + byg + agXg + b^yg 
 
 
 The values of Xg and yg maximizing R ("optimum shipments") are easily shown 
 
 to be 
 
 
 2 
 
 ' 2b 
 
 
 If the constraint x + y^ ■ q, where q is a fixed value, is introduced, 
 
 2 
 
 shipments maximizing f.o.b, returns are given by the expressions: 
 
 
 ^1 ^ b - a + 2b9q 
 2 ^^^2 * ^2^ (B) 
 
 
 Yg = q - 
 
 
 The shipments of winter and summer lemons maximizing f .o.b, returns 
 
 with 
 
 and without constraint for the years 1921-22 to 1940-41 are found in table 
 
 11. One 
 
 set of these figures is based on equations 7s and Iw ~ the other, on equal 
 
 bions 8s 
 
 and 2w solved for f .©.b, price, To determine the constrained optimum shipments. 
 
 f.o.b. returns were maximized under the condition that the sum of optimum 
 
 shipments 
 
 of winter and summer lemons for each marketing year equal the actual quantity 
 
 'shipped during the year. In figure 2 the series of optimum shipments are i 
 
 -epresented 
 
 graphically together with the actual domestic shipments of winter and summer lemons. 
 
 The shading of the area betvreen estimates of optimum shipments, derived foi 
 
 - v/inter 
 
 lemons from equations Iw and 2w and for simmer lemons frcaa equations 7s ant 
 
 i 8s, is 
 
 intended to suggest the existence of a zone of uncertainty for these estimates in 
 
 ^^-/ These equations were chosen because they contain explicitly the relevant 
 variable to which allocation can be applied, namely, domestic shipments. 
 
 
 
TABLE 11 
 
 Allocation of November- April and May-October Lecion •Shipments to Maximize F.O.B. Returns 
 for an Undetermined and for a Fixed Volume of Annual Shipments, 1921-22 to 1940-41 
 
 ■ 
 
 
 
 Unrestricted opt 
 
 imum allocation 
 
 Restricted ortimum allocation 
 
 
 Domestic s 
 
 hipments 
 
 Equations 
 
 Iw and 7s 
 
 Squs-tions 
 
 2w and 8s 
 
 E'^uations 
 
 Iw and 7s 
 
 E^Ui^tions 
 
 2w and 8s 
 
 
 November- 
 
 fjiay- 
 
 Novembe r- 
 
 
 Nove;r.ber- 
 
 iVi&y 
 
 NovsiT^ber- 
 
 May- 
 
 Nove^r/oer- 
 
 May- 
 
 
 April 
 
 October 
 
 April 
 
 October 
 
 April 
 
 October 
 
 April 
 
 October 
 
 April 
 
 October 
 
 
 ^2 
 
 ^2 
 
 4 
 
 0 
 
 ^2 
 
 4 
 
 0 
 
 ^2 
 
 ^2 
 
 1 
 
 ^2 
 
 t 
 
 ^2 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 
 10.000 boxes 
 
 1921-22 
 
 164 
 
 1 
 
 235 
 
 135 
 
 231 
 
 122 
 
 206 
 
 148 
 
 251 
 
 152 
 
 247 
 
 1922-23 
 
 131 
 
 202 
 
 144 
 
 231 
 
 132 
 
 205 
 
 127 
 
 206 
 
 130 
 
 203 
 
 1923-24 
 
 191 
 
 322 
 
 144 
 
 251 
 
 132 
 
 231 
 
 193 
 
 320 
 
 195 
 
 318 
 
 1924-25 
 
 165 
 
 289 
 
 150 
 
 263 
 
 137 
 
 235 
 
 167 
 
 287 
 
 171 
 
 282 
 
 1925-26 
 
 175 
 
 328 
 
 157 
 
 258 
 
 144 
 
 235 
 
 194 
 
 310 
 
 196 
 
 307 
 
 1926-27 
 
 195 
 
 289 
 
 158 
 
 257 
 
 145 
 
 235 
 
 187 
 
 298 
 
 189 
 
 295 
 
 1927-28 
 
 15? 
 
 303 
 
 158 
 
 277 
 
 146 
 
 256 
 
 166 
 
 289 
 
 168 
 
 286 
 
 1928-29 
 
 215 
 
 322 
 
 165 
 
 299 
 
 153 
 
 278 
 
 195 
 
 342 
 
 197 
 
 340 
 
 1929-30 
 
 156 
 
 333 
 
 163 
 
 301 
 
 151 
 
 276 
 
 173 
 
 316 
 
 177 
 
 312 
 
 1930-31 
 
 201 
 
 381 
 
 158 
 
 310 
 
 147 
 
 288 
 
 205 
 
 377 
 
 209 
 
 373 
 
 1931-32 
 
 198 
 
 307 
 
 143 
 
 263 
 
 134 
 
 244 
 
 184 
 
 321 
 
 188 
 
 318 
 
 1932-33 
 
 176 
 
 347 
 
 147 
 
 277 
 
 138 
 
 257 
 
 188 
 
 335 
 
 192 
 
 331 
 
 1933-34 
 
 207 
 
 404 
 
 166 
 
 295 
 
 155 
 
 275 
 
 228 
 
 383 
 
 232 
 
 380 
 
 1934-35 
 
 261 
 
 416 
 
 168 
 
 276 
 
 157 
 
 257 
 
 265 
 
 412 
 
 268 
 
 409 
 
 1935-36 
 
 234 
 
 427 
 
 184 
 
 326 
 
 172 
 
 304 
 
 247 
 
 414 
 
 250 
 
 411 
 
 1936-37 
 
 
 
 
 
 
 
 
 
 
 
 1937-38 
 
 228 
 
 435 
 
 176 
 
 295 
 
 166 
 
 276 
 
 256 
 
 407 
 
 259 
 
 404 
 
 1938-39 
 
 249 
 
 470 
 
 176 
 
 322 
 
 167 
 
 302 
 
 268 
 
 451 
 
 272 
 
 447 
 
 1939-40 
 
 275 
 
 461 
 
 190 
 
 305 
 
 180 
 
 285 
 
 290 
 
 445 
 
 293 
 
 442 
 
 1940-41 
 
 301 
 
 550 
 
 192 
 
 356 
 
 182 
 
 • 335 
 
 318 
 
 533 
 
 323 
 
 529 
 
 Sources of data: 
 
 Col. l: Col. 2 of table 7, 
 Col. 2: Col. 4 of table 2. 
 
 Cols. 3 and 4: Based on expressions (A), see text, applied to equations Iw of table 8 and 7s of table 6. 
 
 Cols. 5 and 6: Based on expressions (A), see text, applied to equations 2w of table 8 and 8s of table 6. 
 
 Cols. 7 and 8: Based on expressions (B), see text, with the constraint ^ ^2 ~ ^^2 * ^2» applied to equations 
 Iw of table 8 and 7s of table 6, , 
 
 Cols. 9 and 10: Based on equations (B), see text, with the constraint ^tg * ~ ^2 * ^2* ^'PP^^®^ ^° equations 2w 
 of table 8 and 8s of table 6. 
 
* : I 
 
 i ' . 
 
 i :. 
 
 , t 
 
 V 
 
 
 
 
 ■ r ; 
 
 - ■ -■ 
 
 • - 
 
 
 • -■ 
 
 : 
 
 ■- ■ 
 ■. - ; 
 
 -■ V? I 
 
 .• .', ; 
 
 1 
 
 ■. -J 
 
 ):_-■*. 
 
 '•1 i 
 
 ^-c- ! 
 
 ■-■?tT '! 
 
 
 
 
 B : 
 
 
 
 
 Mi., : 
 ... i 
 
 
 .; 
 
 :y:. 
 
 
 T 
 
 
 
 
 : ■ . ; 
 
 ■ u 
 
 ^ .. 
 
 
 . ' '■ 
 
 
 ..... 
 "Tj j' 
 
 TT--.'-"- T 
 
 
 
 J 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 i J 
 
 
 
 
 
 :■: - 4 
 
 
 
 
 
 
 
 .V 1 
 
 
 
 
 
 - .. -4 
 
 
 
 
 
 
 
 
 
 
 ; • ■■ I. 
 
 
 
 
 
 
 *' * . 
 
 
 
 
 • 
 
 . . . ^ . 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
to 
 « 
 M 
 O 
 
 o 
 
 ta 
 
 •a 
 
 G 
 
 a 
 « 
 3 
 o 
 
 -p 
 
 V 
 EH 
 
 «9 
 
 <I> 
 
 X 
 
 o 
 
 o 
 » 
 
 c 
 
 OS 
 10 
 
 o 
 
 J3 
 
 a 
 
 500 
 
 400 
 
 300 
 
 200 
 
 300 ■ 
 
 200- 
 
 100 
 
 November-April 
 
 Constrained 
 
 optimun 
 /Shipments 
 
 omestic shipments 
 
 cm 
 
 shipments 
 
 1923-24 -26 
 
 -28 
 
 -30 
 
 -32 
 
 -34 
 
 -36 
 
 -38 
 
 -40 
 
 Fig 
 1921-22 
 
 , 2. — Domestic shipments of (A) winter and (B) simmer lemons and shipm.ents maximizing f.o.b. returns, 
 to 1940-41. (Data from table 11.) 
 
51, 
 
 addition to that implied by the standard errors of the estimates. Since equations 
 with price as the dependent variable and equations vri.th quantity as the dependent 
 variable are a priori equally aopeptable, the differences bebv/een the results secured 
 on the basis of these equations should in some way become a part cf the measure of 
 
 the "true" optimum shipments necessarily lie v/ithin these zones. 
 
 Inspection of figure 2 leads to the following observations: (l) The optiminn 
 shipments of vdnter and summer lemons in the case of the unconstrained maximum arg 
 considerably smaller than the actual shipments. For stunraer lemons in only one 
 season and for winter lemons in only three seasons have the actual shipments been 
 of the same order of magnitude as the shipments maximizing f ,o.b, returns. The gap 
 betv/een the actual and optimum shipments is markedly greater during the latter 
 part of the period than during the earlier years. Furthermore, during the latter 
 half of the period the differences between the actual and optimum shipments of 
 summer lemons are larger than the differences for v/inter lemons. (2) The optimum 
 shipments of vrinter and summer lemons in the case of the constrained maximum do 
 not differ greatly from the actual shipments. Hov/ever, beginning vdth 1933 the 
 optimum shipments of summer lemons are slightly but consistently smaller than the 
 actual shipments. For mnter lemons this tendency is, obviously, in the opposite 
 direction. Thus both sets of calculations, those for the constrained maximum and 
 those for the unconstrained maximum, suggest that during the latter half of the 
 period, relative to prevailing demand conditions, an overshipment of summer lemons 
 has taken place. This conclusion is in harmony v:ith the observation made earlier 
 (page 2 ) concerning the downvrard trend of prices of simmer lemons during roughly 
 
 — » The studies of Frisch and Koopmans are relevant in this connection: 
 Frisoh, R. Statistical confluence analysis by means of complete regression systems. 
 Oslo. 1934; and Koopmans, T. Linear regression analysis of economic time series. 
 Haarlem. 1937. 
 
 uncertainty to accompany 
 
. • t\- ...... 1. 
 
 .9 etB 
 
 - ■ ■ . c 
 
 - • - . --^ ■■ ; :'■ r- ■■ ^■ _ j; :. ■' ■■> 
 
 mil 
 
 ■ '■ » ■:;-v ■;:■:)•= «:.•::•" ■ ■ ■- v •.;..•.>•■• 
 
 - ■ -; • • -■■ I ■' . . ... ■>■• ■;. ■ ; , , 
 
 1 ^iid tot MOila 
 
 ■- • ■•■ t> ■ . ^ ; , w.-..:..' ... . '.■Cr. I i ■ "" . 
 
 ' ■ .:v -t! "<•!■" ;-r. •;!: • i,. J;^':Xo:i' i- • . ' , • 
 
 i 
 
 1 
 
52. 
 
 the same part of the period* 
 
 It may appear from the figures cited in connection with the unconstrained 
 maximum that a drastic curtailment of shipments of summer and winter lemons in many 
 of the years considered would have increased markedly f ♦©•b. returns to the industry 
 for the period. It should be emphasized that such a oonolusion is un^mrranted♦ The 
 formulation employed herein deep not permit aasepament of the long-run effects of 
 an allocation policy* An obvious oonsequenoe of a drastic curijailment of lemon 
 shipments is a shift pn the part of consumers to substitutes* It is probable that 
 within the range of lempn prices which have ijhus far prevailed, the level of prices 
 of technically substitutable oommodities has not had an important influence on the 
 demand for lemons. However, in higher price ranges — effectuated by markedly our- 
 tailed shipments -t^ substitution may beocraie a factor of major importance. 
 
 Introduction of oosts and addition^-l revenues arising fvcsa, the sale of 
 lemons for manufacture has the effect of further decreasing optimum shipments 
 derived for the unconstrained maximum. These nevj- elements are introduced by maxi- 
 mizing for ?L given year "value on tree" defined as 
 
 y « R ^ (g + h) (xg + yg) + (Q - yg) z, 
 where g represents picking and hauling costs per box, h represents the packing- 
 house charge and selling (including advertising costs), Q the total lemon crop, and, 
 finally, z the price "on tree" of lemons used for prooessingi R, as before, denotes 
 f ,o.b, returns for packed and loose fruit. The reader will note the simplifying 
 assumption of constant average "variable" costs and the further assumption of a 
 fixed "on tree" price of lemons diverted to manufaotwe. Cultural costs, interest 
 on investment, and depreciation alloT.mn9e are not included in this formulation. 
 
 The shipments maximizing V are given by 
 
 . x° ^ e,%^ r ^ 
 
 2 2 
 
 (C) 
 
 * 0 e + h + 8 
 
-.t;.; '■. ^ . . \ b-i':.— i. c i: V- J; ^ ^v.;;■■ M:v-.- ::■ •., 
 
 ojii; »>bvj^f;^'4^i;•■^v^> J vcnjt^u C'ini;j.; -.j.f'i- !:■■ •^Z -vg-is^^fUi^c^^ia sr 
 
 ■ v't-gX 
 
 " ' ■ ' ■ ■ - ■ \ ■ fUv«- 
 
53, 
 
 It is apparent from expressions (C) that shipments maximizing 7 will be smaller 
 than shipments maximizing R, that is, that the demand at the "on tree" level is 
 more inelastic than the demand for lemons at the f.o.b, level. The introduction of 
 costs and additional revenue from processing has no effect on the magnitudes of 
 optimum shipments derived for the constrained maximum. 
 
 The application of the remaining criterion involves the maximization of 
 U = + y-g under the condition V = or the minimization of W » R (xg + 72)"^ 
 under the same constraint. The values of x^ and maximizing U or minimizing V/ 
 are given by: 
 
 (D) 
 
 
 (^c 
 
 -F) 
 
 ^2 
 
 (ag 
 
 •.bg) 
 
 
 (^c 
 
 -F) 
 
 
 
 + ^2) 
 
 where P = Qz - agCxg')^ - h^iv^* f • 
 
 In table 12 are indicated the values of optimum shipments for the three 
 years 1937-38 through 1939-40 calculated from (c) and (D). The differences between 
 the optimum shipments maximizing "value on tree" and the shipments minimizing the 
 annual v/eighted average prioo for a fixed "on tree" value are very large. Since 
 the magnitude of such differences is a function of the value selected for V no 
 significance attaches to the particular magnitudes of optimum shipments given in 
 table 12, These are to be viev/ed as numerical illustrations of the expressions (C) 
 and (D) designed to make their meaning more concrete. Of some interest, however, 
 is the following observation. Let d be the difference betiveen the optimum shipments 
 calculated from expressions (C) and (D), that is (x*" - x") or (y'" - y**), and 
 let d' be the value of d for = 0, It is easily seen that 
 
 d 
 
 where is the maximum value of V^., Thus relatively large differences between 
 optimum shipments derived from expressions (C) and (D) are to be expected for a 
 large range of values of V» 
 
I'.xjLSiiiiii ■ - . . v^'V r - -'"^ • !. 
 
 ery- ^0.1 ... 
 
 « r ' ■- ' ' ' ■ ■ ■ ' ■ ' ■ ■ ■ 
 
 T i. 
 
 f ■ 
 
 ■7—' 
 
 f;Si--fi,h7 tie, 0'.'jr 
 
 it ""i »i 
 
 f » » 
 
 >" . s. .j ' • . 
 
 3«f (ffX itfUT (P) 8«ox8ae'?',xd aoi^ fetfvl.te; 
 
 • .. 
 « * 
 
TABLE 12 
 
 Shipments of Summer and Winter Lemons Maximizing Value on Tree 
 and Minimizing Average Annual F.O.B. Price for Fixed Value on Tree 
 
 Year 
 
 Annual 
 pro- 
 duction 
 
 0 
 
 Costs f.o.b. 
 packing house 
 less cultural 
 costs 
 
 e + h 
 
 Price on 
 tree for 
 manufa c- 
 ture 
 
 jg 
 
 Shipments maxi- 
 mizing value on 
 tree 
 
 Ve lue on 
 tree 
 
 V 
 
 Shipments minimizing 
 prices for fixed 
 value on tree 
 
 November- 
 April 
 
 »? 
 3C2 
 
 May- 
 October 
 
 yz 
 
 November- 
 April 
 
 ^2 
 
 May- 
 October 
 
 II ♦ 
 ^2 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 
 10,000 
 
 dollars 
 
 dollars 
 
 10,000 
 
 10,000 
 
 1,000 
 
 10,000 
 
 10,000 
 
 
 boxes 
 
 per box 
 
 per box 
 
 boxes 
 
 boxes 
 
 dollars 
 
 boxes 
 
 boxes 
 
 1937-38 
 
 930 
 
 1.32 
 
 0.11 
 
 150 
 
 259 
 
 12,518 
 
 258 
 
 411 
 
 1938-39 
 
 1,111 
 
 1.32 
 
 0.05 
 
 152 
 
 287 
 
 13,876 
 
 269 
 
 452 
 
 1939-40 
 
 1,198 
 
 1.28 
 
 0.22 
 
 1 
 
 163 
 
 267 
 
 13,040 
 
 291 
 
 447 
 
 Sources of data: 
 
 Cols. 1 and 2: California Fruit Growers Exchange. Marketing Research Department. Statistical information on the 
 
 lemon industry. February, 1942. 
 
 Col. 3; United States Bureau of Agricultural Economics. Agricultural prices. Vi/ashington, D. C. August 28, 1942. 
 (Mimeo. ) 
 
 Cols. 4 and 5: Based on expressions (C), see text, equations Iw and 7s and cols. 1, 2, and 3« 
 
 Col. 6: Estimated on the basis of equations Iw and 7s and data in cols. 1. 2. and 3. cn 
 Cols. 7 and 8: Based on expressions (D), see text, eqiiations Iw and 78, and cols. 1, 2, 3, and 6. 
 
'■'■L'y.-t^'B- 
 
 •i^ t: 
 
 J? 
 
 ■ 'a9 
 
 1 
 
 ■J} i s. • 
 
 . V vrr : 
 
 f * * ' 
 
 ^1 
 
 • ,» - ! 
 ■ . .i • 
 
 
 
 
 a * 
 
 
 
55. 
 
 Summary 
 
 Most of the variation of the average f .o.b, prices of California suramer 
 lemons during the twenty-year period 1922 to 1941 can be accounted for by con- 
 comitant variation in three factors: namely, (l) total quantity of lemons mar- 
 keted as fresh fruit in the United States, (2) nonagricultural income payments in 
 the United States, and (3) maximum temperatures prevailing during the summer months. 
 Most of the variation of the average f .o.b. prices of winter lemons can be accounted 
 for by concomitant changes in (1) domestic shipments for fresh consumption of 
 California winter lemons, (2) nonagricultural income payments in the United States, 
 (3) average lev^l of temperatures prevailing in December, January, and February, 
 and (4) trend factors not individually identified but whose aggregate effect is 
 represented by the variable "time." This variable failed to make a significant 
 contribution in the analysis of summer lemons largely because of the presence of 
 a marked trend in the temperature index. Additional evidence, however, makes it 
 probable that during the period the demand for summer lemons relative to annual 
 changes in the purchasing povrer of consumers and to annual changes in the level of 
 maximum temperatures shifted upvmrd. 
 
 In order to obtain a more comprehensive picture of the characteristics of 
 demand for summer and winter lemons, both price and quantity were employed as 
 dependent variables in the regression analysis. In each case the dependent variable 
 (and its logarithm) was expressed as a linear function of the independent variables 
 (and of their logarithms). In addition, equations based on per-capita quantity and 
 per-capita income were fitted. The results secured with these different treatments 
 were found to be in substantial agreement. 
 
 On the basis of these analyses several major conclusions appear to be 
 warranted: (1) The demand for summer lemons on an f.o.b. basis was inelastic 
 during the period; the demand for v/inter lemons on an f.o.b. basis vms also in- 
 elastic during most of the period. There appears to be little or no difference in 
 the elasticities of demand for sviramer and winter lemons, (g) Changes in income 
 
56. 
 
 have affected the demand for smmner and winter lemons. Increases in nonagricultural 
 income payments have been associated with upward shifts of demand for both summer 
 and winter lemons, (3) Changes in weather conditions, more specifically temperature, 
 have affected the demand for both summer and winter lemons. An upward shift of 
 demand for lemons during the summer months is associated with increase in tempera- 
 tures; an upv/ard shift of demand for lemons during the winter months is associated 
 with decrease in temperatures, (4) During the tv/enty-year period the demand for 
 both summer and winter lemons, relative to the other independent variables, has 
 shifted upvards. It is likely that factors other than growth of population are 
 responsible for a large part of this upv/ard shift. 
 
 The problan of allocation of lemon shipments betv/een the tvro periods of the 
 marketing year, November to April and May to October, v/as given brief consideration. 
 Shipments maximizing f ,o,b, returns or "value on tree" — the latter determined 
 under a set of simplifying assumptions — were found to be, for most of the years 
 of the period, considerably smaller than the actual domestic shipments of winter and 
 summer lemons for fresh consumption. The conclusion that revenue to growers could 
 be increased in the long rim if drastic limitation of shipments were instituted is 
 not implied by the foregoing since long-run effects are not treated in the formula- 
 tions underlying these calculations. 
 
 The allocation of a fixed annual volume of shipments to maximize returns to 
 growers was also considered. For the twenty-year period, the allocation of the 
 actual annual shipments so as to maximize returns to growers was shown to result in 
 shipments of winter and summer lemons not greatly different from the actual shipments. 
 However, since 1932-33 there has been apparently a slight but consistent tendency 
 to vmdership during the months Hovember to April and to overship during the months 
 May to October, This and other evidence suggest that in recent years the shipments 
 of summer lemons were somev/hat large relative to the demand conditions prevailing 
 during the year. 
 
: ..70 -trfd- od' evlrr^. 
 
 U J 
 
 , ooiaeJ to . ,.-r)oXr/' ■ 
 
 ' • '- ■■■'>■»;' ....... . 
 
 • - ■ • — . ' .' - 
 
 .4 ;.j 
 
 o .; 
 
 ;"i:,;;f'i ■..fr-Yvs:^%Nr , ..... . C9i :i3:. . 
 
 ii^.. -i./T;:- .- 
 
57, 
 
 APPEiroiX A 
 
 Series Used in the Study 
 
 The Price Series *— The price series employed in this paper consist of the 
 average prices, f»o.b» basis, received for lemons marketed by the California Fruit 
 Growers Exchange during the six-month periods November through April and May through 
 October, for each of the twenty years 1921-22 through 1940-41 (see table 13 )• The 
 average price for each six-month period was obtained by dividing the total amount 
 of money (reduced to an f .o»b, basis) received by the Exchange for lemons shipped 
 during the period, by the number of boxes shipped* 
 
 It is impossible to determine directly the degree to which the Exchange 
 
 prices are representative of prices received for all California lemons since data 
 
 on sales by other shippers of California lemons are not available to us. Such 
 
 factors as differentiation of product, variation in time and place of shipments, 
 
 and variation in composition of .shipments \vould make for differences between prices 
 
 received by the Exchange and those received by other marketing agencies. However, 
 
 Exchange prices would exert a predominant influence on the weighted average price 
 
 for the industry as a whole. For the period under reviev/ the California Fruit 
 
 Grovrers Exchange has consistently marketed the major proportion of California lemons* 
 
 For winter lemons, on the average, the Exchange handled about 88 per cent of the 
 
 total domestic shipments; for summer lemons the Exchange percentage was even higher, 
 
 approximately 92 per cent. In no year did the Exchange percentage fall below 80 
 
 46/ 
 
 for winter lemons and 86 for summer lemons, ■— ' 
 
 Some notion as to the magnitude of the correlation to be expected between the 
 weightedraverage price of lemons marketed by the California Fruit Growers Exchange 
 and the industry weighted- average price may be obtained by the follovdng calculation. 
 
 These percentages are based on figures given in tables 20 and 21, 
 
vl-j...'.>-3 ni fcsai^ sc. 
 
 > or ; f prt': ■• 
 
 r. ''.t 'ij.^;:! ' yr^ jo:-: f'-'r. f\rr. f •■'lo'rxrjB') '^■-i -f'-''' ' rfp, 'i^ff-^r '.rT ■''^j.'- 
 
 10 
 
 R^pV tocf ;> erf od- a . xo 3 orfcf- lo ei -f 9di bjb noi.-^on 
 
58. 
 
 TABLE 13 
 
 Seasonal Average F.O.B. Prices of California Lemons 
 1921-22 to 1940-41 
 
 
 Period 
 
 
 
 Period 
 
 
 Year 
 
 November- 
 April 
 
 May- 
 October 
 
 Year 
 
 November- 
 April 
 
 May- 
 
 Octob 
 
 3r 
 
 
 dollars 
 per box 
 
 dollars 
 per box 
 
 
 dollars 
 
 per box 
 
 dollars 
 per box 
 
 1921-22 
 
 3.48 
 
 4.48 
 
 1931-32 
 
 2.49 
 
 4.4: 
 
 L 
 
 1922-23 
 
 4.20 
 
 5,23 
 
 1932-33 
 
 3.09 
 
 3.6( 
 
 
 1923-24 
 
 2.38 
 
 2.74 
 
 1933-34 
 
 3.20 
 
 3.8! 
 
 5 
 
 1924-25 
 
 3.87 
 
 4.93 
 
 1934-35 
 
 2.18 
 
 3,3J 
 
 ) 
 
 T Q O C OP. 
 
 ly c 0— CD 
 
 OmOO 
 
 o.2o 
 
 1935-36 
 
 3.72 
 
 4.5: 
 
 L 
 
 1926-27 
 
 2.73 
 
 4.88 
 
 1936-37 
 
 3,79 
 
 4.8e 
 
 
 1927-28 
 
 4.81 
 
 4.86 
 
 1937-38 
 
 3.50 
 
 2.8' 
 
 7 
 
 1928-29 
 
 3.58 
 
 5.36 
 
 1938-39 
 
 2.56 
 
 3.1' 
 
 J 
 
 1929-30 
 
 4.94 
 
 5.18 
 
 1939-40 
 
 2.99 
 
 3.0^ 
 
 
 1930-31 
 
 3.09 
 
 4.50 
 
 , 
 
 1940-41 
 
 2AZ 
 
 3.1£ 
 
 
 Source of data: 
 
 Based on prices received by the California Fruit Growers Exchange 
 for lemons shipped during these periods. Beginning May, 1926, prices 
 of fruit sold loose are included. Beginning November, 1935, prices 
 of exported lemons are excluded. 
 
59. 
 
 On the assumption that the proportion of the total shipments of domestic lemons 
 controlled by the Exchange is constant from year to year and equal to pi, the cor- 
 relation between the Exchange weighted average price and the industry weighted 
 average price is given by the expression, 
 
 Pl + k P2 
 
 where k is the ratio of the standard deviation of the weighted average prices re- 
 ceived by shippers outside the Exchange to the standard deviation the Exchange 
 weighted average prices, r^^g the correlation between the two sets of weighted 
 average prices, and pg = l-p^^* Considering r^^^ as a function of r^g, the minimm 
 value of the former is given for r^g = - k PgP]_"^» namely. 
 
 (kp^)' 
 
 It Pl 
 
 The minimum value of r^^ may thus be calculated for various values of p^ and k« 
 The values of r^^g and r°^ obtained when to p-j^ is assigned the value of the ratio of 
 Exchange domestic shipments to industry domestic shipments and to k plausible limits, 
 are given in table 14» Values of r^^^ obtained when P]^ is assigned the lowest 
 observed value during the period under review are also indicated in the table. 
 Under all assvimptions, and these by no means favored the appearance of high corre- 
 lations, the correlation coefficients secured are very high. These results suggest 
 that a satisfactory use in regression analysis may be made of Exchange prices 
 as approximations to the weighted average industry prices. 
 
 Several observations must be made concerning the year-to-year comparability 
 of the series. Beginning mth May 1926, prices of lemons sold loose are included in 
 our series. Since prices of packed lemons are available for each of the twenty 
 years under consideration, greater homogeneity might have been achieved by exclud- 
 ing data on loose lemons. However, sales of the latter have increased significantly 
 during the period under review. Rather than to disregsird a factor of growing 
 
jj. ..c>x ja '.-.Tii-ij,'!!: ■ 
 
 -too aifi, ^ 
 
 •9 ^btt« ii3;^,v .vj^'^*j&:\;..?'''<3L-,.. v 
 
 fli be' . 
 
 ■o .. <■• 
 
 ■ ^'.i" a©iiv.. 4?f'5i~-^,cf«i. ■4.,-"' - ■ 
 
 .J J 2.' 
 
 i /if-.. 
 
TABL!i 14 
 
 Estimates of Correlation Between California Fruit Growers Exchange 
 and Industry V^eighted Average Prices Under Various Assumptions 
 
 Ratio of C.F.G.E. 
 shipments to 
 industry 
 shipments 
 
 Pi 
 
 P2 = 1 - Pi 
 
 
 Correlation between 
 C.F.G.i. and out- 
 side weighted 
 average prices 
 
 'l2 
 
 Correlation between 
 C.F.G.E. and in- 
 dustry weighted 
 average prices 
 
 ^It 
 
 Minimum 
 value of 
 
 ^t 
 
 r° 
 
 1 1 
 
 0.8752 * 
 
 0.1248 
 
 1 
 
 —0 .1426 
 
 
 n QROfi 
 
 u .yoyo 
 
 0.8752 
 
 0.1248 
 
 2 
 
 -0.2852 
 
 
 0.9584 
 
 0.7961 t 
 
 0.2031 
 
 1 
 
 0 
 
 0.9690 
 
 
 0.9202 + 
 
 0.0798 
 
 1 
 
 -0.0867 
 
 
 0.9962 
 
 0 .9202 
 
 0.0798 
 
 2 
 
 -0.1734 
 
 
 0.9924 
 
 0.8560 4 
 
 0.1440 
 
 1 
 
 0 
 
 0,9862 
 
 
 * Ratio of Exchange domestic shipments of winter lemons 1921-22 through 1940-41 to industry domestic 
 shipments. 
 
 Smallest observed ratio of Exchange domestic shipments of winter lemons to industry domestic shipments 
 
 for the period 1921-22 through 1940-41. 
 
 :^ Ratio of Exchange domestic shipments of summer lemons, 1922 through 1941, to industry domestic shipments, 
 
 ^ smallest observed ratio of Exchange domestic shipments of summer lemons to industry domestic shipments 
 
 for the period 19? 2 through 1941. 
 
i 
 i 
 
 •; 
 
 \ 
 
 i 
 
 t. 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ; 
 
 
 
 
 
 
 
 'f 
 
 
 
 
 
 
 
 
 
 • - 
 
 
 ■ * . '• ■ 
 
 : 
 
 
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 i ■ 
 
 i 
 
 ! 
 
 i 
 
 i 
 
 
 
 ; T ,■ 
 
 ■ r 
 
 ; \ 
 
 
 J 
 
 i 
 
 
 
 4 ■.■ ■;■ 
 
 i. . ; . -^r '., '.. " 
 
 ; 
 
 
 
 
 
 ...... . J.. -J., 
 
 
 
61. 
 
 Mpol'tance, it was thought preferable to attbept the risk of a slight upward bias 
 in the fii»st tour or five observations of -the series. 
 
 Of possibly greater importance as far' as the homogeneity of the price series 
 is concerned is the fact that prior to 1935-36 the series include prices of ex- 
 ported lemons. For the six years for which export data are available, the prices 
 based on domestic shipments differ by as much as 10 cents a box in only one 
 season from prices based on total shipnents (see table 15 )• It is unlikely that 
 differences of this magnitude would be found for the earlier years of the period. 
 
 Total exports during the last six years were greater relatively than during the 
 
 47 / 
 
 previous fourteen years. — « Furthermore, in the more recent years a somewhat 
 larger proportion of lemons than previously was exported to destinations other 
 than Canada; the f ,o.b. prices for the latter country are ordinarily closely in 
 line with prices of like grades and sizes of domestic lemons marketed in continental 
 United States. 
 
 48/ 
 
 Finally, it must be noted that the grade and size composition of shipments 
 varied from year to year (see table 16). The lemons to which the prices refer have 
 not constituted a strictly homogeneous commodity. Had monthly data on grades and 
 sizes been available for the whole of the period, these sources of heterogeneity 
 could have been removed. In the absence of this information we are unable to 
 
 49/ 
 
 assess the contribution of these factors to the variance of the f.o.b. prices. 
 
 47/ 
 
 For the period 1921-22 through 1934-35, exports of domestic winter lemons 
 were 5.8 per cent of total shipments of domestic lemons for fresh consumption; 
 for the period 1935-36 through 1940-41, the percentage of exports v/as 8.1 per cent. 
 Analogous figures for summer lemons are 4.1 per cent and 7.0 per cent. See data on 
 exports given in tables 17 and 18. 
 
 48/ 
 
 — I For the period 1925-26 through 1934-35 exports of lemons to Canada comprised 
 approximately 74 per cent of total lemon exports. The corresponding figure for the 
 period 1935-36 through 1939-40 is somewhat less than 60 per cent. 
 
 49/ 
 
 ._y One other possible source of inoomparability should be mentioned. In 
 November 1929 the California Fruit Growers Exchange extended its operations to 
 Arizona and from that time on prices of Arizona lemons marketed by the Exchange are 
 included in the price series. The volume of Arizona lemons marketed by the Exchange, 
 however, is negligibly small. 
 
 W 
 
W 1 
 
 3-* • . ft ©OA 
 
 ;. ■.■••■J:; -.-..i ; ;;-;.>u;;or> ■iix^J.-; ./ .-,r^,•^ ;r ;.■ 
 
 A 
 
 '■ •■ • .-i;:i:::'v ;^v;.^^.: r;// .^C'-"-* iS^;-?:)^ -^^rw -v:?- ^i:.^: 
 
 t: .■:.:ib vi:.;; -KwA «i-:; fti:-;:?=tr^r •■v-.o.; ,-j:j- ;;v:!;; :.v ■ . ; 
 
 ■■i.Tsb 99Q -iv, O.V i::.; ;;-::^!n -jrr;-!^:!^ •t;^^ 'i^^c*!- 
 
62, 
 
 TABLE 15 
 
 Comparison of F.O.B, Prices of Lemons Excluding and 
 Including Exports, 1935-36 to 1940-41 
 
 
 November- April 
 
 May -October 
 
 
 Year 
 
 F.o.b. price 
 excluding 
 exports 
 
 F.o.b. price 
 
 Xiiv> XUU XXig 
 
 exports 
 
 F.o.b. price 
 
 XUU XZig 
 
 exports 
 
 F.o.b, price 
 j.nc xuu xiig 
 
 exports 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 
 
 dollars 
 
 dollars 
 
 dollars 
 
 dollars 
 
 
 1935-36 
 
 3.72 
 
 3.75 
 
 4,51 
 
 4.49 
 
 
 1936-37 
 
 3.79 
 
 3.81 
 
 4.86 
 
 4.87 
 
 
 1937-38 
 
 3.50 
 
 3.49 
 
 2.87 
 
 2.82 
 
 
 1938-39 
 
 2.56 
 
 2.51 
 
 3.17 
 
 3.07 
 
 
 1939-40 
 
 2.99 
 
 2.99 
 
 3.04 
 
 3.04 
 
 
 1940-41 
 
 2.42 
 
 2.42 
 
 3.19 
 
 3.19 
 
 
 Source of data: 
 
 Prom records of the California Fruit Growers Exchange. 
 
 I 
 I 
 
 r 
 
jr v-:- 
 
 I . . - 1 ^ 
 
 J! 
 
63. 
 
 TABLE 16 
 
 Average Sizes of Lemons Shipped by the California Fruit Growers Exchange 
 and Proportion of Shipments Graded Sunkist, 1930-31 to 1940-41 
 
 
 Aver a 
 
 le size 
 
 shipments 
 prraded Sunkist 
 November-Octobe 
 
 
 I Oc** 
 
 April 
 
 — 
 
 October 
 
 r 
 
 
 J. 
 
 
 3 
 
 
 
 Number 
 
 per box 
 
 Per cent 
 
 
 1930-31 
 
 334 
 
 357 
 
 57,9 
 
 
 1931-32 
 
 341 
 
 363 
 
 57.3 
 
 
 1932-33 
 
 355 
 
 368 
 
 58.8 
 
 
 1933-34 
 
 363 
 
 378 
 
 57.5 
 
 
 1934-35 
 
 361 
 
 355 
 
 59.8 
 
 
 1935-36 
 
 367 
 
 374 
 
 55.0 
 
 
 1936-37 
 
 
 O 1 0 
 
 ^ 
 
 'iOt 1 
 
 
 1937-38 
 
 355 
 
 359 
 
 61.3 
 
 
 1938-39 
 
 364 
 
 367 
 
 54.7 
 
 
 1939-40 
 
 363 
 
 359 
 
 62.0 
 
 
 1940-41 
 
 ! 
 
 354 
 
 i. 
 
 349 
 
 65.3 
 
 
 Sources of data: 
 
 Cols. 1 and 2; Based on packed lemon shipments of the Calif- 
 ornia Fruit Growers Exchange. Average size for each season was 
 computed by weighting the monthly average sizes by the corresponding 
 monthly shipments. 
 
 Col. 3: Based on reports furnished to the California Fruit 
 Growers Exchange by district exchanges. Includes both packed and 
 loose fruit. 
 
4- 
 
 
 t 
 
 
 
 
 
 i 
 
 
 
 t-.. - V ;,^ 
 
 — , 
 
 
 
 
 
 \ • „■ 
 
 ■ y ■ 
 
 J 
 j 
 
 
 
 
 • 
 
 
 
 
 
 
 j. ^ ■ • 
 
 i 
 
 i 
 
 - 
 
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 ' ■ » ■ 
 
 
 
 : : 
 
 ■ 
 
 
 
 
 
 
 ! id 
 
 
 
 
 
 
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 C -. J 
 
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 i 
 
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 t • 1* 
 
 
 
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 ■ -.v 
 
 ] 
 
 
 1 
 
 
 
 
 ■ s • - 
 
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 ^* 
 
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 1 
 
 
 
 
 
 1 
 
 [ 
 
 
 1 
 
 
 
 
 
 
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 1 
 
 1 
 
 
 
 
 
 
 
 eiirto 
 
64. 
 
 The Quantity Series ^— » The quantity series employed in the regression 
 analyiOB are given for winter lemons in table 17 and for summer lemons in table 18, 
 In column 1 of these tables are given estimates of shipments of California and 
 Arizona winter and summer lemons for fresh consumption. Since these are the basic 
 components of the final series, their construction will be described in detail* 
 The sources of the other entries are indicated fully in the notes accompanying the 
 tables. 
 
 Estimates of the industry shipments of domestic lemons for fresh consumption 
 were obtained by adjusting the estimates of packed shipments of domestic lemons by 
 the ratio of packed and loose shipments of lemons by the Exchange to their packed 
 domestic shipments. This step in the construction of the series is based on the 
 assumption that the ratio of sales of loose lemons by the industry to total 
 industry sales of lemons is identical with the analogous ratio for the Exchange. 
 The validity of this plausible assumption cannot be directly examined since reliable 
 estimates of sales of loose lemons by shippers outside of the Exchange are not 
 available for any part of the period under review. However, since the Exchange has 
 marketed the major proportion of the California lemon crop in each of the twenty 
 years, the ratio of loose to packed fruit for the industry as a whole could not be 
 very different from the ratio for the Exchange. 
 
 In turn, estimates of packed shipments of domestic lemons wore obtained by 
 adjusting the Exchange packed shipments by the ratio of industry rail and boat ship- 
 ments of domestic lemons to the Exchange rail and boat shipments. Industry rail 
 and boat shipments cannot be used directly to represent total industry shipments of 
 lemons, because movement of lemons by truck is not included in these figures, and 
 because of the difficulty of determining the proportion of lemons in mixed citrus 
 car shipments. On the other hand, it is probable that the proportion of lemons in 
 mixed citrus car shipments is not greatly different for shippers outside the Exchange 
 from what it is for the Exchange. This is a plausible assumption and one v/hich 
 affects only a relatively minor subtotal. 
 
■■r n:-.;.; ■■ . . .. ' .■ ©Xiv vio'i oij.-^-; «s.-i't j-;..^- 
 
 ■'• -• ■.• ■ -.■ . t€» ^ .i*.-/ v.. , ,'V. 
 
 •11. 
 
 •■^ --';.;-W.'V.>..i. ; .f." rfj;; r r. -v.; v?r^;..;'.-r5.. .V. ....... ^. ; 
 
 i--'Oy..~.^!^''ir'-'^..-":L, _ "^w ■ " '.J Grid 'io .. 
 
 ,r?:fo. '.i3 n<- '/x*.sion f> 
 
TABLS 17 
 
 'A'inter Lemons: Domestic Shipments, Per Capita Domestic Shipments, United States Supply, 
 
 and Per Capita Supply, 1921-22 to 1940-41 
 
 Year 
 
 
 
 
 
 Per capita 
 
 
 
 November- 
 
 Total 
 
 Domestic 
 
 Domestic 
 
 United States 
 
 domestic 
 
 Imports for 
 
 United States 
 
 April 
 
 shipments 
 
 exports 
 
 shipments 
 
 population 
 
 shioments 
 
 consumption 
 
 supply 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 
 thousand 
 
 thousand 
 
 thousand 
 
 thousand 
 
 pounds 
 
 thousand 
 
 thousand 
 
 
 boxes 
 
 boxes 
 
 boxes 
 
 persons 
 
 
 boxes 
 
 boxes 
 
 1921-22 
 
 1,756 
 
 115 
 
 1,641 
 
 109,873 
 
 1.14 
 
 384 
 
 2,025 
 
 1922-23 
 
 1,388 
 
 80 
 
 1,308 
 
 111,537 
 
 0.89 
 
 690 
 
 1,998 
 
 1923-24 
 
 2,034 
 
 123 
 
 1,911 
 
 113,302 
 
 1.28 
 
 137 
 
 2,048 
 
 1924-25 
 
 1,726 
 
 78 
 
 1,648 
 
 114,867 
 
 l.OS 
 
 384 
 
 2,032 
 
 1925-26 
 
 1,860 
 
 110 
 
 1,750 
 
 116,532 
 
 1.14 
 
 309 
 
 2,059 
 
 1926-27 
 
 2,139 
 
 185 
 
 1,954 
 
 118,197 
 
 1.26 
 
 96 
 
 2,050 
 
 1927-28 
 
 1,610 
 
 93 
 
 1,517 
 
 119,862 
 
 0.96 
 
 505 
 
 2,022 
 
 1928-29 
 
 2,291 
 
 145 
 
 2,146 
 
 121,526 
 
 1.34 
 
 156 
 
 2,302 
 
 1929-30 
 
 1,632 
 
 74 
 
 1,558 
 
 123,077 
 
 0.96 
 
 611 
 
 2,169 
 
 1930-31 
 
 2,147 
 
 139 
 
 2,008 
 
 124,039 
 
 1.23 
 
 69 
 
 2,077 
 
 1931-32 
 
 2,122 
 
 138 
 
 1,984 
 
 124,840 
 
 1.21 
 
 36 
 
 2,020 
 
 1932-33 
 
 1,823 
 
 62 
 
 1,761 
 
 125,578 
 
 1.07 
 
 60 
 
 1,821 
 
 1933-34 
 
 2,163 
 
 90 
 
 2,073 
 
 126,373 
 
 1,25 
 
 8 
 
 2,081 
 
 1934-35 
 
 2,779 
 
 170 
 
 2,609 
 
 127,249 
 
 1.56 
 
 3 
 
 2,612 
 
 1935-36 
 
 2,671 
 
 332 
 
 2,339 
 
 128,052 
 
 1.39 
 
 47 
 
 2,386 
 
 1936-37 
 
 2,691 
 
 132 
 
 2,559 
 
 128,823 
 
 1.30 
 
 8 
 
 2,5€7 
 
 1937-38 
 
 2,433 
 
 150 
 
 2,283 
 
 129,823 
 
 1.34 
 
 46 
 
 2,329 
 
 1938-39 
 
 2,790 
 
 299 
 
 2,491 
 
 130,878 
 
 1.45 
 
 
 2,491 
 
 1939-40 
 
 2,964 
 
 218 
 
 2,746 
 
 131,954 
 
 1.5S 
 
 
 2,746 
 
 1940-41 
 
 3.247 
 
 234 
 
 3.013 
 
 133.030 * 
 
 1.72 
 
 
 3.013 
 
 * Estimated. 
 
 Sources of data: 
 
 Col. 1: Col. 4, table 19. 
 
 Col. 2: United States Department of Commerce. Monthly summary of foreign commerce of the United 
 States, monthly issues. 
 
 Col. 3 ; Col. 1 minus col. 2. 
 
 Col. 4: United States Department of Commerce Bureau of the Census. Statistical A^strac^ ol^tTie 
 United States, 1941. Population. Estimated as of July 1 for continental United States. 
 
 Col. 5: Col. 3 divided by col. 4 and multiplied by 76 for conversion to pounds. w 
 
 (Continued on next page) 
 
I 1 J -^iv^-i 
 
 i t . 
 
 
 
 ■ \ ■- > ■ 
 
 
 
 
 1 . . .; • 
 
 
 » /- * ".:.' ' ' ■■ ■ ■ 
 
 1 
 
 \ ^ 
 
 - . * f 
 
 » ■ 
 
 " ♦ '■■ , ; 
 
 
 J ' F 
 
 
 i ■ ^ 
 
 . . . - .J • > *_ . 
 t . ■ - ■ 
 
 : -.»-■. ', 
 
 ■ 
 
 i -I .'i^-.ir - 
 
 ' V. . . J . ■ 
 
 ! - » 1 - .. 
 
 
 * * 
 
 .. • - " • 
 
 •; » ■ 
 
 * 
 
 ; "' ■ 
 
 i 
 
 : 
 
 i ■ 
 f 
 
 ■ ' , ■ 
 
 
 I- ■ K ... 
 
 i ' , " ) 
 
 i J ' ^-e^v . 
 
 ' . - - 4 , . . . . 
 
 ■ " - T ^ ■■ ■ 
 ' ., .»•■ ^, 
 
 i 
 
 ■ \r/: r ♦ 
 
 
 » ■ i - ■ . 
 
 ( "- " 
 1 
 
 ; 
 
 : ■'.'5 ! 
 ; . . / i 
 
 f -.: -'■ ' 
 I .... ^ ■ 
 
 
 
 
 ■-•V. • i'^- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 r ^ .. 
 
 - *■ '. ■. . . 
 
 ■ ■ : 
 
 
 
 
 I..- y . , .. 
 
 
 
 
 
 
 • i . * ' * 
 
 
 
 
 
Table 17 continued. 
 
 Sources of data: 
 
 Col. 6: United States Department of Commerce. Monthly summary of foreign commerce of the Unite 
 States, monthly issues. 1921-22 through 1932-33: "General imports" minus "exports of foreign lemons 
 1933-34 to date: "Imports for consumption." Exports of foreign lemons for November, 1921, through 
 December, 1925, and all import figures converted to feoxes on basis cr 76 pounds per box. 
 
 Col. 7: Col, 3 plus col.. 6. 
 
TABLE 18 
 
 Summer Lemons: Domestic Shipments, United States Supply, and Per Capita United States 
 
 Supply, 1922 to 1941 
 
 Year 
 
 
 
 ■ 
 
 
 United 
 
 United 
 
 Per capita 
 
 ivlay- 
 
 Total 
 
 Domestic 
 
 Domestic 
 
 Imports for 
 
 States 
 
 States 
 
 United States 
 
 October 
 
 shipments 
 
 exports 
 
 shipments 
 
 consumption 
 
 supply 
 
 population 
 
 supply 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 
 thousand 
 
 thousand 
 
 thousand 
 
 thousand 
 
 thousand 
 
 thousand 
 
 pounds 
 
 
 boxe s 
 
 boxes 
 
 boxes 
 
 boxes 
 
 boxes 
 
 persons 
 
 
 1922 
 
 2,425 
 
 78 
 
 2,347 
 
 931 
 
 3,278 
 
 109,873 
 
 2.27 
 
 1923 
 
 2,104 
 
 85 
 
 2,019 
 
 1,096 
 
 3,115 
 
 111,537 
 
 2,13 
 
 1924 
 
 3,335 
 
 118 
 
 3,217 
 
 468 
 
 3,685 
 
 113,202 
 
 2.48 
 
 1925 
 
 2,964 
 
 77 
 
 2,887 
 
 1,101 
 
 3,988 
 
 114,867 
 
 2.64 
 
 1926 
 
 3,442 
 
 160 
 
 3,282 
 
 743 
 
 4,025 
 
 116,532 
 
 2.63 
 
 1927 
 
 3,043 
 
 155 
 
 2,888 
 
 619 
 
 3,507 
 
 118,197 
 
 2.26 
 
 1928 
 
 3,16£ 
 
 131 
 
 3,031 
 
 464 
 
 3,495 
 
 119,862 
 
 2.22 
 
 1929 
 
 3,377 
 
 155 
 
 3,222 
 
 332 
 
 3,554 
 
 121,526 
 
 2.22 
 
 1930 
 
 3,437 
 
 104 
 
 3,333 
 
 549 
 
 3,882 
 
 123,077 
 
 2,40 
 
 1931 
 
 3,941 
 
 129 
 
 3,812 
 
 176 
 
 3,988 
 
 124,039 
 
 2.44 
 
 1932 
 
 3,167 
 
 95 
 
 3,072 
 
 47 
 
 3,119 
 
 124,840 
 
 1.90 
 
 1933 
 
 3,567 
 
 96 
 
 3,471 
 
 69 
 
 3,540 
 
 125,578 
 
 2.14 
 
 1934 
 
 4,180 
 
 140 
 
 4,040 
 
 15 
 
 4,055 
 
 126,373 
 
 2.44 
 
 1935 
 
 4,535 
 
 376 
 
 4,159 
 
 
 4,159 
 
 127,249 
 
 2.48 
 
 1936 
 
 4,576 
 
 302 
 
 4,274 
 
 39 
 
 4,313 
 
 128,052 
 
 2.56 
 
 1937 
 
 3,964 
 
 124 
 
 3,840 
 
 26 
 
 3,866 
 
 128,823 
 
 2.28 
 
 1938 
 
 4,915 
 
 570 
 
 4,345 
 
 
 4,345 
 
 129,823 
 
 2.55 
 
 1939 
 
 5,234 
 
 532 
 
 4,702 
 
 
 4,702 
 
 130,878 
 
 2.73 
 
 1940 
 
 4,857 
 
 252 
 
 4,605 
 
 
 4,605 
 
 131,954 
 
 2.66 
 
 1941 
 
 5.775 
 
 276 
 
 5.499 
 
 
 5.499 
 
 133.030* 
 
 3.14 
 
 * Estimated. 
 Sources of data: 
 
 Col. 1: Col. 8, table 19. 
 
 Col. 2: United States Department of Commerce. Monthly summary of foreign commerce of the 
 United States, monthly issues. 
 Cel., 3: Col, 1 minus col, 2.^ 
 
 Col. 4: United States Department of Commerce. Monthly summary of foreign commerce of the 
 
 United States, monthly issues. For 1922 through 1933: General imports minus exports of foreign 
 
 lemons; 1934 to date: Imports for consumption. Exports of foreign lemons for 1922 through 1925 
 
 and all import figures converted to boxes on basis of 76 pounds per box. / ,\ 
 
 *^ ° I' r (continued; 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . ■■ • 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ;' ■ * ■ . 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 f 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 » . . 
 
 \ 
 1 
 
 
 
 1* 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 t 
 
 
 
 
 
 
 
 • 
 
 
 
 
 
 1 
 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 • ■ • ■ ,; 
 
 
 ; 1 -. 
 
 
 
 
 I 
 { 
 
 
 
 
 
 
 
 ^ » 
 
 
 I 
 
 r .• 
 
 
 
 
 f 
 
 
 
 ; 1 
 
 * 1 
 
 ; ■ » . ■ 
 
 , ■ • ■ . . » . 
 
 . M V. 
 
 
 
 
 .. i 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i ' 
 
 1 ■ ■ '■ ■ 
 
 
 
 
 \ 
 
 
 
 \:"r 
 
 
 
 
 
 
 
 ... 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 f 
 
 
 
 
 
 = . • ». ..■ ,• ; / 
 
Table 18 continued 
 
 Sources of data: 
 
 Col» 5: Col, 3 plus col, 4. 
 
 Col, 6: Col, 4 of table 17. 
 
 Col, 7: Col, 5 divided by col. 6 and multiplied by 76 for conversion to pounds. 
 
TABLE 19 
 
 Industry Shipments of '"anter and Summer Lemons 
 for Fresh Consumption, 1921-22 to 1940-41 
 
 Year 
 
 l&£l-22 
 
 1922- 23 
 
 1923- 24 
 
 1924- 25 
 
 1925- 26 
 
 1926- 27 
 
 1927- 28 
 
 1928- 29 
 
 1929- 30 
 
 1930- 31 
 
 1931- 32 
 
 1932- 33 
 
 1933- 34 
 
 1934- 35 
 
 1935- 36 
 
 1936- 37 
 
 1937- 38 
 
 1938- 39 
 
 1939- 40 
 
 1940- 41 
 
 1941- 42 
 
 November- 
 
 Industry 
 rail and 
 
 boat 
 shipments 
 
 carlots 
 
 3,881 
 3,439 
 4,987 
 4,285 
 4,623 
 5,573 
 4,067 
 5,894 
 4,018 
 5,493 
 5,402 
 4,593 
 5,143 
 6,649 
 6,128 
 5,347 
 5,169 
 5,908 
 6,271 
 6,885 
 6.369 
 
 C.F.G.iii. 
 rail and 
 
 boat 
 shipments 
 
 April 
 
 carlots 
 
 3,368 
 
 3,224 
 
 4,579 
 
 3,879 
 
 4,287 
 
 4,479 
 
 3,735 
 
 5,169 
 
 3,636 
 
 4,685 
 
 4,397 
 
 4,060 
 
 4,513 
 
 5,294 
 
 5,242 
 
 4,803 
 
 4,534 
 
 4,784 
 
 5,000 
 
 5,260 
 
 5.544 
 
 C.F.G.E. 
 
 shipments 
 
 1.000 
 boxes 
 
 1,523 
 
 1,301 
 
 1,867 
 
 1,562 
 
 1,725 
 
 1,719 
 
 1»479 
 
 2,009 
 
 1,477 
 
 1,831 
 
 1,727 
 
 1,610 
 
 1,898 
 
 2,213 
 
 2,285 
 
 2,417 
 
 2,133 
 
 2,260 
 
 2,363 
 
 2,481 
 
 2.621 
 
 May-October 
 
 Sources of data: 
 
 Cols. 1, 
 Exchange and industry 
 Col. 3: 
 packed and loose fruit 
 estimated to be 2»86 p 
 
 
 Industry 
 
 C.F.G.E. 
 
 
 
 Total 
 
 rail and 
 
 rail and 
 
 C.F.G.E. 
 
 Total 
 
 industry 
 
 boat 
 
 boat 
 
 shipments 
 
 industry 
 
 shipments 
 
 shipments 
 
 shipments 
 
 
 shipments 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 1.000 
 
 carlots 
 
 carlots 
 
 1,000 
 
 1,000 
 
 boxes 
 
 
 
 boxes 
 
 boxes 
 
 1,756 
 
 5,751 
 
 4,922 
 
 2,076 
 
 2,425 
 
 1,388 
 
 5,215 
 
 4,972 
 
 2,006 
 
 ? 104. 
 
 2,034 
 
 7,954 
 
 6,819 
 
 2,859 
 
 
 1,726 
 
 7,306 
 
 6,750 
 
 2,738 
 
 
 1,860 
 
 8,771 
 
 8,007 
 
 3,143 
 
 
 2,139 
 
 7,641 
 
 6,860 
 
 2,732 
 
 
 1,610 
 
 8,224 
 
 7,617 
 
 2,928 
 
 w y X u c> 
 
 2,291 
 
 8,460 
 
 7,675 
 
 3,064 
 
 "^77 
 
 1,632 
 
 9,010 
 
 8,319 
 
 3,174 
 
 
 2,147 
 
 10,072 
 
 9,195 
 
 3,598 
 
 
 2,122 
 
 7,910 
 
 7,291 
 
 2,919 
 
 3,167 
 
 1,823 
 
 8,943 
 
 8,004 
 
 3,193 
 
 3,567 
 
 2,163 
 
 10,515 
 
 9,586 
 
 3,810 
 
 4,180 
 
 2,779 
 
 10,877 
 
 9,928 
 
 4,140 
 
 4,535 
 
 2,671 
 
 11,003 
 
 10,123 
 
 4,209 
 
 4,576 
 
 2,691 
 
 8,526 
 
 7,994 
 
 3,717 
 
 3, 964 
 
 2,433 
 
 10,753 
 
 9,793 
 
 4,476 
 
 4,915 
 
 2,790 
 
 11,173 
 
 10,107 
 
 4,734 
 
 5,234 
 
 2,964 
 
 10,215 
 
 8,907 
 
 4,235 
 
 4,857 
 
 3,247 
 
 12,554 
 
 11,067 
 
 5,091 
 
 5,775 
 
 3.011 
 
 10.546 
 
 9.494 
 
 4.376 
 
 4,861 
 
 2, 5, and 6: Reported by the railroads to the California Fruit Growers Exchange, 
 truck shipments are excluded. 
 
 From the records of the California Fruit Growers Exchange. Consists of shipments of 
 For 1921-22 through 1925-26 shipments of loose fruit not available, but were 
 er cent of packed shipments during those years. 
 
 (Continued on next page) 
 
 CO 
 
a-ble 19 continued: 
 
 Sources of data: 
 
 Col. 4: Col. 3 multiplied by col. 1 divided by col, 2. 
 
 V ^ ^ ?°"^* ''j. l^^ records of the California Fruit Growers Exchange. Consists of shipments of 
 
 packed and loose fruit. For 1922 through 1925, shipments of loose fruit not available, but were 
 estimated to be 3.02 per cent of packed shipments during those years. 
 
 Col. 8: Col. 7 multiplied by col, 5 divided by col. 6. 
 
 --3 
 
 O 
 
:■■ -f. 
 
TABLE 20 
 
 71 
 
 Winter Lemons: California Fruit Growers Exchange Domestic Shipments 
 and Outside Domestic Shipments, 1921-22 to 1940-41 I 
 
 Year 
 
 Domestic 
 
 C.F.G.E. 
 
 Estimated 
 
 C • F. G. E. 
 
 Outside 
 
 November- 
 
 shipments 
 
 shipments 
 
 C.F.G.E. 
 
 domestic 
 
 domesti» 
 
 April 
 
 
 
 exports 
 
 shipments 
 
 shipments 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 
 
 1,000 
 
 1,000 
 
 1,000 
 
 1,000 
 
 1,000 
 
 
 boxes 
 
 boxes 
 
 boxes 
 
 boxes 
 
 boxes 
 
 1921-22 
 
 1,641 
 
 1,523 
 
 100 
 
 1,423 
 
 215 
 
 i 
 
 1922-23 
 
 1,308 
 
 1,301 
 
 75 
 
 1,226 
 
 82 
 
 1923-24 
 
 1,911 
 
 1,867 
 
 113 
 
 1,754 
 
 157 
 
 1924-25 
 
 1,648 
 
 1,562 
 
 71 
 
 1,491 
 
 157 
 
 1925-26 
 
 1,750 
 
 1,725 
 
 102 
 
 1,623 
 
 127 
 
 1926-27 
 
 1,954 
 
 1,719 
 
 149 
 
 1,570 
 
 384 
 
 1927-28 
 
 1,517 
 
 1,479 
 
 86 
 
 1,393 
 
 124 
 
 1928-29 
 
 2,146 
 
 2,009 
 
 128 
 
 1,881 
 
 265 
 
 1929-30 
 
 1,558 
 
 1,477 
 
 67 
 
 1,410 
 
 148 
 
 1930-31 
 
 2,008 
 
 1,831 
 
 118 
 
 1,713 
 
 295 
 
 1931-32 
 
 1,984 
 
 1,727 
 
 112 
 
 1,615 
 
 369 
 
 1932-33 
 
 1,761 
 
 1,610 
 
 54 
 
 1,556 
 
 205 
 
 1933-34 
 
 2,073 
 
 1,898 
 
 78 
 
 1,820 
 
 253 
 
 1934-35 
 
 2,609 
 
 2,213 
 
 136 
 
 2,077 
 
 53J 
 
 > 
 
 1935-36 
 
 2,339 
 
 
 
 2,174 
 
 16 J 
 
 
 1936-37 
 
 2,559 
 
 
 
 2,393 
 
 16£ 
 
 
 1937-38 
 
 2,283 
 
 
 
 2,078 
 
 20{ 
 
 
 1938-39 
 
 2,491 
 
 
 
 2,143 
 
 34£ 
 
 i 
 
 1939-40 
 
 2,746 
 
 
 
 2,345 
 
 40] 
 
 [ ■ 
 
 1940-41 
 
 3,013 
 
 
 
 2,459 
 
 554 
 
 
 Sources of data: 
 
 Col. 1: Col. 3, table 17. 
 Col. 2: Col. 3, table 19. 
 
 Col. 3: Col. 2 of table 17 multiplied by the ratio of California 
 Fruit Growers Exchange rail and boat shipments of lemons to industry rail 
 and boat shipments as reported by the railroads to California Fruit Growers 
 Exchange • ^ 
 
 Col, 4: Through 1934-35, col. 2 minus col. 3; beginning 1935-36, 
 reported by the California Fruit Growers Exchange. 
 
 Col. 5: Col. 1 minus col« 4. 
 
351 
 
 3l i.o . 
 
TABLE 21 
 
 Summer Lemons: California Fruit Growers Exchange Domestic 
 Shipments and Outside Supply, 1922-1941 
 
 Year 
 
 
 
 Estimated 
 
 C.F.G.E. 
 
 
 
 
 Hay- 
 
 Domestic 
 
 C.F.G.E. 
 
 C.F.G.E. 
 
 domes t io 
 
 U w lUC a U X U 
 
 Outside 
 
 October 
 
 shipments 
 
 shipments 
 
 exports 
 
 shicmsnta 
 
 
 SUDPlv 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 c 
 
 
 6 
 
 
 1,000 
 
 1,000 
 
 1,000 
 
 1,000 
 
 
 1. 
 
 000 
 
 
 boxes 
 
 boxes 
 
 boxes 
 
 V V "V \^ 1^ 
 
 L/U AC? O 
 
 boxes 
 
 boxes 
 
 1922 
 
 ? ^4.7 
 
 C , \J*t t 
 
 9 n7fi 
 
 d7 
 
 2,009 
 
 338 
 
 
 269 
 
 1923 
 
 
 <c,UUd 
 
 81 
 
 1,925 
 
 94 
 
 1, 
 
 190 
 
 19?4 
 
 O f CI 1 
 
 
 101 
 
 2,758 
 
 459 
 
 
 927 
 
 1925 
 
 9 RH 7 
 
 C , / OO 
 
 71 
 
 2,667 
 
 220 
 
 1. 
 
 321 
 
 1926 
 
 % 9R9 
 O p CO c 
 
 
 146 
 
 2,997 
 
 285 
 
 
 028 
 
 1927 
 
 •L ^ C 1 
 
 9 RRft 
 
 
 139 
 
 2,593 
 
 295 
 
 
 914 
 
 1928 
 
 o , wo J. 
 
 9 Q 9(3 
 
 TOT 
 
 121 
 
 2,807 
 
 224 
 
 
 688 
 
 1929 
 
 3 999 
 
 O , UDrr 
 
 
 2,923 
 
 299 
 
 
 631 
 
 1930 
 
 3 33'^ 
 
 1 74. 
 
 ytj 
 
 3,078 
 
 255 
 
 
 804 
 
 1931 
 
 3 81? 
 
 
 1 J. / 
 
 3,481 
 
 331 
 
 
 507 
 
 1932 
 
 3 07? 
 
 9 Ql Q 
 
 Q 7 
 
 2,832 
 
 240 
 
 
 287 
 
 1933 
 
 3 471 
 
 3 1 Q"^ 
 
 0 , J.«70 
 
 OO 
 
 3, 107 
 
 364 
 
 433 
 
 1934 
 
 4,040 
 
 3,810 
 
 128 
 
 3,682 
 
 358 
 
 373 
 
 1935 
 
 4,159 
 
 4, 140 
 
 349 
 
 7 7Qfl 
 
 o , /yo 
 
 361 
 
 361 
 
 1936 
 
 4,274 
 
 
 
 4,078 
 
 196 
 
 235 
 
 1937 
 
 3,840 
 
 
 
 3,691 
 
 149 
 
 175 
 
 1938 
 
 4,345 
 
 
 
 4,133 
 
 212 
 
 212 
 
 1939 
 
 4,702 
 
 
 
 4,453 
 
 249 
 
 249 
 
 1940 
 
 4,605 
 
 
 
 4,217 
 
 388 
 
 388 
 
 1941 
 
 5,499 
 
 
 
 5,070 
 
 429 
 
 429 
 
 Sources of data: 
 
 Col. 1: Col. 3, table 18. 
 
 Col. 2: Col. 7, table 19, 
 
 Col. 3: Col. 2 of table 18 multiplied by the ratio of California Fruit 
 Growers Exchange rail and boat shipments of lemons to industry rail and boat 
 shipments as reported by the railroads to the California Fruit Growers Exchange, 
 
 Col. 4: Through 1935, Col. 2 minus col. 3; beginning 1936^ reported by 
 the California Fruit Growers Exchange. 
 
 Col. 5: Col. 1 minus col. 4. 
 
 Col. 6: Col. 5 plus col. 4 of table 18. 
 
73. 
 
 The domestic shipments of ^idnter lemons by the California Fruit Growers 
 Exchange and by all other handlers are given in table 20. Similar data for summer 
 lemons are recorded in table 21, For years prior to 1935-36, shipment figures 
 entered in the permanent records of the Exchange include exports. Exchange exports 
 for the period 1921-22 to 1934-35 were estimated by adjusting industry export fig- 
 ures by the ratio of Exchange rail and boat shipments to industry rail and boat 
 shipments. This adjustment is based on the assumption that the ratio of Exohange 
 exports to Exohange shipments is the same as the ratio of exports by other handlers 
 of California and Arizona lemons to their total shipments. 
 
 The Income Series .-- In table 22 are given indexes of nonagri cultural income 
 payments based on data published by the United States Department of Agriculture, 
 The entries in this table are simple averages of the monthly indexes for the six- 
 month periods November through April and May through October. ^2/ It should, 
 perhaps, be noted here that for the years prior to 1929 the index is based on 
 W, I, King's and the Brookings Institution estimates, and since 1929 on United 
 States Department of Commerce estimates of income payments. j 
 
 At least two criticisms may be offered of the use of the index of nonagricul- 
 tural income payments as a measure of consumer purchasing pov/er. Since lemons are 
 produced by a small proportion of the total number of farmers, total income pay- 
 ments would be a more suitable measure of consumer purchasing power than non- 
 agricultural income payments. However, a still more suitable index would be one 
 based on total income payments from which necessitous expenditures have been 
 
 — ' A description of this index is given in: Bean, L, H,, P, H. Bollinger, and 
 0, V. Wells. Nonagri cultural income as a measure of dcsnestic demand. 45p, U.S. 
 Agr. Adjust, Aimin. June 1937. 
 
 51/ 
 
 — ■/ The entire series prior to 1929 is published in Leven, Maurice, Harold G. 
 Moulton, and Clark ViTarburton, America's capacity to consume, p, 152. The Brook- 
 ings Institution, V/ashington, D.C., 1934. 
 
"soflimws, tot 
 
 # - 
 
 '■ ■' '-^l o^rr - ■ ■ 
 
TABLE 22 
 
 Indexes of Total and Per Capita Nonagricultural Income Payments 
 in the United States, 1921-22 to 1940-41 
 
 74. 
 
 Year 
 
 1921- 22 
 
 1922- 23 
 
 1923- 24 
 
 1924- 25 
 
 1925- 26 
 
 1926- 27 
 
 1927- 28 
 
 1928- 29 
 
 1929- 30 
 
 1930- 31 
 
 1931- 32 
 
 1932- 33 
 
 1933- 34 
 
 1934- 35 
 
 1935- 36 
 
 1936- 37 
 
 1937- 38 
 
 1938- 39 
 
 1939- 40 
 
 1940- 41 
 
 Nonagricultural income 
 payments 
 
 November- April 
 1925-29 = 100 
 1 
 
 71 
 83 
 92 
 93 
 100 
 102 
 102 
 106 
 105 
 91 
 75 
 61 
 69 
 74 
 82 
 93 
 88 
 90 
 97 
 109 
 
 May-October 
 1935-39 = 100 
 
 88 
 100 
 101 
 110 
 113 
 116 
 119 
 123 
 111 
 96 
 74 
 71 
 81 
 87 
 104 
 108 
 99 
 107 
 114 
 135 
 
 Index of 
 nonfarm 
 population 
 1922 = 100 
 
 Per capita nonagricultural 
 income payments 
 
 100 
 
 103 
 
 105 
 
 107 
 
 110 
 
 112 
 
 114 
 
 116 
 
 118 
 
 119 
 
 119 
 
 120 
 
 121 
 
 122 
 
 123 
 
 124 
 
 125 
 
 126 
 
 127* 
 
 128* 
 
 November- 
 April 
 
 71 
 
 81 
 
 88 
 
 87 
 
 91 
 
 91 
 
 89 
 
 91 
 
 89 
 
 76 
 
 63 
 
 51 
 
 57 
 
 61 
 
 67 
 
 75 
 
 70 
 
 71 
 
 76 
 
 85 
 
 May- 
 October 
 
 88 
 97 
 96 
 103 
 103 
 104 
 104 
 106 
 94 
 81 
 62 
 69 
 
 Vi 
 
 85 
 87 
 79 
 85 
 90 
 105 
 
 ♦Estimated. 
 
 Sources of data: i 
 
 Col. 1: 1921 to May, 1941: United States Bureau of Agricultural 
 Economics. Nonagricultural income payments. United States, 1919 to date. 2p* 
 T/ashington, D. C, July 21, 1941. (Mimeo.) June, 1941 on: United States 
 Department of Commerce. Survey of Current Business, monthly issues, adjusted 
 by 88.105 per cent. Figures are simple averages of seasonally corrected 
 monthly indexes. Loans and payments to World V/ar veterans on their adjusted 
 service certificates in 1931 and 1936 are excluded. In the other years veteran 
 bonus payments were of little significance. 
 
 Col. 2: United States Bureau of Agricultural Economics. Nonagricul- 
 tural income payments. United States, 1909-41. 2p. Y^ashington, D. C. Feb- 
 ruary 2, 1942. Figures are simple averages of seasonally corrected monthly 
 indexes. Loans and payments to Y.'orld lYar veterans on their adjusted service 
 certificates in 1931 and 1936 are excluded. 
 
 Col. 3: Col. 4 of table 17 minus estimates of farm population given 
 in: United States Bureau of Agricultural Economics. Farm population estimates. 
 Released July, 1940. (Mimeo.) Adjusted as of July 1 of each year. 
 
 Col. 4: Col. 1 divided by col. 3, 
 
 Col. 5: Col. 2 divided by col. 3 
 
' " / - < ■. ■ 
 
 . : ■■■■■■■■ - '■ - ■ ' 
 
 i ; ■ ■ . ■ 
 
75. 
 
 subtracted. The demand for most consumer goods, one would suppose, is affected not 
 so much by total income payments as by the amount of freely disposable income avail- 
 able to the consumers. 
 
 At the time the calculations reported in this paper were made, estimates 
 of total income payments on other than calendar year basis were not available for 
 years prior to 1929, Later, total income payments for November-April and May- 
 October of each year were estimated by the senior author for use in another demand 
 study. Estimates of disposable income were also prepared by subtracting, from total 
 income payments to individuals, necessitous living expenditures, medical expenditures, 
 and selected federal taxes, Ylhile the three indexes ~ namely, nonagrioultural 
 income payments, total income payments to individuals, and disposable income — 
 exhibited some differences, their year-to-year fluctuations were strikingly similar. 
 The correlations betvreen the three November-April indexes for the period 1922-23 
 through 1939-40 were r^^ = ,992, r^^ = ,984, and r^^ = ,996; the correlations for 
 May-October were r^^ = ,991, r^^ = .984, and r^^ = ,998 (a » nonagrioultural income 
 payments, b = total income payments, o = residual income). In view of the magnitude 
 of these correlations it is doubtful that extensive recalculations were warranted. 
 
 Indexes of Summer and Winter Temperatures ,— The construction of a tempera- 
 ture index raises a number of troublesome questions. What should be the basic unit 
 of time in which temperatures are to be collected? Should mean, maximum or minimum 
 temperatures be used? For what localities should temperatures be recorded? Should 
 actual temperatures, departures from normal in a given area, or departures from some 
 arbitrary level constant for all localities be calculated? Eavr should temperatures 
 be combined? Extensive trial may supply appropriate answers to all of these ques- 
 tions, but extensive trial is time-consuming. Practical considerations make it 
 impossible to avoid arbitrariness in the construction of the index. 
 
 The index of summer temperatures constructed for this study consists, for 
 each of the twenty six-month periods, of the sum of weighted daily positive depart- 
 ures of maximum temperatures from 80° Fahrenheit in 39 metropolitan areas (see 
 
■;J\r \'C \fjf ^r; fV^j. 
 
76, 
 
 table 23), Population weights were used in calculating the daily weighted means. 
 
 In order to insure a satisfactory degree of sensitiveness to the index, it 
 appeared advisable to employ as its basic component daily maximum temperatures. 
 Considering the intended use of this variable, it is clear that a geographically 
 representative measure of temperature would not be particularly suitable. Rather 
 an index which summarized temperature conditions in the densely populated areas of 
 this country was required. This led to a consideration of metropolitan districts as 
 areas for which temperature data should be secured. The 39 metropolitan districts 
 selected were the urban centers largest in population. The exclusion of pre- 
 dominantly rural areas is open to criticism, since the available evidence suggests 
 that the per-oapita consumption of lemons in rural areas is nearly on par with the 
 per-capita oonsumptiom in urban districts, ^ The geographical extensiveness of 
 rural regions, however, has precluded their inclusion in the index. 
 
 It is likely that the relation between temperature and consumption of cold 
 drinks has a lower bound within the range of observed temperatures; below a certain 
 point changes in temperature fail to have a measvirable effect on the consumption of 
 cold drinks. This consideration suggests the use of positi-ve departures of maximum 
 temperatures from some level. For this purpose a constant reference point, namely 
 80° Fahrenheit, was employed for all districts and for all days. The use of a 
 changing reference level, such as the "normal" maximum temperature in a certain 
 district for a given day, would have partialled out the effect of differences 
 between the general levels of temperature in the various metropolitan areas. It 
 appeared desirable, however, that the index in part reflect such differences. The 
 selection of 80° Fahrenheit as the reference level is, of course, arbitrary, but 
 the use of any other reference point, provided that it was not extreme, would have, 
 in all likelihood, given approximately the same results, 
 
 52/ 
 
 — ' Annual report of the general manager of the California Fruit Growers Exchange 
 for 1937, 36p, 
 
"i''-'^:^'"" ^-i^^-' •'ir'^jw: c civ ■ 
 
 fit ::-iv;4:o ■, 'rt: 
 
 •> 'Tf^ ;• jfV.^!- ii-; t;,.'!. T. '.1 I; .i ' C V'' '■ 
 
 I: - 
 
 .0 Ci 
 
TABLE 23 
 
 Indexes of ViTinter and Summer Temperatures 
 1921-22 to 1940-41 
 
 77. 
 
 Year 
 
 Index of temperatures 
 
 Year 
 
 Index of temperature 
 
 5S 
 
 December- 
 February * 
 
 May- 
 October f 
 
 December- 
 February * 
 
 I'iay- 
 
 October f 
 
 
 1 
 
 2 
 
 ■ — — — ~— — 
 
 3 
 
 4 
 
 
 
 per cent 
 
 per cent 
 
 
 per cent 
 
 per "cent 
 
 
 81 
 
 100 
 
 1931-32 
 
 100 
 
 lie 
 
 ) 
 
 
 78 
 
 92 
 
 1932-33 
 
 91 
 
 136 
 
 
 T 
 
 85 
 
 80 
 
 1933-34 
 
 76 
 
 142 
 
 
 X ^ c c 0 
 
 82 
 
 120 
 
 1934-35 
 
 79 
 
 106 
 
 
 
 80 
 
 88 
 
 1935-36 
 
 67 
 
 151 
 
 
 1926-27 
 
 82 
 
 75 
 
 1936-37 
 
 90 
 
 127 
 
 
 1927-28 
 
 84 
 
 89 
 
 1937-38 
 
 84 
 
 115 
 
 
 1928-29 
 
 81 
 
 105 
 
 1938-39 
 
 87 
 
 140 
 
 
 1929-30 
 
 86 
 
 138 
 
 1939-40 
 
 77 
 
 106 
 
 
 1930-31 
 
 87 
 
 150 
 
 1840-41 
 
 83 
 
 145 
 
 
 * 1931-32 =100. 
 t 1922 = 100, 
 Sources of data: 
 
 Cols. 1 and 5: United States Weather Bureau, Climatic Summary of the 
 United States, United States Meteorological Yearbook and Climatological 
 Data for the United States by sections. Monthly mean temperatures December 
 through February in 32 cities vreighted by the population in the correspond- 
 ing metropolitan districts. The weights employed are given in table 24, 
 
 Cols, 2 and 4: United States Weather Bureau, Climatological Data for the 
 United States by sections. Positive departures of daily maximum tempera- 
 tures in 39 cities from 80°, May through October, vreighted by the population 
 
 in the corresponding metropolitan districts. The vreights employed are given 
 in table 24. 
 

 
 
 
 
 
 ^ :. . ■ 
 
 
 
 
 
 ■ ( 
 
 
 
 
 
 •.: : ■■ • 
 
 
 
 ... 
 
 .... — I 
 
 
 
 
 
 ; 
 
 
 
 
 
 
 
 
 
 
 
 
 • 
 
 ; i 
 
 . . • \ 
 
 ■ 1 
 
 i 
 
 
 
 
 : 
 
 
 
 ; 
 
 
 
 
 
 
 1 
 
 
 
 
 
 . : 
 
 
 
 
 „-,.. 
 
 
 
 
 
 
 '■■■>.;** ' " ; 
 
 ! I 
 
 
 
 '. 
 
 
 
 
 
 
 i 
 
 \ . 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 ■ 
 
 
 '■■u 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 ... 
 
 ■; . • - .- 
 
 
 
 
 
 
 
 ■Hii. 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 t .. . 
 
 i :..f 
 
 1 
 
 
 
 
 
 
 
 
 
 
 JLc-; . - .r;iJCE v 
 
 . V.,- i,i !f ji-JXl 
 
78. 
 
 On© other item requires mention in connection with the construction of the 
 index, namely the weights employed in the calculation of the daily means. As was 
 indicated previously, the positive departures of maximum temperatures from 80° 
 Fahrenheit in each of the 39 metropolitan districts were weighted by the population 
 in the district. For this purpose the population figures from the censuses of 1920, 
 1930, and 1940 were employed as weights for periods 1922 through 1925, 1926 through 
 1934, and 1935 through 1941 respectively (see table 24), The use of the three sets 
 of weights was deemed sufficient to account for the relative shifts of populations 
 in -ttiese areas. 
 
 Other weights, such as average unloads of lemons in each of the metropolitan 
 
 55/ 
 
 districts — ' or even income figures for each area, might have been employed in 
 place of the weights we have used, or in conjunction with them. The weighting 
 employed is based on the simple hypothesis that, at each level of temperature, 
 consumption of cold drinks is a single-valued monotonically increasing function of 
 the number of persons exposed to the temperature. The weighting disregards possible 
 regional differences in lemon consumption, but it is doubtful that there is marked 
 regional variation in the use of lemons in cold drinks, ^ If simple rather than 
 composite weighting is to be employed, weights based on population appeared to be 
 superior to other feasible types of weights, | 
 
 The index of temperatures employed in the analysis of demand for winter 
 lemons is based on mean temperatures during December, January, and February in 32 
 metropolitan districts. The weighted mean temperature for each of the three months 
 
 5^ 
 5y 
 
 See appendix E for the use of average unloads as weights. 
 
 The data in table 1 suggest the existence of at least one regional difference 
 in consumption of lemons, namely that between the southeastern region of the United 
 States and other regions considered in the Study of Consumer Purchases, The data 
 reported in table 1 were secured during the months May through August of 1936, 
 Analogous data secured during the months September through November, certainly a 
 cooler period, reveal about the same difference between lemon consumption in the 
 southeast and in the other regions. Thus it is not clear that this regional differ- 
 tial is related to the use of lemons in thirst-quenching beverages. ; 
 
©or 
 
 .■^rl> yj 
 
 .as! iioqoad-sm erirf lo liom 
 
 't'.; lie. i'tfc'.'^'' 
 
 Ji) 8.;. V 
 
 '! i ' ■ 
 
 >,..j%- n.i. nt: 
 
TABLE 24 
 
 Population Weights Employed in the Construction of Indexes 
 of Summer and Winter Temperatures 
 
 Metropolitan districts 
 
 Mi 
 
 ay-October ii 
 
 idex 
 
 Decernber-Ffthrnqrv inrio^ 
 
 1922 
 through 
 1925 
 
 1926 
 through 
 1934' 
 
 1935 
 through 
 1941 
 
 1921-22 
 through 
 1924-25 
 
 1925-26 
 through 
 1933-34 
 
 1935-36 
 through 
 1940-41 
 
 Albany - Schenectady - Troy, N. Y. 
 
 Atlanta, Georgia 
 
 Baltimore, Maryland 
 
 Birmingham, Alabama 
 
 Boston, Massachusetts 
 
 Buffalo, New York 
 
 Chicago, Illinois 
 
 Cincinnati, Ohio 
 
 Cleveland, Ohio 
 
 Columbus, Ohio 
 
 Dallas, Texas i 
 
 Denver, Colorado 
 
 Detroit, Michigan 
 
 Hartford, Connecticut 
 
 Houston, Texas 
 
 Indianapolis, Indiana 
 
 Kansas City (Kansas, Missouri) 
 
 Los Angeles, California 
 
 Louisville, Kentucky 
 
 Memphis, Tennessee 
 
 Milwaukee, 'Aisconsin 
 
 Minneapolis - St, Paul, Minnesota 
 
 New Orleans, Louisiana 
 
 New York - Northeastern New Jersey 
 
 Oklahoma City, Oklah.oma 
 
 Omaha, Neb, - Council Bluffs, Iowa 
 
 Philadelphia, Pennsylvania 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 .011 
 
 .008 
 
 ,024 
 
 .008 
 
 .058 
 
 .019 
 
 .095 
 
 .018 
 
 ,027 
 
 .008 
 
 ,006 
 
 .008 
 
 .036 
 
 .011 
 
 .005 
 
 .010 
 
 .014 
 
 .031 
 
 .010 
 
 .005 
 
 .016 
 
 .020 
 
 .012 
 
 .247 
 
 .003 
 
 .007 
 
 .010 
 .008 
 .021 
 .009 
 .052 
 .018 
 .098 
 .017 
 .027 
 .008 
 .007 
 .007 
 .047 
 .011 
 .008 
 .009 
 .014 
 .052 
 .009 
 .006 
 7 
 
 .019 
 .011 
 .245 
 .005 
 .006 
 
 .009 
 
 .009 
 
 .022 
 
 .009 
 
 .049 
 
 .018 
 
 .094 
 
 .016 
 
 .025 
 
 .008 
 
 .008 
 
 .008 
 
 .048 
 
 .010 
 
 .011 
 
 .009 
 
 .013 
 
 .061 
 
 .009 
 
 .007 
 
 • UXO 
 
 .019 
 .011 
 .244 
 .005 
 .006 
 
 .012 
 
 .026 
 
 .064 
 .022 
 .105 
 .020 
 .030 
 .009 
 
 .009 
 .040 
 .012 
 
 .011 
 .015 
 
 .011 
 .006 
 .018 
 .022 
 
 .273 
 .003 
 .008 
 
 .011 
 
 .024 
 
 .059 
 .021 
 .112 
 .019 
 .031 
 .009 
 
 .008 
 .054 
 .012 
 
 .011 
 .016 
 
 .010 
 .007 
 ,019 
 ,021 
 
 ,279 
 .005 
 .007 
 
 .011 
 
 .025 
 
 .057 
 .021 
 .109 
 .019 
 .029 
 .009 
 
 .009 
 .056 
 .012 
 
 .011 
 .015 
 
 .011 
 .008 
 .019 
 .022 
 
 .283 
 .005 
 .007 
 
 Pittsburgh, Pennsylvania 
 Portland, Oregon 
 
 fOTl 
 ,049 
 .009 
 
 v664 
 .044 
 .009 
 
 .060 
 
 .042 
 .008 
 
 .079 
 .055 
 .010 
 
 .073 
 .050 
 .010 
 
 .070 
 .048 
 .010 
 
 Providence. Rhode Island 
 
 .025 1 .022 
 
 .021 
 
 .028 
 
 .025 
 
 .024 
 
 (Continued on next page) 
 
I 
 
 V- ■ 
 
 ':;!■: 
 
 ■ . V 
 
 i 
 
 i 
 
 
 ' ■■ T^: •" " 1 ; ;'" .■ - "' ' 
 .1 ' ■ 
 
 \r:: i. 
 
 ■ : ! 
 
 
 
 
Table 24 continued. 
 
 
 May- 
 
 October index 
 
 December-February index 
 
 
 1922 
 
 1926 
 
 1935 
 
 1921-22 
 
 1925-26 
 
 
 Metropolitan districts 
 
 through 
 
 through 
 
 through 
 
 throuffh 
 
 V 1 11 LI E^l 1 
 
 + Vi y*A 1 1 crVi 
 
 
 1925 
 
 1934 
 
 1941 
 
 1924-25 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 
 Richmond, Virginia 
 
 ,006 
 
 .005 
 
 .005 
 
 .006 
 
 .006 
 
 .006 
 
 Rochester, New York 
 
 .010 
 
 .009 
 
 .009 
 
 -0] 1 
 
 ♦ \JJ. -1. 
 
 m n 
 
 
 St, Louis, Missouri 
 
 .031 
 
 .029 
 
 .029 
 
 .034 
 
 .033 
 
 .033 
 
 Salt Lake City, Utah 
 
 .004 
 
 .004 
 
 .004 
 
 .005 
 
 .005 
 
 .005 
 
 San Francisco - Oakland, California 
 
 .028 
 
 .029 
 
 .030 
 
 
 
 
 Scranton - Wilkes Barre, Pa, 
 
 .017 
 
 .015 
 
 .013 
 
 .019 
 
 .017 
 
 ;oi5 
 
 Seattle, Washington 
 
 .010 
 
 .009 
 
 .009 
 
 .011 
 
 .011 
 
 .011 
 
 Toledo, Ohio 
 
 .008 
 
 .008 
 
 .007 
 
 .009 
 
 .009 
 
 .008 
 
 Washington, D,C, 
 
 .015 
 
 .014 
 
 .019 
 
 .017 
 
 .016 
 
 .022 
 
 Total population 
 
 34,489,191 
 
 44,519,745 
 
 47,950,608 
 
 31,144,016 
 
 39,009,662 
 
 41,340,367 
 
 Sources of data: 
 
 Cols, 1 and 4: Population figures for 1920 from United States Bureau of the Census, Fifteenth Census of 
 the United States, 1930. Metropolitan Districts, Population and Area, Govt. Print. Off., '.'ashington, 1932, 
 expressed as ratios of the total population in the cited metropolitan districts. 
 
 Cols, 2, 3, 5, and 6: Population figures for 1930 and 1940 from United States Bureau of the Census, 
 Sixteenth Census of the United States, 1940, Population, first series. Number of Inhabitants, United States 
 Suratnary. Govt. Print. Off,, Washington, 1941, expressed as ratios of the total population in the cited metro- 
 politan districts. 
 
 CO 
 
 o 
 
1 
 
 h{ 
 
 4 
 
 
 
 
 
 '■■ . I \ ' r" 
 
 
 
 i 
 
 
 1 
 
 . ■ ; i 
 
 
 
 
 : -'t » ■ i.- . '. 
 
 i 
 
 
 
 i 
 
 I 
 
 / 
 
 ♦ i 
 
 • ■ • ■ , ■' 
 
 * 
 
 • ■- 
 
 i 
 
 1 ' 
 
 
 
 
 : i- 
 
 .• J - , ..' 
 1 .1- ' ■■ 
 
 ! 
 
 ; 
 
 » ■ . I - ' . 
 
 ' : 
 
 t. 
 
 1 
 
 • , 
 
 
 
 
 r-v— ' i 
 
 
 - . t 
 
 ! 
 
 t 
 
 
 i 
 
 I' 
 
 ; 
 
 — - i 
 
 — j 
 t 
 
 
 
 
 
 
 
 
 
 
81. 
 
 was obtained by weighting the mean monthly temperatxires in the 82 districts by the 
 population in each district. As before, three different sets of population figures 
 were employed, based on the 1920, 1930, and 1940 population counts and applied 
 respectively to the periods 1921-22 through 1924-25, 1925-26 tlirough 1933-34, and 
 1934-35 through 1940-41 (see table 24). The final figure for each year is the sum 
 of the weighted mean temperatures in December, January, and February adjusted for 
 the difference in the number of days in these months. j 
 
 Index of Influenza .— The index of influenza given in table 25 is based on 
 the incidence of influenza statistics reported by the various state health boards to 
 the United States Public Health Service. Considerable caution must be exercised in 
 the use of this index. Incidence of influenza figures are far from complete for 
 even the most recent years. Not all of the states have or are reporting nonfatal 
 cases of influenza and, for states which do report, varous degrees of underreport- 
 ing are to be expected. | 
 
 The index was constructed by calculating the link relatives of the incidences 
 for states reporting influenza in two successive years. The nvnnber of states on 
 which the relatives are based varied, of course, from year to year. An alternative 
 procedure would have been to base the index on a constant sample of states, that 
 is, on states that have reported for each year of the period under reviev^. It is 
 felt that the first procedure yields a more reliable index since it utilizes a 
 larger number of reports. However, an index based on data secured from states 
 •vrfiioh have reported influenza cases throughout the period showed excellent agree- 
 ment with the index reported in table 25. The major difference between the two 
 indexes was the greater magnitude for epidemic years of the values of the iniex 
 based on a constant number of states. 
 
 i 
 
.. . ■ • ' ; ; • \ ■ ■ ■' - ■ ' 
 
 ■. -t ,,tbf.'' 
 
TABLE 25 
 
 82 
 
 Index of the Incidence of Influenza, 1921-22 to 1940-41 
 
 Year, 
 November- 
 April 
 
 Index of 
 incidence of 
 influenza 
 
 Year, 
 November- 
 April 
 
 Index of 
 incidencfi of 
 influenza 
 
 
 per cent 
 
 
 per cent 
 
 1921-22 
 
 64 
 
 1931-32 
 
 21 
 
 1922-23 
 
 100 
 
 1932-33 
 
 90 
 
 1923-24 
 
 15 
 
 1933-34 
 
 13 
 
 1924-25 
 
 44 
 
 1934-35 
 
 28 
 
 1925-26 
 
 64 
 
 1935-36 
 
 38 
 
 1926-27 
 
 21 
 
 1936-37 
 
 
 1927-28 
 
 24 
 
 1937-38 
 
 15 
 
 1928-29 
 
 176 
 
 1938-39 
 
 33 
 
 1929-30 
 
 12 
 
 1939-40 
 
 44 
 
 1930-31 
 
 26 
 
 1940-41 
 
 162 
 
 Source of data: 
 
 United States Public Health Service, Public Health 
 Reports. The figures are link relatives reduced to 1922-23 
 base* 
 
83, 
 
 APPENDIX B 
 
 Price and Quantity Residuals and 
 Tests of Randomness 
 
i 
 
TABLE 26 
 
 Summer Lemons: Price and Quantity Residuals 
 
 84* 
 
 Year 
 
 Equation 
 
 
 Mav- 
 
 October 
 
 Is 
 
 2s 
 
 3s 
 
 4s 
 
 5s 
 
 6s 
 
 7s 
 
 8s 
 
 9s 
 
 
 10s 
 
 
 
 10 000 
 
 
 
 
 
 
 in onn 
 
 Uu J. XUFB 
 
 
 10,000 
 
 
 
 boxes 
 
 
 
 
 
 
 boxes 
 
 
 boxes 
 
 
 0,12 
 
 3 
 
 0,23 
 
 0,04 
 
 0,005 
 
 -0,002 
 
 0,03 
 
 4 
 
 0,06 
 
 
 4 
 
 
 0,24 
 
 3 
 
 0,16 
 
 0,00 
 
 -0,004 
 
 *0,012 
 
 0,15 
 
 4 
 
 0.20 
 
 
 4 
 
 
 -0,79 
 
 -28 
 
 -0,65 
 
 -0.12 
 
 -0,099 
 
 »-0»034 
 
 -0,78 
 
 -27 
 
 -0,81 
 
 
 -28 
 
 T Q o r 
 
 0,48 
 
 18 
 
 0,64 
 
 0,15 
 
 0,059 
 
 0.022 
 
 0,32 
 
 20 
 
 0,40 
 
 
 20 
 
 
 -0,37 
 
 -11 
 
 -0,22 
 
 -0,01 
 
 -0,021 
 
 -0,002 
 
 -0.44 
 
 -10 
 
 -0,40 
 
 
 -10 
 
 TOOT 
 
 0.45 
 
 17 
 
 0.37 
 
 0.07 
 
 0,061 
 
 0,022 
 
 0.49 
 
 17 
 
 0,46 
 
 
 17 
 
 
 -0,12 
 
 -10 
 
 -0.18 
 
 -0,07 
 
 -0,001 
 
 -0,007 
 
 -0.05 
 
 -11 
 
 -0,08 
 
 
 -11 
 
 
 -0,14 
 
 -15 
 
 -0,23 
 
 -0,10 
 
 -0.012 
 
 -0.015 
 
 -0.05 
 
 -16 
 
 -0.10 
 
 
 -16 
 
 lyou 
 
 -0.04 
 
 -10 
 
 -0.04 
 
 -0.03 
 
 -0.007 
 
 -0.012 
 
 -0.08 
 
 -9 
 
 -0.07 
 
 
 -9 
 
 iyol 
 
 -0.17 
 
 -12 
 
 -0.09 
 
 -0.04 
 
 -0.016 
 
 -0.012 
 
 -0.17 
 
 -11 
 
 -0,18 
 
 
 -11 
 
 iyo<: 
 
 0,07 
 
 0 
 
 0.00 
 
 -0.03 
 
 -0.001 
 
 -0.005 
 
 0.15 
 
 -1 
 
 0,12 
 
 
 -2 
 
 1933 
 
 -0,48 
 
 -21 
 
 -0.46 
 
 -0.12 
 
 -0.040 
 
 -0.017 
 
 -0.47 
 
 -21 
 
 -0,48 
 
 
 -21 
 
 19o4 
 
 0,22 
 
 12 
 
 0.27 
 
 0.07 
 
 0.034 
 
 0.017 
 
 0.22 
 
 12 
 
 0,21 
 
 
 12 
 
 1 Q C 
 
 0,71 
 
 39 
 
 0.71 
 
 0.21 
 
 0,085 
 
 0,046 
 
 0.74 
 
 39 
 
 0.73 
 
 
 39 
 
 i90D 
 
 0.11 
 
 3 
 
 0,11 
 
 0.01 
 
 0,016 
 
 0.004 
 
 0,13 
 
 2 
 
 0,13 
 
 
 2 
 
 1937 
 
 0.06 
 
 -2 
 
 -0.03 
 
 -0.04 
 
 0.011 
 
 -0.001 
 
 0,15 
 
 -3 
 
 0.12 
 
 
 -4 
 
 1938 
 
 -0.21 
 
 -1 
 
 -0,25 
 
 -0.02 
 
 -0.034 
 
 -0.004 
 
 -0.17 
 
 -1 
 
 -0.17 
 
 
 -2 
 
 1939 
 
 -0.25 
 
 -5 
 
 -0.31 
 
 -0.04 
 
 -0,036 
 
 -0.001 
 
 -0.25 
 
 -5 
 
 -0.24 
 
 
 -5 
 
 1940 
 
 0.08 
 
 13 
 
 -0.06 
 
 0.03 
 
 0.010 
 
 0.015 
 
 0.13 
 
 12 
 
 0.10 
 
 
 12 
 
 1941 
 
 0.02 
 
 10 
 
 -0.06 
 
 0.04 
 
 -0.012 
 
 0.004 
 
 0.01 
 
 10 
 
 0.00 
 
 
 10 
 
 Sourfce of data: Derived from equations Is through 10s of tables 3 and 6 
 applied to data given in table 2, 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 *f • -i 
 
 — "T 
 
 
 
 
 
 
 
 
 
 
 
 
 " i 
 
 
 
 
 
 
 * 
 
 
 
 
 ... — j,. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ■ » 
 
 
 1 i 
 
 i 
 
 1 
 
 
 
 
 
 
 
 .i 
 
 .0 i 
 
 
 
 
 1 
 
 
 
 
 
 • .' f ' ' 
 
 f 
 
 ■ 
 
 ■• 
 
 « i ; 
 
 
 
 
 
 
 - 
 
 
 
 
 '}•■'■'■ 
 
 
 1 
 
 
 
 
 
 
 
 
 
 • 
 
 
 i; • 
 
 ^';>*' 
 
 ;, 
 
 
 
 ■ • ■■■ J 
 
 • 
 
 
 
 
 - 
 
 
 
 : ^ *J ■ ■ ■-' 
 
 *; 
 
 r 
 
 
 r 
 
 
 
 
 
 
 
 ; 
 
 
 1 
 
 ■ ■ ■• ; . I: 
 
 ,■ 
 
 i 
 
 
 n ■ 
 
 ?.-<SX-', 
 
 
 
 ; 
 
 
 
 
 
 . 
 
 
 - 
 
 
 , ; . » ■ 
 
 
 - 
 
 
 
 
 
 
 
 ! ■' 
 
 
 
 
 
 
 
 
 
 4 
 
 
 
 * ' / - 
 
 ; , ! ' 
 
 ( i • 
 
 * 
 
 
 
 1 it'. 
 
 
 
 
 
 
 
 : ' f '. ■ 
 
 ■ 
 
 *.,Vf. C 
 
 i 
 
 ' ■>■ ^» ' ■ 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 • 
 
 ; 
 
 ■* N;. ^. • 
 i' 
 
 .•lv.;o • 
 
 \'i ■ 
 
 
 
 
 
 
 
 
 
 (■;«■;■ 
 
 ( 
 
 t 
 
 
 
 ' T t 
 
 
 
 
 
 
 
 
 
 f . 
 
 
 
 ■ 'N 
 
 
 i 
 
 * 
 
 -■ 
 
 
 
 
 
 
 ■ ■ (• 
 
 
 
 i 
 
 •• 
 
 ' 
 
 
 
 
 
 
 
 
 
 vi-i-i .•".)( 
 
 ! , 
 
 • 
 
 .1^.0. ■ 
 
 
 
 
 
 
 
 
 
 
 I 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 < 
 
 
 
 
 
 
TABLE 27 
 
 Summer Lemons: Tests of Randomness of Residuals 
 
 Eauation 
 
 Lagged oo- 
 
 * W J» cat V.f>^Ai 
 
 coefficient 
 
 Wallis and Moore test 
 
 2 
 
 
 
 1 
 
 2 
 
 3 
 
 Is 
 
 -0.3563 
 
 0.816 
 
 0,70 
 
 2s 
 
 -0.0706 
 
 3,149 
 
 0.26 
 
 3s 
 
 -0.2349 
 
 0,298 
 
 0.88 
 
 4s 
 
 0,3848 
 
 1.502 
 
 0.53 
 
 5s 
 
 -0.1399 
 
 0.416 
 
 0.84 
 
 6s 
 
 0,1304 
 
 2.395 
 
 0.36 
 
 7s 
 
 -0.2982 
 
 0.816 
 
 0,70 
 
 8s 
 
 -0.0802 
 
 3,149 
 
 0.26 
 
 9s 
 
 -0.3280 
 
 0.816 
 
 0.70 
 
 10s 
 
 -0.0785 
 
 3,149 
 
 0.26 
 
 Sources of data: 
 
 Col. 1: Correlations of residuals lagged one year, based 
 on data given in table 26. The 1 per cent significance point 
 for n = 20 at the negative tail is -0.524. (Anderson, R. L, 
 Distribution of the serial correlation coefficient. Annals 
 of Mathematical Statistics 13:1-13, 1942.) 
 
 Cols. 2 and 3: Based on data given in table 26 and calcu- 
 lated by combining all phases of more than two years. A given 
 entry in col. 3 gives the probability that a Xp of the magni- 
 tude of the corresponding entry in col, 2 or larger would be 
 obtained in a random time series. For details of the test, 
 see Vifallis, W, A, and G. H. Moore, A significance test for 
 time series and other ordered observations. National Bureau 
 of Economic Research Tech, Paper 1, September, 1941. 
 
:r.<- 
 
 » i 
 
 i; 
 
 i 
 
 t •' 
 
 ! 
 
 
 1 
 
 
 ii 
 
 asV- ■ 
 
 
 
 !; 
 
 i 
 
 
 a^: i 
 
 ! 
 
 80X 1 
 
 —■»;■.--■■ :?;.-.-&■ - " 
 
 if." J.'t' 
 
 «rft>©T xio 
 
86. 
 
 TABLE 28 
 
 Winter Lemons: Price and Quantity Residuals 
 
 Year 
 
 
 Equat ion 
 
 
 November- 
 
 
 
 
 
 
 
 
 April 
 
 Iw 
 
 2w 
 
 3w 
 
 4w 
 
 
 
 \J w 
 
 
 dollars 
 
 1,000 
 boxes 
 
 dollars 
 
 pounds 
 
 10|S_ 
 
 1 
 
 
 1921-22 
 
 0.59 
 
 219 
 
 0.61 
 
 0.14 
 
 0.070 
 
 0 
 
 .045 
 
 1922-23 
 
 -0.15 
 
 -86 
 
 -0.27 
 
 -0.08 
 
 -0.067 
 
 -0 
 
 
 1923-24 
 
 -0.30 
 
 -24 
 
 -0.28 
 
 -0.01 
 
 -0.047 
 
 -0 
 
 .VJUD 
 
 1924-25 
 
 0.17 
 
 48 
 
 0.15 
 
 0.02 
 
 0.029 
 
 0 
 
 
 1926-26 
 
 -0.47 
 
 -142 
 
 -0.46 
 
 -0.09 
 
 -0.038 
 
 -0 
 
 
 1926-27 
 
 -0.58 
 
 -148 
 
 -0.62 
 
 -0.08 
 
 -0.056 
 
 -0 
 
 
 1927-28 
 
 0.26 
 
 11 
 
 0.26 
 
 0.01 
 
 0.017 
 
 -0 
 
 
 1928-29 
 
 0.40 
 
 151 
 
 0.45 
 
 0.10 
 
 0.086 
 
 0 
 
 
 1929-30 
 
 0.28 
 
 1 
 
 0.30 
 
 0.00 
 
 0.023 
 
 -0 
 
 .OOQ 
 
 1930-31 
 
 -0.10 
 
 -26 
 
 -0.08 
 
 -0.01 
 
 0.013 
 
 0 
 
 .009 
 
 1931-32 
 
 0.10 
 
 48 
 
 0,07 
 
 0.02 
 
 0.003 
 
 0 
 
 
 1932-33 
 
 -0.16 
 
 -89 
 
 -0,18 
 
 -0.06 
 
 -0.005 
 
 -0 
 
 .012 
 
 1933-34 
 
 -0.23 
 
 -91 
 
 -0,22 
 
 -0.05 
 
 -0.008 
 
 -0 
 
 UUcS 
 
 1934-35 
 
 0.13 
 
 105 
 
 0.09 
 
 0.06 
 
 -0.025 
 
 0, 
 
 OAT 
 
 1935-36 
 
 0,04 
 
 -10 
 
 0.06 
 
 0.00 
 
 0.014 
 
 0. 
 
 003 
 
 1936-37 
 
 
 
 
 
 
 
 
 1937-38 
 
 0.10 
 
 -3 
 
 0.16 
 
 0.01 
 
 0.040 
 
 0. 
 
 014 
 
 1938-39 
 
 -0.29 
 
 -89 
 
 -0.27 
 
 -0.05 
 
 -0.036 
 
 -0. 
 
 019 
 
 1939-40 
 
 0.07 
 
 33 
 
 0,05 
 
 0.02 
 
 0.008 
 
 0. 
 
 006 
 
 1940-41 
 
 0.13 
 
 90 
 
 0.07 
 
 0.04 
 
 -0.022 
 
 -0. 
 
 003 
 
 Source of data: 
 
 Derived from equations Iw through 6w of table 8 applied to data given 
 in table 7. 
 
: -<3 x : 
 
 
 
 
 
 
 
 
 
 ■■■•f 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 l 
 
 
 i 
 
 
 
 ■■ 
 
 
 
 ! ■* ■ . 
 1 . .. « ' ■ ■" 
 
 ■' ~. » * 
 
 i 
 
 f 
 
 t 
 
 1 
 
 i 
 
 > ■ 
 
 
 
 
 
 i 
 
 i 
 
 i 
 
 
 
 
 
 f 
 
 • . ' .' * 
 ■ '. ' 
 
 • 
 
 
 ! 
 
 t 
 t 
 
 t 
 
 t 
 
 
 
 i ■ ". * - 
 S 
 
 1 j 
 
 i 
 
 
 
 ii ■ 
 
 
 
 
 
 
 
8 7, 
 
 TABLE 29 
 
 Winter Lemons: Tests of Randomness of Residuals 
 
 Equation 
 
 Lagged cor- 
 relation 
 coefficient 
 
 Wallls and Moore test 
 
 
 
 
 1 
 
 2 
 
 3 
 
 Iw 
 
 0.0583 
 
 3,399 
 
 0.23 
 
 2w 
 
 -0.0888 
 
 6.862 
 
 0.05 
 
 Sw 
 
 0,0668 
 
 3.399 
 
 0.23 
 
 4w 
 
 -0,1399 
 
 1.468 
 
 0,53 
 
 5w 
 
 -0,0471 
 
 5.668 
 
 0,09 
 
 6w 
 
 -0,1040 
 
 4.399 
 
 0.15 
 
 Sources of data; 
 
 Col, 1: Correlations of residuals lagged one year, based 
 on data given in table 28. The 1 per cent significance point 
 for N = 15 at the negative tail is -0.597. (Anderson, R, L, 
 Distribution of the serial correlation coefficient, Aimals ■ 
 of Mathematical Statistics 13:1-13, 1942.) 
 
 Cols, 2 and 3: Based on data given in table 28 for 1921- 
 22 through 1935-36 and calculated by combining all phases of 
 more than two years, A given entry in col, 3 gives the 
 probability that a of the magnitude of the corresponding 
 entry in col, 2 or larger v;ould be obtained in a random time 
 series. For details of the test, see V/allis, YJ, A. and 
 G. H. Moore, A significance test for time series and other 
 ordered observations. National Bureau of Economic Research 
 Tech, Paper 1, September, 1941, 
 

 
 
 
 
 
 
 
 
 • 
 
 4 
 
 
 
 
 
 
 
 • 
 
 
 
 
 
 
 
 
 
 
 
 
 •— -t ■v.- - 1 
 
 
 
 
 
 .,1 
 
 ■.,r 
 
APPENDIX C 
 Net Regression Charts 
 
6.00 
 5.50 
 5.00 
 4.50 
 
 o 
 
 I 4.00 
 
 ^ 3.50 
 
 0) 
 
 3.00 
 
 ^ 2.50 
 
 o 
 
 2.00 
 
 1.50 
 1.00 
 
 310 350 390 430 470 510 550 
 
 United States supply (Xp) 
 10,000 boxes 
 
 70 30 
 
 100 110 120 150 
 
 Index of nonagricultural income (x^) 
 
 70 80 90 100 110 120 130 140 150 
 Index of temperature (x^) 
 
 Fig. 5. — Summer lemons: Net regressions of price on (A) United States 
 supply (xip = 12.1858 - 0.0205 Xg), (B) index of nonagricultural income payments 
 (x^5 = -0.4630 + 0.0445 X3), and (C) index of temperature (x^^ = 0.8536 + 
 0.0282 X4), 1922-1941. Arithmetic form. 
 
CQ 
 g 
 
 o 
 o 
 o 
 
 o 
 
 rH 
 
 I 
 I 
 
 >f400 
 
 450 - 
 
 3.00 3.50 4.00 4.50 5.00 
 
 F.o.b. price (x^) — dollars 
 
 a, 
 
 §• 
 
 to 
 
 CO 
 
 o 
 -p 
 cd 
 +3 
 
 CO 
 
 -d 
 
 0) 
 
 -p 
 
 •H 
 
 c 
 
 350 
 
 300 
 
 70 80 90 100 110 120 130 
 Index of nonagricultural 
 income (x^ ) 
 
 140 150 160 
 
 Index of temperature (x^) 
 
 Fig. 4. — Summer lemons: Net regressions of United States supply on 
 (a) price (xgi = 563.4914 - 41,2473 x^), (B) index of nonagricultural inco:ne 
 payments (xgs = 175.3518 + 2.1239 X3), and (C) index of temperature (X24 - 
 234.5614 + 1.3774 X4), 1922-1941. Arithmetic form. 
 
91. 
 
 70 80 90 100 110 120 130 140 150 
 Index of temperature (x^) 
 
 Fig. 5. — Siunmer lemons: Net regressions of price on (A) per capita United 
 States supply (x^po = 13.0064 - 3.6517 xg), (3) index of per capita nonagricul- 
 tural income payments (xi^o = -0.8778 + 0.565 x§), and (C) index of temperature 
 (^14 " + 0.0272 X4), 1922-1941. Arithmetic form. 
 
1^- 
 
92. 
 
 2.9 
 2.8 
 
 n 
 
 5 2.7 
 
 (X 
 
 \ 2.6 
 
 2.5- 
 
 rH 
 
 & 2.4 
 
 P 
 (0 
 
 ^ 2.3 
 
 •H 
 
 & 
 
 Q 2.2 
 
 u 
 
 0) 
 
 ^ 2.1 
 
 2.0 
 
 2 
 
 
 .35 
 
 A 
 
 
 .40 
 \.41 
 
 
 - 24 
 
 3'^\ -34 
 
 
 - 
 
 \' 36 
 32 .\ . 
 
 31' X 
 
 . 25 
 
 27 
 
 
 37" 
 
 • 
 
 28* 
 
 ox 
 
 
 t 1 1,1 
 
 3o\ 
 29* 
 
 o^<^'2.4 
 
 ,50 3. 
 F. 
 
 00 3.50 4.00 4.50 5.00 5.50 
 o.b. price (x-j^) — dollars 
 
 1 I I 1 L 
 
 50 70 80 90 100 110 120 
 
 Index of per capita non- 
 agriculUiral income (x°) 
 
 
 2.8 - 
 
 w 
 
 
 x> 
 
 2.7 - 
 
 o 
 
 
 a, 
 
 
 1 
 
 2.6 - 
 
 ^ 2.4 
 
 §• 
 
 2.3 
 
 cS 
 ■P 
 •H 
 
 2.2 
 
 o 
 
 2.1 
 
 2.0 
 
 c 
 
 
 
 34 36 y 
 
 
 
 .25 
 
 4lX 
 / -31 
 
 
 
 .35 
 
 /<39 
 
 
 
 
 ^0* 
 
 
 
 ^° ^38 
 
 '33 
 
 
 22 
 
 'y^ 32 
 
 
 .27 y 
 
 ^23 
 •^26 
 
 '^8 
 
 •29 
 
 
 ' .24 
 
 
 
 
 ' . . 1 I ... 
 
 
 1 . ( 
 
 1 ! 1 
 
 70 80 90 100 110 120 130 140 150 160 
 Index of temperature (x^) 
 
 Fig. 6. — Rummer lemons: Net regressions of per capita United States supply 
 on (A) price (x^i =,3.3727 - 0,2295 x^), (B) index of per capita nonagricultujral 
 income payments (xlso = 1.1373 + 0,0146 x§), and (C) index of temperature (x^4 = 
 1.5834 + 0.0073 X4), 1922-1941. Arithmetic form. 
 
J. 
 
95. 
 
 (D 
 O 
 •H 
 
 o 
 
 o 
 
 O 
 
 O 
 
 O 
 
 u 
 
 o 
 
 o 
 
 o 
 (-1 
 
 •^2° -15 2.50 
 
 ,00 
 
 .70 
 
 to 
 o 
 
 .60 
 
 .50 
 
 .40 
 
 .33 
 
 2.55 2.60 2.65 
 
 Log of supply (log xg) 
 
 .30 
 
 2.70 2.75 
 
 X.70 
 
 to 
 o 
 
 O 
 
 t£0 
 
 Q4 
 
 O 
 
 HO 
 O 
 
 .50 
 
 40 
 
 
 
 
 
 C 
 
 
 35- 
 
 25 • 
 
 37. . 
 
 54' 
 *53 
 
 36. 
 
 y"b\ 
 ) 41 
 
 59 
 
 .27 
 
 40./^ 
 
 ?2 /'^^ 
 
 3 
 
 •38 
 
 
 
 16 
 
 
 
 
 
 - .24 
 
 • • 
 
 
 
 1 
 
 1.85 
 
 1.95 
 
 2.05 
 
 Log of income (log x^) 
 
 2.15 70 80 90 100 110 120 130 140 150 160 
 Index of temperature (x.) 
 
 Fig. 7. — Summer lemons: Net regressions of price on (A) United States 
 supply (log x^g = 6.0075 - 2.0854 log x^), (B) index of nonagricultural income 
 payments (log x-j^^ = -1.4737 + 1.0356 log Xg), and (C) index of temperature 
 (log x^^ = 0.2300 + 0.0032 x^), 1922-1941. Logarithmic form. 
 
i 
 
94. 
 
 2.70- 
 
 to 
 o 
 
 V) 
 
 o 
 f-3 
 
 2.70 
 
 1.85 1.95 2,05 2.15 
 
 Log of income (log x™) 
 
 90 100 110 120 130 140 150 160 
 Index of temperature (x^). 
 
 Fig. 8. — Summer lemons: Net regressions of United States supply on 
 (a) price (log x^^ =» 2.8305 - 0.3965 log x^), (B) index of nonagricultural income 
 payments (log Xg^ - 1.6148 + 0.4865 log Xj), and (C) index of temperature 
 (log x^4 = 2.4125 + 0.0015 x^), 1922-1941. Logaritlimic form. 
 

 4.5C- 
 
 u 
 
 
 
 
 H 
 iH 
 
 4.0C- 
 
 O 
 
 
 j 
 
 3»5C~ 
 
 '"In 
 
 
 
 3.0C- 
 
 0) 
 
 
 o 
 
 •H 
 
 2.5C- 
 
 !h 
 
 
 
 
 • 
 • 
 
 2.0C- 
 
 o 
 
 
 
 
 o 
 
 « 
 
 m 
 u 
 
 ns 
 (H 
 iH 
 O 
 
 I 
 I 
 
 A 3.50 
 
 0) 
 
 o 
 
 •H 
 U 
 P. 
 
 80 90 
 Index of temperature (x^ 
 
 100 
 
 ) 
 
 14 16 18 20 22 24 26 28 50 
 Domestic shipments (xg) — 100,000 boxes 
 
 J__, .. , 1 L_t- 
 
 1951 
 Seasons 
 
 1935 
 
 90 100 110 
 
 Index of no nagri cultural income (xj) 
 
 Fig. 9. — Winter lemons: Net regressions of price on (A) domestic shipments (x^g = 8.9058 - 0.0028 
 (B) index of nonagricultural income payments (x{^ = 1.2950 + 0,0225 X3), (C) index of temperature (xf4 = 
 0.0484 X4), and (D) time (x^5 = 3.5295 + 0.0656 X5), 1921-22 to 1940-41. Arithmetic form. 
 
 ■ 7.2948 
 
 CD 
 
 cn 
 
2.00 3.00 4.00 5.00 
 
 F.o.b. price (x^) — dollars 
 
 Index of temperature (x^) 
 
 (0 
 
 -p 
 
 a ro 
 
 a. o 
 
 Id-" 
 
 to 
 
 o 
 
 •H 
 
 -P 
 
 to 
 
 O 
 O 
 
 o 
 
 o 
 o 
 
 o 
 
 23 
 
 22 
 
 21 
 
 20 
 
 19 - 
 
 18 
 
 B 
 
 
 
 
 
 
 
 
 
 29 . 
 
 41 . 
 
 - 
 
 22 
 
 35 
 
 
 „^ 40 28^^-^^ 
 
 
 
 .32 
 
 '56 
 • 
 
 38 31 _ .27 
 
 26 
 
 39 ^^'^ 
 
 - 
 
 
 
 
 
 
 - 34 
 
 
 
 
 •33 
 
 
 
 1 
 
 
 70 80 90 100 
 
 Index of nonagricultural income (x^) 
 
 1922 
 
 1925 
 
 1930 
 Seasons 
 
 1935 
 
 1940 
 
 Fig . 10. — — Winter lemons: Net regressions of domestic shipments on (A) price (xg-^ = 3,010,03 - 294,93 Xj|)y^ 
 
 (B) index of nonagricultural income payments (xgj = 1,388.5 + 7.3125 Xj), (G) index of temperature 
 
 (X24 = 3,355.1 - 15.927 X4), and (D) time (X25 = 2,053.3 + 24.805 X5), 1921-22 to 1940-41. Arithmetic form. 
 
 CO 
 
Index of temperature (x^) Seasons (xg) 
 
 Fig. 11. — Winter lemons: Net regressions of price on (A) per capita domestic shipments (x^^po = 8.9028 - 
 4.4674 Xg), (B) index of per capita nonagricultural income payments (x^^^o = 1.4173 + 0.0245 Xg), (C) index of tempera- 
 ture (x^^ = 7.2061 - 0.0474 x^), and (D) time (x£g = 3.3204 + 0,0479 x^), 1921-22 to 1940-41. Arithmetic form. 
 
4 
 
 ft 
 '^1 
 
 ■Ji- 
 ll 
 
 n 
 4 
 
2.50 
 
 m 
 
 3.00 3.50 
 F.o.b. price (x^) 
 
 4.00 
 
 dollars 
 
 4.50 
 
 50 60 70 80 90 
 
 Index of per capita nonagricultural income (x°) 
 
 to 
 -p 
 
 2 
 p- 
 
 •H 
 
 CO 
 
 1.50- 
 
 1.40- 
 
 -P 
 
 CO 
 
 i 
 
 1.30- 
 
 1.20- 
 
 •H ^ 1.10 
 
 1.00 
 
 g 
 
 p-i 
 
 1.00 
 
 1921-22 
 
 -25 
 
 -30 
 
 -35 
 
 -40 
 
 Index of temperature (x^) 
 
 Seasons (xp 
 
 0.1825 
 ture 
 
 Fig. 12. — Winter lemons: Net regressions of per capita domestic^ shipments on (A) price (x^^ = 1.8569 
 
 5 xn ), (B) index of per capita nonagricultural income payments (xg^o = 0.8746 + 0 
 (xg^ = 2.0503 - 0.0096 X4), and (D) time (xgg = 1.2625 + 0,0115 X5), 1921-22 to 1 
 
 0050 X5), (C) index of tempera- 
 
 1940-41. Arithmetic form. 
 
 CO 
 
 CO 
 
id V r 
 
 i,.V J' .' I 
 
 V 
 
 
 
 
 
 
 
 
 J 
 
 
 
 
 
 i 
 
 
 
 
 T 
 
 
 1 
 
 
 'y': 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ; \ 
 
 
 
 
 
 ft 
 
 ?-5 
 
 '00' 
 
 Ojyt.-?.."; 
 
 o."0 i 
 
 V,:... 
 
0) 
 
 o 
 
 •H 
 
 S-, 
 
 o 
 
 o 
 
 to 
 o 
 
 1-5 
 
 bO 
 O 
 H 
 
 '2:10 2.20 2.30 2.40 2.50 
 
 Log of domestic shipments (log x^) 
 
 o 
 
 •H 
 
 U 
 
 a, 
 
 O 
 
 <+H q 
 o 
 
 tiD 
 O 
 1-5 
 
 .60 
 
 .50 
 
 .40 
 
 .36 
 
 
 C 
 
 
 •22 
 
 ^\ . 40 
 
 34^\^^ 25- .38 
 
 
 - 
 
 ^\ 28 
 
 \^ * .30 
 
 35 • 
 
 26- \:31 
 
 27 24. • 33\ 
 
 
 
 39 
 
 J . ... 
 
 ^\32 
 
 1.85 1.90 1.95 
 
 Log of temperature (log x^) 
 
 2.00 
 
 1.75 1.85 1.95 2.05 
 
 Log of nonagricultural income (log x^) 
 
 1921-22 -25 
 
 -30 
 Seasons 
 
 -35 
 
 (X5) 
 
 -40 
 
 Fig. 13— Winter lemons: Net regressions of price on (A) domestic shipments (log x{z " 4.1432 - 1.5816 
 log xp), (B) index of nonagricultural income payments (log xis = -0.3898 + 0.4610 log X5), (C) index of tempera- 
 ture (log xi'4 = 2.7348 - 1.1632 log X4), and (D) time (log xfg = 0.5105 + 0.0073 x^), 1921-22 to 1940-41. 
 Logarithmic form. 
 
2.40 
 
 CO 
 -p 
 
 n 
 
 a, 
 
 •H 
 
 w 
 
 o --^ 
 
 •H CS2 
 -P H 
 
 m 
 
 m bO 
 S O 
 O rH 
 tJ ^ 
 
 «H 
 
 O 
 
 w 
 o 
 1-5 
 
 0) 
 
 -p 
 
 to 
 
 -P « 
 
 w 
 
 23 ^ 
 fi o 
 
 O rH 
 O 
 
 2.30 
 
 2.20 
 
 .30 
 
 2.40 — 
 
 2.40 
 
 2.30 
 
 2.2CI 
 
 .40 .50 .60 
 
 Log of f .o.b, price (log x^) 
 
 1.75 1.85 1.95 2.05 
 
 Log of nonagricultural income (log x^) 
 
 m 
 -p 
 
 a 
 
 CO 
 o ^ 
 -P X 
 
 to 
 
 e o 
 
 O H 
 O 
 
 2.30 
 
 2.20 
 
 3 
 
 1.75 
 
 1.85 
 
 1.95 
 
 2 JDS 
 
 Log of temperature (log x^) 
 
 2.40 
 
 CO 
 
 t 
 
 •rt 
 
 to 
 
 •H CV 
 •P X 
 03 
 
 O iH 
 
 2.30 
 
 o 
 
 3 
 
 2.2C- 
 
 1921-22 -25 
 
 -30 
 Seasons 
 
 -35 
 
 -40 
 
 (X5) 
 
 Fig. 14^-^ Winter lemons: Net regressions of domestic shipments on (A) price (log Xgi—*— 2.5518 - 0.4984 
 
 i Xg. J--r. ^^.u^ii<j . ii^^j i ^j^i ^„.v^w -..^x — — . V--/ I ^ ° <,!. 
 
 log Xt), (B) index of nonagricultural income payments (log Xgg = 1.8008 + 0.2566 log xj), (0) index of temperature 
 
 log x^4 = 3.5279 - 0.6412 log X4), and (D) time (log Xg5 
 Logarithmic form. 
 
 2.3024 + 0.0051 X5), 1921-22 to 1940-41. 
 
APPEiroiX D 
 Auxiliary Tables 
 
TABLE 30 
 
 Winter Lemons: The Effect of Adjusting Domestic Shipments in 1936-37 
 on the Net Regression Coefficients and on the Coefficients of Multiple Correlation 
 
 
 
 Net regressi 
 
 on coefficients * 
 
 
 Adjusted 
 
 Equation 
 
 Dependent 
 variable 
 
 F.o.b. price 
 
 Domestic 
 shipments 
 
 Nonagri- 
 cultural 
 income 
 
 Index of 
 tempera- 
 tures 
 
 Time 
 
 coefficient 
 of multiple 
 correlation 
 
 
 
 ""l 
 
 "^2 
 
 ^3 
 
 ^4 
 
 ^5 
 
 R 
 
 Including 1936-37, 
 not adjusted 
 
 ^1 
 
 
 -0 .0027 
 (0.0005) 
 
 0.0232 
 (0.0082) 
 
 -0.0352 
 (0.0176 
 
 0.0652 
 (0.0191) 
 
 0.7867 
 
 
 ^2 
 
 -240.5343 
 (46.5887) 
 
 
 6.8369 
 (2.5069) 
 
 -12.9784 
 (4.9377) 
 
 27.3906 
 (2.9472) 
 
 0..9494 
 
 Adjusting 1936-37 
 shipment observa- 
 Uon to 2,204,000 
 boxes 
 
 ^1 
 
 -285.5297 
 (36.2236) 
 
 -0.0028 
 (0.0004) 
 
 0.0233 
 (0.0060) 
 
 7.3266 
 (1.9156) 
 
 -0.0451 
 (0.0124) 
 
 -14.8370 
 (3.8206) 
 
 0.0677 
 (0.0131) 
 
 25,4577 
 (2.2611) 
 
 0,8941 
 0.9686 
 
 X = Seasonal average f.o.b. price in dollars per box. 
 
 Xg = Domestic shipments of California and Arizona lemons in units of 1,000 boxes. 
 
 X, = Index of nonagricultural income payments, 1924-25 to 1928-29 = 100. 
 
 ^ and 
 x^ = Index of mean temperatures in December, Januaryj/February in 32 metropolitan districts, 
 1931-32 =100. 
 
 X5 = Time in units of ha lf years, origin halfway between 1930-31 and 1931-32. 
 
TABLE 31 
 
 Summer Lemons: Intercorrelations of the Series Employed in the Regression Analyses 
 
 
 ""l 
 
 
 
 "^3 
 
 0 
 
 V 
 
 ^4 
 
 ^2d 
 
 2i 
 
 V 
 
 2e 
 
 20 
 
 1 CiP IT 
 
 1 
 
 iOg Xg 
 
 ^2 
 
 -0.572288 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 0 
 
 ^2 
 
 -0.548529 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 0.118360 
 
 a.452897 
 
 
 1 
 
 
 
 
 
 
 
 
 
 0 
 
 U vc / cOUO 
 
 
 
 
 1 
 
 A. 
 
 
 
 
 
 
 
 
 \ 
 
 -0 .026852 
 
 0.514790 
 
 0.347067 
 
 -0.130167 
 
 -0 •405177 
 
 1 
 
 
 
 
 
 
 
 ^2d 
 
 -0,606340 
 
 
 
 0 .236590 
 
 
 0.592982 
 
 1 
 
 
 
 
 
 
 ^2i 
 
 0.469018 
 
 
 
 0.160461 
 
 
 -0,519741 
 
 -0.807169 
 
 1 
 
 
 
 
 
 ^2e 
 
 -0.562579 
 
 
 
 0.248953 
 
 
 0.613403 
 
 
 
 1 
 
 
 
 
 ^2o 
 
 0.343487 
 
 
 
 0.157795 
 
 
 -0.543965 
 
 
 
 -0.772969 
 
 1 
 
 
 
 log Xj^ 
 
 
 
 
 
 
 0.005085 
 
 
 
 
 
 1 
 
 
 log 
 
 
 
 
 
 
 0.520499 
 
 
 
 
 
 -0.570926 
 
 1 
 
 log X3 
 
 
 
 
 
 
 ^0.144313 
 
 
 
 
 
 0*088095 
 
 0,430650 
 
 x, = 
 
 x„ = 
 
 Seasonal average f.o,b. price of summer lemons. 
 
 United States supply of summer lemons. 
 
 Per capita United States supply of summer lemons, 
 
 Index of nonagricultural income. 
 
 Index x>f per capi^ nonagri cultural income. ^ 
 
 Index of temperature. 
 
 "2d 
 X2i 
 
 ^26 
 
 - Domestic shipments of summer lemons, 
 
 = Imports of summer lemons for consumption, 
 
 = Domestic shipments of summer lemons by California 
 Fruit Growers Exchange, 
 
 -= Domestic shipments of summer lemons outside 
 
 California Fruit Growers Exchange plus imports of 
 summer lemons for consumption. 
 
 o 
 
. 1 ! » ■ 
 
 ■ \ ■ 
 
 .... , 
 
 pi . 
 
 ~i 
 
TABLE 32 
 
 Summer Lemons: Reciprocal Correlation tlatrices 
 
 
 Eauations Is and 2s 
 
 
 Equations 6s and 7s 
 
 
 
 
 ^3 
 
 
 
 ""l 
 
 ''2d 
 
 21 
 
 ''3 
 
 ''4 
 
 X 
 
 6.562543 
 
 
 
 
 X 
 
 6.808934 
 
 
 
 
 
 2 
 
 8.833359 
 
 14.063709 
 
 
 
 Xo J 
 
 2d 
 
 12,769370 
 
 30.168585 
 
 
 
 
 ^3 
 
 -5 .438465 
 
 -8.469953 
 
 6,132164 
 
 
 ^21 
 
 5.165902 
 
 14.248319 
 
 8.648916 
 
 
 
 4 
 
 -5.079015 
 
 -8,105168 
 
 5,012417 
 
 5.688528 
 
 x. 
 
 -5,359076 
 
 -12.466534 
 
 -5.967977 
 
 6.185965 
 
 
 
 Equations 3s and 4s 
 
 
 -5 .401821 
 
 -11.763851 
 
 -4.591926 
 
 4.951939 
 
 6.088672 
 
 
 
 x° 
 
 
 
 ''4 
 
 
 
 
 1 
 
 ^2 
 
 3 
 
 X4 
 
 
 Eauations 8s and 9s 
 
 1 
 
 0 
 
 X 
 
 2 
 
 6.829170 
 
 
 
 
 
 ^1 
 
 ^2e 
 
 ^20 
 
 ^3 
 
 ^4 
 
 7,659574 
 
 10.223064 
 
 
 
 ^1 
 
 6,643819 
 
 
 
 
 
 o 
 
 ""3 
 
 -6.467930 
 
 -8,176593 
 
 7.843269 
 
 
 ^2e 
 
 12.375084 
 
 28.082392 
 
 
 
 
 Y 
 
 -5.095665 
 
 -6.655381 
 
 5.842061 
 
 5.540103 
 
 ^2e 
 
 5,282716 
 
 13.224280 
 
 7,912748 
 
 
 
 
 
 Equations 5s and 6s 
 
 -5.382782 
 
 -12.008727 
 
 -5.740498 
 
 5.170648 
 
 
 
 log x^ 
 
 log 
 
 log x^ 
 
 ^4 
 
 ^3 
 
 
 Log 
 
 5.823581 
 
 
 
 
 ""4 
 
 -5,239562 
 
 -11.263123 
 
 -4.412927 
 
 4.902235 
 
 6.005772 
 
 log Xg 
 
 7,710820 
 
 12.347127 
 
 
 
 
 
 
 
 
 
 log Xj 
 
 -4.511113 
 
 -7.077073 
 
 5.085974 
 
 
 
 
 
 
 
 
 \ 
 
 -4.694097 
 
 -7.487188 
 
 4.440520 
 
 5.561766 
 
 
 
 
 
 
 
 Tor the meaning of the various x's, see table 51« 
 
r 
 
TABLS 33 
 
 Winter Lemons: Intercorrelations of the Series Employed in the Regression Analyses 
 
 
 1 
 
 X 
 
 2 
 
 2 
 
 1 
 
 3 
 
 0 
 
 
 
 log X 
 
 X 
 
 log X 
 
 log X 
 
 ^2 
 
 
 — U •O'iOODVJ 
 
 X 
 
 
 
 
 
 
 
 
 
 x° 
 2 
 
 ^3 
 
 
 -0*710609 
 
 U »JL ooooo 
 
 1 
 
 X 
 
 1 
 
 ±. 
 
 
 
 
 
 
 
 0 
 
 ^3 
 
 
 0.340976 
 
 
 -0.169203 
 
 
 i 
 
 
 
 • 
 
 
 
 ^4 
 
 
 -0.209951 
 
 -0.174066 
 
 -0.207 373 
 
 -0.082620 
 
 -0.095509 
 
 1 
 
 
 
 
 
 
 
 
 0 .fi49398 
 
 0.740809 
 
 0.011540 
 
 -0 .427189 
 
 -0.042935 
 
 1 
 
 
 
 
 log 
 
 \ 
 
 
 
 
 
 
 
 -0.367142 
 
 1 
 
 
 
 log 
 log 
 log 
 
 ^2 
 ^3 
 ^4 
 
 
 
 
 
 
 
 0,840508 
 0.003982 
 -0.059772 
 
 -0.666677 
 0.201064 
 -0,234293 
 
 1 
 
 0,106258 
 -0.163422 
 
 1 
 
 -0.071114 
 
 -5 Seasonal average f.o.b. price of winter lemons. 
 Xg = Domestic shipments of winter lemons. 
 x° = Per capita domestic shipments of winter lemons. 
 Xj = Index of nonagricultural income. 
 x° = Index of per capita nonagricultural income. 
 
 c Index of temperature, 
 
 x- = Time. t-- 
 
TABLE 34 
 
 '/Vinter Lemons: Reciprocal Correlation Matrices 
 
 
 Equations Iw and 2w 
 
 
 
 Equations 3w and 4w 
 
 
 
 ^2 
 
 ''3 
 
 ^4 
 
 ^5 
 
 
 
 ^1 
 
 xo 
 
 iZ 
 
 
 ^4 
 
 
 ^1 
 
 6,913313 
 
 
 
 
 
 
 
 ^1 
 
 
 6.905547 
 
 
 
 
 
 2 
 
 10.986835 
 
 21.511390 
 
 
 
 
 
 r\ 
 
 ^2 
 
 
 8.734010 
 
 13,545363 
 
 
 
 
 ^3 
 
 -2*770949 
 
 -4,861574 
 
 2.169333 
 
 
 
 
 0 
 ^3 
 
 
 -2,753762 
 
 -3.878092 
 
 d ,403504 
 
 
 
 ^4 
 
 2,848864 
 
 
 5,048229 
 
 -1.117880 
 
 2,249574 
 
 
 
 
 
 2.782599 
 
 3.913811 
 
 -1,030239 
 
 2.201530 
 
 
 ^5 
 
 -6.663260 
 
 -14,002538 
 
 3.048479 
 
 -3.142227 
 
 10,299944 
 
 
 
 -5.015852 
 
 -8.346937 
 
 2.854046 
 
 -2,233046 
 
 6,482752 
 
 
 
 
 
 
 
 
 Equations 
 
 5w 
 
 and 6w 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 log X^ 
 
 log Kg 
 
 log x^ 
 
 log 
 
 X 
 
 5 
 
 
 
 
 
 
 log x^i^ 
 
 6.171160 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 log Xg 
 
 9,195382 
 
 17.382883 
 
 
 
 
 
 
 
 
 
 
 
 
 log X3 
 
 -2.019832 
 
 -3.360642 
 
 1 .699643 
 
 
 
 
 
 
 
 
 
 
 
 log X4 
 
 2.487777 
 
 4.100113 
 
 -0,780249 
 
 
 2.053562 
 
 
 
 
 
 
 
 
 ^5 
 
 -5,306360 
 
 -10,975990 
 
 2.029677 
 
 
 -2.406959 
 
 
 8.125271 
 
 
 
 For the meaning of the various x's, see table 33, 
 
 O 
 
107* 
 
 APPENDIX E 
 
 The Use of Mean Monthly Maximum Temperatures in the 
 Summer Lemons Regression Analysis 
 
 The chief drav/back of the index of summer temperatures described in 
 
 appendix A is that it is laborious to calculate. In this appendix are reported 
 
 the results secured with the use of another temperature variable (see table 35 )# 
 
 the extension of which to future seasons is relatively easy. This series consists 
 
 of monthly mean maximum temperatures. May through September, in 22 cities weighted 
 
 55 / 
 
 by 1931-38 average unloads of lemons in these cities for corresponding months. — ' 
 The weights used are given in table 36. YiThile less sensitive than the index 
 described in appendix A, this temperature variable yields quite similar results in 
 the seasonal analysis* 
 
 In table 37 are given the regression coefficients and auxiliary constants 
 obtained when mean maximvim teiaperatures were used in place of the index of summer 
 temperatures described previously. The other variables in the two equations pre- 
 sented in table 37 are those used in equations Is and 2s of table 3. It is seen 
 that with f.o.b, price as dependent variable, the adjusted coefficient of multiple 
 correlation is of the same magnitude as that corresponding to equation Is (0.9031 as 
 against 0.9050 secured with equation Is). With the United States supply as 
 dependent variable, the adjusted coefficient of multiple correlation is somewhat 
 lower than the coefficient of equation 2s (0.9482 as against 0.9569), but the 
 difference between them is not large. The magnitudes of the regression coefficients 
 of these equations differ somewhat from those of comparable coefficients of 
 equations Is and 2s, but here, too, the discrepancies are not large. It is clear 
 from the foregoing that the equations described in table 37 are acceptable substitutes 
 
 55 / 
 
 — ' Wellman, H. R. Statistics pertaining to lemons, California Agr. Exp* Sta« 
 October, 1940. (Processed). 
 
i'■^rJ.i•;.■. ■:••■! ,'\:r' .■•■<^::yy,i '(.r-:,^::. >.i'j:i'' c-'i-. ••c:.:;:-i.^.. • ' 
 ii'V/^. M-f;- ■-i,ivo.-;:^- ;■(; » tc'.f^.; Ij:> ' , -;• .;• ■ • .■ . ; .' ' • . ■ Ih,":--.-' 
 
 ( :v!i';.i;u.7r;-. *r:; -;-.'.;f--.u :J- acn-?' £"-:..-"i:-v:; 'f * 
 
 « rrxn-.. '..•■i .:■ I- .-i.;; ■ r. .. 
 
 t ■;;<. >;i>i-,\.l v;;.J- 'io Or?;:^' a.'. !:.!;-;; ;r!>«i.!f:; ,;*i';:7 f K': . i. ; i;;; :v ■ ;. .! •;. 
 
 1 i->.!::;0 ■■■.■i:}- f r.-' i:l ^ird^i^ri a-T , vi".;i.; vfi^, bu-'ru v,^;: 
 
 '1:'\H,:-:: i'ii ■•.•■'>,r.-.l;/Or> !>^:^:^:j\l-n o-'J ^ -ii-v ;K.-;..f:j. :: ,:i>: •; v 
 
 v.! ' ' V'-.?'/:'..' -7!;; :k:].\: ,{':r ji- ; rl-/;- ; ; :■. ■•;;•;>•,>•; ,fr:rf.' • 
 
 Rv-i::!? cr>;:".;'i.-.;i-:^ ;,!'::■ ': o "'-.i-^c^i-ir.:. •■ 5 »!■ .!. ' r>v-f vi' ur^/y;- ■-•■'I't/'j 
 
 •t:.^.!.,:- j ;! r'j't.-;/' om, vi t'.'.-:- ; 'j'siJiT.: ■■> m';- ^-^ : «-^-: i-n,.; Z'-i 
 
108, 
 
 for equations Is and 2s presented in the text* 
 
 In table 37 are also indicated the coefficients of separate determination 
 pertaining to the two equations. It is seen that the bulk of the variation of 
 f.o.b. price is attributable to variation in the United States supply, and that 
 income, and especially temperature, are relatively unimportant. These results are 
 similar to those secured vn.th equation Is, and it is thus evident that the minor 
 role played by temperature, as indicated by coefficients of separate determination, 
 is not a consequence of the idiosyncracies of the index of summer temperatures 
 described in appendix A. But here also it should be observed that from the point 
 of view of goodness of fit, temperature is an important and, in fact, an indispens- 
 able independent variable, since its omission results in a marked lowering of the 
 
 56/ 
 
 fit of both equations, — ' 
 
 One other point should be mentioned, namely, that the introduction of "time" 
 as an additional independent variable does not improve significantly the fit of 
 these equations. The ratios of the net regression coefficients of the added 
 variable "time" to their standard errors are ,329 and 1,846 respectively with f«o,b, 
 price and United States supply as the dependent variable. The null hypothesis here 
 cannot be rejected since for 15 degrees of freedom the t-ratio at the 5 per cent 
 level is 2,131, The explanation of the failure of "time" to contribute significantly, 
 advanced in the text in connection viith. equations Is and 2s, is applicable here, 
 for mean maximum temperatures also exhibit an upward trend during the period under 
 review, 
 
 5§/ The coefficients of multiple correlation with f.o.b, price as the dependent 
 variable obtained when United States supply, index of nonagri cultural income, and 
 the temperature variable are omitted in turn are ^1(340) " 0,1416, ^'1(240) = 0.5627, 
 RiC9'z\ " 0.6699, The first multiple correlation coefficient was not adjusted be- 
 cause the adjustment resulted in an imaginary value of the coefficient. 
 
 67/ 
 
 The equation of the trend in mean maximum temperatures is: 
 
 x°' = 79,5950 + 0,0683 x_ 
 
 4 5 
 
 where x^ is time measured in half-years with the origin half-way between 1931 and 
 □ 
 
 1932, The standard error of the coefficient of Xg is 0,0276 yielding t = 2,478, 
 For 18 degrees of freedom the t-ratio at the 5 per cent level is 2,101, 
 
.•3 i/l 
 
 bX 31. 
 
 a t5 
 
 ■ ; -Zip .$,4.., , : ,. . 
 
 ■■ ..-r.^bfl't . ■.: 
 
 ».--'-'--■*.■- 
 
 ■ vff l^.r«?^ -^:4yx;iJ3if:7. . .. . . 
 
 f.r. 
 
109. 
 
 TABLE 35 
 
 Mean Maximum Temperatures in 22 Cities 
 
 
 May-September 
 
 , 1922 to 1941 
 
 
 
 Year 
 May- 
 September 
 
 Mean 
 maximum 
 temperatures 
 
 Year 
 May- 
 September 
 
 Mean 
 maximum 
 temperatures 
 
 
 
 degrees 
 
 
 degrees 
 
 
 1922 
 
 79.5 
 
 1932 
 
 80.2 
 
 
 1923 
 
 79.0 
 
 1933 
 
 81.1 
 
 
 1924 
 
 76.6 
 
 1934 
 
 82.3 
 
 
 1925 
 
 79,9 
 
 1935 
 
 78,7 
 
 
 1926 
 
 77.8 
 
 1936 
 
 81,4 
 
 
 1927 
 
 76.6 
 
 1937 
 
 80.1 
 
 
 1928 
 
 77.6 
 
 1938 
 
 79.8 
 
 
 1929 
 
 78.7 
 
 1939 
 
 80.9 
 
 
 1930 
 
 31.2 
 
 1940 
 
 78.8 
 
 
 1931 
 
 80.7 
 
 1941 
 
 81.0 
 
 
 Source of data: 
 
 Wellman, H. R. Statistics pertaining to lemons. California Agr* 
 Exp. Sta. October, 1940, (Processed). Extended through 1941. The 
 
 entries are monthly mean maximum temperatures May through September in 
 22 cities weighted by 1931-38 average unloads of lemons for correspond- 
 ing months. For cities included see table 36, 
 

 
 
 
 
 I 
 
 
 
 
 X 
 
 
 ; 
 
 
 
 
 ■ r ' '** 
 
 I 
 
 ••• • ■ 
 
 
 
 
 ! 
 
 1 
 
 • '. > 
 
 
 
 ^ . '' 
 
 
 
 ^' . . ■ -. 
 
 
 
 1 ^ 
 
 
 
 
 ! 
 
 
 
 „ ■• " . 
 
 
TABLE 36 
 
 110. 
 
 Average Kail emd Boat Unloads of Lomons iu May« Juiio« July* August 
 and September in 22 Cities, 1931 to 1938 
 
 
 Average unloads 
 
 
 Cities 
 
 May 
 
 June 
 
 July 
 
 August 
 
 September 
 
 
 Carlots 
 
 
 Atlanta, Ga» 
 
 25.1 
 
 34.4 
 
 25.6 
 
 24.4 
 
 
 
 Baltimore, Md. 
 
 49.1 
 
 95.1 
 
 100.4 
 
 69.9 
 
 
 
 Boston, Mass. 
 
 65.9 
 
 88.9 
 
 99.1 
 
 74.7 
 
 
 
 Buffalo, N. y. 
 
 19.4 
 
 26.4 
 
 19.4 
 
 18.5 
 
 
 Q c; 
 
 Chicago, 111. 
 
 114.9 
 
 164.5 
 
 191.8 
 
 129.5 
 
 
 
 Cincinnati, Ohio 
 
 44.4 
 
 81.2 
 
 86.7 
 
 55.9 
 
 
 
 Cleveland, Ohio 
 
 47,4 
 
 65.4 
 
 58.6 
 
 40.1 
 
 
 
 Dallas, Texas 
 
 20.5 
 
 21.4 
 
 19.7 
 
 20.4 
 
 
 
 Denver, Colo. 
 
 15.4 
 
 23.0 
 
 22.8 
 
 14.9 
 
 
 7.0 
 
 Detroit, Mich. 
 
 59.9 
 
 93.1 
 
 79.7 
 
 52.0 
 
 
 28.0 
 
 Houston, Texas 
 
 18.1 
 
 25.3 
 
 19.2 
 
 18.4 
 
 
 14. R 
 
 Kansas City, Mo. 
 
 24.5 
 
 38.7 
 
 38.0 
 
 26.5 
 
 
 in R 
 
 Memphis, Tenn. 
 
 18.9 
 
 26.6 
 
 24.0 
 
 18.4 
 
 
 is.l 
 
 Minneapolis-St. Paul, Minn. 
 
 29.0 
 
 39.1 
 
 38.1 
 
 23.7 
 
 
 
 New Orleans, La. 
 
 34.4 
 
 46.6 
 
 42.9 
 
 34.5 
 
 
 
 New York, N. Y. 
 
 259.9 
 
 387.5 
 
 387.2 
 
 310,4 
 
 
 190,1 
 
 Omaha, Neb» 
 
 10.2 
 
 17.1 
 
 19.5 
 
 10.8 
 
 
 4.9 
 
 Philadelphia, Pa. 
 
 91.0 
 
 153.4 
 
 152.5 
 
 113.6 
 
 
 52.5 
 
 Pittsburgh, Pa. 
 
 49.8 
 
 76.7 
 
 78,4 
 
 56.1 
 
 
 29.0 
 
 Portland, Ore» 
 
 17.2 
 
 15.9 
 
 12.4 
 
 12.7 
 
 
 9.5 
 
 St. Louis, Mo. 
 
 44.0 
 
 95.9 
 
 99.9 
 
 59,6 
 
 
 27.9 
 
 Seattle, T/ash. 
 
 19.0 
 
 20.3 
 
 13.1 
 
 16,8 
 
 
 11.2 
 
 Source of data: United States Department of Agriculture. Agricultural Marketing 
 Service. Carlot unloads of certain fruits and vegetables in 66 cities and im- 
 ports in 4 cities for Canada. Annual issues. VJ^ashington, D. C. (Processed) 
 
 1 
 
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TABLE 37 
 
 Summer Lemons: Regression Coefficients and Auxiliary Constants Obtained When Mean 
 Maximum Temperature in 22 Cities is Used as the Temperature Variable 
 (Figures in parentheses are standard errors) 
 
 Dependent 
 variable 
 
 Net recression coefficients * 
 
 Adjusted 
 coeffic- 
 ient of 
 multiple 
 correla- 
 tion 
 
 R 
 
 flexi- 
 bility 
 
 of 
 price 
 
 Elas- 
 ticity 
 
 of 
 demand 
 
 Percentage of variance of 
 dependent variable ascribable 
 to 
 
 Constant 
 term 
 
 F.o.b. 
 
 price 
 
 ^1 
 
 United 
 States 
 supply 
 
 ^2 
 
 Nonagri- 
 cultural 
 income 
 
 ^3 
 
 Mean 
 maximum 
 tempera- 
 tures 
 
 0 
 
 ^4 
 
 
 ^2 
 
 ^3 
 
 o 
 \ 
 
 X 
 
 -26.1255 
 
 
 -0.0189 
 
 0.0490 
 
 0.4100 
 
 0.9031 
 
 -1.8067 
 
 
 
 70.9 
 
 10.8 
 
 2.7 
 
 1 
 
 
 
 (0.0020) 
 
 (0.0071) 
 
 (0.0695) 
 
 
 
 
 
 
 
 
 ^2 
 
 -1,381,9485 
 
 -44.5889 
 
 
 2.5302 
 
 21,3450 
 
 0.9482 
 
 
 -0.4658 
 
 38.9 
 
 
 32.5 
 
 20.1 
 
 - 
 
 
 (4.8363) 
 
 
 (0.2732) 
 
 (2.7835) 
 
 I 
 
 
 
 
 
 
 
 
 X, = Seasonal average f.o.b. price in dollars per box. 
 
 Xg = United States supply of lemons in units of 10,000 boxes. 
 Xj = Index of nonagri cultural income payments, 1935-39 = 100. 
 x° = Mean monthly maximum temperature in 22 cities. May through September. 
 'f' At the centroid. 
 
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 f 
 
 
 
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112, 
 
 TABLE 38 
 
 Sumner Lemons: Correlation Matrix and its Inverse Obtained 
 When Mean Maximum Temperature in 22 Cities is Used as the Temperature Variable 
 
 
 Correlation matrix 
 
 
 Reciprocal matrix 
 
 
 ^1 
 
 ^2 
 
 ^3 
 
 0 
 
 ^4 
 
 ^1 
 
 ^^2 
 
 ^3 
 
 
 X° 
 
 ""4 
 
 ^1 
 
 ^2 
 ^3 
 
 0 
 
 =^4 
 
 1 
 
 -0.572288 
 0.118360 
 0.036886 
 
 1 
 
 0,452897 
 0.341278 
 
 1 
 
 -0.312107 
 
 1 
 
 6.441653 
 7.984304 
 -5,875439 
 -4.796239 
 
 11.759235 
 -S.437056 
 -6.940941 
 
 7.182498 
 5.337810 
 
 c 
 
 5.211672 
 
 For the meaning of the x*s# see table 37. 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
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