UNIVERSITY OF CALIFORNIA COLLEGE OF AGRICULTURE AGRICULTURAL EXPERIMENT STATION BERKELEY, CALIFORNIA MAINTENANCE OF « SUBSTANTIAL EQUITY IN THE POOLING OF LEMONS H. R. WELLMAN and M. D. STREET BULLETIN 619 MAY, 1938 CONTRIBUTION FROM THE GIANNINI FOUNDATION OF AGRICULTURAL ECONOMICS UNIVERSITY OF CALIFORNIA BERKELEY, CALIFORNIA CONTENTS PAGE Introduction 5 Purpose of study 5 Typical method of handling lemons 6 Grade pools 8 Division of total net returns between growers: grade pools vs. no-grade pools 9 Variations between growers in the proportions of the several grades contributed 9 Differences between the average selling prices of the several grades ... 10 Differences in returns to individual growers with separate pools for each grade as compared with no-grade pools 10 Determination of the number of units of each grade contributed by indi- vidual growers 12 Estimating cleanups 14 Combining lots containing only a few boxes each 17 Differences in grade occasioned by length of time in storage 19 Determination of price differentials between grades 23 Size pools 25 Division of total net returns between growers with and without size pools .... 25 Variations between growers in the proportions of the several sizes contributed 26 Differences between the prices of the several sizes of the same grade of lemons 28 Differences in returns to individual growers without size pools as com- pared with pooling on the basis of sizes 31 Determination of the number of units of each size contributed by indi- vidual growers 33 Determination of sizes on cleanups 35 Determination of sizes in combination lots 35 Mechanical sizers and electric counters 36 Determination of price differentials between sizes 38 Pooling on the basis of size groups 39 Time pools 40 Division of annual returns between growers: multiple time pools vs. annual pool 41 Variation in time when fruit of individual growers can be shipped 41 Seasonal variation in prices of lemons 45 Differences in returns to individual growers with multiple time pools as compared with an annual pool i 50 Seasonal variation in shipments 51 Transition from one pooling period to another with multiple time pools. ... 53 Multiple time pools based upon shipments 53 Multiple time pools based upon picks 55 Price risks in time pools *. 60 Total returns to all growers combined 62 Relation of the length of pooling period to orderly marketing 62 Relation of the length of pooling period to costs of operation 63 [3] PAGE Color pools 64 By-products pools 67 Adjustments between time pools 70 Adjustments between color classifications 72 Adjustments between grade pools 73 Adjustments between sizes 75 Summary 75 Grade pools 76 Size pools 77 Time pools 78 Color pools 80 By-products pools 80 Acknowledgments 81 Appendix A: Computation of pool returns based upon grades determined at end of normal storage periods 83 Appendix B: Computation of rates of payments to growers based upon simple averages of market price differentials between grades and between sizes. ... 88 Appendix C: Methods of calculating adjustments between time pools when merchantable lemons are sent to the products plant 94 Appendix D: Method of calculating adjustments between color classifications when merchantable fruit is sent to the products plant 100 Appendix E: Method of calculating adjustments between grades and between sizes when merchantable fruit is sent to the products plant 108 Appendix F: Illustration of adjustments between time pools, color classifica- tions, and grades when merchantable lemons are sent to the products plant 111 Appendix G: Data on variation between growers in proportions of the several brands, sizes, and grades contributed 120 [4] MAINTENANCE OF SUBSTANTIAL EQUITY IN THE POOLING OF LEMONS 2 H. R. WELLMAN 3 and M. D. STREET 4 INTRODUCTION Purpose of the Study. — The essential question to which this study is di- rected is : What are likely to be the effects of variations in grade, size, color, and time pools upon the division of the total returns between the individual members of an association? This division involves problems relating to maintenance of substantial equity and to distribution of market risks. The term "pooling" as used in this study refers to a particular method by which a cooperative marketing association may handle the products of its members. It involves (a) the physical mingling of the products, (b) the combining of sales returns, (c) the merging of operating ex- penses, and (d) the division of the net returns among the several members. The chief purposes of pooling are (1) to spread the risks of marketing among the individual members, (2) to promote orderly marketing, and (3) to reduce the costs of operation. The extent to which these purposes can be realized under given conditions may be limited by the necessity of maintaining substantial equity between individual growers. The term "equity" is essentially a subjective concept and may have different meanings to different persons. As used in this report, "sub- stantial equity" occurs when the division among its members of the total net returns received by an association is based upon the characteristics of lemons which the market signifies to be important as indicated by price differentials that tend to persist over a period of several years. Thus a pooling system is deemed to be equitable if the returns paid the individual growers over a period of several years closely reflect the aver- age differences in the market values of their lemons. The establishment of a pooling plan requires determination with respect to: (1) the number and content of concurrent size pools; (2) the number and content of concurrent grade pools ; (3) the number and 1 Received for publication October 19, 1937. 2 Paper Xo. 71. The Gianniiii Foundation of Agricultural Economics. 3 Associate Professor of Agricultural Economics, Associate Agricultural Economist in the Experiment Station and Associate Agricultural Economist on the Giannini Foundation. * Research Assistant on the Giannini Foundation. [5] 6 University of California — Experiment Station content of concurrent color pools; (4) the number of pooling periods during the season, the length of each, and whether such time pools are to be based upon when the lemons are picked or upon when they are shipped. Since each of the above is capable of independent variation, numerous pooling systems, each differing in some degree from the others, are pos- sible. This study was undertaken at the request of the Board of Directors of the Santa Paula Citrus Fruit Association who desired an analysis made of their pooling operations that would serve as a guide to the mem- bers in determining what, if any, changes should be made in the pooling system then employed. A progress report was presented to the Board in November, 1936. 5 Since that time the scope of the study has been broad- ened. This report is designed to be of value to all persons interested in the pooling of lemons. Some parts of it will also be of use to those inter- ested in the pooling of other agricultural products. Because of the prospective increase in lemon production, the pooling problems which arise from deterioration in quality and shrinkage of lemons in storage and from the sending of merchantable lemons to the products plant are likely to become acute. Under such situations certain adjustments not now employed will be needed if substantial equity be- tween growers is to be maintained. The technical aspects of these adjust- ments, which may not be of interest to the general reader but which are of importance to those directly responsible for managing the associations, are given in the appendixes. The allocation of the expenses of associations to the different classes of fruit is not covered in this report. It is, however, an important aspect of pooling. Its investigation would require a careful study of the cost- accounting methods employed by the several associations, and would take a considerable period of time. To delay the publication of the mate- rial contained herein until such an investigation could be made was not considered advisable. TYPICAL METHOD OF HANDLING LEMONS Although there is some variation in the methods of handling lemons both as between associations and within an association at different times of the year and under different conditions, the following procedure is fairly typical. Each lemon orchard is generally picked in rotation from seven to ten 5 Wellman, H. E., and M. D. Street. The pooling of lemons with special reference to the Santa Paula Citrus Fruit Association. A progress report. Univ. of California Giannini Foundation Mimeo. Eept. 55:1-67. 1936. (Out of print.) Bul. 619] Maintenance of Equity in Pooling of Lemons 7 times during the year at intervals of from four to seven weeks. Modifi- cations in the picking schedule, however, are made to meet special con- ditions. Picking is done in most instances by crews employed by the association. The lemons are picked according to size and color. On each "pick-around" all yellow lemons and all those which are likely to turn yellow shortly are picked irrespective of size, w r hile only those green lemons which are above a minimum size are picked. In most associations, rings are used by the pickers as an aid in determining the sizes of green lemons. The lemons are delivered to the packing-house in field boxes, which are piled in tiers on the receiving floor. From the receiving floor the lemons are trucked by hand to the washer. After being washed, they pass over a mechanical sizer which removes the smallest sizes, known as "lemonettes." The remainder go onto a sorting belt, where the culls are removed and the merchantable lemons sorted into a number of different color classifications and placed in storage boxes. The color classifications most frequently used are dark green, light green, silver, and yellow, although some associations at times make two separations of one or more of these colors. The chief reason for sorting by color arises from the differences in the length of time in which lemons of different colors can be marketed after being picked and differences in the length of time they can be held in storage without deterioration in quality. In general, yel- low lemons can be shipped immediately after being picked, but green lemons must first be cured, which process requires from several days to several weeks. On the other hand, green lemons can be held in storage much longer than yellow lemons. The different color segregations are stacked in separate blocks in the storage room, where they are held for varying lengths of time awaiting shipment. Within each color classification the order of shipments is usually based upon the time of arrival at the packing-house, while be- tween color classifications the order of shipments is usually based upon the condition of the fruit with respect to the length of time it can be held in storage without becoming unmerchantable. As given lots of fruit are to be shipped, they are taken out of storage, graded and packed, and then either stacked on the loading platform or loaded directly into the cars. The fruit is sorted into the several grades by means of inspection. The usual grades employed are Extra Choice, Choice, and Standard. Lemons which do not meet the specifications of Standard are termed "culls" and are sent to the products plant. Occa- sionally some lots, instead of being graded, are shipped as orchard-run. Each of the grades is packed separately. In the process of packing the 8 University of California — Experiment Station lemons are sorted by size, only those of the same approximate size being placed in the same box. The standard sizes of lemons are as follows : 180's, 210's, 240's, 270's, 300's, 360's, 432's, 490's, 540's, and 588's. The figures refer to the number of lemons in a standard packed box. In associations packing from trays the identity of the individual lots is maintained until after they have been graded, while in associations packing from belts, tubs, or bins, the identity of the individual lots is generally maintained until after they are packed. Thereafter one grower's fruit becomes commingled with that of other growers. Payments to growers are based upon grades and, in most associa- tions, upon sizes. Each grower receives the same price per unit for the same class of fruit contributed during a specified pooling period. GRADE POOLS In the Santa Paula Citrus Fruit Association the bulk of the lemons is sorted into the following grades : Extra Choice, Choice, Standard, and culls. Lemons which do not meet the specifications of either Extra Choice, Choice, or Standard, but which are merchantable are classed as offgrade. Occasionally some lots of lemons are sold as orchard-run instead of being graded. Lemonettes, those smaller than 588's, are re- moved at the washer by means of a mechanical sizer, but are not subse- quently graded for quality, except that the culls are taken out. In the Extra Choice and Choice grades, cured and tree-ripe lemons are kept separate. In the Standard grade, however, they are combined. Pooling is on the basis of brands, which with their corresponding grades are as follows : Brand Grade Excellent Extra Choice (cured) El Merito Extra Choice (tree-ripe) Sunside Choice (cured) Superba Choice (tree-ripe) Wave Standard (cured and tree-ripe) Stock Offgrade (cured and tree-ripe) Lemons which are sold as orchard-run are pooled with Choice tree- ripe under Superba. Lemonettes, loose fruit, and culls are each pooled separately. 6 The bulk of the loose-fruit sales consists of Standard tree-ripe lemons, although other grades are at times included. Bul. 619] Maintenance of Equity in Pooling of Lemons DIVISION OF TOTAL NET RETURNS BETWEEN GROWERS: GRADE POOLS VS. NO-GRADE POOLS At the outset it should be recognized that pooling on the basis of grades may or may not result in a division of the total net returns different from the division in the absence of grade pools. A difference will occur if: (1) there are variations between growers in the proportions of the several grades contributed by them during the period under considera- tion; and (2) the average selling prices of the several grades for the TABLE 1 Percentage of Total Packed-Lemon Shipments Under Excel- lent Brand; 56 Growers from the Santa Paula Citrus Fruit Association ; Average 1925-26 to 1934-35 Per cent of shipments Number of growers 1 Per cent of growers 1 S 29.9 to 32. 3 1 2 11 24 10 8 1.8 32.4to37.3 3.6 37.4 to 42. 3 19.6 42.4 to 47. 3 42.9 47.4 to 52. 3 17.8 52.4 to 56.8 14.3 Total 56 100.0 specified period of time are unequal. In the absence of either of the two sets of conditions, however, even though the other is present, the division of the total net returns would be the same. Variations between Growers in the Proportions of the Several Grades Contributed. — During the ten years 1925-26 to 1934-35, approximately 47 per cent of the lemon shipments of the Association consisted of Extra Choice cured fruit, marketed under the Excellent brand. This same per- centage of Excellent fruit, however, was not produced by each grower. Table 1 shows the extent of the variation between the 56 growers in the average proportions of their total shipments which graded Excellent for the period 1925-26 to 1934-35. The consistency with which the ship- ments of the 56 growers contained a larger or smaller percentage of Excellent lemons than the average of the Association during the ten years is shown in table 2. From the data presented in these two tables it is evident that the fruit of some growers consistently ran heavily to first grade, while that of other growers consistently ran light to first grade, and that over a period of years there was substantial variation between growers in the proportions of first-grade fruit produced. 10 University of California — Experiment Station An analysis of shipments shows that much the same situation which existed with respect to the variations between growers in the proportions of Excellent lemons contributed also prevailed with respect to each of the other brands. 7 Differences between the Average Selling Prices of the Several Grades. — Table 3 shows the amount per packed box that the weighted-average f .o.b. prices of El Merito, Sunside, Superba, and Wave have been below TABLE 2 Distribution of 56 Growers with Eespect to Number of Years Their Percentage of Excellent Brand (on Basis of Total Packed-Lemon Shipments) Was Below the Santa Paula Citrus Fruit Association Average ; 1925-26 to 1934-35 Number of years below association average Number of growers Per cent of growers 1 2 10 6 3 10 9 4 7 3 4 3 5 2 10.7 9 5.4 8 17.8 7 16.1 6 7.1 5 12.5 4 5.4 3 7.1 2 5 4 1 8.9 3.6 Total. 56 100 or above the weighted-average f.o.b. price of Excellent each year from 1925-26 to 1934-35. 8 The chief tendencies exhibited in this table are (1) for the price differentials between the several brands to be sub- stantial in each year, (2) for Excellent to bring more than El Merito, El Merito more than Sunside, Sunside more than Superba, and Superba more than Wave, and (3) for the price differentials between the several brands to narrow. Differences in Returns to Individual Growers with Separate Pools for Each Grade as Compared with No-Grade Pools. — Table 4 is designed to show the differences in the average returns per packed box to indi- vidual growers for the ten-year period from 1925-26 to 1934-35 with separate pools for each grade as compared with no-grade pools. With all 7 See table 69, Appendix G. 8 The question whether or not the weighted-average-priee differentials correctly reflect the differences in the market value of the several grades is discussed under the section entitled "Determination of Price Differentials Between Grades." Bul. 619] Maintenance op Equity in Pooling of Lemons 11 grades combined, about 68 per cent of the growers would have received over this ten-year period within 5 cents a packed box of the average price which they actually received with the grade pools. Over 21 per cent of the growers, however, would have received from 6 to 10 cents a box different (either more or less) from the average price which they TABLE 3 Weighted-Avekage F.O.B. Prices per Packed Box of Excellent Lemons, and Differentials Between the Prices of Excellent and Other Brands; Santa Paula Citrus Fruit Association ; 1925-26 to 1934-35 F.o.b. price Excellent Price differentials from Excellent of Year November-October El Merito Sunside Superba Wave 1 2 3 4 5 1925-26 dollars per box 4.08 5.40 5.55 5.72 5.85 4.81 4.38 4.00 4.29 3.66 5.32 4.23 4.77 dollars per box -0.82 -0.96 -0.78 -0.79 -0.77 -0.10 -0.84 -0.55 -0 34 -0.56 -0.82 -0.48 -0.65 dollars per box -0.94 -1.05 -0.77 -0.83 — 1.07 -0.92 -0.36 -0.85 -0.86 -0.74 -0.93 -0.75 -0.84 dollars per box -1.32 -1.97 — 1.53 -1.26 -0.94 -0.57 -0.97 -1.05 -0.67 -0.25 -1.40 -0.70 -1 05 dollars per box -1.31 1926-27 -1.15 1927-28 -1.82 1928-29 -1.63 1929-30 -1.84 1930-31 -1.57 1931-32 +0.24 1932-33 -1 81 1933-34 -1 53 1934-35 -0.73 Averages : 1925-26 to 1929-30 -1.55 1930-31 to 1934-35 -1.18 1925-26 to 1934-35 -1 36 actually received, while about 9 per cent of the growers would have received from 11 to 15 cents a box more or less. Judging from the variations between growers in the proportions of the first grade contributed (table 1) and from the differentials between the average f.o.b. prices of the several grades (table 3), it may be con- cluded that much the same situation as is shown in table 4 characterizes each of the ten years from 1925-26 to 1934-35. In each of the years the variations between growers in the proportions of the several grades contributed was greater than the average of the ten years. In some years, however, the price differentials between the several grades were con- siderably smaller than the average of the ten years, while in other years they were considerably larger. In those years in which the price differ- entials between the several grades were larger than the average of the ten-year period, the differences in returns to growers with separate grade pools as compared with no-grade pools would have been larger than those shown in table 4. 12 University of California — Experiment Station In table 4 two assumptions are made : (1) that the total net returns of the Association would have been the same without grade pools as they were with grade pools, and (2) that the proportions of the several grades contributed by each grower would have been the same without grade pools as with grade pools. While such a situation may exist for a short period it is not likely to continue for ten years and certainly would not continue indefinitely. Payment to growers of a flat rate per unit irrespec- TABLE 4 Differences in Lemon Returns per Packed Box to 56 Grow- ers with Separate Pools for Each Grade as Compared with No-Grade Pools; Santa Paula Citrus Fruit Association; Average 1925-26 to 1934-35 Differences, cents per box Number of growers Per cent of growers 1 g Oto 5 6 to 10 38 12 5 1 67.9 21.4 11 to 15 8.9 10 to 20. 1.8 Total... 56 100 tive of the character of the fruit contributed by each would sooner or later discourage the production of high-quality lemons. Under such conditions, growers who produced high-quality fruit would tend either to leave the Association or allow their fruit to deteriorate to the general level. On the other hand, growers who produced poor-quality lemons would have no particular incentive to increase the quality of their fruit. DETERMINATION OF THE NUMBER OF UNITS OF EACH GRADE CONTRIBUTED BY INDIVIDUAL GROWERS If each grower is to be credited with the number of units of each of the grades which the fruit that he contributed to a given time pool actually contained, the following requirements must be met : 9 1. The sorting must be done in such a w r ay that all the lemons in each of the grades are reasonably uniform in quality and that the average quality of the lemons in one grade is significantly different from the average quality in another. 2. The sorting must be reasonably uniform as between the fruit of the several growers. 9 The problem relating to differences in grades arising from variations in the length of time the individual lots are kept in storage is discussed later (p. 19-23). Bul. 619] Maintenance of Equity in Pooling of Lemons 13 3. The fruit of each grower must be sorted separately. 4. The number of units of each grade must be determined before one grower's fruit has become commingled with that of other growers. In general, it appears that each of these four requirements has been met satisfactorily by associations which pack from trays, and that the first two requirements have been satisfactorily fulfilled by associations packing from belts, bins, or tubs. In all associations the fruit is sorted into the several grades by inspec- tion rather than by mechanical means. The bulk of the lemons in any one lot would be sorted in about the same way by different graders or by the same graders at different times. The difficulty in securing uniformity of grading is in connection with those lemons which fall at the extremes of the grade limits. With such lemons there may be differences of opinion, even among the most expert graders, whether they should be placed in the higher or in the lower grade, and the same expert may decide one way at one time and the other way at another time. Consequently, the grade-outs obtained on a given lot would probably not be identical with those obtained if the same lot were run again. At best, grading of lemons under commercial operations is approximate rather than precise. Never- theless, when done by experienced people under careful supervision, the grading is usually sufficiently uniform so that buyers seldom discrim- inate between lemons of the same grade packed from different lots of fruit in the same association. As a general rule, if grading is sufficiently uniform for the purposes of selling, it is also sufficiently uniform for the purposes of pooling. In associations which grade into and pack from trays, the individual lots of fruit, however small, are kept entirely separate until after they have been graded and the number of pounds of each grade in each lot determined. Thus, each grower is credited not only with the total num- ber of pounds of lemons (less shrinkage) delivered to the packing-house from his orchard, but also with the number of pounds of each grade which his fruit contained at the time it was graded, since the identity of the individual lots is maintained until after the weight of the fruit in the trays has been determined. Within the past ten years many of the lemon packing-houses in the state have discarded grading tables and packing trays and installed grading belts with either packing belts, tubs, or bins. Packing belts are the most numerous. The two reasons generally given for this change relate to costs of operation and to size pools. 10 10 The use of packing belts, tubs, and bins in connection with pooling on the basis of size is discussed under "Size Pools." 14 University of California — Experiment Station Packing-house managers who have operated with both the tray and the belt systems are unanimous in the opinion that costs of grading and packing are at least 5 cents a packed box less with belts than with trays, and some managers claim a saving in costs of as much as 15 cents a packed box. Although comparable records relative to the costs of the two systems are not available, careful observation supports the claim of a reduction in costs, provided fairly continuous operation is secured. 11 The difficulty is that the continuity of operation which is essential in order to secure low costs prevents the keeping of small lots of fruit entirely separate until after the number of units of each grade has been determined. The pooling unit employed by associations packing from belts, tubs, or bins is the packed box. The number of packed boxes of each grade of fruit obtained from a given lot cannot be precisely determined until after the lot has been packed. But to keep small lots of fruit entirely separate until after they have been packed would result in much idle time on the part of both the workers and the equipment. The cost which this would entail apparently is so great that no association with nu- merous members actually does it. Instead they have resorted to two de- vices : (1) estimating cleanups, and (2) combining lots containing only a few boxes each. Estimating Cleanups. — After each lot of fruit has passed over the grading belt and has been sorted into the several grades, the amount of fruit of each grade remaining on the packing belts (or in the tubs or bins) and in the partially packed boxes is determined by experienced estimaters on the basis of inspection. The estimated amounts are then added to the number of boxes of each grade packed from that lot and subtracted from the number of boxes of each grade packed from the next succeeding lot. The two problems involved here are (1) the deter- mination of the total quantity of all grades combined and (2) the deter- mination of the total quantity of each of the grades. The first of these two problems is less difficult than the second. When grading begins, the total number of storage boxes in each lot is known, and if desired the net weight of the fruit in each lot can be ascertained. The amount of culls obtained from the lots and the amounts of the grades set back for packing later can be determined either in terms of storage boxes or pounds. By subtracting the culls and "set- backs" from the original quantity, the quantity of fruit actually packed from the lot can be closely approximated, either in terms of pounds, 11 The largest part of the reduction appears to be in the cost of grading rather than in the cost of packing, although some saving in the cost of packing is apparently secured. Bul. 619] Maintenance of Equity in Pooling of Lemons 15 storage boxes, or equivalent packed boxes, whichever is desired. 12 With the use of some such system as outlined above, the total quantity of packed fruit credited to each grower would not be significantly different from the quantity that would be obtained if each lot were kept entirely separate. The greatest difficulty in connection with estimating cleanups is in determining the quantity of each grade and size. 13 The number of storage TABLE 5 Number of Packed Boxes of Lemons Estimated on Cleanups; 10 Individual Lots ; Association A ; 1936 Extra Choice Choice Lot number On belt Partially packed Total On belt Partially packed Total 1 2 5 4 5 6 1 2 boxes* 9 11 9 8 10 12 11 14 14 14 boxes* 16 5 10 8 6 28 8 8 12 12 boxes* 25 16 19 16 16 40 19 22 26 26 boxes* 5 5 8 11 7 3 5 4 11 5 boxes* 6 3 6 5 2 6 6 9 9 boxes* 11 8 3 14 4 5 6 11 12 5 7 8 11 10 9 10 20 14 * Equivalent packed boxes. boxes in or the net weight of the lot is of use only in checking the total number of boxes of all grades packed, but not in checking the number of boxes of each grade packed. In the absence of some device for recording the quantity of each grade between grading and packing, the number of units of each grade credited growers is subject to the errors of estimate. The volume of fruit remaining on the belts (or in the tubs or bins) and in the partially packed boxes at the end of the grading of each lot tends to vary within rather wide limits, as is shown in table 5. In the case of lots containing a relatively few boxes, the entire determination of the number of units of each of the grades being packed at a given time is based upon estimates, while in the case of lots containing a large number of boxes the major part of the determination is based upon actual pack- out with only a minor part based upon estimate. This is illustrated in table 6. 12 Some associations consistently check the estimates of cleanups in this fashion ; other associations make only occasional checks. 13 The problem of estimating the number of units of each size is discussed under "Size Pools." 16 University of California — Experiment Station In most associations only Extra Choice and Choice are packed at the same time, while Standards are set back for packing later. Now even when the sum of the estimates of both of these grades of a particular lot is correct, the Extra Choice may be overestimated and the Choice under- estimated, or vice versa. It should also be recognized that each lot except the first and last between complete cleanups is subject to two estimates, and that any errors in the two estimates on a given lot are as likely to be in the same as in the opposite direction. Suppose, for example, on the first lot after a complete cleanup the estimates show 2 boxes more Extra TABLE 6 Number of Boxes of Lemons Packed Out, Estimated on Cleanups, and Total Credited Growers; 4 Individual Lots ; Association B ; 1936 Extra Choice Choice Lot number Packed out Estimated Total Packed out Estimated Total / 2 3 4 5 6 1 2 3 boxes* 53 84 282 boxes* 23 24 29 30 boxes* 23 77 113 312 boxes* 14 22 61 boxes* 12 23 9 12 boxes* 12 37 31 4 73 * Equivalent packed boxes. Choice and 2 boxes less Choice than the fruit actually contains. Since these estimates are added to lot No. 1 and subtracted from lot No. 2, the second lot would show 2 boxes less Extra Choice and 2 boxes more Choice than it contains, providing that the estimates of the cleanup on lot No. 2 were correct. The estimates of the cleanup of the second lot, however, may show 2 boxes more Choice and 2 boxes less Extra Choice than the actual amounts of fruit on the belt and in the partially packed boxes. Under this situation lot No. 2 would be credited with 4 more boxes of Choice and 4 fewer boxes of Extra Choice than it would if the fruit had been packed separately. In order to obtain some idea of the accuracy of the estimates of clean- ups, a limited test covering 15 lots was made. Estimates were made by the regular estimater. Then the fruit was completely packed out. The differences between the actual pack-outs and the amounts credited growers are shown in table 7. The results of this test, while by no means conclusive, since it was conducted in only one packing-house and in- cluded only a few lots, check with the consensus of opinion among pack- ing-house managers, which is that the estimates for any given grade are not likely to be more than 2 or 3 packed boxes different from the actual amounts. Bul. 619] Maintenance of Equity in Pooling of Lemons 17 Over a period of time errors in estimates of this sort tend to be com- pensating rather than cumulative, so that the net error involved in an entire season's operation tends to be less than the error in connection with a single lot ; and likewise, the net error over a period of several years tends to be less than the net error in a given year. With fairly large individual lots, the net error on a year's deliveries cannot be very sig- nificant, while over a period of years it will be negligible. As the indi- TABLE 7 Differences Between Actual Pack-outs of Lemons and Amounts Credited Growers ; 15 Individual Lots ; Association C; 1937 ....... ..i Number of lots Differences, number of packed boxes Extra Choice Choice 1 2 to0.5 2 5 5 2 1 15 3 0.6to 1.5 1.6 to 2 5 6 4 2.6 to 3 5 2 3.6to4 5 Total 15 vidual lots become smaller, however, the error in estimating constitutes a larger proportion of the delivery. With fairly small lots such errors may be significant in amount. Combining Lots Containing Only a Few Boxes Each. — In order to secure economical operation, associations packing from belts, tubs, or bins combine several lots containing only a few boxes each and run them as one lot. In most cases the total number of packed boxes of each grade obtained from the combination lot is prorated among the several growers f on the basis of the number of storage boxes contributed by each. Thus each grower is credited with the average grade-out of the combination lot irrespective of whether his particular fruit was above or below the average. By recognizing that there is substantial variation in the proportions of the several grades in small as well as in large lots, some associations follow the practice of combining lots which appear to be similar in quality and of placing fruit which is known to be markedly different in separate combination lots. At least one association has gone a step fur- ther. With lots containing from 11 to 50 storage boxes which are com- bined, it separately grades each lot, determines the quantity of culls and Standards, and estimates the percentage of Extra Choice in the remain- 18 University of California — Experiment Station der. These percentages are then used in prorating the pack-out from the combination lot among the several growers. Methods such as these are an improvement over straight combination lots containing fruit markedly different in quality, but they do not appear to provide sufficient accuracy to justify the claim that fruit in combination lots is pooled on the basis of grade. The usual pool statement shows the total shipments of a grower's fruit broken down by grades, but with no indication of the amount of such fruit in combination lots. To the extent that such lots are employed, the pool statements of individual growers give an impression of much greater accuracy than actually exists. Unless growers are fully ac- quainted with the operations of their association, they naturally believe that their pool statements show the precise grades obtained from their fruit, when as a matter of fact this may not be true, particularly in the case of growers having relatively small quantities of lemons. From the standpoint of revealing the actual situation, pool statements of indi- vidual growers might well show the number of storage boxes placed in combination lots. At least one association handling grapefruit does this. A number of suggestions have been made for overcoming the disad- vantages of no-grade pools for fruit in combination lots when packing from belts, tubs, or bins, while at the same time retaining the low costs arising from continuous operation. Three which appear to justify experi- mentation are (1) mechanical sizers and electric counters, (2) sample grading, and (3) automatic weighing devices. 14 When the grades are determined by sorting the entire lot, the chief problem peculiar to combination lots is that of determining the number of units of each grade between grading and packing. Individual lots con- taining as few as 5 storage boxes can be graded separately without undue cost, but cannot be packed separately. Under the present methods of operation, however, the number of units of each grade cannot be de- termined until after the fruit is packed. If it should prove commercially feasible to record, by means of automatic weighing devices installed between the grading and packing equipment, the number of pounds of each grade of fruit prior to packing, growers with fruit in combination lots could be paid in accordance with the particular grades of their fruit. The pooling unit for combination lots would then be the pound rather than the storage box. In the Santa Paula Citrus Fruit Association the individual lots run considerably larger than the average of all the associations in the state, 14 The problems connected with mechanical sizers and electric counters are dis- cussed under "Size Pools"; those relating to sample grading are discussed later in this part of the report. Bul. 619] Maintenance of Equity in Pooling of Lemons 19 but even in this association there are many small lots. An individual lot consists not of the entire crop of the grower, but of only the part of the fruit from one picking, and there are usually from seven to ten pickings. After taking out the washer culls and lemonettes, each picking of each grower is divided into at least as many individual lots as there are sep- arate color classifications, of which there are generally four or five. 16 In addition, a given color of fruit of a grower may be placed in two or more TABLE 8 Percentages of Total Annual Lemon Deliveries in Lots of 50 Storage Boxes and Less; 101 Growers from the Santa Paula Citrus Fruit Association; 1933-34 and 1934-35 Number of growers Per cent of deliveries 1933-34 1934-35 1 2 0.0 to 9.9 45 30 11 8 7 69 lO.Oto 29.9 20 30.0 to 49.9 8 50.0to 74.9 2 75.0 to 100.0 2 Total 101 101 different blocks in the storage room. An individual grower's lot, there- fore, consists of only the lemons of a given color from one picking which are stored in the same block. Table 8 is designed to show the proportions of the annual deliveries of the growers in the Santa Paula Citrus Fruit Association that were in individual lots of 50 storage boxes and less in 1933-34 and 1934-35. Table 8 shows that in 1933-34, a year of about average yields per acre, 26 of the growers had 30 per cent or more of their fruit in lots of 50 storage boxes and less, while 7 of the 101 growers had 75 per cent or more of their fruit in such lots. In 1934^35, however, when yields per acre were much above average, considerably fewer growers had a relatively large proportion of their annual deliveries in lots of 50 storage boxes and less. On the other hand, in years of low yields per acre, it would be expected that the number of growers having a relatively large propor- tion of their crops in such lots would be increased. Differences in Grade Occasioned by Length of Time in Storage. — Thus far the assumption has been that the grades obtained from differ- ent lots correctly reflect the inherent differences in the quality of the 15 The division into the several color classifications is not, of course, equal. 20 University of California — Experiment Station fruit. This assumption is valid only if the lots are graded after being in storage for comparable lengths of time under uniform storage condi- tions. The quality of the fruit is affected by the length of time it is held in storage and by the conditions under which it is held as well as by its inherent characteristics. In all associations the lemons are held in storage for the accounts of the individual growers. Grading is done after the fruit is taken from storage and just prior to the time it is shipped. During a considerable TABLE 9 Number of Days That Individual Lots of Light-Green and Silver Lemons Delivered in December, 1934, Were Held in Storage at the Santa Paula Citrus Fruit Association Light green Silver Number of days Number of lots Per cent of lots Number of lots Per cent of lots 1 2 3 4 60 and less 15 24 25 23.4 37.5 39.1 31 19 20 44 3 61 to 90 91 to 120 27.1 28.6 121 to 150 0.0 Total 64 100.0 70 100 part of the year there is a larger volume of lemons available for ship- ment than can be marketed. Since all of the fruit, particularly that received during the winter months, cannot be marketed as soon as it is ready for shipment, the manager must select the particular fruit to be shipped at any given time, and the remainder must stay in storage. This situation occasions little difficulty with respect to the determination of the grades of each grower's fruit at the time of shipments in years when the supply and demand conditions are such that all of the fruit can be shipped before it has begun to deteriorate in quality. But in years like 1934—35, when considerable quantities of lemons had to be held in storage long past their prime, the problem may be acute. Some growers may secure relatively large gains while others may experience substan- tial losses merely by reason of their position in the picking schedule or by reason of the choice of the manager in shipping fruit of one color classification rather than of another. 16 An example of an extreme situation with respect to variations in the 16 Within each color classification the order of shipments is usually based upon the time of arrival at the packing-house, while between color classifications the order of shipments is usually based upon the condition of the fruit with respect to the length of time it can be held in storage without becoming unmerchantable. Bul. 619] Maintenance of Equity in Pooling of Lemons 21 length of time lemons of the same color classification were held in storage is shown in table 9. Probably the lots of light-green lemons which were held in storage between four and five months suffered considerably more from deterioration in grade and shrinkage than those held in storage three months or less. Likewise, the lots of silver lemons which were held in storage between three and four months probably experi- enced more deterioration in grade and shrinkage than those held in storage two months or less. In order to handle this problem adequately, some method must be employed to determine, before the fruit deteriorates, the grades of the individual lots that are held in storage beyond their prime. It does not appear at all impossible for an association to establish the normal lengths of time the fruit in each color classification can be held in storage without appreciable loss from deterioration in quality and shrinkage. Such normal storage periods may be different at one part of the season from those at another. If each lot that has been held in storage for the estab- lished normal length of time could be graded immediately, the individ- ual growers could then be paid in accordance with the inherent qualities of their fruit. In the opinion of packing-house managers, such a pro- cedure would be very expensive. Much the same results, however, might be secured without excessive costs by determining the grades on the basis of respresentative samples taken at the washer. Although the grades of many agricultural products are determined on the basis of samples, this system has never been used for lemons. Whether or not it would prove satisfactory for lemons cannot be de- termined in advance of careful experimentation. The two chief objec- tions against it relate to the securing of a representative sample and the proper curing of the sample. If these two problems could be solved, then a sample from each grower's deliveries would be taken just after the fruit was washed. It would then be sorted by color and placed in storage. At the end of the normal storage period for each color classification, the fruit of that color in the sample would be graded and the grades thus obtained would be applied to the entire lot for the purpose of determin- ing the grower's grade credits. 17 If this method is used, a separate room for storing the samples would probably be desirable in order to insure that every sample is stored under uniform temperature and humidity conditions, and to provide easy access for inspection. Separate equip- ment for grading the samples would probably also be desirable. Such equipment could be designed especially for grading small quantities of fruit, and possibly special devices, which would be too expensive to use 17 Each grower's size credits could also be obtained from the sample. 22 University op California — Experiment Station in the regular operations, could be employed. Also the most expert graders could be assigned to grade the samples. The method of determining growers' grade and size credits from samples, if it should prove to be feasible, would go far toward solving some of the most difficult problems in the pooling of lemons. Estimates of cleanup and combination lots could then be eliminated and continuous operation in the packing-house could be secured. Differences in grades and sizes arising from variations in the length of time fruit was held in storage would be much reduced, and the grades and sizes of merchant- able fruit sent to the products plant could be readily ascertained. Instead of taking samples at the washer and placing them in storage, there is the possibility that it might be feasible to select samples from the individual lots after they are stacked in the storage rooms. From the entire lot a few boxes would be selected at random or in accordance with a definite pattern. The boxes thus selected would be removed from the stacks and the grades and sizes of the lemons contained therein deter- mined. The chief problems in this method relate to the additional han- dling required in the tearing down and restacking of the fruit in storage and to the securing of samples which are representative of the entire lot. One advantage of this method over that of selecting samples at the washer is that samples would have to be taken from only those lots which were left in storage beyond their normal storage periods. The grades and sizes of the lemons in lots which were shipped before the end of their normal storage periods would be determined in the usual way. Another proposal which is sometimes advanced is that the grades of each grower's lemons be determined before they are placed in storage. This proposal, however, does not appear to be a feasible one. Difference in quality cannot be readily detected before the lemons are cured. In many instances neither the external appearance nor the internal condi- tion of the lemons at the time they would normally be shipped can be determined at the time they are delivered to the packing-house. External defects, for example, cannot be easily seen while the fruit is still green. Also, the degree of susceptibility to decay cannot in many cases be as- certained at delivery. Thus, two lots of lemons which appear to be identi- cal at the time of delivery may be considerably different in quality after being in storage for the same length of time. Even though it were possible to determine the relative grades of the lemons with a reasonable degree of accuracy at the time of delivery, this would not avoid the necessity of grading them at the time of packing. From the standpoint of pooling it is only necessary to determine the proportions of the entire quantity in each grade, but from the standpoint Bul. 619] Maintenance of Equity in Pooling of Lemons 23 of selling it is important to separate the several grades physically. And since the quality of lemons may change, the physical separation should be made as close to the time of sale as practicable. Thus, if the relative grades at the time of delivery were determined from the sorting of the entire lot, two complete grading processes would be entailed. On the other hand, the relative grades at the time of delivery might be deter- mined from samples, which would avoid the double grading of all the fruit. However, if the relative grades are to be determined from samples, these could probably be cured before they are graded instead of being graded immediately, and this would overcome the difficulties mentioned in the preceding paragraph. DETERMINATION OF PRICE DIFFERENTIALS BETWEEN GRADES When pooling is on the basis of grade the question arises of how to de- termine the price rates to be applied to each grade in setting up the money credits to growers. The simplest method, and the one which is universally used by lemon packing-houses, is merely to divide the total net amount of money received for each grade during the period of the pool by the number of units of that grade sold. This gives a weighted- average net price per unit. Another method, which has some advantages, although involving more clerical work, is to base the rates upon a simple average of the price differentials between the several grades prevailing on the same markets on the same days. If the proportions of the several grades were the same in each car shipped during the time pool, the two methods would give identical results. But this situation seldom prevails. The general situation is that some cars contain a larger proportion of certain grades than do others. The result is that the weighted-average prices of each grade may vary because of either (1) differences in prices between grades on the same market on the same day, (2) differences in the level of prices of all grades on the same market on different days, or (3) differences in the level of prices of all grades on different markets on the same day. In most cases the differences between the weighted- average prices of the several grades for a given pooling period are the result of a combination of the three. There is considerable basis for contending that the price rates used in determining the money credit to growers should reflect only the price differentials between the several grades on the same markets on the same days, and not the differences in the level of prices of all grades, which occur by reason of the market to which they were shipped or by reason of the time at which they were shipped. In order to obtain the largest total returns for all growers combined, the manager, rather than the 24 University of California — Experiment Station individual growers, should determine the time and place of shipments. Yet his decisions, although resulting in the largest possible total returns to the association, under the existing conditions, may cause certain grades to bring either more or less than they would have brought if his decisions had been different. Table 10 shows a comparison of the price differentials between Excel- lent and Sunside and between Excellent and Wave computed from the TABLE 10 Comparison of Price Differentials between Selected Brands of Lemons, Based upon Weighted- Average Lemon Prices and upon Simple Average of Prices in Corresponding Months ; Santa Paula Citrus Fruit Association; 1925-26 to 1934-35 Differential of Sunside from Excellent Differential of Wave from Excellent Year November-October Weighted average Simple average Weighted average Simple average 1 2 3 4 1925-26 dollars per box -0.94 -1 05 -0.77 -0.83 -1.07 -0.92 -0.36 -0.85 -0.86 -0.74 -0.93 -0.75 -0.84 dollars per box -0 75 — 1 10 -0.60 -0.99 -1.00 -1 00 -0.70 -0.86 -0.88 -0.85 -0.89 -0.86 -0.87 dollars per box -1 31 -1.15 -1.82 -1.63 -1.84 -1.57 +0.24 -1.81 -1 53 -0 73 -1.55 -1.18 — 1 36 dollars per box -1.27 1926-27 -2 13 1927-28 — 1.47 1928-29 -2.28 1929-30 —2.17 1930-31 —2 51 1931-32 1932-33 -1.98 -1.87 1933-34 — 1.73 1934-35 -1 81 Averages: 1925-26 to 1929-30 -1.86 1930-31 to 1934-35 — 1 98 1925-26 to 1934-35 -1.92 weighted-average prices and from the simple averages of prices in cor- responding months. Substantial differences in the results are obtained by the two methods of computation, in both amount and direction. The use of the weighted-average prices indicates a material decrease in the average price differentials during the five years 1930-31 to 1934-35 as compared with the previous five years, yet the use of the simple average of prices in corresponding months shows no significant narrowing. In general, the differentials based upon weighted-average prices are less than those based upon simple-average prices. This is most pronounced in the case of Wave. In 1931-32 the weighted-average price of Wave was $0.24 a packed box above the weighted-average price of Excellent, yet at no time during that year did Wave sell for as much as Excellent. During the months in Bul. 619] Maintenance of Equity in Pooling of Lemons 25 which both brands were sold the price of Wave averaged $1.98 a packed box below the price of Excellent. In this case the weighted-average prices of the two brands reflected not the differences in the quality, but the dif- ferences in the time they were shipped. The simple average of the prices during the months both brands were sold provided a much closer ap- proximation to the price differentials occasioned by differences in quality alone. While this example represents an extreme case, a careful examina- tion of table 10 shows that somewhat the same type of situation has occurred rather frequently during the past ten years. Methods of computing rates of payments to growers based upon a simple average of the price differentials between the several grades pre- vailing in the same markets on corresponding days are discussed in Appendix B. SIZE POOLS Packed lemons, which constitute the bulk of the lemons destined for fresh consumption, are sold on the basis of size as well as of grade. In past years lemons were packed in both the standard box and the jumbo box, but since 1935-36 the use of the jumbo box has largely been dis- continued. Throughout this report the term "size" will refer to the number of lemons contained in a standard packed box, unless the words "jumbo box" are specifically mentioned in connection therewith. The standard sizes of lemons are as follows : 180's, 210's, 240's, 270's, 300's, 360's, 432's, 490's, 540's, and 588's. In the Santa Paula Citrus Fruit Association, lemonettes are sorted out at the washer by means of a mechanical sizer and are pooled sep- arately. Until recently the remaining lemons were pooled by grade but not by size within a grade pool. Each grower received the same price per pound for the same grade of lemons irrespective of the particular sizes of his lemons in that grade. This was formerly the practice employed by all lemon cooperative packing associations. For several years, however, numerous associations have pooled, at least to some extent, on the basis of size. Some associations pool each size separately ; others group the sizes in various combinations. DIVISION OF TOTAL NET RETURNS BETWEEN GROWERS WITH AND WITHOUT SIZE POOLS As in the case of pooling on the basis of grades, the division of the total net returns with size pools or without size pools may or may not be different among the individual growers. A difference will depend upon (1) the extent of the variation between growers in the proportions of the several sizes of a given grade contributed during the period under con- 26 University of California — Experiment Station sideration and upon (2) the extent of the differences between the aver- age selling prices of the several sizes of that grade for the specified period of time. Variations between Growers in the Proportions of the Several Sizes Contributed. — Records from the Santa Paula Citrus Fruit Association are not available on the nature and extent of the variations between its growers in the proportions of the several sizes of each of the different TABLE 11 Proportions of the Several Sizes of Extra Choice Lemons Contributed to a Given Time Pool by 4 Growers from Association D in 1933-34 Percentage of total boxes contributed by Sizes Grower No. 11 Grower No. 15 Grower No. 12 Grower No. 16 1 2 8 4 number per box 210 per cent 0.2 0.0 0.2 6.3 19 3 21.1 17.6 17.3 18.0 per cent 0.0 5 32.4 43.9 16.2 5.8 1.2 0.0 0.0 per cent 0.0 0.0 0.0 22.4 42 5 19.3 11.0 3.6 1.2 per cent 0.0 240 2.0 270 2.0 300 25 3 360 35 6 432 20.5 490 11.7 540 2.9 588 0.0 Total 100.0 100.0 100 100.0 Average number of lemons per box 466 810 884 876 grades delivered during specific pooling periods and over a period of several years. Some data, however, were secured from two other asso- ciations. 18 Table 11 shows the relative distribution of sizes in the shipments of Extra Choice lemons of 4 growers during a given time pool in 1933-34. The fruit of grower No. 11 ran heavily to small sizes, while that of grower No. 15 ran heavily to large sizes. Even though the average size of the fruit was nearly the same for grower No. 12 and grower No. 16 there was a significant difference in the proportions of 360's. The extent of the variation between 12 growers in another association in the proportions of Extra Choice lemons contributed to each size pool by years from 1929-30 to 1934-35 is shown in table 12. 19 In each year the variation in sizes was considerable. Over the six-year period the 18 In addition to tables 11, 12, and 13, see tables 70, 71, and 72 in Appendix G. 19 The situation with respect to Choice and Standard lemons is shown in tables 71 and 72, respectively, Appendix G. Bul. 619] Maintenance of Equity in Pooling of Lemons 27 l-i 4. co o o PM M OQ B o <1 o n w Eh P n n OS Eh o Q m o h-H w o Sg 05 X H r-l oh 1§ IS 85 P-l o o Pn o O 02 05 02 B Eh CO C3 W I O (M © o < o ►H Eh < « l> - «"■ "cS «a ro CO oo CO o M c© w >H a to -o ao CO ■* o> OS o B 1— 1 PH CI Cl »— 1 CO CM b( C o S3 "3 K O h3 »o OB =; c-. >o Cl r-- I S >H CC ■M "" U3 ■« CM CO n -a c 1 i S3 _co cm CO > 3?>.2 Jh s ® -+3 »H lO «5 CO OS >* C s3 SO *- "? Tt< X Cl o ■^ 00 OS © "r-* OS CO o CO o IO o g ~^ i-H rH " .a fe C a as ae CO CO CO r^ be ©4 ffi ■■->« ^^ r- r^ o 'J: «o CO OD -r -# 90 ■* ^r •^ •^ M a c3 P3 C i-H 1 »H a> CO CO CO «M CO CM B9 n i—i Cl Cl - H CM CM © CO co , < -a to K n. *> CO OB <* oc O go >o c e-8 f a GO -*r Cl o o a OS ■■£. CO r^ IO as t^ CO a GO co cc CO CO CO CO r4 t£ - t^ Cl CM CO c •O >o te a s3 % >~ "s •^ r^ t^ ■«< i-H CO o J^ to ^ a. ■» C CM CM o t- IO r^ t^ ■<*< si e «s ag "5 CO Cl o CM Cl rH CM CM g rr -f ■* Tt< -r CO ■«f JH, -* to ^» a. « ** to 00 — Cl OS or oo »o CM o CO 01 — 1 CI CM »— Cl CM CM bt S3 CD is J. "5 to ^* a * 06 00 00 <5X CO CO o M s3 O eo rc BQ ■H •X ^ - 1 •"J" C S3 33 o e* to ^ a. " CO CI o Cl «5 00 o CM c S3 v "5 t- vc t^ o rt CM OS CD *■< a m CI Cl ^H r^ _ O o § i-H rH Fh CD ,fl O +3 o *Q e to be 9 S3 > Im o 5 a o i-^ Cl co f iC > M? cc CO co CO CO a> o ^^ Cl co 'U' CM cc co co co CO ~ 0D 0B :r. cr- os ^^ ♦^ •— i i— * '-" 1 r^-t 28 University of California — Experiment Station average variation tended to be less than in any single year, but was nevertheless significant. Not only did some growers' fruit contain, on the average, a larger pro- portion of large, medium, or small sizes than did that of other growers, but the fruit of some growers consistently ran heavily to large sizes while that of other growers consistently ran heavily to small sizes. This is shown in table 13. Also, some growers consistently produced fruit con- TABLE 13 Distribution of 12 Growers with Respect to Number of Years That Their Percentages of Shipments of Extra Choice Lemons in Each Size Pool Were Above the Average for Association E, 1929-30 to 1934-35 Number of years above average Size pools 270's and larger 300's 360's 432's and smaller 1 2 S 4 6. number of growers 3 number of growers 3 number of growers 2 number of groirers 3 5. 3 1 4. 2 2 3. 1 2 1 2 2 1 1 2 2 2 2... 1 1 . . 3 2 2 5 Total 12 12 12 12 taining more than the average percentage of 300's or of 360's, while other growers consistently produced fruit containing less than the average percentage of these sizes. The above evidence indicates that, during any given pooling period and over a period of several years, there is likely to be substantial va- riation between growers in the proportions of the several sizes of each of the different grades delivered. The extent of the variation in any given year tends to be greater than the average variation over a period of several years. The latter, however, is substantial. Differences between the Prices of the Several Sizes of the Same Grade of Lemons. — This part of the report deals mainly with an analysis of the price differentials between the more important sizes of Extra Choice lemons sold at auction in New York City during the period, November, 1930, to August, 1936. The data were computed to show the differentials between the prices of 360's and each of the other sizes from 240's to 588's, inclusive. These price differentials were then analyzed from the stand- points of (1) the averages for a given year, (2) the averages for the Bul. 619] Maintenance of Equity in Pooling of Lemons 29 five-year period, 1930-31 to 1934-35, and (3) the trends since 1930-31. The tendency is for the price differentials between the several sizes to be continually changing from month to month, rather than to remain constant. This is illustrated in table 14. Certain sizes, however, tend to sell at a premium, while others tend to sell at a discount. Table 15 shows the annual average price differentials between 360's and each of the other sizes of Extra Choice lemons at New York each TABLE 14 Average Monthly Price Differentials from 360's of Each of the Other Sizes of Extra Choice Lemons from 240's to 588's on the New York Auction Market, 1933-34 Month November. . . . December .... January February March April May June July August September October Average 240's* 270's* 300's 432's 490's 540's 1 2 S 4 5 6 dollars dollars dollars dollars dollars dollars per box per box per box per box per box per box +0.09 +0 53 +0.76 -0.73 -0.92 -1.27 -0 03 +0.27 +0 31 -1.25 -1.32 — 1 23 -0.04 +0.13 +0.12 -0.02 -0.08 -0.28 -0.40 -0.28 -0.45 -0.30 -0.82 -1.39 -0.57 -0.28 -0.44 +0.03 -0.02 -0.49 -0.47 -0.56 -0.32 -0.48 -0 70 -0.37 -0.06 +0.03 —0.41 -0.54 -0.75 -0.62 -0 35 —0 11 +0.21 +0.20 +0.53 -0.60 -0.40 +0.01 +0.02 -0 23 -0.07 -0.47 -0.27 -0.06 +0.01 -0.08 -0 30 +0.21 +0.50 +0.45 -0.90 -1.37 -1.26 +0.11 +0.81 +0.80 -1 54 -1.98 -2.57 -0.26 +0.01 +0.07 -0 43 -0.64 -0.84 588's dollars per box -1.70 t -0.44 -1.15 -0 70 +0.37 -0.08 -0.36 -1.99 -2.67 -0.97 * Jumbo boxes. t Dashes indicate data not available. Source of data: Computed from New York Daily Fruit Reporter. year from 1930-31 to 1935-36. In each of these six years there were dif- ferences between the prices of the several sizes, except with respect to (1) the prices of 300's and 360's in 1932^-33, and (2) the prices of 270's and 300's in 1934-35. For the five-year period, 1930-31 to 1934-35, the prices of 270's and 300's averaged the same. 20 There were substantial dif- ferences, however, between the average prices of each of the other sizes. On the average, 270's and 300's commanded a premium over 360's, while each of the other sizes sold at a discount. The average discount was smallest on 240's. Of the sizes smaller than 360's the average discount was least on 432's and greatest on 588's. The tendency is for the differ- ences in prices between the intermediate sizes to be relatively small and 20 However, since 270's were packed in jumbo boxes and 300's in standard boxes, it is likely that if both sizes had been packed in the same boxes, 300's would have com- manded a premium over 270's. Roughly, lemons packing a given size in jumbo boxes will pack the next larger size in standard boxes. 30 University of California — Experiment Station for the differences between the prices of the small sizes to be relatively large. Two trends are apparent in table 15 : (1) for the large sizes instead of selling at a premium over 360's to sell at a discount ; and (2) for the dis- count on the small sizes to narrow, but not to disappear. Much the same general situation that has existed with respect to the price differentials between the several sizes of Extra Choice lemons has also prevailed with respect to the price differentials between the sizes of TABLE 15 Average Annual Price Differentials from 360's of Each of the Other Sizes of Extra Choice Lemons from 240's to 588's on the New York Auction Market, 1930-31 to 1935-36 Year November-October 1930-31 1931-32 1932-33 1933-34 1934-35 1935-36 Average: 1930-31 to 1934-35 240's* 270's* 300's 432's 490's 540's 1 2 5 4 5 6 dollars dollars dollars dollars dollars dollars per box per box per box per box per box per box +0.12 +0 43 +0 38 -0 49 -0.96 1 +0.14 +0 34 +0.24 -0 35 -0 76 -1.72 -0 24 -0.11 0.00 -0 29 -0 49 -0 82 -0.26 +0 01 +0 07 -0 43 -0 64 -0 84 -0.14 -0 03 -0 03 -0 10 —0 19 -0 32 -0.82 -0.48 -0.09 -0 36 —0 81 -1 02 -0.08 +0.13 +0.13 -0 33 —0 61 -0 92 588's dollars per box -2 01 -2.42 -0 95 -0 97 —0 41 -1.28 1 35 * Jumbo boxes. t Dash indicates data not available. Source of data: Computed from New York Daily Fruit Reporter. both Choice and Standard lemons. This is illustrated in table 16. It should be noted, however, that the discounts on the small sizes in 1933-34 were considerably less in the case of Standard Lemons than of Extra Choice. The foregoing analysis does not forecast with any great degree of certainty the extent to which the prices of the several sizes will differ during the next several years. A number of distinct tendencies, however, are discernible: (1) The differentials between the prices of the several sizes are likely to continue to fluctuate rather sharply from month to month and from year to year rather than to remain constant. (2) Over a period of years the prices of the intermediate sizes are likely to aver- age above the prices of both the large sizes and the small sizes. (3) On the average, the differentials between the prices of the intermediate sizes are likely to be small, whereas the average differentials between the prices of the large sizes and between the prices of the small sizes are likely to be substantial. Bul. 619] Maintenance of Equity in Pooling of Lemons 31 Differences in Returns to Individual Growers without Size Pools as Compared with Pooling on the Basis of Sizes. — Table 17 is designed to show the differences in returns per packed box to 25 individual growers under three different size-pool arrangements as compared with separate pools for each size. In column 1 all sizes of Extra Choice lemons are com- bined in one pool ; in column 2 all sizes from 180's to 490's, inclusive, are combined in one pool while the 540's and 588's are placed in a second pool ; and in column 3 the 270's and larger are placed in one pool, the TABLE 16 Average Price Differentials from 360's of Each of the Other Sizes of Lemons from 250's to 588's, by Grades, on the New York Auction Market, 1933-34 Size Extra Choice Choice Standard 1 2 3 240's* dollars per box -0.26 +0.01 +0.07 -0.43 -0.64 -0.84 -0.97 dollars per box -0.28 -0.01 +0.14 -0.29 -0.36 -0.46 -0.74 dollars per box -0.32 270's* -0.29 300's +0.03 432's 490's -0.15 -0.05 540's 588's -0.18 -0.28 * Jumbo boxes. Source of data: Computed from New York Daily Fruit Reporter. 300's in a second pool, the 360's in a third pool, and the 432's and smaller in a fourth pool. Table 17 shows that, without size pools, only 52 per cent of. the growers would have received within 5 cents a packed box of the same price that they would have obtained with separate pools for each size, whereas with two size pools, 72 per cent would have been in this class, and with four size pools, 96 per cent would have been included. In calculating the data given in table 17, the percentages of each size shipped by 25 growers in a given time pool in 1933-34 and the average price differentials between the several sizes for the five years 1930-31 to 1934-35 were used. The use of the five-year average price differentials is entirely appropriate, but the use of the percentages of each size shipped in only one year exaggerates the average differences in returns to grow- ers over a period of several years. It has already been shown that the variation between growers in the proportions of the several sizes con- tributed tends to be less over a period of years than in any given year (pp. 26-28) . A careful study of the shipments by sizes of the 12 growers in Association E from 1929-30 to 1934-35 (table 12) shows that, although a grower may have had either extremely large or extremely small sizes 32 University of California — Experiment Station in one year, he did not average such extreme sizes over a period of several 21 years Of the 2 growers in column 1, table 17, in the class interval "21 to 25 cents," one had 40 per cent more than the average of the 25 growers and the other 27 per cent less in the size group 432's and smaller. Among the 12 growers in Association E, the greatest deviation from the average percentage of 432's and smaller in any one of the six years 1929-30 to TABLE 17 Differences in Beturns per Packed Box of Extra Choice Lemons to 25 Growers with No Size Pools, Two Size Pools, and Four Size Pools, as Compared with Separate Pools for Each Size* Differences With no size pools With two size pools With four size pools / 2 5 Oto 5 6 to 10 cents per box number of growers 13 5 5 2 number of growers 18 4 2 1 number of growers 24 11 to 15 16 to 20 1 21 to 25 ' Total. . . 25 25 25 * Based upon shipments by sizes of 25 growers from Association D, in 1933-34 and average price differentials between the several sizes at New York from 1930-31 to 1934-35. 1934-35 was 24 per cent. Over the six-year period, however, the devia- tion from the average for this grower was only 9 per cent. Table 18 is designed to show, over the five years 1930-31 to 1934-35, the average differences in returns per packed box to the 12 growers in Association E without size pools as compared with each size pooled separately. In this table it will be noted that differences in returns to growers are not nearly so wide as those shown in table 17, column 1. If the trends with respect to the price differentials between the sizes continue, the average differ- ences in returns to individual growers over the next several years, with one rather than another of the various size-pool arrangements, are likely to be less than the average differences for the past several years. As nearly as can be determined from the available data, the placing of all sizes 490's and larger in one pool and 540's and 588's in a second pool would result in all growers' receiving over a period of several years within 5 cents a packed box of the price that they would receive if each size were pooled separately. In any one year, however, some growers may receive considerably more than 5 cents a packed box above or below that price. The differences in average returns to growers over a period of 21 The 12 growers in Association E were selected so as to include the extreme cases. Bul. 619] Maintenance of Equity in Pooling of Lemons 33 years with four size pools as compared with each size pooled separately are likely to be negligible, while in any given year no appreciable differ- ences are likely to occur except in the most extreme cases. On the other hand, if all sizes of each grade are combined in a single pool some growers are likely to be paid considerably more and others considerably less than the market value of their fruit over a period of several years. TABLE 18 Estimated Differences in Eeturns per Packed Box of Extra Choice Lemons to 12 Growers with No Size Pools as Compared with Separate Pools for Each Size ; Aver- age 1930-31 to 1934-35* Differences, cents per box Number of growers to 5 8 6 to 10 4 11 to 15 Total 12 * Based upon shipments by sizes of 12 growers from Associa- tion E and average price differentials between the several sizes at New York. DETERMINATION OF THE NUMBER OF UNITS OF EACH SIZE CONTRIBUTED BY INDIVIDUAL GROWERS If each grower is to be credited with the number of units of each of the several sizes which the fruit of a given grade that he contributed to a time pool actually contains, the same requirements must be met that were outlined in the case of grade pools, namely : 1. The sorting must be done in such a way that all the lemons in each of the separate classifications are reasonably uniform in size and that the average size of the lemons in one classification is significantly different from the average size in another. 2. The sorting must be reasonably uniform as between the fruit of the several growers. 3. The fruit of each grower must be sorted separately. 4. The number of units of each size must be determined before one grower's fruit has become commingled with that of other growers. The first two of these requirements offer no serious difficulties and ap- pear to be met satisfactorily by most associations. All associations irre- spective of whether they employ size pools or not, sort the lemons sold as packed fruit into size classifications, which are precisely defined and uni- versally accepted. The particular size of lemons in a packed box is 34 University of California — Experiment Station plainly marked on the outside of the box and the packed lemons are sold by the association on the basis of size as well as of grade. The size of lemons is determined by the number of lemons packed in accordance with definite patterns in a standard box. A standard packed box may contain any one of the following numbers of lemons : 180, 210, 240, 270, 300, 360, 432, 490, 540, and 588. It never, however, contains a number in between these numbers, except that 442's are sometimes packed. The lemons are sorted into the several sizes by the packers in the proc- ess of packing. The sorting is done by inspection rather than by mechan- ical means. When packed by experienced people under careful super- vision, reasonable uniformity is maintained with respect to (1) the sizes of the individual lemons in a particular box and (2) the average size of the lemons in different boxes containing the same number of lemons. If the sorting by size is sufficiently uniform so that buyers do not discrimi- nate between boxes containing the same number of lemons of the same quality, it is also sufficiently uniform for the purpose of pooling. Since all packed lemons are sorted by size in the process of packing, the question arises why pooling on the basis of these same size classifica- tions involves any additional expense other than for accounting. The reason is to be found in the third and fourth requirements mentioned above. For the purpose of marketing, the lemons need only be packed by size without regard to the identity of the fruit, but for the purposes of pooling on the basis of size, the sizes of each grower's fruit must be deter- mined separately. The cost of keeping each grower's fruit entirely sep- arate until after it has been packed and the number of boxes of each size recorded is apparently so great that as far as the authors have been able to learn, no association with numerous members actually does this. The customary practice among associations packing from trays is to keep each grower's fruit entirely separate until after it has been graded and weighed, but thereafter the identity of the individual lot is no longer maintained. Although each grower's packed fruit is eventually sorted by size in the process of packing, the sizes thus obtained are not used as the basis for pooling, since there is no means of determining which grower's fruit is contained in each packed box. Associations packing from belts, tubs, or bins generally employ size pools for the Extra Choice and Choice grades. Standards, however, are seldom pooled on the basis of size. The usual practice is to credit growers with the total number of pounds of Standards without reference to the size of the fruit. In the case of the Extra Choice and Choice grades, each grower is credited with a definite number of boxes of each size or size Bul. 619] Maintenance of Equity in Pooling of Lemons 35 group. Except in the case of large lots, however, there is no assurance that the sizes credited to each grower are the same that his fruit actually contained. Determination of Sizes on Cleanups. — Apparently the difficulty of estimating accurately the number of units of each size on the belts (or in the tubs and bins ) at the end of the run of each lot is so great that most associations make no attempt to do it. Instead they merely credit each lot with the particular sizes in the boxes which reach the lidding machine immediately after the estimate. Thus, if the estimate shows that there are the equivalent of 15 packed boxes of Extra Choice lemons remaining on the packing belt and in the partially packed boxes, that lot is credited with the next 15 boxes of Extra Choice lemons which reach the lidding machine. The advantages of this method lie in its simplicity. It involves practically no additional labor either in the plant or in the office. At any particular time the number of packed boxes of each size credited to all growers is in balance with the number actually packed. The disadvan- tages relate to the question of equity. There is no certainty that these boxes contain only the fruit of the grower to whom they are credited or in fact contain any of that grower's fruit. Consequently, the sizes cred- ited to the growers may be considerably different from the sizes of his fruit. With a fairly large lot, there could not be any material difference be- tween the total number of boxes of each size credited to the grower under this system and the total number of boxes of each size that would have been secured if the lot had been kept entirely separate. But with a small lot there could be a significant difference. In order to overcome this difficulty at least partially in connection with small lots, some associations have, as far as seemed practical, avoided packing a lot running heavily to small sizes immediately after a lot running heavily to large sizes and vice versa. This procedure has merit, but it may not credit each grower who has a considerable propor- tion of his fruit in small lots with the precise sizes which they contained. The average difference over a period of years, however, would tend to be less than the difference in any given year. Determination of Sizes in Combination Lots. — Several individual lots containing only a few boxes each are combined in order to secure suffi- cient volume for economical operation when packing from belts, tubs, or bins. In most such cases the total number of boxes of each size or size group in each grade are simply prorated among the several growers on the basis of the number of units of that grade contributed by each. Thus each grower with fruit in a given combination lot is credited with the 36 University of California — Experiment Station same proportions of the several sizes that such combination lot con- tained, irrespective of the sizes of his particular fruit. This in essence involves no pooling on the basis of sizes for the combination lots. Some associations make an effort to avoid placing fruit markedly dif- ferent in sizes in the same combination lots. To the extent that this is done, growers tend to be paid more nearly in accordance with the par- ticular sizes which they contributed. It is doubtful, however, whether even the use of this method justifies the implication given by the usual type of pool statement furnished growers that all of their fruit is pooled on the basis of sizes. Mechanical Sizers and Electric Counters. — Several lemon associations use mechanical sizers, which provide some degree of presorting on the basis of size, before packing. Recently two lemon associations installed electric counters in connection with the mechanical sizers along the same general lines as those employed in most orange cooperative packing asso- ciations. It was hoped that this equipment would make it possible to determine the number of units of each grade and size or size group in each individual lot, however small, and at the same time maintain con- tinuous operation in the packing-house. This system, however, is more difficult to use for lemons than for oranges. The number of oranges in a standard packed box depends almost entirely upon the diameter of the oranges, since they are virtually round. On the other hand, the number of lemons in a standard packed box depends not only upon the diameter of the lemons, but also upon the length. Even though all the lemons in a given lot have the same diameter, if they do not also have the same length, there will be considerable variation in size as measured by the number of lemons in a standard packed box. With the present type of equipment the most that can be expected is that the mechanical sizers will sort the lemons accurately on the basis of diameter and that the electric counters will record the actual number of lemons in each diameter group. Even if these conditions were fulfilled, however, it does not necessarily follow that, from the records thus ob- tained, each grower would be credited with the same number of boxes of each size that his fruit actually contained. If the number of lemons in each diameter group were converted to packed boxes by the use of com- mon conversion factors, those growers whose lemons tended to be round would be credited with more packed boxes in total and with a higher proportion of the larger sizes than their lots actually contained, while those whose lemons tended to be oblong would be credited with fewer packed boxes and with a smaller proportion of the larger sizes than their lots actuallv contained. Bul. 619] Maintenance of Equity in Pooling of Lemons 37 Under practical operating conditions, with the speed at which the sizers must be run in order to secure reasonable costs, the lemons are not sorted into well-defined diameter groups. In general, many of the smaller lemons are carried beyond the tubs which they are intended to enter, because of being either crosswise on the belts or on top of larger lemons. This, together with the fact that the diameter of the lemons is not the only factor determining their size, appears to be the chief reason why several different sizes of lemons are commonly found in the same tub and the same-sized lemons are commonly found in each of three and even four consecutive tubs. For the purpose of securing some information relative to the possibili- ties of pooling lemons by grade and size on the basis of the records ob- tainable from the use of mechanical sizers and electric counters, a limited test covering 24 individual lots was made. While many more lots would need to be included in the test before final conclusions could be reached, the results obtained from the 24 lots indicate certain limitations and probabilities as follows i 22 1. If the growers' credits are based upon the number of lemons in each count group converted to equivalent packed boxes by the use of common conversion factors, the total number of packed boxes, the number of packed boxes of each grade, and the number of packed boxes of each size or size group within each grade credited to a grower may all be consider- ably different from the quantities, grades, and sizes which the fruit of that grower actually contained. 2. If the total number of packed boxes of Extra Choice and Choice combined in each individual lot is known, the number of packed boxes in each grade can be closely approximated on the basis of the relative number of lemons in each grade. 23 3. If the number of packed boxes in each grade in each individual lot is known, such number can probably be divided, with a fair degree of accuracy, into two size groups on the basis of the relative number of lemons in the corresponding count groups. 22 It is assumed that the electric counters accurately record the number of lemons. In the test which was run, however, the electric counters were far from accurate. This may have been the result of mechanical difficulties which can be overcome. It is ob- vious, of course, that unless the electric counters are accurate, the recordings cannot be used as the basis for pooling. 23 Since the total number of storage boxes in each individual lot is known, and if desired, the net weight of the fruit in each lot can be ascertained, it would appear that the total number of packed boxes of Extra Choice and Choice combined could be closely approximated by subtracting from the total number of storage boxes the amount of culls, setbacks, and Standards, and converting the remainder to equivalent packed boxes. 38 University of California — Experiment Station DETERMINATION OF PRICE DIFFERENTIALS BETWEEN SIZES The same types of problems arise in connection with the establishment of the price rates to be applied to each size or size group in setting up the money credits to growers as occur in connection with the price rates to be applied to each grade. The universal practice among associations pool- ing by sizes is to base the price rates on the weighted-average prices of each size or size group. The returns to growers thus reflect not only the differences in the prices of the several sizes on the same market on the same day, but also the differences in the level of prices between markets and over a period of time. From the standpoint of paying growers in ac- cordance with the market value of the sizes which they contribute, the determination of price rates on the basis of a simple average of the price differentials between the several grades on the same markets on corre- sponding days appears to be superior to the use of weighted-average prices. In selling lemons on the auction markets, the general practice is to include in each car the run of the sizes packed from the particular lot or lots. Occasionally, however, discount sizes are set back for later ship- ment. At the time they are eventually shipped, these sizes may bring either more or less relative to the prices of the sizes that were originally shipped, solely by reason of a change in the market level. This same situa- tion applies to lemons sold in private-sale markets. In addition to a change in the market level over a period of time, some sizes may bring more or less than other sizes merely by reason of differ- ences in the level of prices on the same day in the particular markets to which they were sent. The largest total amount of money may be secured from a given volume of shipments by selling the smaller sizes in some markets and the larger sizes in other markets, yet the differences between the weighted-average prices of the several sizes might have been mate- rially modified if the distribution of the sizes between the markets had been changed. In private-sale markets, cars containing a number of different sizes of the same grade are frequently sold at a flat price per box, on the grounds that the entire car brings more total money than it would if each size were priced separately. That each size was worth the same price to the buyer, however, does not necessarily follow. In deciding whether to pay the flat price, he probably estimated, at least roughly, the prices at which he could sell each of the sizes, and, knowing the number of boxes of each size in the car, arrived at the total amount of money which he felt he could pay for that particular car. If each size had been priced separately, he Bul. 619] Maintenance of Equity in Pooling of Lemons 39 would have paid more than the flat price for some sizes and less for others. Methods of computing rates of payments to growers based upon a simple average of the price differentials between sizes on the same mar- kets in corresponding days are discussed in Appendix B. POOLING ON THE BASIS OF SIZE GROUPS Only a few associations have separate pools for each size. Most of them pool on the basis of size groups. Although there is considerable difference between associations in the precise groupings of sizes, the general prac- tice is to combine the large sizes in one group, the small sizes in another group, and to keep the intermediate sizes separate. The reason generally given by packing-house managers for combining sizes instead of pooling each separately is that it results in a saving in costs without sacrificing substantial equity between the growers. The question of the extent of differences in returns to individual grow- ers with pooling on the basis of size groups as compared with separate pools for each size has already been discussed (pp. 31-33) . The conclusion reached was that the average differences over a period of years are likely to be negligible, while the differences in any one year are likely to be insignificant except in extreme cases. 24 Although no cost figures are available, careful observation supports the claim that it is less expensive to pool on the basis of size groups than to pool each size separately. This saving in cost, however, is not great and is confined almost entirely to the calculation of the pool statements of the individual growers. With present methods, most of the expense con- nected with pooling on the basis of sizes must be incurred whether pool- ing is by each size or by groups of sizes. Pooling by size groups involves the combining of the separate sizes into a smaller number, both with respect to the number of units and the price rates. Thus, as usually done, the number of units of each size of each grower's fruit must first be de- termined before the number of units in each size group can be calcu- lated. In determining the price rates to be applied to the size groups, both the number of boxes sold and the money received for each size in the size group have to be added. When three sizes are combined in one size group, the calculation of the price rate involves one division instead of three and one subtraction of the association packing charge instead of three. The saving here is negligible. The chief reduction in expense has to do with the preparation of the individual grower's pool state- ments. The total number of calculations involved in closing a pool, par- 24 This conclusion is predicated on the assumption of at least four size groups such as 270's and larger, 300's, 360's, and 432's and smaller; or 240's and larger, 270's and 300's, 360's and 432's, and 490's and smaller. 40 University of California — Experiment Station ticularly if there are many growers, runs into the thousands. The doubling of the number of size pools nearly doubles the number of cal- culations required. The combining of the separate sizes into size groups avoids none of the serious difficulties involved in pooling each size separately. The prob- lems relating to cleanups, combination lots, and determination of price rates are identical in both cases. As far as sizes are concerned, the difficulties connected with cleanups and combination lots could be eliminated by taking out the smallest sizes such as 588's and 540's with a second mechanical sizer at the washer. 25 Pooling would then be on the basis of two size groups, 490's and larger and 540's and smaller. The extent of the differences in returns between individual growers with this system as compared with separate pools for each size has already been discussed. The use of a mechanical sizer, how- ever, introduces the problem discussed under the section entitled "Me- chanical Sizer and Counter." If the sizer is set so as to remove round lemons which would pack 540's, it would also remove a considerable number of oblong lemons which would pack 490's, while if set so that oblong lemons which would pack 490's would not be removed, a consid- erable proportion of the round lemons which would pack 540's would not be removed. This same type of situation, of course, already exists with respect to lemonettes. Another problem that would arise under this system relates to the increase in the number of separate lots into which each grower's deliveries would be divided. At least one additional lot would be required, and, if the 540's and smaller are sorted by color, as many additional lots would be created as there are color classifications. It appears likely, however, that seldom would more than two color classi- fications be needed for these small lemons. While many of them are green, they tend to be more similar to tree-ripe lemons than to the larger green lemons, as far as keeping quality is concerned. The possibilities of sorting individual lots into two size groups by means of mechanical sizers and electric counters have already been dis- cussed. TIME POOLS The type of time pool employed by the Santa Paula Citrus Fruit Asso- ciation during the ten years 1925-26 to 1934-35 was the annual ship- ping pool. Every grower was paid the same price per pound for all lemons of the same grade shipped during the twelve months November 23 It is now common practice to remove lemonettes at the washer by means of a mechanical sizer. Bul. 619] Maintenance of Equity in Pooling of Lemons 41 through October, irrespective of the time they were shipped. Any lemons in the packing-house at the end of the crop year were carried over into the following crop year for the accounts of the individual growers. A number of the other lemon cooperative packing associations also employ an annual shipping pool. The large majority, however, employs multiple time pools based either on shipments or on picks. Those based on picks are the most numerous. TABLE 19 Percentage of Annual Lemon Shipments during November through April; 56 Growers from the Santa Paula Citrus Fruit Association ; Average 1925-26 to 1934-35 Per cent of annual shipments Number of growers Per cent of growers / 8 8.2to 16.0 17 26 7 5 1 30.4 16.1 to 26.0 46 4 26.1 to 36.0 12 5 36.1 to 46.0 8 9 46.1 to 49. 4 1 8 Total.... 56 100 DIVISION OF ANNUAL RETURNS BETWEEN GROWERS: MULTIPLE TIME POOLS VS. ANNUAL POOL The possibility of obtaining additional returns over a period of years from marketing lemons during one part of the season rather than dur- ing another depends upon (1) the existence of price changes that tend to be repeated year after year at about the same part of the season, or (2) the existence of changes in the volume of consumption that tend to be repeated year after year at about the same part of the season. How- ever, from the standpoint of making the returns paid the individual growers over a period of several years reflect closely the average differ- ences in the market value of their fruit, the existence of definite seasonal variation in prices or consumption will not be of significance unless there also exist distinct variations in the time of the season during which the lemons of individual growers can be shipped. Likewise, the existence of distinct variations between individual growers in the time of the season during which their lemons can be shipped is of significance only when there are also present definite seasonal variations in prices or in consumption. Variation in Time when Fruit of Individual Growers Can Be Shipped. — Records of the monthly shipments and deliveries of 56 growers who had delivered lemons to the Santa Paula Citrus Fruit Association from 42 University of California — Experiment Station the same orchards for the ten-year period 1925-26 to 1934-35 were ob- tained. As shown later (pp. 45, 51), the crop year November through October is, from the standpoint of both prices and consumption of lem- ons, about evenly divided into two six-month periods ; namely, the winter months, November through April, and the summer months, May through October. Table 19 shows the average percentages of the annual shipments of the 56 growers that were shipped during the winter months. It will be noted TABLE 20 Distribution of 56 Growers with Bespect to Number of Years That Their Percentages of Annual Lemon Ship- ments During November through April Fell Below the Santa Paula Citrus Fruit Association Average ; 1925-26 to 1934-35 Number of years under association average Number of growers Per cent of growers / 2 10 13 13 6 7 3 2 3 3 1 3 2 23 3 9 23 3 8 10.7 7 12.5 6 5.3 5 3.6 4 5 3 3 5.3 2 1.8 1 5 3 3 6 Total.. 56 100.0 that there has been substantial variation between these growers' ship- ments. On the average for the ten-year period, a much smaller percent- age of the annual shipments of some growers was made in the winter months than of other growers. Table 20 shows the consistency with which the percentage of the annual shipments of the individual growers during the winter months has been under or over the Association average. Thir- teen of the growers were under the Association average in each of the ten years, while two of the growers were over the Association average in each of the ten years. The variation between growers in the average percentages of annual shipments in the winter months is associated in part with the locations of the orchards, as shown in table 21. The area served by the Santa Paula Citrus Fruit Association was divided into three parts : west of Santa Paula, east of Santa Paula, and the canyon which lies north of Santa Bul. 619] Maintenance of Equity in Pooling of Lemons 43 Paula. In general, growers having the largest percentage of their annual shipments in the winter months are located east of Santa Paula, while growers having the smallest percentage of their annual shipments in the winter months are located west of Santa Paula and in the canyon. There are, however, some important exceptions. Much the same situation that has prevailed with respect to variations between growers in the percentage of annual shipments in the winter TABLE 21 Percentage of Annual Lemon Shipments during November through April, by Districts ; 56 Growers from the Santa Paula Citrus Fruit Association; Average 1925-26 to 1934-35 Number of growers Per cent of annual shipments West Canyon East Total 1 2 3 4 8 2 to 16.0 9 18 1 6 4 1 2 4 5 5 1 17 16.1 to 26.0 26 26.1 to 36.0 7 36 1 to 46.0 5 46.1 to 49. 4 1 Total 28 11 17 56 months has also existed with respect to variations in the percentage of deliveries to the packing-house, as shown in tables 22 and 23. That there would be a close relation between the percentage of deliv- eries and the percentage of shipments is a natural expectation, since within each color classification the order of shipments is based upon the order of deliveries. The failure of these two series to show virtually per- fect correlation is accounted for chiefly by the differences between grow- ers in the proportion of their lemons in the several color classifications, and to some extent by the positions of the growers in the picking schedule. The data presented in tables 19 to 23 merely show the extent of the variation between individual growers in the time of picking and ship- ping under the conditions which existed during the ten years 1925-26 to 1934-35. One of these conditions was an annual pool. It does not neces- sarily follow that the same differences between the growers with respect to the time of picking and shipping would have occurred under multiple time pools. Under an annual pool it is a matter of indifference to the individual grower when his particular fruit is shipped, since he receives the same price per unit if his fruit is shipped at one time as at another. 28 With 26 This assumes that all fruit is graded before there is significant loss from deteri- oration in quality and shrinkage. 44 University of California — Experiment Station respect to picking, the grower's chief concern is to have his fruit picked at the time the largest quantity of the most desirable grades and sizes can be obtained without seriously inconveniencing his farm operations. In the Santa Paula Citrus Fruit Association, because of differences in TABLE 22 Percentage of Annual Lemon Deliveries during November through February ; 56 Growers from the Santa Paula Citrus Fruit Association ; Average 1925-26 to 1934-35 Per cent of annual deliveries Number of growers Percent of growers / 2 6 4 to 14.1 9 33 12 2 16.1 14 2 to 24.1 58.9 24 . 2 to 34 . 1 21.4 34 2 to 41. 8 3.6 Total.... 56 100.0 TABLE 23 Percentage of Annual Lemon Deliveries during November through February, by Districts ; 56 Growers from the Santa Paula Citrus Fruit Association; Average 1925-26 to 1934-35 Number of growers Per cent of annual deliveries West Canyon East Total / 2 S 4 6.4 to 14.1 14.2to24.1 24.2 to 34.1 5 21 2 2 8 1 2 4 9 2 9 33 12 34.2 to 41. 8 2 Total 28 11 17 56 topography and soil, some orchards can be picked sooner after a rain than others. As a matter of convenience to the Association, owners of such orchards have permitted the lemons thereon to be picked out of turn. This has enabled the Association to secure more effective utilization of its labor and equipment, and to provide a more continuous supply of lemons to its customers. Under multiple time pools, however, growers whose orchards could, on account of topography and character of soil, be picked early would not generally permit this to be done. Instead, they would tend to delay pick- Bul. 619] Maintenance of Equity in Pooling of Lemons 45 ing in order to have a larger proportion of their fruit in later pools. 27 Not only have prices of lemons during the summer months averaged con- siderably above prices in the winter months, but the proportion of the deliveries shipped has also been larger in the summer than in the winter (pp. 45, 51). To the extent that orchards in the Santa Paula Citrus Fruit Associa- tion were picked out of turn, the differences with respect to the time of picking shown in tables 22 and 23 were larger than those inherent in the orchards. The use of the annual pool tended to accentuate the variation between growers in the time of picking. Nevertheless, there are substan- tial inherent differences between orchards with respect to the time of picking in the Association, and significant variation would exist under multiple time pools. From the standpoint of returns to growers the time of picking is im- portant only as it affects the time of shipment. Whether or not one grower can have a larger proportion of his crop on the summer market than can another depends not only upon the time the fruit is picked, but also upon the length of time it can be kept in storage without undue loss. 28 The crux of the situation lies in the extent of the differences between orchards with respect to the time of the year the fruit from such orchards can be shipped. Seasonal Variation in Prices of Lemons. — Although lemon prices are characterized by wide fluctuations from month to month, they have nevertheless exhibited over a period of years a definite seasonal varia- tion. An index of seasonal variation in the f.o.b. prices received for lemons shipped by the California Fruit Growers' Exchange from 1913- 14 to 1934-35 is shown in table 24. During this twenty-two year period there was a definite tendency for prices to be low in the winter months as compared with the summer months. In each of the months, November through April, the index was below 100 (that is, the average price for the year) ; in each of the months, May through October, the index was above 100. Table 25 shows the number of years during the twenty-two-year period 1913-14 to 1934—35 that the prices in each month were below or above the average for the crop year. Thus prices in November were below the average of the crop year in fourteen of the twenty-two years and were above in eight of the twenty-two years. On the other hand, the situation for September was just reversed. The general situation shown by table 27 It should, of course, be recognized that, on the assumption that the same condi- tions exist with respect to prices, quality of fruit, and convenience of farm operations, it is generally to the interest of the individual grower to have his fruit picked early rather than late in order to avoid the risk of frost and wind damage. 28 This is discussed later under the section entitled "Color Pools." 46 University of California — Experiment Station TABLE 24 Indexes or Seasonal Variation in F.O.B. Prices Received for Lemons by the California Fruit Growers' Exchange and by the Santa Paula Citrus Fruit Association Month November December January . . February . March .... April May June July August . . . September October. . . C.F.G.E. 1913-14 to 1934-35 1 per cent 93 87 87 84 80 85 104 109 119 116 121 115 1925-26 to 1934-35 C.F.G.E. per cent 97 97 83 80 80 81 99 103 122 116 127 115 S.P.C.F.A. 3 percent 96 95 83 81 82 85 103 105 124 118 123 105 1930-31 to 1934-35 C.F.G.E. per cent 89 96 81 79 77 77 99 109 123 119 133 118 S.P.C.F.A. per cent 90 94 81 79 78 78 99 110 126 121 132 112 Sources of data: Cols. 1, 2, and 4: Computed from records of the California Fruit Growers' Exchange. Cols. 3 and 5: Computed from records of the Santa Paula Citrus Fruit Association. TABLE 25 Number of Years from 1913-1914 to 1934-35 that Monthly Index of F.O.B. Prices Received for Lemons by California Fruit Growers' Exchange Was below or above the Average for the Year Month Under average price for year Over average price for year Month Under average price for year Over average price for year 1 2 1 2 November. . years 14 17 19 19 19 18 years 8 5 3 3 3 4 May years 9 11 6 6 8 11 years 13 December. . June 11 January February March April July August September October 16 16 14 11 Source of data: Computed from records of the California Fruit Growers' Exchange. 25 is that in most of the past twenty-two years prices in the winter months were relatively low, while prices in the summer months were relatively high. A comparison of the index of seasonal variation in prices received for lemons shipped by the Santa Paula Citrus Fruit Association with the index of seasonal variation in prices received by the California Fruit Growers' Exchange for the ten years 1925-26 to 1934-35 and for the five years 1930-31 to 1934-35 is shown in table 24. It will be noted that the Bul. 619] Maintenance of Equity in Pooling of Lemons 47 two indexes are very similar. This is accounted for by the fact that the conditions which have caused the prices of lemons to be relatively high in the summer months and relatively low in the winter months were industry-wide and not confined to the Santa Paula Citrus Fruit Associa- tion. There is no evidence which indicates that the seasonal variation in prices received by this Association was affected by the particular pooling system which it had. About the same seasonal variation in prices would TABLE 26 Percentages that California F.O.B. Prices and Shipments of Lemons in May-October Were of Previous November-April Prices and Shipments, Respectively, and June-September Temperature Departures from Normal in 14 Eastern Markets Per cent May-October of November-April Temperature departures Five-year averages Prices Shipments 1 2 S 1915-16 to 1919-20 per cent 138 149 127 143 per cent 137 161 178 178 degrees F +0.2 1920-21 to 1924-25 +1.1 1925-26 to 1929-30 -0.1 1930-31 to 1934-35 +2.2 Sources of data: Cols. 1 and 2: Computed from records of the California Fruit Growers' Exchange. Col. 3: Computed from United States Department of Agriculture Weather Bureau, Monthly Weather Review, monthly issues. apparently have prevailed under any other type of pooling system. The level of prices may have been different under another type of pooling system, but the relative changes in prices during the season would have remained approximately the same. Although over a long period prices of summer lemons have averaged substantially above those of winter lemons (table 26), certain factors are at work which will tend to narrow this price differential during the coming years; but apparently it will not be entirely eliminated. The factors tending to narrow the price differential are (1) the increase in the shipments of summer lemons in relation to the shipments of winter lemons, and (2) the decrease in summer temperatures in consuming markets from the high level of recent years. The conditions which will tend to prevent the average differential between the prices of summer and winter lemons from being entirely eliminated are (1) the costs and risks involved in carrying lemons available for shipment in the winter months into the summer months, (2) the possibility of carrying summer lemons into the following winter, and (3) the probability of occasional high summer temperatures. 48 University of California — Experiment Station Over the next few years it appears likely that the shipments of lemons in the summer months will increase in relation to the shipments in the winter months, and that this increase in shipments will tend to reduce the price differential between summer and winter lemons. The two con- ditions tending to cause the relative increase in shipments of summer lemons are (1) the increase in storage facilities under refrigeration, and (2) the increase in the acreage of lemons in late-maturing districts. Many local lemon packing associations throughout the lemon-produc- ing sections of the state have, in recent years, not only expanded their storage space but of even more significance, have provided cooling facili- ties of one sort or another. Two incentives have been chiefly responsible for this situation : the relatively high prices of lemons in the summer months, and the proration of shipments under the Exchange Lemon Agreement on the basis of volume of lemons in storage. The second condition tending to increase the shipments of summer lemons in relation to the shipments of winter lemons is the heavy plant- ings in the coastal sections, particularly in Ventura and Santa Barbara counties, where the bulk of recent lemon plantings has been made. All of the acreage in Santa Barbara County and most of the new plantings in Ventura County are located near the coast. In this section the production of summer fruit is much heavier than the average for the state. In addition to the relative increase in the shipments of summer lemons in prospect as a result of the expansion of storage facilities under refrig- eration and of the increase in acreage of later-maturing lemons, the prob- ability of lower average summer temperatures in the consuming markets points toward a narrowing of the price differential between summer and winter lemons. During the five years 1931 to 1935, temperature depar- tures in the 14 principal lemon markets of the United States during the four months June through September averaged 2.2° Fahrenheit above normal. There are no grounds for expecting these abnormally high sum- mer temperatures to continue indefinitely. From 1908 to 1935 summer- temperature departures averaged 0.7° Fahrenheit above normal. Over this period summer temperatures have exhibited a cyclical tendency. The average departures from normal during the past twenty years, by five- year periods, are shown in table 26. The available evidence indicates that, with summer-temperature de- partures from normal equal to the average of the past twenty-eight years, shipments of lemons during the six months May through October twice as large as shipments during the six months November through April would tend to keep average prices of lemons during each of the six-month periods closely in line. Bul. 619] Maintenance of Equity in Pooling of Lemons 49 With the expansion of refrigerated storage and the increase in produc- tion of summer lemons, it may be physically possible to ship sufficient lemons during the summer months in years of average summer tempera- tures or below to keep the price of summer lemons closely in line with the price of winter lemons. However, over a period of years the price of TABLE 27 Differences in Lemon Returns per Packed Box with 2 Six-Month Shipping Pools as Compared with an Annual Shipping Pool ; 56 Growers from the Santa Paula Citrus Fruit Association; Average 1925-26 to 1934-35 Differences, cents per box Number of growers Per cent of growers 1 2 Oto 5 6 to 10 13 16 19 6 2 23.2 28.6 11 to 15 33.9 16 to 20 10.7 21 to 25 3.6 Total... 56 100 TABLE 28 Differences in Lemon Returns per Packed Box with Monthly Shipping Pools as Compared with 2 Six-Month Shipping Pools ; 56 Growers from the Santa Paula Citrus Fruit Association; Average 1925-26 to 1934-35 Differences, cents per box Number of growers Per cent of growers / 2 Oto 5 6 to 10 50 5 1 89.3 8.9 11 to 15 1.8 Total... 56 100 lemons shipped during the summer months will not necessarily average as low as the price of those shipped during the winter months. Over a period of years the price during the summer months would need to be sufficiently higher than the price during the winter months to compen- sate for the cost and risk involved in carrying the lemons. The storing of lemons involves two types of risks : physical deterioration and price declines. The price of lemons during the summer months is influenced to so great an extent by temperatures in the consuming markets, which cannot them- 50 University of California — Experiment Station selves be forecast, that uncertainty always exists whether or not a large supply of lemons can be moved into consumption at a reasonable level of prices to growers. There is no certainty at all that, with a heavy supply of lemons available for shipment during the summer months, the price in any particular summer will be above the price of the preceding winter, and there is always the possibility that it will be lower, unless of course, the price during the winter in question was at a very low level. From the analysis presented in this section two conclusions appear justified: (1) that the differential between the prices of summer and TABLE 29 Index of Seasonal Variation in Total California Lemon Shipments, 1925-26 to 1934-35 Month November. December. January . . . February. . March April Per cent Cumulative per cent 1 » 4.08 4.08 5.12 9.20 5.84 15.04 4.92 19.96 7.50 27.46 8.73 36.19 Month May June July August September. October. . . . Per cent / 14.09 16 31 14.08 9.08 4.95 5.30 Cumulative per cent 50.28 66.59 80.67 89.75 94.70 100 00 Source of data: Computed from records of the California Fruit Growers' Exchange. winter lemons will be materially reduced during the coming years, and (2) that the prices of summer lemons during the next several years will average somewhat above the prices of winter lemons. Differences in Returns to Individual Growers with Multiple Time Pools as Compared with an Annual Pool. — Table 27 is based on the as- sumption that the total net returns of the Association would have been the same with multiple time pools as with an annual pool. This table is designed to show the differences in returns to the 56 growers over the ten- year period 1925-26 to 1934-35 which would have occurred, if instead of an annual shipping pool, the Association had employed two six-month shipping pools. 29 It will be noted that a considerable proportion of the growers would have received substantially more or less than they were actually paid. Under the conditions which have existed, the differences in returns to individual growers with the two six-month shipping pools as compared with an annual pool were greater than either (1) the dif- ferences in returns with separate pools for each grade as compared with no grade pools (table 4), or (2) the differences in returns with separate pools for each size as compared with no size pools (table 18) . 29 It is also assumed that the time of shipment of each of the growers' fruit would have remained unchanged. Bul. 619] Maintenance of Equity in Pooling of Lemons 51 On the other hand, the differences in returns to the 56 growers, over the ten-year period, with monthly shipping pools as compared with two six-month shipping pools are relatively small, as shown in table 28. Almost 90 per cent of the growers would have received within 5 cents a packed box of the same price under either system. Seasonal Variation in Shipments. — An index of seasonal variation in the total shipments of California lemons for the ten years 1925-26 to TABLE 30 Indexes of Seasonal Variation in Lemon Shipments and in Deliveries to the Packing Plant; Santa Paula Citrus Fruit Association; 1925-26 to 1934-35 Shipments Deliveries Month Per cent Cumulative per cent Per cent Cumulative per cent 1 2 8 4 November December 2.00 2.15 2.00 4.15 2.55 4.46 2.55 7.01 January 3.60 7.75 7.70 14.71 February 3.49 11.24 9.49 24.20 March 6.57 17.81 15.43 39.63 April May June 8.35 14.85 18.25 26.16 41.01 59.26 14.82 16.60 11.42 54.45 71 05 82.47 July August September October 18.11 11.48 5.17 5.98 77.37 88.85 94.02 100.00 5.66 3.97 3.74 4.16 88.13 92.10 95.84 100.00 1934-35 is shown in table 29. On the average, shipments have been rela- tively light in each of the months from September through February, with only minor differences between these months. Beginning in March, the volume of shipments has usually increased, with the peak in June. There has usually been a moderate decrease in July, a sharp drop in August, and a further marked decline in September. A comparison of the index of seasonal variation in shipments with the index of seasonal variation in prices (table 24) shows that in general both prices and ship- ments have been relatively lower in the winter months than in the sum- mer months. The seasonal index of total lemon shipments from the state roughly corresponds to the index of lemon consumption in this country, if an allowance is made for a lag of about three weeks. It is evident, therefore, that the period of heaviest consumer demand is in the summer months and the period of lightest consumer demand in the winter months. 52 University of California — Experiment Station On the average, shipments of lemons from the Santa Paula Citrus Fruit Association have been relatively lighter in the winter months and relatively heavier in the summer months than from the state as a whole. During the ten years 1925-26 to 1934-35 an average of only 26 per cent of the annual shipments of this association was made during the six months November through April as compared with 36 per cent for the entire state. Table 30 shows a comparison between the index of seasonal variation in shipments and the index of seasonal variation in deliveries of the TABLE 31 Percentages of Annual Lemon Deliveries Sent to the Products Plant; Santa Paula Citrus Fruit Association; 1925-26 to 1934-35 Year November-October Per cent Year November-October Per cent 1925-26 11.60 19.40 8.60 11.70 4.70 1930-31 1931-32 1932-33 15 80 1926-27 17.30 1927-28 12.86 1928-29 1933-34 7.58 1929-30 1934-35 26.64 Santa Paula Citrus Fruit Association for the period 1925-26 to 1934—35. On the average, deliveries have been relatively heavier than shipments during the winter months, while shipments have been relatively heavier than deliveries during the summer months. During the past ten years there has frequently been a surplus of lemons in the winter months, but seldom one in the summer months. Table 31 shows the percentages of the total deliveries of lemons of the Santa Paula Citrus Fruit Association sent to the products plant during each of the past ten years. In only three of the ten years was the per- centage less than 10 per cent, while in four of the ten years it was over 15 per cent. Judging from the seasonal movement of deliveries and ship- ments shown in table 30, it appears that virtually all the merchantable fruit sent to the products plant was picked in the winter months, and that practically no merchantable fruit picked in the summer months was used for by-products. This situation suggests that, where the loss on merchantable fruit sent to the products plant is borne by the Association rather than by the indi- vidual growers of the particular fruit so sent, two time pools during the crop year are needed. As a general proposition, the burden of surplus production should fall on those who produced it and not upon those who did not contribute to it. Even though the selling prices of lemons during the coming years should average the same in the summer months as in Bul. 619] Maintenance of Equity in Pooling of Lemons 53 the winter months, growers having the bulk of their fruit shipped in the summer months will, in years of excessive production, be able to market a much larger proportion of their crops than will growers with fruit which must be marketed mostly in the winter months. From a market standpoint some growers have lemons available for sale at the time of the year when consumers desire them keenly, while others have lemons avail- able at the time when consumers' demand is much more limited. One of the characteristics of lemons, which the market has determined to be important, is the time of the year that they are available for consumption. In associations where merchantable fruit sent to the products plant is for the account of the individual growers of that particular fruit (and this has been the customary practice), the length of the pooling period has little effect upon the relative proportions of the crops shipped as between growers of early and of late fruit. As long as this practice is con- tinued, there is no need for multiple time pools from the standpoint of seasonal variation in shipment alone. The problems which arise under this practice are discussed in connection with by-products pools. TRANSITION PROM ONE POOLING PERIOD TO ANOTHER WITH MULTIPLE TIME POOLS One of the most serious problems which arises when multiple time pools are employed relates to the transition from one pooling period to the next. This problem is present even with an annual pool, but the amount of fruit involved in the transition is usually such a small proportion of the total in the pool that no particular difficulty occurs. As the number of separate pooling periods during the season is increased, however, the difficulty is accentuated, since the amount of fruit involved in the transi- tion in relation to the amount of fruit in a specific time pool is increased. The annual pool is ended at a time of the year when there is usually little fruit in the packing-house, but some of the multiple time pools are ended at times when there is a large amount of fruit on hand. Multiple Time Pools Based upon Shipments. — A few lemon associa- tions employ multiple time pools based upon shipments. The most usual lengths of the pooling periods are either one month, three months, or four months. Although shipping pools have several advantages, they have one serious disadvantage which accounts for their limited use. This has to do with the determination of whose fruit is to be included and whose is to be excluded from a given time pool. 30 During most of the season there is more fruit in the house available 30 Another serious disadvantage has to do with the making of adjustments between multiple time pools when merchantable fruit is sent to the products plant (see p. 70). 54 University of California — Experiment Station for shipment than can be shipped within a specified short period. Some of the fruit must be shipped but all of it cannot be shipped. Consequently, the manager must choose from the available supply the particular fruit to be shipped, and the choosing of that fruit automatically precludes the shipment of other fruit in that time pool. The manager's choice, what- ever it may be, is likely to affect some growers advantageously and others disadvantageously, since the returns per unit from two adjoining ship- ping pools are seldom the same. In selecting from the available supply the particular lots to be shipped next, the manager must decide both between lots within the same color classification and between lots in dif- ferent color classifications. The general practice is to base the order of shipments within each color classification upon the time of arrival at the packing-house, and to base the order of shipments between color classifi- cations upon the condition of the fruit with respect to the length of time it can be kept in storage without undue loss from deterioration in grade and shrinkage. Even if all growers' lemons were comparable with respect to rate of maturity and keeping quality, the employment of multiple time pools based upon shipments would subject the individual grower to the risk of having a larger-than-average percentage of his fruit in a low-priced pool. For purposes of illustration, assume that each grower's fruit con- sists of dark-green lemons, and that each lot is shipped in the order in which it was received. Assume further that grower A's delivery was made in the morning and grower B's delivery was made in the afternoon of the same day, and that subsequently grower A's fruit was packed in the afternoon and grower B's fruit the following morning. Now if the end of one shipping pool and the beginning of another happened to occur at that particular time, grower A's delivery would be in the first pool and grower B's would be in the second. To the extent that the re- turns per unit from the two pools were different, one of the growers would lose while the other would gain merely by reason of their respec- tive positions in the picking schedule. If their positions in the picking schedule had been reversed, their returns per unit would have been re- versed. With multiple shipping pools this type of situation occurs fre- quently, and the larger the number of separate pooling periods during the season the more often will this happen. With differences between growers in the proportions of their respec- tive deliveries in the several color classifications, there is the further risk with multiple shipping pools, arising from the choice of the particular color classification to be shipped during the latter part of one pool and the first part of another. For example, suppose that both silver and light- Bul. 619] Maintenance of Equity in Pooling of Lemons 55 green lemons can be shipped either during the last week in pool No. 1 or during the first week in pool No. 2. The light-green lemons, however, can be kept in storage longer than the silver, so the manager decided to ship the latter in the first pool, and the former in the second pool. If, however, the returns per unit in the first pool happen to be considerably above those in the second, the grower who had a large proportion of light-green lemons may well ask why they were not shipped instead of the silver lemons, since the latter could have been held in storage without deterioration in grade until the beginning of the second pool. On the other hand, if the returns per unit happened to be higher in the second pool than in the first, the grower who had a large proportion of silver lemons may ask why they were not held until the beginning of the second pool. The foregoing problems arise only in connection with fruit that is available for shipment in either of two shipping pools. They do not arise in connection with fruit that is not sufficiently cured to be shipped within a given pool or with fruit that cannot be held until the next pool. The time during which these problems are most acute is at the beginning and end of the pooling periods. One association, in the attempt to eliminate the extreme differences in returns per unit between growers who deliver fruit of the same color classifications within a short space of time, adjusts the shipments of the individual growers so as, in effect, to place a portion of the shipments made during the latter part of one pool into the following pool and a portion of shipments made during the first part of a pool into the previous pool. A sliding-scale arrangement is used which provides a gradual rather than an abrupt change from one pool to another. The adjustments are made within each color classification, but not between color classifications. Multiple Time Pools Based upon Picks. — Because of the difficulties which arise in connection with shipping pools, most associations that employ multiple time pools base such pools upon picks rather than upon shipments. The most common is known as the "pick-around pools." Under this system the orchards of the growers are picked in rotation, each orchard being picked usually from seven to ten times a year. At the beginning of the crop year all the fruit picked from each orchard on the first pick-around is placed in pool No. 1 ; all the fruit picked on the second pick-around, in pool No. 2; and so on through the season. Thus, there are as many separate time pools as there are pick-arounds. The grade-out, shipments, and sales returns of the fruit in each pool are kept separate, and the payments to growers are based upon the average prices 56 University of California — Experiment Station received for comparable grades and sizes of all the fruit in the pool, irrespective of the time any particular lot was shipped. 31 Some associations, instead of having separate pools for each pick- around, combine two or more pick-arounds into one pool, which thus extends the length of each pooling period and reduces the number of time pools during the season. One association has only two time pools. All fruit picked during the six months, November through April, is placed in the first pool and all picked during the six months, May through October, in the last pool. The management attempts to pick each orchard at the time the fruit thereon is in prime condition, without particular reference to a picking rotation among the growers. If, on each pick-around, all orchards in an association were picked on the same day or even in the same week, the problems of transition from one pooling period to the next would disappear. But such a procedure would be extremely expensive. In order to secure reasonable operating costs, a fairly uniform flow of fruit is necessary from the orchards to the packing-house. This requires fairly continuous picking. Assume for the time being that all orchards in an association are picked on each pick-around and that a definite picking schedule can be followed without undue delay ; there may, nevertheless, be substantial differences in the annual returns per unit between growers having com- parable fruit in all respects. One grower may have a much larger pro- portion of his total crop in a given pick-around pool than another grower merely because of his position in the picking schedule. The most extreme case of such a difference in proportions arises at the time of the year when the picks are the heaviest and between the growers whose fruit is picked at the beginning of the picking schedule and those whose fruit is picked at the end. Suppose, for example, that the fourth pick is made between March 15 and April 30, inclusive ; that grower A's orchard is picked on March 15 and grower B's orchard on April 30; and that the period of heaviest production on both orchards occurs during this inter- val of time. Under this situation grower B would have his heaviest pick of the year in pool No. 4, while grower A's heaviest pick would be in pool No. 5, although the period of heaviest production on both orchards coin- cided. To the extent that the returns per unit in the two pools were dif- ferent (and this is usually the case), one of the growers would lose and the other would gain, not because of inherent differences in their fruit but because of chance. There is no certainty that gains and losses from this source will aver- age out over a period of several years. In sections in which lemons mature 31 Some associations also pool on the basis of color classifications. This is discussed later (p. 64). Bul. 619] Maintenance of Equity in Pooling of Lemons 57 the year around, it is no easy matter to change the picking schedule radically from one year to another. Only moderate changes can be made without danger of loss from deterioration of the fruit in the orchard. With only moderate changes in the picking schedule made each year, several years might be required to effect a complete shift in the order of pickings. Risks of the sort described above cannot be entirely eliminated with multiple time pools, but they can be materially reduced by two methods : (1) by extending the length of the pooling periods, and (2) by picking the orchards in the order of the relative rates of maturity of the fruit. When time pools are based upon picks, extension of the pooling period requires the inclusion of one or more additional pick-arounds in the pool. The fewer the number of time pools in a year, the fewer are the number of transitions between pools and the smaller is the proportion of the fruit involved in the transitions. To the extent that the orchards are picked in the order of the relative rates of maturity of the fruit, the differences in returns over a period of several years between growers, occasioned by having varying propor- tions of their total crops in one pool rather than in another, tend to reflect the inherent differences in the characteristics of their fruit. In any one year, however, the differences in returns may arise solely from temporary fluctuations in the supply and demand situation. The employment of multiple time pools based upon picks presupposes that the beginning and end of each pick-around is precisely determined. Otherwise, the assignment of each lot of fruit to a specific pool would be impossible. If each orchard were picked in rotation and each picked the same number of times in a given year, the determination could easily be made. Under the conditions existing in the area served by the Santa Paula Citrus Fruit Association, however, such a procedure appears im- practical to follow at all times. During the rainy season, a predetermined picking schedule is frequently impossible to adhere to strictly and still secure economical operation. A given rain may not be uniform over the entire area, with the result that some orchards are less affected by it than are others. And even when the rain is fairly uniform, some orchards, because of the soil and topography, can be picked much sooner after the rain than can others. Furthermore, the fruit in some orchards grows faster or matures more rapidly than it does in other orchards. Conse- quently, some orchards need to be picked more frequently than do others. These conditions suggest that in this association the picking schedule should be flexible rather than rigid. Flexibility in the picking schedule, however, does not preclude the 58 University of California — Experiment Station determination of the beginning and end of each pick-around, although it does introduce a degree of artificiality. For example, the first pick- around of an association in each year can be considered to begin with the crop year. Between the middle of October and the first of November there is usually relatively little mature fruit on the trees. The first pick- around can be considered finished when all the orchards of the growers have been picked once, except (1) orchards, which in the opinion of the management do not have a sufficient volume of fruit available at ap- proximately their assigned time in the picking schedule, (2) orchards which, because of weather conditions or the condition of the land, can- not be picked at approximately their assigned time in the schedule, and (3) orchards whose owners refuse to allow picking at the assigned time. The second pick-around can be considered to begin immediately upon the close of the first and to end when all orchards except as provided above have been picked twice, and so on. There is necessity for more rigidity in picking when each pick-around constitutes a pool than when a number of pick-arounds are combined, if each grower is to receive impartial treatment. When a number of pick- arounds are combined in one time pool considerable flexibility may be permitted on each pick-around except the last one in each time pool. Such flexibility may be of considerable advantage to some growers and to the association as a whole without detriment to any grower. Thus, in each of the earlier pick-arounds some orchards may not be picked at all, while other orchards may be picked twice. The order of picking may be modified to suit the convenience of individual growers and the size of the rings used in picking may be adapted to the desires of the individual growers. On the last pick-around in each time pool, however, there is need for a high degree of uniformity. 32 Associations which combine two or more pick-arounds in one time pool generally require that all orchards be picked once on the last pick- around. This requirement can be met without serious disadvantage to any grower provided weather conditions do not unduly delay the pick- ing of his fruit. In the territory of the Santa Paula Citrus Fruit Associa- tion, picking has been reasonably free from delay occasioned by weather conditions from the first of May until November, but in each of the other months and particularly in February and March the picking on some orchards has had to be postponed for several weeks. Suppose, for example, that two time pools are to be established during the crop year based upon picks, and that the first pool is to include 32 When each pick-around constitutes a pool every pick-around is the last in some time pool. Bul. 619] Maintenance of Equity in Pooling of Lemons 59 mainly fruit which must be shipped in the six months, November through April, and the second pool to include mainly fruit which can be shipped in the six months, May through October. 33 If this is to be accomplished the last pick-around in the first pool should end sometime before May 1, and the last pick-around in the second pool should end before November 1. In this case the closing of the second pool would not usually be inter- fered with by weather conditions, but the closing of the first pool might be interfered with in any year and is certain to be interfered with in some years. From 1925-26 to 1934-35 an average of 26 per cent of the annual shipments of the Association was made in the six months, No- vember through April, while an average of 24 per cent of the annual deliveries occurred in the four months, November through February. It appears from these figures that, if deliveries in the first pool are to con- form closely with the shipments in the winter months, the end of the last pick-around in the first pool would need to be in March, preferably in the first half. This is precisely the time, however, when picking is likely to be delayed because of rain. Under such conditions some modification in the requirement that each orchard be picked once on the last pick-around in a time pool appears necessary to avoid penalizing some growers at times because of their position in the picking schedule. To continue with the above example, let us assume that, in the absence of interference with the picking sched- ule, the first pool can be closed about March 15. On March 10, however, an extended rainy period occurs which delays picking for two weeks. About 90 per cent of the orchards were picked before March 10, but 10 per cent of them still remained to be picked. By the time these were eventually picked a larger quantity of fruit was secured from them than would have been obtained if they had been picked two weeks earlier. If all of the fruit is placed in the first pool, and if it is the lower-priced one, these growers will be penalized, while if all of the fruit is placed in the last pool and it is the higher-priced one, they would receive an undue advantage. What is needed in this situation is a basis for dividing the deliveries between the two pools in accordance with the relative amounts of fruit that would have been in each if the picking had not been delayed. The suggestion has been made that the division be based upon the number of days between pickings. For example, assume that on the last pick-around in the first pool, grower A's orchard would have been picked 40 days after the previous picking had weather conditions not inter- fered, but because of such interference it was picked 10 days later, and that 100 field boxes were obtained. With this situation four-fifths of the 33 The relation of separate color pools to this problem is discussed later (p. 65). 60 University of California — Experiment Station 100 boxes, or 80 boxes, would be placed in the first pool and one-fifth of the 100 boxes, or 20 boxes, would be placed in the second pool. When the delay in picking is caused by conditions over which the indi- vidual grower has control, no adjustments in his delivery as between pools appear warranted. In the event that the picking on the last pick- around in the first time pool is delayed by the grower, all the fruit from that pick might well be placed in the first pool. On the other hand, if the picking on the last pick-around in the second time pool is delayed by the grower, all the fruit from that pick might well be placed in the first time pool of the following year. This assumes that there are only two time pools during the crop year and that on the average the returns per unit from the first time pool are lower than those from the second time pool. With regard to the sizes of the rings used in picking, it would seem that, with the exception of the last pick-arounds in each time pool, con- siderable variation between orchards might be permitted, particularly if size pools are employed. On the last pick-around in each time pool, however, impartial treatment of all growers requires that the same ring size be used, except that on the last pick-around in the first time pool a smaller ring size may be used if desired by the grower, while on the last pick-around in the second time pool a larger ring size may be used if desired by the grower. PRICE RISKS IN TIME POOLS The chief source of risk in the marketing of lemons relates to sharp fluc- tuations in prices from day to day, from week to week, and from month to month. Table 32 is designed to show the extent of the changes in the prices of lemons on the New York auction market from one day to the next during 1933-34 and 1934-35. The significant facts illustrated in this table are that prices of lemons change rapidly and that the changes are frequently pronounced. The pooling of lemons provides a type of insurance for growers against the risk of loss from having the bulk of their lemons sold on days when prices are low. Losses from sharp drops in market prices may fall on any of the numerous growers, but actually they will fall upon only a few of the entire number. Pooling does not free the growers from loss, but it does distribute among all the growers the burden of losses which would otherwise fall heavily upon a few. Short time pools such as the monthly shipping pool or the pick-around pool are effective in insuring growers against losses from price declines within a short space of time, but do not provide adequate insurance against price decreases from one month to another. Table 33 shows the Bul. 619] Maintenance of Equity in Pooling of Lemons 61 TABLE 32 Distribution of Changes in Weighted- Average Prices of Lemons per Packed Box between Consecutive Days; New York Auction Market; 1933-34 and 1934-35 1933-34 1934-35 Changes, cents per box Number of days Per cent of days Cumulative per cent of days Number of days Per cent of days Cumulative per cent of days 1 2 S 4 5 6 80 and over 4 4 4 6 12 20 52 59 88 249 1.6 1.6 1.6 2.4 4.8 8.0 20.9 23.7 35.4 1.6 3.2 4.8 7.2 12.0 20.0 40.9 64.6 100 5 1 8 6 12 19 31 64 103 249 2.0 0.4 3.2 2.4 4.8 7.6 12.5 25.7 41.4 2.0 71 to 80 2.4 61 to 70 5.6 51 to 60 8.0 41 to 50 12.8 31 to 40 20.4 21 to 30 32.9 11 to 20 58.6 Oto 10 100.0 Total 100.0 100.0 Source of data: Computed from New York Daily Fruit Reporter. TABLE 33 Distribution of First Differences between Monthly F.O.B. Prices of Lemons after Adjusting for a Normal Seasonal Variation; Santa Paula Citrus Fruit Association; November, 1933 to October, 1935 Dollars per box Number of first differences Oto 0.25 7 26 to 0.50 8 0.51 to 1.00 5 1.01 to 1.50 2 1.51 to 2. 00 1 Total 23 extent of the changes from November, 1933, to October, 1935, in the monthly average f .o.b. prices received for lemons shipped by the Santa Panla Citrus Fruit Association, after adjusting the monthly prices for the normal seasonal variation in prices given in table 24, column 3. In seven months during this period, the average price was within $0.25 a packed box of the average price in the preceding month, but in five of the months the average price was from $0.51 to $1.00 a box above or below the average price of the preceding month, while in three months it was from $1.01 to $2.00 above or below the average price of the preceding- month. With short time pools some growers would have secured rela- 62 University of California — Experiment Station tively large gains during this period while others would have suffered relatively large losses, mainly as the result of chance. An increase in the lengths of the pooling periods reduces the chance both of large gains and of large losses. From the standpoint of reducing the hazards to individual growers arising out of the unpredictable de- clines in prices an annual pool is superior to multiple time pools. Two time pools during the season are inferior to an annual pool but are supe- rior to shorter time pools, such as the pick-around pool. TOTAL RETURNS TO ALL GROWERS COMBINED The foregoing sections of this part of the report have largely dealt with the effects of variations in the length of the pooling periods upon the division of the total net returns of an association between the individual growers. This is important, but it is also important to determine what effects variations in the length of the pooling periods have upon the size of the total net returns, that is, whether the total amount of money avail- able for division between the individual growers is likely to be larger or smaller with one type of time pool than with another. From the stand- point of time pools, the two factors affecting the total amount of the net returns of an association relate to orderly marketing and costs of operation. Relation of the Length of Pooling Period to Orderly Marketing. — By orderly marketing we mean the regulation of shipments for quantity, quality, time, and place in accordance with market demands. Only by regulating shipments in such fashion is an association able to obtain the largest gross returns possible under the particular circumstances with respect to the national supply and demand situation which prevails during a given crop year. The total weekly lemon shipments of associations affiliated with the California Fruit Growers' Exchange are, during most of the season, determined by allotments received under the Exchange Lemon Agree- ment. The allotments to the several associations are based upon the volume of lemons which they have in storage, and no association is permitted to exceed its allotment. Thus, as far as regulation of lemon shipments with regard to time is concerned, most associations operate under a coordinated program rather than individually. No evidence was found that the length of the pooling periods employed by associations in any way affected their ability to fit into the coordinated program. Although the total weekly shipments may be fixed for an association, the character of lemons to be shipped is left to the individual association. It was found that in some cases the character of fruit shipped during a Bul. 619] Maintenance of Equity in Pooling of Lemons 63 specific short period was affected by the length of the pooling period. The tendency among a number of associations employing pick-around pools was to ship dark-green lemons from an earlier pick in order to close that particular pool, when from the standpoint of the association as a whole it would have been better to have shipped silver lemons from a later pick. Growers naturally wish to obtain full payment on their fruit at an early date. When multiple time pools based upon picks are employed they frequently ask the manager "When are we going to receive final payment on this particular pool?" In order to make an early final payment, managers are at times forced to ship fruit which in their judgment should be held and to hold fruit which in their judg- ment should be shipped. Relation of the Length of Pooling Period to Costs of Operation. — There appears to be little difference in the costs of operation between multiple time pools based upon shipments and an annual pool based either upon shipments or picks. The accounting costs incident to the pool settlement are increased with the increase in the number of pools during the season, but this is in part offset by the additional costs of making advance payments when the pooling periods are long. Careful observa- tion also indicates that the accounting costs are somewhat larger with multiple time pools based upon picks than with an annual pool. With pick-around pools, for example, there is frequently fruit from two pools and sometimes from three and even four pools in the same car. The identity of the fruit from each of the pools must be maintained until after the car has been sold, and the sales returns must be divided between the several pools. In order to avoid mistakes, great care must be exercised both in the packing plant and in the office. Most associations employing pick-around pools make advance pay- ments on green lemons, since these are generally held in storage for some months after being delivered. The expense of so doing is not much less than the cost of making advance payments under an annual pool. The cost of making the final payments is, of course, greater with pick-around pools than with an annual pool since there are usually from six to nine more final settlements to make. An element of cost which may at times be affected by the length of the pooling period relates to picking. Under both the annual pool and the multiple time pools based upon picks, some growers are inclined to inter- fere with the picking schedule of the association. With an annual pool some growers may want to pick out of turn in order to avoid weather hazards or to carry on a particular cultural operation at a given time. With pick-around pools these same incentives are present, and in addi- 64 University of California — Experiment Station tion there is the incentive for growers to have their fruit in a high-priced rather than in a low-priced pool. In an attempt to do so, some growers are inclined to manipulate their cultural operation for the purpose of delay- ing the picking on their orchards, or to bring pressure upon the manager to have their orchards picked early. To the extent that such practices interfere with the normal picking schedule of the association, costs of operation may be increased. COLOR POOLS When conditions are such that multiple time pools based upon picks are indicated, separate pools for the several color classifications are also likely to be needed in order to preserve substantial equity between growers. 34 The presence of definite seasonal variations in prices and in consumption of lemons indicates that lemons which can be shipped in the summer months are, from a market standpoint, usually worth more per unit than are those of the same grades and sizes which can be shipped only in the winter months. The time of the year during which lemons can be shipped depends not only upon the time they are picked but also upon the length of time they can be kept in storage without physical loss. In general, the latter is closely associated with the color of the lemons at the time of delivery. There is wide variation in the length of time lemons in the different color classifications can be kept in storage without serious loss from de- terioration in grade and shrinkage. According to the inherent character- istics of the lemons and the storage conditions, the average lengths of time for the different colors are roughly as follows : dark green, four to six months ; light green, three to four months ; silver, one and a half to two and a half months; and yellow, one to one and a half months. Dark- green lemons delivered in March can be shipped in the early summer months, but yellow lemons delivered in March must ordinarily be shipped before the usual advance in prices and consumption occurs. There is considerable variation between the growers in the Santa Paula Citrus Fruit Association with respect to the proportions of their fruit in the several color classifications. This is illustrated in table 34. Over the four-year period 1931-32 to 1934-35, a relatively large per- centage of some growers' fruit consisted of dark-green and light-green lemons, while a relatively large percentage of other growers' fruit con- sisted of yellow and silver lemons. One association which has four time pools based upon picks, in addi- Si When multiple time pools are based upon shipments, the only reason for also having separate color pools relates to grades. Bul. 619] Maintenance of Equity in Pooling of Lemons 65 tion to pooling by grade and size, also pools on the basis of three color classifications. The additional work which color pools entail relates en- tirely to accounting. The physical handling of the fruit is the same with as without color pools. The number of units of each grade and size in each color classification of the individual growers' fruit can be readily ascer- tained since the several color classifications are packed separately. The determination of the price rates on the same grades and sizes in different color pools, however, requires that the sales of the fruit from each color TABLE 34 Percentages of Total Lemon Deliveries from November through April That Were Green ; 56 Growers from the Santa Paula Citrus Fruit Association ; Average 1931-32 to 1934-35 Per cent of total deliveries Number of growers Per cent of growers 1 2 20.0 to 29. 9 2 20 20 11 2 1 3.6 30.0to39.9 40.0to49.9 50.0 to 59. 9 35.7 35.7 19.6 60.0 to 69.9 3.6 70.0to79.9 1.8 Total 56 100.0 classification be recorded separately. Also, the time required to make out the individual growers' pool statements is increased. When two or more pick-arounds are combined in one time pool it does not necessarily follow that there should be the same length of pooling period for each color classification. In fact, if the fruit in a given time pool is to conform most closely to a definite shipping period, the number of pick-arounds in each color pool would need to be varied. Again if two time pools are assumed during the crop year to be divided so as to include in the first chiefly fruit which must be shipped in the winter months and in the second chiefly that which can be shipped in the summer months, at least one more pick of yellow and silver lemons than of light- and dark- green lemons should be in the first time pool, while one less pick should be in the second time pool. For example, instead of having the first time pool include all lemons picked in the first three pick-arounds and the second time pool include all lemons picked in the fourth to the last pick- arounds, the first time pool could include all lemons picked in the first three pick-arounds plus all silver and yellow lemons from the fourth pick- around. The second time pool would then include all lemons picked in the fourth to the last pick-arounds, except those silver and yellow lemons 66 University of California — Experiment Station from the fourth pick-around. If pooling is on the basis of color classifica- tions, the above type of arrangement would involve practically no addi- tional work. As contrasted with the determination of price differentials between the several grades and sizes discussed previously (pp. 23, 38 ) , the price differ- entials between color classifications should be based upon weighted-aver- age prices rather than upon a simple average of prices on corresponding days. A color pool is a type of time pool. Consequently, the price differ- entials between fruit from different color classifications should reflect the difference in time at which they were shipped. Under some condi- tions, however, it appears that the price rates to growers for comparable grades and sizes of two or more of the several color classifications should be the same even though the weighted-average selling prices were different. For example the price of lemons tends to fluctuate sharply within rela- tively short periods, and these fluctuations can seldom be forecast very far in advance. During a given period of time when the market level is relatively favorable, an association may be shipping yellow and silver lemons and holding the light- and dark-green lemons delivered at the same time, although the green lemons are also ready for shipment. At the time the green lemons are eventually shipped prices may be materially reduced. The result of such a situation is that green lemons bring less than silver and yellow lemons of comparable grades and sizes. Although the decision of the manager to hold the green lemons may have resulted in the largest total returns to all growers combined, nevertheless those growers whose deliveries consisted mainly of green lemons would have individually secured larger returns if his decision in this particular case had been different. The contention that fruit of long-keeping quality is always worth as much and frequently is worth more than fruit of short-keeping quality has considerable merit. It can be shipped during the same time that the latter can, and, in addition, can be shipped after the latter is no longer fit for consumption. One method of giving recognition to the wider market opportunity possessed by fruit of long-keeping quality would be to base the price rates to growers on the weighted-average prices, whenever they are higher, on the longer-lived fruit than on the shorter-lived fruit, but to combine both in one pool when they are not. Thus, two or more separate color pools would be combined within each time pool in the event the following con- ditions are found to exist : (1) if a given grade of dark green brings as low a price per unit or lower than the same grade of light green, silver, Bul. 619] Maintenance of Equity in Pooling of Lemons 67 or yellow; (2) if a given grade of light green brings as low a price per unit or lower than the same grade of silver and yellow ; and (3 ) if a given grade of silver brings as low a price per unit or lower than the same grade of yellow. BY-PRODUCTS POOLS Lemons sent to the products plant are of two classes: (1) fruit which during its normal life does not meet the minimum requirements for fresh shipment, and (2) fruit which was physically fit for consumption at the end of the normal storage period of its particular color classifica- tion. In this report the first class will be termed "cull fruit" and the second class will be termed "merchantable fruit." In most of the years since 1924—25, considerable quantities of lemons, which were at one time physically fit for fresh shipments, have been used in the manufacture of by-products. Returns to growers from mer- chantable lemons sent to the products plant have generally been lower than the returns on comparable grades and sizes of lemons shipped fresh. Under the California Fruit Growers' Exchange Lemon Agree- ment, which was instituted in 1924, attempts are made to regulate ship- ments of lemons for fresh consumption in accordance with the effective market demand. Quantities in excess of the amounts which could be shipped fresh at prices deemed to provide a reasonable return to grow- ers were eventually sent to the products plant. Because of the inelastic demand for lemons, limitation of the total supply marketed fresh in years of large crops not only resulted in higher prices to growers but also in larger total returns. The problems in pooling that arise when merchantable lemons are sent to the products plant center around the division among the individ- ual members of the total net returns received by an association from the sale of its entire deliveries. Who is to take the loss when an association sends merchantable lemons to the products plant? Is such loss to be borne entirely by the individual growers of the particular fruit sent to the products plant, or is such loss to be shared by all of the members of the association f If the loss is to be shared by all the members of the asso- ciation, how is the distribution of the loss between the members to be de- termined ? In most associations all fruit sent to the products plant has been for the account of the individual growers of such fruit. In some associations the gross returns received from the products plant were distributed among the several growers, but in other associations a handling charge was first deducted. In any event, the returns which the growers received 68 University of California — Experiment Station for merchantable fruit sent to the products plant were much smaller than those which other growers received for similar grades and sizes of lemons that were shipped fresh. In considering this problem a clear distinction must be made between strictly cull lemons and those which were one time merchantable. 30 There appears to be little doubt that strictly cull fruit should receive only the by-products returns, and there is considerable merit in assessing such fruit with at least the direct costs of handling it. In the case of lemons which were one time merchantable, however, there are strong grounds for contending that such fruit should receive more than the by-products returns whenever similar grades and sizes shipped fresh are bringing more than by-products returns ; for the merchantable fruit, by being withheld from the fresh market, contributed to the prorate under which other fruit was shipped and to the price received for the fruit that was shipped. Under the Exchange Lemon Agreement, the total quantity of lemons deemed advisable to ship each week is divided among the member associa- tions on the basis of the amount of lemons which each has in storage. The storage counts are made as of the first and fifteenth of each month. All merchantable lemons, irrespective of color, grade, and size, in storage when the count is made, are included in determining the total storage volume of the association as of that date, and this total storage volume constitutes the basis upon which the weekly shipping allotments for the next two weeks are calculated. 36 Each unit of merchantable lemons in storage on a given date is equally as important as every other unit in determining the amount of fruit which the association is permitted to ship. Thus when fruit which was counted in storage is later sent to the products plant, it contributed to the shipping allotment on which other fruit in storage at the same time was shipped. An analysis of the relation between the total shipments of California lemons and the average f .o.b. prices shows clearly that, on the average, a reduction in shipments for the season is accompanied by an increase in the price, while an increase in shipments for the season is accompanied by a decrease in the price. The sending of merchantable lemons to the products plant results in a decrease in shipments below what they other- wise would have been and in an increase in the price received for the 35 The important thing here is not the condition of the lemons at the time they are actually sent to the products plant, but their condition at the end of the normal stor- age period for that particular class of lemons (see p. 19). 38 Because of the varying number of full weeks between storage-count dates, it is occasionally necessary to base the shipping allotments for three consecutive weeks upon the same storage count. Bul. 619] Maintenance of Equity in Pooling of Lemons 69 lemons shipped. The fact that the merchantable lemons sent to the prod- ucts plant consist chiefly of the lower grades and less desirable sizes does not significantly change the general conclusion stated above. The with- holding of any particular grade or size of lemons from the market results not only in a higher price for the lemons of that particular grade and size which are shipped, but also in a higher price for each of the other grades and sizes. The effect, however, is somewhat more pronounced upon the price of the particular grade and size than upon the prices of the other grades and sizes. From the above discussion it is evident that the key problem which needs to be solved when merchantable lemons are sent to the products plant relates to methods of making the adjustments necessary to main- tain substantial equity between the members of an association without unduly sacrificing total net returns to the association as a whole. It does not appear feasible to have such adjustments apply directly to the separate lots of fruit of the individual members of an association. Instead, it is proposed that the adjustments be made between classes of fruit based upon size, grade, color, and time of picking. Thus, the position of any individual grower will depend upon the particular class of fruit which he delivers, and every grower with the same class of fruit will be accorded the same treatment. Equity between groups of growers deliver- ing different classes of fruit will be maintained through adjustments in the total net returns credited to the different classes of fruit. Such ad- justments may involve : (1) adjustments between time pools ; (2) adjust- ments between color pools within a given time pool; (3) adjustments between grade pools within a given color pool ; and (4) adjustments be- tween size pools within a given grade pool. In developing the methods for making adjustments when merchant- able lemons are sent to the products plant the following assumptions were made : 1. That the total volume of lemons in storage provides an equitable basis for determining shipping allotments. 2. That the only lemons sent to the products plant which are entitled to additional payment are those which, during their normal shipping period, would have brought more than the by-products return if they had been shipped and an equal quantity of other lemons had been withheld from the market. 3. That the amount of the additional payment to which such lemons are entitled is the difference between what they would have brought if they had been shipped during their normal shipping period and the by- products return, with no change in the total volume of shipments. 70 University of California — Experiment Station Although the validity of each of the foregoing assumptions is open to question, they do not appear to be unreasonable. Under the Exchange Lemon Agreement, shipping allotments to the member associations are based upon their respective volumes in storage. From the standpoint of equity, and as long as this procedure is followed, the local association in turn should divide up its shipping allotment among the various classes of fruit on the same basis. The second assumption is based upon the reasoning that a shipping allotment is of no value per se; that it is of value only if it is used to ship fruit of a character which will bring more than by-products returns. A certain class of fruit, by reason of having been counted in storage, may be entitled to a portion of the total shipping allotment received by the association. But if the fruit in that class is of such a character that under the prevailing market conditions during its normal shipping period it cannot be sold for fresh consumption at prices above by-products returns, then the growers of such fruit have lost nothing by its having been sent to the products plant. The fact that that portion of the shipping allot- ment which was obtained on such fruit was used to ship other fruit does not in itself justify additional compensation. The maintenance of sub- stantial equity does not require that growers be paid more than market value of the particular class of fruit which they produce. The third assumption is based upon the reasoning that the individual growers of merchantable fruit sent to the products plant should be com- pensated for any loss incurred on that particular class of fruit because of its having been used for by-products rather than shipped fresh. Under this proposal growers of merchantable fruit that was sent to the products plant would participate in those gains to the association which arise from a higher level of prices occasioned by the limitation of total shipments, but would not participate in those gains to the association which arise from shipping the better grades and more desirable sizes rather than the poorer grades and less desirable sizes. However, growers of the latter grades and sizes would in no way be penalized under this proposal, since they would be paid the full market value of the particular class of fruit which they produce, and the market value of the lower grades and less desirable sizes along with the other grades and sizes would be increased from limitation of total shipments in years of excessively large crops. Adjustments betiveen Time Pools. — When multiple time pools are based upon shipments, there appears to be no satisfactory way of deter- mining the extent of adjustments required from the standpoint of main- taining substantial equity when merchantable fruit is sent to the prod- ucts plant. That there are grave possibilities of substantial inequities Bul. 619] Maintenance of Equity in Pooling of Lemons 71 unless appropriate adjustments are made can scarcely be doubted. When each of the multiple shipping pools is charged with the total volume sent to the products plant during the particular period of time covered by such shipping pool, one shipping pool may easily happen to be charged with a very large volume of by-products and another shipping pool with a very small volume merely by reason of the particular pooling periods employed. An even greater cause of inequity arises out of the lag in movement to the products plant as compared with the shipments for fresh consumption. Ordinarily, merchantable fruit sent to the products plant is held in storage until it has so deteriorated in quality that it is no longer fit for fresh consumption. Consequently, during the winter and early spring months when deliveries are normally in excess of shipments, there is a large accumulation of lemons in storage. In years of large crops relative to demand conditions, a portion of the accumulated volume in storage eventually has to be sent to the products plant. This generally occurs in the late spring and early summer months. Thus, of the deliv- eries of merchantable fruit to the packing-house during a given period of time, that portion which is utilized for fresh shipment may be credited to one shipping pool and that portion which is sent to the products plant charged to the following shipping pool. As far as is known, no association employing multiple shipping pools has attempted to work out adjust- ments between them. Instead they have generally avoided the necessity of making such adjustments between time pools as such by simply charg- ing all fruit sent to the products plant to the accounts of the individual growers of such fruit. In doing so, of course, they did not avoid inequities as between growers. Such study as we have been able to make of this problem leads us to the conclusion that the most feasible way of handling it is to employ multiple time pools based upon picks rather than upon shipments and then to make appropriate adjustments between the picking pools. When multiple time pools are based upon picks, methods of making adjustments between them to take into account their respective contri- butions to the total shipping allotments received by the association are not especially difficult. The need for making such adjustments when merchantable fruit is sent to the products plant arises out of three con- ditions : ( 1 ) There are periods during which lemons from two or more time pools are in storage at the same time and upon which shipping allot- ments are being received. (2) There is substantial variation between growers with respect to the percentages of their total deliveries which they contribute to each time pool. (3) Physical division of the total ship- ping allotments which an association receives between the time pools dur- 72 University of California — Experiment Station ing the overlapping storage period on the basis of the amount of fruit from each time pool in storage would tend to reduce the total net returns to the association. An association might divide the total shipping allotments which it receives between the several time pools during the overlapping storage periods based upon the respective amounts of fruit from each time pool in storage. To do so, however, would result in some additional expenses in the packing-house. Of even more importance would be the effect of doing so upon the gross returns of the association. At times the manager would be compelled to ship fruit which, because of lower grades or less desirable sizes, would return less money than other fruit that he had available for shipment. Also such a procedure may at times result in ship- ping fruit which is physically capable of being held for a considerable period without undue deterioration and which could eventually be shipped, and at the same time having to hold other fruit until it became unmerchantable. Unless, however, an association does divide its shipping allotments during the overlapping storage period between the time pools based upon their respective amounts of fruit in storage, it may find that it has actu- ally shipped an undue proportion of the fruit from one time pool and sent an undue proportion of the fruit from another time pool to the products plant. In such a situation, one time pool is benefited and the other penalized, unless an appropriate adjustment is made between them. A suggested method for making appropriate adjustments between time pools based upon picks is explained in Appendix C. In making such adjustments it should be recognized that the larger the number of time pools during the season the more complicated is the problem. With pick- around pools, for example, lemons from three or even four pools may happen to be in storage at the same time. Thus with pick-around pools it would be necessary to deal with three or four time pools in each of eight or ten overlapping storage periods. On the other hand, with only two time pools during a year, it would be necessary to deal with only two overlapping storage periods and with only two time pools in each such period. Fortunately from the standpoints of both largest total returns to the association and the maintenance of substantial equity between grow- ers, two time pools during the year are probably superior to three or more time pools. Adjustments between Color Classifications. — When the shipping allot- ments received by local associations are based upon the amounts of fruit which each has in storage, a given quantity of lemons of a long storage life generally contributes more to the total shipping allotment received Bul. 619] Maintenance of Equity in Pooling of Lemons 73 by an association than does the same quantity of lemons of a short storage life, since the former is in storage for more storage-count dates than the latter. In general, the length of time lemons can be held in storage is closely associated with the color classifications into which they are sorted after being washed. Dark-green lemons can be held in storage the longest, followed by light green, silver, and yellow in the order named. In order to secure the largest total net returns from all lemons in the time pool, it may at times be desirable to ship all of one color classification and send all of another color classification to the products plant, or at least to ship a much larger proportion of one color classification than of another. In doing so, however, the fruit in one color classification may be shipped on the allotment received on fruit in another color classification with the latter eventually going to the products plant. The problem, therefore, is to determine the extent of adjustments required between color classifications from the standpoint of their respective contributions to the shipping allotments received by an association under the Exchange Lemon Agreement. Suggested methods for making such adjustments are explained in Appendix D. Adjustments between Grade Pools. — When there are more lemons available for shipment than can be shipped, an individual association will find that confining its shipments to the fruit which is highest in price and sending the lower-priced fruit to the products plant will result in the largest total returns to itself. 87 Since at any given time Extra Choice fruit commands a premium over Choice, and Choice fruit over Standard, the bulk of the merchantable by-products fruit consists of Standard and Choice grades. Granting the desirability of an individual association's sending the lower grades and least desirable sizes to the products plant in years when all of the merchantable fruit cannot be marketed, it does not necessarily follow that the growers who produced such grades and sizes should bear the full burden of the lower returns. Did not the withholding of that fruit from the market result in a higher price for the fruit that was shipped f The answer to this question is definitely in the affirmative. This in itself, however, does not justify additional payments on such fruit. If an association can secure at least as large net returns for a given class of fruit sent to the products plant as it could if such fruit were shipped, no loss is entailed by so doing, and no grower is paid less than the market 37 Whereas it will pay an individual association to send only the lower grades and least desirable sizes to the products plant, it may at times pay the industry as a whole to send some of the higher grades and more desirable sizes to the products plant and to ship some of the lower grades and least desirable sizes. 74 University of California — Experiment Station value of his fruit. On the other hand, when certain grades and sizes are sent to the products plant which, if they had been shipped and an equal volume of other grades and sizes withheld, would have brought more than the by-products return, growers of such grades and sizes are not paid in accordance with the market value of their fruit when they receive only the by-products return. If growers of merchantable by-products fruit are to be paid a higher price per unit than the association receives for such fruit, the first ques- tion to be determined is whether the additional compensation is to be a flat rate irrespective of the quality of the fruit or is to vary with the grade. In 1934-35 one association made an additional payment of $5.00 a ton on all merchantable by-products fruit. This procedure made the determination of the grades sent to the products plant unnecessary. The cost of the payment was treated as an operating expense against all fruit shipped. Varying the compensation on by-products fruit with the grade gives rise to three questions : (1) How are the number of units of each grade in the individual lots to be determined? (2) What rates are to be paid for each grade ? (3) From what source is the money to be obtained? Thus far, associations sending merchantable fruit to the products plant have employed either of two methods for determining the grades : (1) actually grading the lots and (2) estimating the proportions of the several grades in the lots, commonly termed "pencil-packing." The indi- vidual lots are graded only if the association intends to ship the Extra Choice fruit. The difficulty with this method is that the grades obtained may reflect not so much the inherent characteristics of the fruit in the lot as the length of time it has been in storage. This problem has already been discussed (p. 19). The method known as "pencil-packing" represents simply the best guess of the manager or packing-house foreman with respect to the grades contained in a given lot. These men are, of course, familiar with the general type of fruit produced by each grower, and consequently, on the average, their guesses are likely to be much closer than those of a stranger. Nevertheless, there is no certainty that, with respect to any individual lot, the grades credited growers by this method even closely approximate the grades which the lot actually contained. Apparently the determination of grades based upon samples taken at the washer is likely to be more accurate than either of the two methods mentioned above. Once the grades of the by-products fruit are determined, the next problem is to fix the rates of payment for each grade. The general prac- tice among associations which have settled for by-products fruit on the Bul. 619] Maintenance of Equity in Pooling of Lemons 75 basis of grade has been to pay the same rate for the same grade of fruit sent to the products plant that is paid for the fruit of that grade which is shipped. The usual procedure is to combine within each grade pool both the fruit shipped and the fruit sent to the products plant, and to divide the total net returns from that grade among the several growers irrespective of the disposition of the individual grower's fruit. The ad- justment of loss on by-products fruit (that is, the difference in price between shipped fruit and by-products fruit) is made entirely within the grade ; no returns from other grades enter into it. While the foregoing method recognizes that the burden of low returns on particular lots of merchantable fruit sent to the products plant should not be borne entirely by the growers of those lots, it fails to recognize that withholding a portion of certain grades and sizes from the market results in higher prices on other grades and sizes. In order to spread the loss incurred on those particular grades and sizes sent to the products plant over all grades and sizes in such a manner that the total returns to each grade and size will reflect their respective market values, adjust- ments need to be made between them. A convenient method of calculating such adjustments is illustrated in Appendix E. Adjustments between Sizes. — When pooling is on the basis of sizes or size groups, the adjusted net returns to each grade will need to be distrib- uted among the several sizes or size groups. The procedure required is simply an extension of the method employed in determining the adjust- ments between grades. If the number of units of each size within a grade and the price differentials between the several sizes are known, it is a rela- tively simple matter to calculate the rates of payment to growers by sizes or size groups. This is illustrated in Appendix E. SUMMARY In the cooperative marketing of lemons, pooling is done by the local packing associations. The problem which these associations have in their pooling operations is twofold : (1) the handling of the fruit in such a way as to secure under the existing market conditions the largest total net returns for the association as a whole ; and (2) the division of the total net returns among the members of the association on an equitable basis. Each of these can be done effectively if the other is disregarded. The dif- ficult problem is to accomplish both at the same time. The principal solu- tion of this problem lies in handling all the fruit as if it belonged to one person, and then in manipulating the money returns so that the pay- ments to the individual members will, over a period of several years 76 University of California — Experiment Station closely reflect the average differences in the market value of the lemons which each contributes. If the growers are to be paid in accordance with the respective market values of their lemons, the pooling system employed by an association should be based upon the characteristics of lemons which the market signifies to be important, as indicated by price differentials which tend to persist over a period of several years. Such characteristics relate to the quality and size of lemons and to the time of the year during which they are available for fresh shipment. This latter is determined primarily by the time of the year during which the lemons are picked and the length of time they can be held in storage. The storage life of lemons under given storage conditions is closely related to the color of the fruit at the time of delivery to the packing-house. The constituent parts of a pooling sys- tem for lemons, therefore, consist of grade pools, size pools, time pools, and color pools. Grade Pools. — In most associations, if not in all, a substantial varia- tion exists between growers in the proportions of the several grades con- tributed to a given time pool. Over a period of years the fruit of some growers consistently contains a larger proportion of the higher-priced grades than does the fruit of other growers. On the same markets on the same days, Extra Choice consistently brings a higher price than Choice, while Choice consistently brings a higher price than Standard. Under these conditions, the establishment of separate pools for each grade appears to be the only certain way of assuring that the returns paid the individual growers, either for a given time pool or over a period of sev- eral years, will fully reflect the average differences in the market value of their fruit arising from the differences in quality. In associations which pack from trays, each individual lot is kept entirely separate until after it has been graded and the number of units of each grade determined. Thus, each grower is credited with the precise grades which his fruit contained at the time it was graded. In associa- tions which pack from belts, tubs, or bins, the number of units of each grade is determined only after the fruit has been packed. The large lots are kept sufficiently separate until after they have been packed to provide a very close approximation to the actual number of units of each grade in such lots. This, however, is not done with small lots, because of the expense that would be entailed. Instead, several of the small lots, those containing usually 50 storage boxes and less, are combined before grad- ing and run as one lot. In most cases the grades obtained from the com- bination lot are simply prorated among the several growers on the basis of the number of storage boxes which each had in that combination lot. Bul. 619] Maintenance of Equity in Pooling of Lemons 77 In such cases, fruit in combination lots is not pooled on the basis of grade. In order to pay growers having any significant proportions of their fruit in small lots in accordance with the particular grades of their fruit, the number of units of each grade must be determined between grading and packing, unless each grower's grade credits are determined from samples. When grading on belts and packing from belts, tubs, or bins, the instal- lation of an automatic weighing device, or, in the case where mechanical sizers are employed, the installation of counters between the grading and packing equipment may enable this to be done. The grades obtained at the time the fruit is graded depend upon the length of time the fruit has been held in storage and the conditions under which it was held as well as by its inherent characteristics. In years of excessive supplies, some growers may secure relatively large gains while other growers may experience substantial losses because of the differ- ences in the length of time between delivery and grading of their respec- tive fruit. Adequate handling of this problem necessitates the employ- ment of some method for determining the grades of the individual lots which are held in storage beyond their prime before the fruit begins to deteriorate in grade. The determination of the grades on the basis of samples may afford a solution to this problem. In determining the money credits to growers, the use of a simple aver- age of the price differentials between the several grades on the same markets on corresponding days has some advantages over the use of weighted-average prices by grades, although it would involve somewhat more clerical work. For a given time pool, the weighted-average price of Standard may be above the weighted-average price of Extra Choice, yet at all times during that period the price of Standards may have been considerably below the price of Extra Choice. Size Pools. — The establishment of separate size pools within each grade pool appears to be the only certain way of assuring that the returns paid the individual growers will, over a period of several years, fully reflect the average differences in the market value of their products occasioned by the differences in the sizes of their fruit. It will also result in each grower's receiving for the particular sizes he contributes to each time pool the average net prices realized by the association for those particular sizes. Pooling on the basis of size groups involves less accounting expense than pooling each size separately, but lacks the certainty of the latter with respect to each grower's being paid in accordance with the market prices of the particular fruit he contributes to a given time pool. Over a period of years, however, the division of the returns between the indi- 78 University of California — Experiment Station vidual growers is likely to be substantially the same under both systems. Under the methods now employed, lemons are sorted by sizes in the process of packing, with the result that the number of units of each size or size group in each lot cannot be precisely determined until after the lemons are packed. Associations packing from trays make no attempt, because of the expense involved, to keep each lot separate until it has been packed and consequently do not pool on the basis of size. Associa- tions packing from belts, tubs, or bins are able without undue expense to keep large lots sufficiently separate until after they have been packed and thus provide a very close approximation to the number of units of each size in such lots. In the case of small lots, however, the cost of keep- ing them separate until after they have been packed is apparently so great that no association does this. Instead they place several lots, each of which contains usually 50 storage boxes and less, in a combination lot and prorate the sizes packed from the combination lot among the several growers. The fruit in such combination lots is not pooled on the basis of size. There is a reasonable prospect that the combining of all sizes except the smallest within each grade would, over the next several years, tend to result in about the same division of the total net amount of money among the individual growers as would occur if each size were pooled separately. For any given pooling period, however, the division would most likely be considerably different. The number of units of each size group in each individual lot might be determined by sampling or by means of mechanical sizers and electric counters. Careful experimentation, however, would be required before their potentialities could be definitely ascertained. The use of weighted-average prices as a basis for determining the price rates by sizes in setting up the money credits to growers has some disadvantages which could be overcome by the use of a simple average of price differentials between sizes in the same markets on corresponding days. Time Pools. — Under the conditions which are likely to prevail over the next several years, comparable grades and sizes of lemons produced by some growers in a given association will, from a market standpoint, tend to be worth more per unit than those of other growers. Within the area covered by many associations there are inherent differences between orchards in the time of the season during which the lemons produced on them can be shipped. A larger proportion of the lemons from some or- chards than from others can be shipped during the summer months. Although the prospects are that the wide differential between the prices Bul. 619] Maintenance of Equity in Pooling of Lemons 79 of summer and winter lemons which has prevailed will be materially narrower during the coming years, it does not seem that this differential will entirely disappear. Over the next several years the prices received for lemons shipped during the summer months will tend to average some- what above the prices received for those shipped during the winter months. The consumption of lemons in the United States is also much higher in the summer months than in the winter months. Relative to consumption, however, supplies available for shipment have been heavy in the winter months and light in the summer months. There has seldom been a surplus of lemons in the summer months, but there has frequently been a surplus in the winter months. Thus, the available evidence indi- cates that growers whose fruit can be shipped during the summer months will, on the average, not only receive a somewhat higher price per unit, but will also be able to market a larger proportion of their crops than will growers whose lemons must be marketed in the winter months. From the standpoint of closely reflecting in the returns to individual growers the average differences in the market value of their respective crops over a period of several years, multiple time pools are superior to an annual pool. In most associations, the inclusion and exclusion of orchards on an area basis would not give a high degree of uniformity, since within very small areas there are significant differences between orchards in the time of the season during which the lemons produced on them can be shipped. The available evidence indicates that at least two time pools during the season are necessary in order to maintain substan- tial equity between growers, but that no more than two time pools are needed. From the standpoint of both prices and consumption there are two fairly distinct marketing periods during the season ; namely, Novem- ber through April and May through October. Within each of these the tendency is for the monthly prices over a number of years to average about the same. The first time pool, therefore, might well include mainly fruit which must be shipped during the winter months and the second mainly that which can be shipped during the summer months. Most associations employing multiple time pools base them upon picks rather than upon shipments. Under both types difficulties arise in con- nection with the transition from one pooling period to the next, and the larger the number of time pools the greater are the difficulties. On the whole it appears that the difficulties of transition are less with multiple time pools based upon picks than with those based upon shipments. From the standpoint of insuring individual growers against the risks of marketing, two time pools during the season are inferior to the annual pool, but are superior to three or more time pools. 80 University of California — Experiment Station From the standpoint of securing the maximum total returns to all growers combined, two time pools during the season are no better than the annual pool and probably are inferior, but they are at least as good as three or more time pools and probably superior. Color Pools. — When conditions are such that multiple time pools are needed in order to maintain substantial equity between the members of an association, separate color pools also appear to be necessary if the time pools are based upon picks. The time of the year that lemons can be shipped depends not only upon the time they are picked but also upon their keeping quality, which is closely related to their color. In most associations there is considerable variation as between growers in the proportions of their fruit in the several color classifications. From a market standpoint lemons of long-keeping quality tend to be worth more than comparable grades and sizes of short-keeping quality, since they have a wider market opportunity. When two or more picks are combined in one time pool, it may be desirable to have more picks of one color than of another in a given time pool. By-Products Pools. — When merchantable lemons are sent to the prod- ucts plant adjustments may be required between time pools, between color classifications within a given time pool, between the grades in a given color classification, and between the sizes in a given grade. The need for making such adjustments arises from the fact that merchant- able fruit, by being withheld from the market, contributed to the price received for the fruit that was shipped, and in those associations affiliated with the California Fruit Growers' Exchange from the fact that such fruit contributed to the shipping allotment on which other fruit was shipped. In the event that suitable means can be developed for determin- ing the grades and sizes of merchantable lemons sent to the products plant at the end of the normal storage periods for this fruit, such as might be done on the basis of samples, methods for calculating the neces- sary adjustments will not be particularly difficult. Bul. 619] Maintenance of Equity in Pooling of Lemons 81 ACKNOWLEDGMENTS Much of the detailed analysis is based upon the records of the Santa Paula Citrus Fruit Association. The Board of Directors of that associa- tion made available to us all of the records covering a period of ten years and provided considerable clerical help for copying them. Detailed records on various aspects of the study were also obtained from the Central Lemon Association, Fillmore Lemon Association, Glendora Lemon Growers' Association, La Verne Lemon Association, Johnston Fruit Company, North Whittier Citrus Association, Upland Lemon Growers' Association, Whittier Select Citrus Association, and the Cali- fornia Fruit Growers' Exchange. In addition to the local associations from which specific data were secured, we visited some twenty other local associations and obtained a general picture of their respective pooling systems. In all, numerous persons actively engaged in the lemon industry were consulted on one or more aspects of the study. Many of the ideas developed herein origi- nated in such interviews. Bul. 619] Maintenance of Equity in Pooling of Lemons 83 APPENDIX A COMPUTATION OF POOL RETURNS BASED UPON GRADES DETERMINED AT END OF NORMAL STORAGE PERIODS Data are not available regarding the extent of deterioration in quality and of shrinkage from holding lemons in storage beyond their prime. Consequently, it is impossible to use actual records in the following dis- cussion. Instead, hypothetical examples have been used. These examples, TABLE 35 Illustration of Pack-out of Lemons and Net Returns by Grades in a Given Time Pool Grade Packout Net returns Price per box Price differentials from Extra Choice 1 2 S 4 Extra Choice boxes* 390 240 170 dollars 975 00 420.00 170.00 dollars 2 50 1.75 1 00 dollars 0.00 Choice Standard -0.75 -1.50 Subtotal 800 1,565.00 Culls Shrinkage 100 100 Total 1,000 * Equivalent packed boxes. Sources of data : Col. 1: Assumed number of boxes packed out by grades. Col. 2: Assumed returns by grades. Col. 3: Figures in col. 2 divided by corresponding figures in col. 1. Col. 4: Figures in col. 3 minus 2.50. however, although simplified, are believed to be well within the range of actual occurrences. The difficult problem relates to the determination of the grades of each lot of lemons at comparable times with respect to its normal storage period (see p. 19) . Once such grades have been determined, the computa- tion of pool payments by grades is a relatively simple matter. In the following example we shall consider only lemons placed in storage and assume that the total quantity in a given time pool amounts to the equivalent of 1,000 packed boxes. We shall further assume that a portion of the fruit was held in storage beyond its prime. Table 35, column 1, shows the number of boxes of each of the several grades obtained at the time the fruit was packed. The shrinkage of 100 boxes represents the difference between the volume placed in storage and the volume taken out of storage. The total net returns from the sale of each 84 University of California — Experiment Station grade of merchantable fruit are shown in column 2 and the weighted- average prices per box in column 3. In table 36, column 1 shows the number of boxes of each grade which we assumed would have been obtained from the 1,000 boxes if each lot had been graded at the end of its normal storage period. The problem is to divide the total net returns received for the lemons sold between the grades determined on the basis of the assumed grade-out. The total net TABLE 36 Illustration of Pool Payments for Lemons, Based upon Grades Determined at End of Normal Storage Periods r Jrade Grade-out Price rate per box Total payments 1 2 S Extra Choice boxes* 450 250 150 dollars 2.32647 1.57647 0.82647 dollars 1,046 91 Choice 394.12 Standard 123 97 Subtotal Culls Shrinkage 850 70 80 1,565 00 Total 1,000 * Equivalent packed boxes. Sources of data: Col. 1: Assumed number of boxes by grades determined at end of normal storage periods. Col. 2: From equation 450X + 250(X - $0.75) + 150(X - $1.50) = $1,565.00 850X - $412.50 = $1,565.00 850X= $1,565.00 + $412.50 X - 0.75 - $1.57647 X - 1.50 = $0.82647 Col. 3: Figures in col. 1 multiplied by corresponding figures in col. 2. returns from the sale of merchantable fruit amounted to $1,565.00, as shown in table 35, column 2. This represents the total amount of money available for payments to growers in the pool, exclusive of returns from cull lemons sent to the products plant. If we assume that the weighted- average prices per packed box shown in table 35, column 3, correctly reflect the price differentials between the grades occasioned by differ- ences in quality, the price rates may be determined by means of the following equation i 38 aX+b(X + Y)+c(X + Z)=R 38 If desired, the equation may first be written as : E — bY — cZ X = Then : X = a + b + c $1,565.00— (250) (—$0.75)— (150) (—$1.50) 450 + 250 + 150 Bul. 619] Maintenance of Equity in Pooling of Lemons 85 Where X equals the price rate on Extra Choice, Y equals the price dif- ferential between Extra Choice and Choice ; Z equals the price differ- ential between Extra Choice and Standard ; a, b, and c equal the number of boxes of Extra Choice, Choice, and Standard, respectively; and B equals the total net returns. By substituting the appropriate values in the above equation and solving, the value of X is $2.32647. This is the required price rate for TABLE 37 Alternative Method of Determining Pool Payments for Lemons Based upon Grades at End of Normal Storage Periods Grade Grade- out Price per box Col. 1 X Col. 2 Total payments Price rate per box Price rate differentials from Extra Choice / i S 4 5 6 Extra Choice boxes* 450 250 150 dollars 2.50 1.75 1.00 dollars 1,125.00 437.50 150.00 dollars 1,028.10 399.82 137.08 dollars 2.28467 1.59927 0.91387 dollars Choice Standard -0.68540 -1.37080 Subtotal 850 70 80 1,712 50 1,565.00 Culls Shrinkage Total 1,000 * Equivalent packed boxes. Sources of data: Col. 1: From table 36, col. 1. Col. 2: From table 35, col. 3. Col. 3: Figures in col. 1 multiplied by corresponding figures in col. 2. Col. 4: Figures in col. 3 multiplied by 0.913869 which was obtained by dividing 1,565.00 by 1,712.50. Col. 5: Figures in col. 4 divided by corresponding figures in col. 1; or by multiplying figures in col. 2 by 0.913869. Col. 6: Based upon price rates shown in col. 5. Extra Choice. The price rate for Choice is $2.32647 minus $0.75 or $1.57647 ; and the price rate for Standard is $2.32647 minus $1.50 or $0.82647. These price rates are shown in table 36, column 2. A simple way of solving the equation is illustrated in table 41 (p. 91) . The total payments to be made to each grade pool are shown in table 36, column 3. It will be noted that the sum of those total payments equals the total net returns shown in table 35, column 2, and that the differ- entials between the price rates are the same as the differentials between the actual prices. When the return from the 100 boxes of culls is received, 70 per cent of it should be credited to the cull pool and 30 per cent should be distributed among the several grades on the basis of the number of boxes in each as shown by the grade-out (table 36, col. 1) . Table 37 shows an alternative method of determining pool-payment 86 University of California — Experiment Station price rates by grades. The number of boxes of each grade as determined at the end of the normal storage periods (col. 1) is multiplied by the actual price received for that grade (col. 2). The sum of the products (col. 3) is then divided into the total net returns actually received. The quotient thus obtained is multiplied by each of the products, and the resulting figures (col. 4) represent the total payments by grades. Divid- ing these total payments by grades by the corresponding number of boxes TABLE 38 Illustration of Differences in Lemon Eeturns to 2 Growers, Arising Out of Differences in Length of Time Their Fruit Was Held in Storage Based upon pack-out Based upon grade-out Grade Price per box Grower A Grower B Price rate per box Each grower Volume Returns Volume Returns Volume Returns 1 2 S 4 5 6 7 8 Extra Choice Choice Standard dollars 2.50 1.75 1.00 boxes* 48 27 16 dollars 120.00 47.25 16.00 boxes* 34 21 20 dollars 85.00 36.75 20.00 dollars 2.32647 1.57647 0.82647 boxes* 45 25 15 dollars 104.69 39 41 12.40 Subtotal Culls Shrinkage 91 5 4 183.25 75 10 15 141 75 85 7 8 156 50 Total 100 100 100 * Equivalent packed boxes. Sources of data: Col. 1: From table 35, col. 3. Cols. 2 and 4: Assumed. Cols. 3 and 5: Figures in col. 1 multiplied by corresponding figures in cols. 2 and 4 respectively. Col. 6: From table 36, col. 2. Col. 7: Assumed number of boxes by grades determined at end of normal storage periods. The figures are assumed to be the same for each of the 2 growers. Col. 8: Figures in col. 6 multiplied by corresponding figures in col. 7. in each grade (col. 1) gives the price rates per box (col. 5). The price rates per box may be obtained directly by multiplying each of the actual prices (col. 2) by the quotient mentioned above. This method, although perhaps easier to understand than that involv- ing the use of the algebraic equation, has the serious disadvantage of failing to preserve the correct price differentials between grades except when the sum of the products (col. 3) is identical with the total net returns. A comparison of the price rates in table 37, column 5, with those in table 36, column 2, shows the differences in the results obtained by the two methods in this particular instance. In most cases, when this alternative method is used, the sum of the products will most likely exceed the total net returns. When such is the case the resulting price differentials will be smaller than the correct Bul. 619] Maintenance of Equity in Pooling of Lemons 87 price differentials. On the other hand, if the sum of the products is less than the total net returns, the resulting price differentials will be larger than the correct price differentials. As mentioned above, it is only when the sum of the products is identical with the total net returns that the resulting price differentials will be correct. Since there is no certainty that such a situation will occur, this alternative method is not recom- mended. The differences in returns which two growers might receive solely because of the differences in the length of time their respective fruit was kept in storage is shown in table 38. In this table it is assumed that each grower's grade credits are determined at the time the fruit is packed ; and that if each grower's fruit had been graded at the end of the normal storage period, the grade-outs would have been identical and would have been those shown in column 7. It is further assumed that grower A's fruit was packed out within a relatively short time after being placed in storage and that grower B's fruit was held beyond the normal storage period. The number of boxes of each grade assumed to have been obtained at the time each grower's fruit was packed is shown in columns 2 and 4. If the pool payments were based upon the weighted-average prices (col. 1) and the actual pack-outs (cols. 2 and 4), grower A would have received nearly 30 per cent more money than grower B from the mer- chantable fruit pool. Only a small part of this difference would have been offset by the larger return which grower B would have received from cull fruit. If the pool payments had been based upon the grades determined at the end of the normal storage periods, both growers would, of course, have received the same total returns (table 38, col. 8). 88 University of California — Experiment Station APPENDIX B COMPUTATION OF RATES OF PAYMENTS TO GROWERS BASED UPON SIMPLE AVERAGES OF MARKET PRICE DIFFERENTIALS BETWEEN GRADES AND BETWEEN SIZES When the record of daily sales in the various markets is segregated by grades and sizes, it is a relatively easy matter to compute the price dif- ferentials between each of the grades and sizes which prevailed on the same markets on the same days. The daily price differentials may then be averaged for the particular pooling period employed. The average price differentials thus obtained may be used in calculating the rates of payment by grades and sizes for the purpose of determining the money credits to growers. While an association may calculate price differentials from its own records, those based upon the sales of representative brands in one or more of the large markets would probably be better. Many of the indi- vidual associations do not have sufficient volume to have a complete line of grades and sizes in the same markets each day. Consequently their own records alone are likely to contain many gaps. On the other hand, if the records of sales from a number of associations are used, a much more complete tabulation can be secured. Price differentials between grades and sizes based upon sales at auction in New York City will probably be adequate in most cases. New York is the largest of the lemon markets. Sales at auction are by brands and sizes. Ordinarily representative brands, each containing a fairly wide run of sizes, are sold each business day. Consequently a fairly complete tabula- tion of daily price differentials by grades and sizes can generally be secured from this market. Considerable expense would be saved if price differentials between grades and sizes were computed by the central sales organization instead of by each association. A simple procedure would be for the central sales organization to issue each week a simple average of the price differentials between grades for a given size for cured and tree-ripe lemons separately and a simple average of the price differentials between the sizes of each of the grades. Each of the local associations could then average these weekly price differentials for whatever length of pooling period it employed. In years when merchantable lemons are sent to the products plant, some adjustments in the price differentials calculated from current sales records may be required. Since the merchantable fruit sent to the prod- ucts plant generally consists chiefly of grades and sizes which are the Bul. 619] Maintenance of Equity in Pooling of Lemons 89 lowest in price, the volume of these which is shipped is reduced relative to the volume of the other grades and sizes, and as a result their prices tend to rise relative to the prices of the other grades and sizes. Conse- quently, the price differentials actually prevailing on the markets during such periods of time may be considerably different from those which would have prevailed if equal proportions of the various grades and sizes had been sent to the products plant. When price differentials are TABLE 39 Price Differentials for Cured Lemons between Sizes by Grades and Prices by Grades and Sizes ; New York Auction Market; 1933-34 Row Extra Choice Choice Standard Size Differential from 360's Price Differential from 360's Price Differential from 360's Price 1 2 3 4 5 6 number per box 270 1 dollars per box +0.01 dollars per box 5.26 dollars per box -0 01 dollars per box 4.44 dollars per box -0.29 dollars per box 3.50 300 2 +0.07 5 32 +0.14 4.59 +0.03 3.82 360 3 00 5.25 00 4.45 0.00 3.79 432 4 -0 43 4.82 -0.29 4.16 -0.15 3.64 490 5 -0.64 4.61 -0 36 4.09 -0.05 3.74 588 6 -0.97 4.28 -0.74 3.71 -0.28 3.51 Sources of data: Cols. 1,3, and 5: From table 16. Cols. 2, 4, and 6: The price of $5.25 in row 3, col. 2 is the simple average of daily prices of Extra Choice size 360's, on the New York auction market in 1933-34. The prices of $4.45 in row 3, col. 4, and $3.79 in row 3, col. 6, were obtained by adding to the price of Extra Choice 360's, the average price differentials between Extra Choice and Choice of —$0.80 and between Extra Choice and Standard of —$1.46. The prices of each of the other sizes were obtained by adding to the prices of 360's the price differentials shown in cols. 1, 3, and 5. used in calculating adjustments between time pools, color classifications, grades, and sizes, they should reflect what might be termed "normal" differences in prices rather than the abnormal differences occasioned by the withholding of much larger proportions of some grades and sizes than of others from the market. Otherwise, the particular grades and sizes which are withheld from the market will be paid relatively more and those which are not withheld will be paid relatively less than their respective market values. "Normal" price differentials as used here are those which presumably would have existed if a proportionate withholding of various grades and sizes had been made. A close approximation to normal price differentials for a given period of time could be arrived at by analyzing price differ- entials in previous years and also the current market situation. The determination of normal price differentials between grades and between sizes can best be done by the central sales organization rather than by the individual local associations. 90 University of California — Experiment Station Once the price differentials between grades and between sizes in each grade have been calculated for the pooling period they can be used in arriving at representative prices by grades and sizes. For purposes of illustration we shall use the average price differentials between grades and sizes of cured lemons on the New York auction market during 1933-34. In that year on size 360's, Extra Choice brought $0.80 a packed TABLE 40 Computation of Price Differentials between Grades for Cured Lemons Extra Choice Choice Standard Size Price New York Volume Value Price New York Volume Value Price New York Volume Value ; 2 boxes* 84 826 708 224 63 16 1,921 3 4 5 6 7 8 9 number per box 270 dollars per box 5.26 5.32 5.25 4.82 4.61 4.28 5 20 00 dollars 442 4,394 3.717 1,080 290 68 dollars per box 4 44 4 59 4.45 4.16 4.09 3.71 4.38 -0.82 boxes* 10 117 156 80 35 14 412 dollars 44 537 694 333 143 52 dollars per box 3 50 3 82 3.79 3.64 3 74 3 51 3.75 -1.45 boxes* 2 18 23 11 4 2 60 dollars 7 300 69 360 87 432 40 490 15 588 7 Total or average Price differential from Extra Choice 9,991 1,803 225 * Equivalent packed boxes. Sources of data: Cols. 1, 4, and 7: From table 39. Cols. 2, 5, and 8: Based upon shipments of the Santa Paula Citrus Fruit Association in 1933-34, and dropping two ciphers. Col. 3: Figures in col. 2 multiplied by corresponding figures in col. 1. Col. 6: Figures in col. 5 multiplied by corresponding figures in col. 4. Col. 9: Figures in col. 8 multiplied by corresponding figures in col. 7. box more than Choice and $1.46 a packed box more than Standard. The simple average of the daily prices of representative brands of Extra Choice, size 360's, on the New York auction market in 1933-34 amounted to $5.25 a packed box. This figure can be taken as the base price from which to compute the prices of each of the other grades and sizes. 39 Using the figure of $5.25 as the base price for Extra Choice, size 360's, the price on Choice, size 360's, is $4.45 ($5.25 — $0.80) , and the price on Standard, size 360's, is $3.79 ($5.25 — $1.46). These computed prices of the three grades, size 360's, are shown in table 39, row 3, columns 2, 4, and 6. The average price differentials between the several sizes of Extra Choice, Choice, and Standard on the New York auction market during 39 Since we are dealing with the absolute rather than the relative price differentials between grades and between sizes, it makes no difference whether the base price used is correct or not. Instead of $5.25 an arbitrary figure such as $4.00 or $6.00 could just as well be used for the base price. The important thing is to have the price differentials correct. Bul. 619] Maintenance of Equity in Pooling of Lemons 91 1933-34 are shown in table 39, columns 1, 3, and 5, respectively. By adding the price differentials between 360's and each of the other sizes to the base prices established for 360's we obtain a series of prices for each grade and size. 40 These are shown in table 39, columns 2, 4, and 6. If the relative distribution of the total number of boxes in each grade among the several sizes were the same, the price differentials between the grades computed on the basis of 360's could safely be used in deter- TABLE 41 Computation of Grade Price Kates and Payments for Cured Lemons in a Given Time Pool Grade Price differential from Extra Choice Volume Col. 1 X col. 2 Price rate Total payment 1 2 3 4 5 Extra Choice dollars per box 0.00 -0.82 — 1 45 boxes* 1,921 412 60 dollars 0.00 -337.84 - 87.00 dollars per box 3.311676 2.491676 1.861676 dollars 6,361.73 Choice 1,026.57 Standard 111.70 Total 2,393 -424.84 7,500.00 * Equivalent packed boxes. Sources of data: Cols. 1 and 2: From table 40. Col. 3: Figures in col. 2 multiplied by corresponding figures in col. 1. Col. 4: Price rate of Extra Choice calculated from the following equation: 2,393* - $424.84 = $7,500.00 Transposing: 2.393X = $7,500.00 + $424.84 Solving: _ $7,924.84 _ M , 11fi7R "TW ~ $3 - 311676 Price rates of Choice and Standard obtained by adding the price differentials of those grades (col. 1) to the price rate of Extra Choice. Col. 5: Figures in col. 2 multiplied by corresponding figures in col. 4. mining the rates of payment by grades. In most cases, however, the rela- tive distribution of sizes is different in one grade from that in another. In such cases the differences in the relative distribution of the sizes must be taken into account in order to obtain the correct price differentials between grades. A method of doing this is illustrated in table 40. The prices by sizes and grades obtained from table 39 are shown in table 40, columns 1, 4, and 7. The number of boxes of each size in each grade is shown in table 40, columns 2, 5, and 8. The total value of each size, obtained by multiplying the number of boxes of each size by the price of that size, is shown in columns 3, 6, and 9. The total value for all sizes of each grade divided by the total number of boxes for all sizes in that grade gives the average price per packed box of each grade. From the average prices thus obtained the correct price differentials between grades may be computed. In the example in table 40, the price 40 In adding the price differentials to the base prices, signs must be maintained. Thus, a minus price differential is subtracted from the base price. 92 University of California — Experiment Station differential between Extra Choice and Choice is $0.82, and between Extra Choice and Standard, $1.45. In this particular case, the price dif- ferentials thus computed are not greatly different from the price differ- entials of 360's. In other situations, however, considerable differences might easily occur. The problem now is to divide the total net returns received from all merchantable fruit in the time pool between the several grades on the TABLE 42 Computation of Size Price Bates and Payments for Cured Lemons in a Given Grade Pool Size Price differential from 360's Volume Col. 2 X col. 3 Price rate Total payment 1 * S 4 5 number per box 270 dollars per box +0 01 +0.07 00 -0.43 -0 64 -0.97 boxes* 84 826 708 224 63 16 dollars + 0.84 +57.82 00 -96.32 -40 32 -15.52 dollars per box 3 37035 3 43035 3.36035 2 93035 2 72035 2.39035 dollars 283.11 300 2,833.47 360 2,379.13 432 656.40 490 171.38 588 38.24 Total 1,921 -93.50 6,361.73 * Equivalent packed boxes. Sources of data : Col. 1: From table 39, col. 1. Col. 2: From table 40, col. 2. Col. 3: Figures in col. 2 multiplied by corresponding figures in col. 1. Col. 4: Price rate of 360's calculated from the following equation: 1.92LY - $93.50 = $6,361.73 Transposing: 1.921X = $6,361.73 + $93.50 Solving: X - -^j~~= $3.36035 Price rates of each of the other sizes obtained by adding the price differentials of those sizes (col. 1) to the price rate of 360's. Col. 5: Figures in col. 2 multiplied by corresponding figures in col. 4. basis of the number of boxes of each and the computed price differentials. This may be done by using the equation given in Appendix A (p. 84). If the total net returns amount to $7,500.00, this figure, together with the totals in columns 2 and 3 of table 41, gives the necessary data for solving the equation. The price rates thus obtained are shown in table 41, column 4; the total payments to each grade pool, column 5, are obtained by multiplying the number of boxes of each grade (table 41, column 2) by its corre- sponding price rate. After the total net payments to each grade pool are obtained by the method mentioned above, the price rates by sizes for each grade may be calculated by using the same type of equation as before. In the case of the Extra Choice grade pool, for example, table 41 shows that the 1,921 Bul. 619] Maintenance of Equity in Pooling of Lemons 93 boxes of Extra Choice are entitled to receive a total of $6,361.73. Table 42 shows how this amount is distributed between the various sizes on the basis of the number of boxes of each size and the average price differen- tials between 360's and each of the other sizes. The price rates by sizes thus determined may be used in setting up the money credits to growers. 94 University of California — Experiment Station APPENDIX C METHODS OF CALCULATING ADJUSTMENTS BETWEEN TIME POOLS WHEN MERCHANTABLE LEMONS ARE SENT TO THE PRODUCTS PLANT When the situation requires that adjustment be made between time pools (based upon picks) , the computations of such adjustments may be based upon either cumulative volumes in storage or hypothetical shipping allotments. The use of cumulative volumes in storage during the overlapping stor- age period as the basis for determining the extent of under- or overship- ments in each of the time pools has several disadvantages. The total cum- ulative volume from each time pool in storage during the overlapping storage period is determined to a considerable extent by the particular decisions made by the manager with respect to shipments. The same problem arises in connection with the use of this basis for calculating adjustments between color classifications and is discussed in more detail in Appendix D. Furthermore, when used in connection with time pools this method implies that a given volume of fruit in storage is worth the same from the standpoint of shipments during each part of the overlapping storage period. However, when the first time pool contains chiefly fruit which must be shipped during the winter months and the second time pool chiefly fruit which can be shipped during the summer months, a given volume in storage will generally permit the shipment of a larger propor- tion of it at the end of the overlapping storage period than at the begin- ning. Also during such overlapping storage period the quantity of fruit from the first pool which is in storage is decreasing, whereas the quantity of fruit from the second pool which is in storage is increasing. The gen- eral situation, therefore, is that during the first part of the overlapping storage period, when the percentage shipping allotment tends to be small, a large proportion of the total volume in storage will consist of fruit from the first pool ; while during the last part, when the percentage shipping allotment tends to be large, most of the total volume in storage will consist of fruit from the second pool. The foregoing difficulties are largely overcome when adjustments be- tween time pools are based upon hypothetical shipping allotments. The method of determining the extent of the adjustments required between two time pools in terms of physical units is illustrated in tables 43 to 46 inclusive. The overlapping storage period may be considered as beginning with Bul. 619] Maintenance of Equity in Pooling of Lemons 95 the date that the fruit from pool No. 2 was first counted in storage, and it may be considered as ending when fruit from pool No. 1 was last counted in storage, advance storage counts being included. Table 43 shows for each of two time pools the deliveries, shipments, and by-products of merchantable fruit by two-week intervals during the overlapping storage period, and the volume of fruit from each time pool TABLE 43 Lemon Deliveries, Storage, Shipments, and By-Products During Overlapping Pooling Periods; Association F; 1934-35 Pool No. 1 Pool No. 2 Period ending Deliveries Storage at beginning of period Ship- ments By- products Deliveries Storage at beginning of period Ship- ments By- products / 2 3 4 5 6 7 8 Feb. 11 25 Mar. 11 25 April 8 22 May 6 20 June 3 17 July 1 boxes* • ■t 226 boxes* 45,720 35,527 28,591 24,805 16,840 12,441 10,106 6,379 6,031 3,692 boxes* 3,584 4,907 3,515 5,220 3,411 1,844 2,854 348 2,088 2,888 boxes* 6,609 2,029 497 2,745 988 491 873 251 804 boxes* 6,219 12,660 13,913 9,566 11,387 8,484 12,438 3,156 2,025 2,627 3,076 boxes* 6,219 18,879 24,628 34,194 43,288 46,980 51,584 48,866 40,354 36,359 boxes* 313 4,037 4,420 2,749 9,779 4,698 4,907 boxes* 8,164 1,980 755 3,414 3,125 758 1,924 1,169 15 Totals 190, 132 30,659 15,287 351,351 30.903 21,289 * Equivalent packed boxes. t Leaders indicate data are of no significance to the problem. Sources of data: Cols. 1, 3, 4, 5, 7, and 8: From records of Association compiled by two-week periods. Cols. 2 and 6: From records of Association at beginning of each two-week period, adjusted so that the storage at the beginning of a period plus the deliveries during that period minus the ship- ments and by-products during that period equals the storage at the beginning of the next period. in storage at the beginning of each two-week interval. The percentage shipping allotments for each two-w T eek interval during the overlapping storage period may be computed from the total storage at the beginning of each interval and the shipments during such interval (see table 44). From the data on deliveries, volumes in storage at the beginning of the overlapping storage period, quantities sent to the products plant, and percentage prorates, hypothetical shipping allotments may be computed. This is illustrated in table 45. In working out table 45 certain assumptions were made. In connection with the quantities sent to the products plant (cols. 4 and 8) the first assumption was that this fruit had been held as long as it was eligible to be counted in storage. When advance storage counts are received on fruit 96 University of California — Experiment Station sent to the products plant while it is still fit for fresh shipment, such fruit should be shown as being in storage until after the last advance storage-count date and as going to the products plant immediately after that date. The second assumption was that no fruit in pool No. 1 would have been fit for fresh shipment after July 1 and that consequently all fruit in pool No. 1 on hand after July 1 would have to go to the products TABLE 44 Computation of Prorate Percentages for Lemons During Overlapping Pooling Periods ; Association F ; 1934-35 Period ending Feb. 25 Mar. 11 25 Apr. 8 22 May 6 20 June 3 17 July 1 15 Storage at beginning of period Shipments during period Pool Pool Pool Pool No. 1 No. 2 Total No. 1 No. 2 Total 1 2 S 4 5 6 boxes* boxes* boxes* boxes* boxes* boxes* 45,720 6,219 51,939 3,584 3,584 35,527 18,879 54,406 4,907 4,907 28,591 24,628 53,219 3,515 3,515 24,805 34,194 58.999 5,220 313 5,533 16,840 43,288 60,128 3,411 4,037 7,448 12,441 46,980 59,421 1,844 4,420 6,264 10,106 51,584 61,690 2,854 2,749 5,603 6,379 48,866 55,245 348 9,779 10,127 6,031 40,354 46,385 2,088 4,698 6,786 3,692 36,359 40,051 2,888 4,907 7,795 t Prorate per cent 6.90 9 02 6.60 9 38 12 39 10 54 9 08 18 33 14.63 19.46 * Equivalent packed boxes. t Leaders indicate data are of no significance to the problem. Sources of data: Col. 1: From table 43, col. 2. Col. 2: From table 43, col. 6. Col. 3: Figures in col. 1 plus corresponding figures in col. 2. Col. 4: From table 43, col. 3. Col. 5: From table 43, col. 7. Col. 6: Figures in col. 4 plus corresponding figures in col. 5. Col. 7: Figures in col. 6 divided by corresponding figures in col. 3 and the quotients multiplied by 100. plant. Thus, in table 45 (col. 4), 6,997 boxes of fruit in pool No. 1 are shown as going to the products plant immediately after July 1. In using this method of calculating adjustments between time pools, the length of time fruit from pool No. 1 is entitled to be counted in storage will need to be determined, and some date will need to be selected after which any fruit in pool No. 1 not previously sent to the products plant or entitled to be shipped under its hypothetical shipping allotment will be deemed unfit for fresh shipment. Table 45 shows that, based on the hypothetical shipping allotment, 23,662 boxes from pool No. 1 and 37,897 boxes from pool No. 2 were en- titled to be shipped during the overlapping storage period. As shown in table 43, actual shipments during this period from pool No. 1 amounted Bul. 619] Maintenance of Equity in Pooling of Lemons 97 to 30,659 boxes and from pool No. 2 to 30,903 boxes. Thus pool No. 2 was undershipped to the extent of 6,994 boxes (37,897 — 30,903) and pool No. 1 overshipped by about the same amount — 6,997 boxes (30,659 — 23,662). " The next thing to be determined, therefore, is the quantities of fruit from pool No. 2 sent to the products plant which could have been shipped TABLE 45 Computation of Lemon Shipping Allotments by Time Pools During Overlapping Pooling Periods ; Association F ; 1934-35 Pro- rate Pool No. 1 Pool No. 2 Period ending Storage at be- ginning of period Ship- ping allot- ment By- prod- ucts Deliv- eries Storage at be- ginning of period Ship- ping allot- ment By- prod- ucts Deliv- eries 1 2 3 4 5 6 7 8 9 Feb. 25 percent 6.90 9.02 6.60 9.38 12.39 10.54 9.0? 18.33 14.63 19.46 boxes* 45,720 35,956 30,684 28,388 22,980 19,145 16,636 14,252 11,640 9,686 boxes* 3,155 3,243 2,025 2,663 2,847 2,018 1,511 2,612 1,703 1,885 boxes* 6,609 2,029 497 2,745 988 491 873 251 804 6,997 boxes* 226 boxes* 6,219 18,450 22,535 30,614 37,149 40,275 45,054 40,994 34,747 30,367 26,365 boxes* 429 1,664 1,487 2,872 4,603 4,245 4,091 7,514 5,083 5,909 boxes* 8,164 1,980 755 3,414 3,125 758 1,924 1,169 boxes* 12,660 Mar. 11 13,913 25 9,566 Apri] 8 11,387 22 8,484 May 6 12,438 20 3,156 June 3 2,025 17 2,627 July 1 3,076 15 Total 23,662 37,897 * Equivalent packed boxes. t Leaders indicate data are of no significance for the problem. Sources of data: Col. 1: From table 44, col. 7. Cols. 2 and 6: Figures in first line from table 43, cols. 2 and 6. Each succeeding figure is obtained by taking the storage at the beginning of a period plus the deliveries during that period minus the shipping allotment and by-products during that period. Cols. 3 and 7: Figures in col. 1 multiplied by corresponding figures in cols. 2 and 6, respectively. Cols. 4 and 8: From table 43, cols. 4 and 8, with the exception of the last figure in col. 4. This figure represents the amount of fruit still in storage after July 1 which, under the assumption that it is no longer fit for fresh shipment, must go to the products plant. Cols. 5 and 9: From table 43, cols. 1 and 5. under its hypothetical shipping allotments. A method of determining such quantities is illustrated in table 46. The total quantity is the sum of the figures in column 7, if the last figure in column 9 is positive, or the sum of the figures in column 7 minus the last figure in column 9, if such figure is negative as in this illustration. Therefore, the total quantity of fruit in pool No. 2 sent to the products plant that could have been shipped under its hypothetical shipping allotments amounts to 6,994 boxes 41 The undershipments and overshipments in the two pools would be identical if the computations were carried out to a sufficient number of decimal places. 98 University of California — Experiment Station (7,872 — 878) . In this instance, the total quantity thus calculated is the same as the undershipments in pool No. 2. If the total quantity thus calculated, however, had been larger than the undershipments in pool No. 2, then the amount of the undershipments would be taken as the TABLE 46 Computation of Amount of Lemons in Pool No. 2 Sent to the Products Plant Which Could Have Been Shipped Under Its Prorate During the Overlapping Pooling Periods ; Association F ; 1934—35 Period ending Prorate carried over from previous period Period prorate Total prorate Ship- ments Total prorate minus ship- ments By- products By- product which could have been shipped By- product which could not have been shipped Prorate carried over into next period 1 2 S 4 5 6 7 8 9 Feb. 25 boxes* 429 1,487 2,066 1,877 -2,265 -1,880 boxes* 429 1,664 1,487 2,872 4,603 4,245 4.091 7,514 5,083 5,909 boxes* 429 2,093 1,487 4,359 6,669 6,122 4.091 7,514 2,818 4,029 boxes* 313 4,037 4,420 2,749 9,779 4,698 4,907 boxes* 429 2,093 1,487 4,046 2,632 1,702 1,342 -2,265 -1,880 - 878 boxes* 8,164 1,980 755 3,414 3,125 758 1,924 1,169 boxes* 2,093 1,980 755 1,702 1,342 7,872 boxes* 6,071 1,712 1,783 758 1,924 1,169 boxes* 429 Mar. 11 25 1,487 April 8 2,066 22 May 6 1,877 20 June 3 -2,265 17 July 1 -1,880 - 878 Total t * Equivalent packed boxes. t Leaders indicate data are of no significance to the problem. Sources of data: Col. 1: The first figure opposite Feb. 25 is taken as zero since there was no fruit from pool No. 2 in storage at the beginning of the previous two-week period, and consequently during that period pool No. 2 was not entitled to a shipping allotment. The other figures are from the preceding period in col. 9. Col. 2: From table 45, col. 7. Col. 3 : Figures in col. 1 plus corresponding figures in col. 2. Col. 4: From table 43, col. 7. Col. 5: Figures in col. 3 minus corresponding figures in col. 4. Col. 6: From table 43, col. 8. Col. 7: When either the figures in col. 6 are zeros or the figures in col. 5 are a minus quantity, the corresponding figures in col. 7 are zeros. The other figures in col. 7 are the same as the smallest of the two corresponding figures in cols. 5 and 6. Col. 8: Figures in col. 6 minus corresponding figures in col. 7. Col. 9: Figures in col. 5 minus corresponding figures in col. 7. basis for adjustments. On the other hand, if the total quantity of by- products which could have been shipped had been smaller than the undershipments, it, instead of the volume of undershipments, would constitute the basis for adjustments. The general rule to be followed is to use whichever of the two amounts is the smaller. 42 42 This general rule, however, may need to be modified under certain conditions. For example, it is possible during the overlapping storage period for actual shipments from pool No. 2 to be considerably less than its prorate contribution and for only small quantities of lemons to be sent to the products plant, but shortly thereafter for large quantities to be sent to the products plant. In such a case the correct adjustment amount would be between the volume of by-products that could have been shipped and the amount of undershipments. Bul. 619] Maintenance of Equity in Pooling of Lemons 99 Table 46 also provides the information needed for determining the particular intervals of time during which the undershipment of pool No. 2 could have been shipped under its prorates. Column 7 shows that pool No. 2 was entitled to ship the 6,994 additional boxes as follows : Time interval Boxes Feb. 12-Mar. 11 2,093 Mar. 12-Apr. 8 1,980 Apr. 9-Apr. 22 755 Apr. 23-May 6 1,702 May 7-May 20 464 The money adjustment to which pool No. 2 is entitled is the net returns which could have been obtained if the 6,994 boxes from pool No. 2 had been shipped during the periods indicated above and the same volume of fruit from pool No. 1 had been withheld from the market. In deter- mining the net returns which would have been received from the 6,994 boxes, if they had been shipped, it is necessary to know the grades and sizes of the fruit sent to the products plant and the prevailing market prices on similar grades and sizes. If the grades and sizes of each lot of fruit sent to the products plant are known, the grades and sizes of the undershipments can be estimated with a reasonable degree of accuracy. For example, the 2,093 boxes (table 46, col. 7) can be assumed to have the same relative grade and size distribution as the entire 8,164 boxes (table 46, col. 6). 43 The most dif- ficult problem has to do with determining the grades and sizes of fruit sent to the products plant when such fruit was in its prime (see p. 19) . The net prices of the grades and sizes estimated to be contained in the undershipments can be calculated from the prices received for similar grades and sizes actually shipped, or upon estimated normal price dif- ferentials between the several grades and sizes (pp. 23, 38) . The method of calculating adjustments between two time pools during the season, discussed above, is equally applicable in calculating adjust- ments between the last time pool in one season and the first time pool in the following season. Also the same principle can be used in calculating adjustments when three or more time pools are employed. The calcula- tions required, however, may be exceedingly laborious. 43 It may, of course, be assumed that, if the 2,093 boxes had been shipped, only the higher grades and more desirable sizes of the entire 8,164 boxes would have been selected. 100 University of California — Experiment Station APPENDIX D METHOD OF CALCULATING ADJUSTMENTS BETWEEN COLOR CLASSIFICATIONS WHEN MERCHANTABLE FRUIT IS SENT TO THE PRODUCTS PLANT Calculations of the amount which each color classification contributed to the shipping allotment may be based upon either (1) normal storage periods, (2) cumulative volume in storage, or (3) hypothetical shipping allotments. The deliveries, shipments, and amounts sent to the products plant by one association during a given time pool in 1934r-35 are used for purposes of illustration (table 47) . Prorate Contributions Based upon Normal Storage Periods. — Under its particular conditions an association can probably determine with a TABLE 47 Lemon Deliveries, Shipments, and By-Products of Merchant- able Fruit by Color Classifications ; Pool No. 3 ; Association F; 1934-35 Color classification Deliveries* Shipments By-products 1 2 8 Dark green Light green Silver boxes t 1,065 5,394 22,794 6,960 fcoxesf 922 4,562 15,489 306 boxes\ 143 832 7,305 Yellow 6,654 Total 36,213 21,279 14,934 * Includes only fruit placed in storage exclusive of culls and shrinkage, t Equivalent packed boxes. reasonable degree of accuracy the average lengths of time which fruit in each color classification can be kept in storage and still be counted in the determination of the shipping allotment. Such determinations can be made at the end of the time pool and be based upon the actual expe- rience had with the particular fruit. The storage periods may be different at one part of the season than at another. Suppose, for example, that for a given time pool each color classifica- tion can normally be kept in storage for the periods shown in table 48, column 1. Converting these normal storage periods into relatives (col. 2) — using the longest storage period as the base — provides a series, which, when multiplied by the corresponding deliveries (col. 3) , serves to estab- lish the relative prorate contributions of each color classification as shown in column 5. The relative prorate contributions applied to the total shipments of all fruit give the prorate contributions of each color Bul. 619] Maintenance of Equity in Pooling of Lemons 101 classification in physical units (col. 6) .** In those cases where one or more of the prorate contributions are in excess of the deliveries a further adjustment is necessary. In the case of dark-green lemons, for example, column 6 shows the calculated prorate contribution amounted to 1,236 boxes, whereas the deliveries as shown in column 3 amounted to only 1,065 boxes. On the principle that the largest shipments to which any TABLE 48 Calculation of Contributions Made by Color Classifications to Lemon Shipping Allotments Based Upon Normal Storage Periods ; Pool No. 3 ; Association F ; 1934-35 Normal storage Deliveries Prorate contributions Color classification Period Index Unadjusted Index First adjustment Final adjustment V 1 2 8 4 5 6 7 Dark green Light green Silver months 5.0 3.5 2.5 1.5 per cent 100 70 50 30 boxes* 1,065 5,394 22,794 6,960 boxes* 1,065 3,776 11,397 2,088 percent 5.81 20.61 62.19 11.39 boxes* 1,236 4,386 13,233 2,424 boxes* 1,065 4,423 13,346 Yellow 2,445 Total 36,213 18,326 100.00 21,279 21,279 * Equivalent packed boxes. Sources of data: Col. 1: Assumed. Col. 2: Based upon 5.0 in col. 1 equals 100. Col. 3: From table 47, col. 1. Col. 4: Figures in col. 3 multiplied by corresponding figures in col. 2, and products multiplied by 100. Col. 5: Figures in col. 4 divided by 18,326 and resultant multiplied by 100. Col. 6: Figures in col. 5 multiplied by 21,279. Col. 7: Since the first adjustment on dark green exceeds the total volume of dark green delivered, the volume delivered was taken. The excess, amounting to 171 boxes, was apportioned among the other color classifications on the basis of their respective first adjustments; each of the first approxi- mations being multiplied by 1.0085, which was obtained by dividing 20,214 (21,279-1,065) by 20,043 (21,279-1,236). classification of lemons is entitled are its total deliveries of merchantable fruit less normal shrinkage, the prorate contribution of dark-green lemons was reduced from 1,236 boxes to 1,065 boxes as shown in column 7. The prorate contributions of the other color classifications were rat- ably increased. Column 7, therefore, shows the number of boxes which each color classification was entitled to have shipped according to its normal storage period. Calculated Adjustments between Color Classifications. — 1 Table 49 shows the detailed adjustments between color classifications based upon their respective prorate contributions. The figures in column 1 show for each color classification the volume of deliveries and shipments and the 44 The shipping allotment which the association received is assumed to be the same as its actual shipments of 21,279 boxes. 102 University of California — Experiment Station < Eh 02 Q O »-H OS W Ph w § E-i O o p 02 PP 02 !? o 3 3 i 02 ••» O i— i Eh ««J O l-H 02 o W2 M < 02 d^ §« *l CO CO o «4 55 w w £ &H fa pq 02 H 525 w Eh 02 P t-s O <1 O 125 i— ( I H Eh W w W CO W o 55 »-i » -^< »h co 1-I « a> -e io o «0 <33 CM t— CO CO X! cu.2" 1-H e oo r- os oo ^ Eg oo co o co r»» Cj «o CO >C CO i-> 3 V. ^5 o e oo ^^ os J5 CU >-1 E3 *h c (h ■« Q 83 B 3d 3 CO M CU o .OJ2 Ph CU OS dollars 0.85 0.85 • a # CO OS CO OS CO ^* CO ^* CO +3 3 00 — 1 — a CU ► iQ B +j GO CO US »o o 3 to a *^ ollars 121.5 818.1 939.7 "d 0) -« ^ ^ a> o .OX) to 00 ,2 oo oo Ph cu a *o O O 0) a * CO OS CO OJ oo ^< co ^* co ? »o Hj — — i—l .— 1 o O -O 1 o> 3 ■JS.O # »c co to m cs a^ a 60 CO C3 ^< ■»»< t>- §£.S ~* go •"»< CO ■* C> cg _ O O O O o « 3 55 1 eo g •>*< •**< CO (M CO C r- ic — d ^*« ~ CO >o CO c« t^ O "0 t~ CO ti «-i CU -« t-l r-l t» CD CO IM CO '3 3 01 o fc o o o o o ,» ^- t^ t-- t^ t^ +3 ©* « O CO "Cft CO 05 •>*< 00 CO CM -^ OS CO CO OIQOO CO O "0 i— I f^ CO 3 ■*— ( J> OOH CO «0 OO t^-fcO OSCOCO CNI (M OS o O i—l IO -^< IMUJN CO CO CO i— l •*»< > "© C^ i— l CO CM i— 1 o rHCNPS'flHOCONOOOlOrtNcOflOtONOOaO Pi BE a CC K a • -f^ • +? • s-= • +s r^ « «^ W ™^ °3 ri "3 «, CO C a a E a e 1 +- C a. E c 1 > PC g a. a '1 a 1 "a c +s C a £ c 1 > PC i a T > c ->- C £ E 1 1 ■a 2 > P ->- c a £ c X a: 1 1 c E- CG "C -i- c a. £ c X i > PC i > co cu t, 3 M tfl M 13 a o a co 0) u M O « S CO 3 ti 3 T3 C a 3 tsfi 3 CD a . . _■ "- 1 a o -a °o^ o o « .3 ™ 3 ^ ° "*-> 3 CO""' M.„ * M ® m « 3 a 3 £ fc M 3 be 3 c qa Men Jo c e ° «•! o3. g^ 3 a • 3 o'Sc^ u >s fl Mo'" CO^H a>-S"3 M - 3 S^ a O J2 -o X! cu 03 ^ +s o C3 a a o .fe -ri * la-s _ a cm o : S— ;oo I co O-* Os eg "3 cu _ « 2 •CM "3 *■ _ a 03 T3^ ; oO CO 0) U cu'3.3\e^ *%£ « i ^ | 3 a^ CU co 83 I 3 3 Q - " co co co ** co 0) cu cu . . o I- s- t-. oo tj 3 3 3 -3 S-SP.SP.2P It? .-Oi-HCM Ni-lHrt O O O o o o o o OOOOU 3 o CC Bul. 619] Maintenance of Equity in Pooling of Lemons 103 amounts sent to the products plant.* 5 The figures in column 2 show the average net price per box received for fruit shipped, and those in column 3 show the total net returns received for such shipments. The prorate contributions of each color classification, as determined in table 48, are entered in the appropriate rows in column 4 of table 49. These prorate contributions provide the basis for making adjustments in the amounts of fruit of each color classification shipped and sent to the products plant. These adjustments are shown in columns 5 and 8. In the case of dark-green lemons, for example, the prorate contribu- tion was 1,065 boxes.* 8 Shipments, however, amounted to only 922 boxes. This indicates an upward adjustment in shipments of 143 boxes. This figure is entered in column 5, row 3. If an additional 143 boxes of dark- green lemons had been shipped, however, it is obvious that they could not also have been sent to the products plant. Consequently, a downward adjustment of 143 boxes on dark-green lemons sent to the products plant is required. This downward adjustment is shown in column 8, row 4. A similar upward adjustment on shipments and a downward adjust- ment on fruit sent to the products plant are indicated in the case of yellow lemons, since the actual shipments of this color classification were less than its prorate contribution. In the cases of light-green and silver lemons, however, the indicated adjustments are in the opposite direction. Silver lemons, for example, were overshipped to the extent of 2,143 boxes ; that is, actual shipments of 15,489 boxes were 2,143 boxes larger than the calculated prorate con- tribution of 13,346 boxes. Consequently, this overshipment of 2,143 boxes is subtracted (col. 8, row 11) and the same amount is added to the by-products (col. 5, row 12). After the adjustments in physical units are thus determined, the next problem is to calculate the price rates to be applied to these physical units in order to obtain the required money adjustments. In the case of shipments it will be most convenient to carry out the necessary adjust- ments in terms of money, but in the case of by-products the necessary adjustments can easily be carried out in terms of fruit. For undership- ments the most appropriate basis for establishing price rates is the esti- mated market value of the particular grades and sizes sent to the products plant. "What the undershipments would have brought if they had been marketed minus the by-products return gives the net loss to the particular color classification from such undershipments. As shown in 45 Only fruit which was one time merchantable is included. The deliveries represent actual deliveries of merchantable fruit less normal shrinkage. 46 It so happens in this particular case that the prorate contribution was as large as the delivery. 104 University of California — Experiment Station column 5, row 3, the undershipment of dark-green lemons amounted to 143 boxes, and these were sent to the products plant. In order to deter- mine how much these 143 boxes would have brought if they had been shipped, the grades and sizes of this particular fruit must first be as- certained. 47 It is then necessary to ascertain the net prices being received for similar grades and sizes during the period this particular fruit was TABLE 50 Calculation of Contributions Made by Color Classifications to Lemon Shipping Allotments, Based Upon Cumulative Volume in Storage; Pool No. 3 ; Association F ; 1934-35 Deliveries Cumulative storage Prorate contributions Color classification Volume Index Unadjusted Adjusted 1 B S 4 5 Dark green Light green boxes* 1,065 5,394 22,794 6,960 boxes* 7,604 41,318 96,250 16,116 per cent 4.71 25.62 59.68 9.99 boxes* 1,002 5,452 12,699 2,126 boxes* 1,006 5,394 Silver 12,745 Yellow 2,134 Total 36,213 161,288 100.00 21,279 21,279 * Equivalent packed boxes. Sources of data : Col. 1: From table 47, col. 1. Col. 2: The sum of the amounts of each color classification in storage at each storage-count date during the pooling period. Advance storage counts are included. Col. 3: Figures in col. 2 divided by 161,288 and the quotients multiplied by 100. Col. 4: Total shipments of 21,279 boxes multiplied by the figures in col. 3 and the products di- vided by 100. Col. 5: Since the unadjusted prorate contribution of 5,452 boxes (col. 4) for light green exceeds the deliveries of 5,394 (col. 1), the volume delivered was taken. The excess of 58 boxes was then ap- portioned among the other classifications on the basis of their respective unadjusted prorate contri- butions. Each of the unadjusted figures was multiplied by 1.00374, which was obtained by dividing 15,885 (21,279-5,394) by 15,827 (21,279-5,452). available for shipment. 48 Once these two sets of data are determined the market value of the undershipments can be readily computed. In table 49 it is assumed that the undershipments of dark-green and yellow lemons consisted of the lower grades and less desirable sizes and that they would have brought only $0.85 a box if they had been shipped. Multiplying the volume of undershipments (col. 5) by the calculated price rate (col. 6) gives the market value of the undershipments (col. 7 ) . These amounts are added to the returns from shipments shown in column 3, and the sums give the adjusted returns from shipments as shown in column 11. Since the total net return from shipments of all color classifications 47 Methods of ascertaining the grades and sizes of lemons sent to the products plant are discussed on pages 74—75. 48 Methods of ascertaining the net prices being received for grades and sizes similar to those sent to the products plant are discussed on pages 88-89. Bul. 619] Maintenance of Equity in Pooling of Lemons 105 combined is the maximum amount of money, exclusive of returns from by-products, available for distribution between the color classifications, the addition to the returns on dark-green and yellow lemons must be accompanied by a subtraction of the same amount from one or both of the other color classifications. As shown in column 7, row 17, the total return added to dark-green and yellow lemons amounted to $1,939.70, TABLE 51 Computation of Hypothetical Lemon Shipping Allotments by Color Classifications ; Pool No. 3 ; Association F ; 1934-35 Associa- tion prorate Dark green Light green Sil ver Yellow Storage count date Storage Ship- ments Storage Ship- ments Storage Ship- ments Storage Ship- ments 1 8 S 4 5 6 7 8 9 per cent boxes* boxes* boxes* boxes* boxes* boxes* boxes* boxes* Feb. 15 6.90 1,065 73 5,394 372 22,794 1,573 6,960 480 Mar. 1 9.02 992 89 5,022 453 21,221 1,914 6,480 584 15 6.60 903 60 4,569 302 19,307 1,274 5,896 389 Apr. 1 9.38 843 79 4,267 400 18,033 1,691 15 12.39 764 95 3,867 479 16,342 2,025 May 1 10 54 669 71 3,388 357 15 9.08 598 54 3,031 275 June 1 18.33 544 100 15 14 63 444 65 Julv 1 19.46 379 74 Total 760 2,638 8.477 1,453 * Equivalent packed boxes. Sources of data: Col. 1: Figures represent the total allotments received by the Association divided by its total volume in storage on each storage-count date. Cols. 2, 4, 6, and 8: The first figures in each of these columns are from table 47, col. 1. Here it is assumed that all deliveries were in storage on Feb. 15. The other figures were obtained by subtracting the figures in cols. 3, 5, 7, and 9 from the corresponding figures in cols. 2, 4, 6, and 8, respectively. Thus, in col. 2 the figure 992 was obtained by subtracting 73 from 1,065 and the figure 903 was obtained by subtracting the 89 from 992. Blanks indicate that remaining fruit was no longer merchantable. Cols. 3, 5, 7, and 9: Figures obtained by multiplying the figures in cols. 2, 4, 6, and 8 by the cor- responding figures in col. 1. and as shown in column 10, row 17, the total return subtracted from light-green and silver lemons was the same amount. The total deduction from light-green and silver lemons combined was distributed between these two color classifications on the basis of their respective over- shipments. Alternative Methods of Calculating Prorate Contributions. — Instead of basing the prorate contributions of each color classification upon their normal storage periods, they may be based upon either cumulative vol- ume in storage or hypothetical shipping allotments. The method of calculating prorate contributions based upon cumula- tive volume in storage is shown in table 50. With this method the extent of adjustments between the color classifications will depend in part upon 106 University op California — Experiment Station the particular pattern of shipments followed by the management. Since the management can modify the pattern of shipments within a fairly wide range, the cumulative volumes of each color classification in storage are materially affected by its decisions. For any one color classification the cumulative volume in storage will be maximized by holding all of the lemons of that color in storage as TABLE 52 Calculation of Prorate Contributions by Color Classifications, Based Upon Hypothetical Lemon Shipping Allotments ; Pool No. 3 ; Association F ; 1934-35 Deliveries Hypothetical shipping allotment Prorate contribution Color classiBcation Volume Index Unadjusted Adjusted 1 2 S 4 5 Dark green boxes* 1,065 5,394 22,794 6,960 boxes* 760 2,638 8,477 1,453 per cent 5.70 19.79 63.61 10 90 boxes* 1,213 4,211 13,536 2,319 boxes* 1,065 Light green Silver 4,242 13,636 Yellow 2,336 Total 36.213 13,328 100.00 21,279 21,279 * Equivalent packed boxes. Sources of data : Col. 1: Figures equal to storage on Feb. 15, table 51, cols. 2, 4, 6, and 8. Col. 2: Totals of cols. 3, 5, 7, and 9 in table 51. Col. 3: Figures in col. 2 divided by 13,328 and the quotients multiplied by 100. Col. 4: Total shipments of 21,279 boxes multiplied by the figures in col. 3 and the products di- vided by 100. Col. 5: Since the unadjusted prorate contribution of 1,213 boxes (col. 4) for dark green exceeds the deliveries of 1,065 boxes (col. 1) the volume delivered was taken. The excess of 148 cars was then apportioned among the other color classifications on the basis of their respective unadjusted prorate contributions. Each of the unadjusted figures was multiplied by 1.00737 which was obtained by dividing 20,214 (21,279-1,065) by 20,066 (21,279-1,213). long as they continue to be counted at each storage-count date. Accord- ingly it would be to the interest of those growers having a larger-than- average proportion of yellow lemons, for example, for such lemons to be held as long as possible and for the shipping allotment of the association to be filled with the other color classifications. However, such a procedure would be to the disadvantage of those growers having a larger-than- average proportion of the other color classifications. Possibilities of inequity appear to be inherent in the method of calculating prorate con- tributions on the basis of the cumulative volume in storage. The method of calculating adjustments between color classifications based upon hypothetical shipping allotments is essentially the same as that outlined for calculating adjustments between time pools (Appendix C) . Because of the number of separate color classifications and the vary- ing length of time which each can be held in storage, this method is Bul. 619] Maintenance of Equity in Pooling of Lemons 107 somewhat complicated when applied to color classifications. A much simplified illustration is presented in tables 51 and 52. This method requires the determination of the length of time which each color classi- fication can be held in storage. In table 51 it was assumed that dark-green lemons could be held in storage for ten storage-count periods, light-green lemons for seven, silver lemons for five, and yellow lemons for three. 108 University of California — Experiment Station APPENDIX E METHOD OF CALCULATING ADJUSTMENTS BETWEEN GRADES AND BETWEEN SIZES WHEN MERCHANTABLE FRUIT IS SENT TO THE PRODUCTS PLANT The method of calculating the necessary adjustments between grades within a given color classification and between sizes within a given grade, when a larger proportion of some grades and sizes than of others is shipped, consists essentially in the determination of the rates of pay- ments by grades and sizes, based upon the volume grade-outs at the end of the normal storage period and upon the price differentials between TABLE 53 Illustration of Disposition of Merchantable Light-Green Lemons and Net Returns from Shipments by Grades in a Given Time Pool Grade Volume grade-out By-products Shipments Net returns from shipments Net price per box 1 S S 4 6 Extra Choice boxes* 450 250 150 boxes* 125 150 boxes* 450 125 dollars 900.00 187.50 00 dollars 2 00 Choice Standard 1 50 00 Total 850 275 575 1,087.50 * Equivalent packed boxes. Source of data: All figures are assumed. grades and sizes on the same markets on corresponding days. This method, therefore, is very similar to those discussed in Appendix A and Appendix B. For the purpose of illustration let us assume the situation shown in table 53. Unless adjustments between grades are made, Standard fruit would receive only the by-products return, Choice fruit would receive either $1.50 a box on one-half of the volume and by-products return on the other half, or if both the shipments and by-products are pooled together, $0.75 a box for the entire volume plus the by-products return on one-half of it, while Extra Choice fruit would receive $2.00 a box on its entire volume. Let us assume further that on the same markets on corresponding days, the simple average of the price differentials between Extra Choice lemons and Choice was $0.82 a box and between Extra Choice and Standard was $1.45 a box. Under the foregoing assumptions the appropriate adjustments be- tween the grades are shown in table 54. It will be noted that the adjust- ments result in a decrease in the total payments to Extra Choice and an increase in the total payments to both Choice and Standard. Bul. 619] Maintenance of Equity in Pooling of Lemons 109 TABLE 54 Computation of Adjustment Between Grades "Within a Given Color Classification When Merchantable Light-Green Lemons Are Sent to the Products Plant Grade Price differential from Extra Choice Volume grade-out Col. 1 X col. 2 Price rate Total payments 1 2 3 4 5 Extra Choice dollars per box 00 -0.82 -1 45 boxes* 450 250 150 dollars 00 -205.00 -217.50 dollars per box 1.77647 0.95647 0.32647 dollars 799.41 Choice 239.12 Standard 48.97 Total 850 -422.50 1,087. 50 * Equivalent packed boxes. Sources of data: Col. 1: From table 40. Col. 2: From table 53, col. 1. 3: Figures in col. 2 multiplied by corresponding figures in col. 1. 4: Price rate of Extra Choice calculated from following equation: 850X - $422.50 = $1,087.50 Transposing: 850X = $1,087.50 + $422.50 a i • v <1.510.00 t1 __,._ Solving: X = — — = $1.77647 Col. Col. Price rates of Choice and Standard obtained by adding to the price rate of Extra Choice the price differentials between Extra Choice and Choice and between Extra Choice and Standard shown in col. 1. Col. 5: Figures in col. 2 multiplied by corresponding figures in col. 4. TABLE 55 Computation of Adjustments Between Sizes Within a Given Grade When Merchantable Extra Choice Light-Green Lemons Are Sent to the Products Plant Size Price differentials from 360's Volume Col. 1 X col. 2 Price rate Total payment 1 t 3 4 5 number per box 270 300 dollars per box +0.01 +0.07 0.00 -0.43 -0.64 -0.97 boxes* 20 193 166 52 15 4 dollars + 0.20 +13.51 0.00 -22.36 - 9.60 - 3.88 dollars per box 1.83564 1.89564 1.82564 1.39564 1 . 18564 0.85564 dollars 36.71 365 86 360 303.06 432 72.57 490 17.79 588 3.42 Total 450 -22.13 799.41 * Equivalent packed boxes. Sources of data: Col. 1: From table 39, col. 1. Col. 2: Total from table 54, col. 2, volume grade-out of Extra Choice. Distribution by sizes assumed. Col. 3: Figures in col. 2 multiplied by corresponding figures in col. 1. Col. 4: Price rate of 360's calculated from following equation: 450X - $22.13 = $799.41 450X = $799.41 + $22.13 x = $82L54 = M 4o0 Price rates of other sizes obtained by adding to the price rate of 360's the price differentials between 360's and the several sizes shown in col. 2. Col. 5: Figures in col. 2 multiplied by corresponding figures in col. 4. 110 University of California — Experiment Station . When the return from the 275 boxes (table 53, col. 2) sent to the products plant is received it is distributed among the grades on the basis of their respective volume grade-outs. Once the total payments to each grade are determined, they can be distributed among the several sizes within the grade by the method illustrated in table 55. It is assumed that the required price differentials between the sizes of Extra Choice lemons are those shown in column 1, and that the number of boxes of each size as determined at the end of the normal storage period are those shown in column 2. The computed price rates by sizes are shown in column 4, and the total payments to each size in column 5. There is no point in distributing the returns from by-products to a given grade among the several sizes in that grade, since, as far as the individual growers are concerned, the same result can be more simply achieved by prorating the by-products returns to a given grade among the several growers on the basis of the number of boxes of that grade which each contributed to the pool. Bul. 619] Maintenance of Equity in Pooling of Lemons 111 APPENDIX F ILLUSTRATION OF ADJUSTMENTS BETWEEN TIME POOLS, COLOR CLASSIFICATIONS, AND GRADES WHEN MERCHANTABLE LEMONS ARE SENT TO THE PRODUCTS PLANT In appendixes C, D, and E, each of the adjustments which may be re- quired when merchantable lemons are sent to the products plant was worked out separately from the others. Under actual conditions, how- ever, the several adjustments will be interrelated, and a definite order should be followed in calculating them. Ordinarily it will be desirable, TABLE 56 Balance Sheet Showing Adjustments Between Time Pools for Lemons Actual Adjustment Pool Add Subtract Adjusted Ship- ments Net returns By- products Returns By- products Returns By- products Returns By- products 1 2 3 4 5 6 7 8 9 No. 1 No. 2 boxes* 21,279 21,279 dollars 36,174.30 36,174.30 boxes* 14,934 14,934 dollars 3,000.00 boxes* 3,480 dollars 3,000.00 boxes* 3,480 dollars 33,174.30 39,174.30 boxes* 18,414 11,454 * Equivalent packed boxes. Sources of data: Cols. 1 and 3: From table 47, totals in cols. 2 and 3. Col. 2: From table 49, total in col. 3. Cols. 4 to 7: Based upon undershipments in pool No. 2 amounting to 3,480 boxes which, if they had been shipped, would have returned $3,000.00. Col. 8: Figures in col. 2 plus or minus corresponding figures in cols. 4 and 6. Col. 9: Figures in col. 3 plus or minus corresponding figures in cols. 5 and 7. first, to calculate the adjustments between time pools, second, to calcu- late the adjustments between color classifications within each time pool, third, to calculate the adjustments between grades within each color classification, and finally to calculate the adjustments between the sizes of each grade. This procedure is followed in the illustration given in this appendix, except that the final step, that of calculating the adjustments between sizes within each grade pool, is not taken, since the method of calculating adjustments between sizes is essentially the same as that of calculating adjustments between grades. Table 56 summarizes the adjustments on shipments and by-products between two time pools (based upon picks). For the sake of simplicity the actual shipments, net returns from shipments, and by-products of merchantable fruit for each time pool are taken as the same amounts. The extent of the undershipment of pool No. 2, according to hypothetical shipping allotments during the overlapping period (Appendix C), is 112 University of California — Experiment Station 3,480 boxes. The total returns to pool No. 2 from shipments should, there- fore, be increased and a corresponding reduction made in the total net returns from shipments to pool No. 1. In the case of by-products the adjustment is in the opposite direction; that is, the merchantable by- TABLE 57 Illustration of Deliveries, Disposition, and Net Returns from Shipments of Merchantable Lemons in a Given Time Pool by Color Classifications and Grades Color classification Grade Deliveries By- products Ship- ments Net returns from ship- ments 1 2 8 4 Dark green < Extra Choice Choice Standard Total boxes* 564 320 181 boxes* 143 boxes* dollars 1,065 143 922 1,567.40 < Extra Choice 2,859 1,618 917 832 Choice Standard Total 5,394 832 4,562 7,755.40 • Extra Choice 12,081 6,838 3,875 3,430 3,875 Choice Silver Standard Total 22,794 7,305 15,489 26,331 30 . Extra Choice 1,740 2,436 2,784 1,434 2,436 2,784 Choice Yellow Standard Total 6,960 6,654 306 520.20 Total 36,213 14,934 21,279 36,174.30 * Equivalent packed boxes. Sources of data: Cols. 1, 2, and 3: Totals are from table 47. The deliveries and by-products by grades are based upon the grades determined at the end of the normal storage periods for each color classification, such as might be done from representative samples of each lot. Col. 4: From table 49, col. 3. products of pool No. 2 are reduced by 3,480 boxes and a corresponding amount added to the merchantable by-products of pool No. 1. The money value of the undershipments of pool No. 2 is based upon the grades and sizes of the lemons sent to the products plant which could have been shipped under its prorate and the prices prevailing on similar grades and sizes during the periods such lemons were physically fit for fresh consumption. Table 57 shows the detail figures for pool No. 1 with respect to the Bul. 619] Maintenance of Equity in Pooling of Lemons 113 volume of merchantable lemons delivered and quantities sent to the products plant by color classifications and grades, together with ship- ments and net returns from shipments by color classifications. The grades of the deliveries and by-products are assumed to have been de- termined at the end of the normal storage periods for each color classifi- cation. 49 Ordinarily the total deliveries thus determined will be less than the volume actually placed in storage because of the shrinkage and cull- TABLE 58 Division of Adjustments in Pool No. 1 Between Color Classifications for Lemons Color classification Prorate contribution Returns subtracted By-products added 1 2 3 4 Dark green boxes* 1,065 4,423 13,346 2,445 per cent 5.005 20.786 62.719 11.490 dollars 150.15 623.58 1,881.57 344.70 boxes* 174 Light green 723 Silver 2,183 Yellow 400 Total 21,279 100.000 3,000.00 3,480 * Equivalent packed boxes. Sources of data: Col. 1: From table 48, col. 7. Col. 2: Figures in col. 1 divided by 21,279 and the quotients multiplied by 100. Col. 3: Figures in col. 2 multiplied by 3,000 and the products divided by 100. Col. 4: Figures in col. 2 multiplied by 3,480 and the products divided by 100. age during the normal storage period. On the other hand, the total amount of merchantable fruit credited as by-products will generally be larger than the actual volume because of the shrinkage between the end of the normal storage periods and the time the fruit is sent to the prod- ucts plant. Also, the grades actually shipped may be considerably differ- ent from the grades determined at the end of the normal storage periods. Such situations, however, do not cause any difficulties as far as calcula- tions of adjustments are concerned, since they are based upon the quantities and grades determined at the end of the normal storage periods. From table 56 it was found that the total net returns from pool No. 1 should be reduced by $3,000 and that the volume of by-products should be increased by 3,480 boxes. The distribution of these adjustments among the different color classifications in pool No. 1 is shown in table 58. In the case of both net returns and by-products, the division between the color classifications is based upon their respective prorate contributions. The next step is to determine the extent of the adjustments required 49 The determination of the grades and sizes in each lot by means of samples is dis- cussed on pages 21-22. 114 University of California — Experiment Station between color classifications. Using the method based upon normal stor- age periods outlined in Appendix A, the adjustments thus determined are given in table 59, columns 3 and 4. The adjustments between time pools, as distributed among the color classifications in pool No. 1, are given in columns 5 and 6. These two sets of adjustments applied to the actual net returns and by-products (cols. 1 and 2) give the amount of money and volume of by-products to be credited to each of the color classifications. The distribution of the adjusted returns and by-products credited to each color classification between the several grades within TABLE 59 Computation of Adjusted Returns from Lemon Shipments and Adjusted Volume of By-Products by Color Classifications, Pool No. 1 Actual Adj ustment between color classifications Adjustment between time pools Adjusted Color classification Returns By- prod- ucts Returns By- prod- ucts Returns By- prod- ucts Returns prod- ucts 1 2 5 4 5 6 7 8 Dark green Light green Silver dollars 1,567.40 7,755.40 26,331.30 520.20 boxes* 143 832 7,305 6,654 dollars + 121.55 - 118.15 -1,821.55 +1,818.15 boxes* - 143 + 139 +2,143 -2,139 dollars - 150.15 - 623.58 -1,881.57 - 344.70 boxes* + 174 + 723 +2,183 + 400 dollars 1,538.80 7,013.67 22,628.18 1,993.65 boxes* 174 1,694 11,631 Yellow 4,915 Total 36,174.30 14,934 0.00 -3,000.00 +3,480 33,174 30 18,414 * Equivalent packed boxes. Sources of data: Cols. 1 and 2: From table 57, cols. 4 and 2. Cols. 3 and 4: From table 49, cols. 5, 7, 8, and 10. Cols. 5 and 6: From table 58, cols. 3 and 4. Col. 7: Figures in col. 1 plus corresponding figures in cols. 3 and 5. Col. 8: Figures in col. 2 plus corresponding figures in cols. 4 and 6. each of them are given in tables 60 to 67. In calculating the distributions of the adjusted returns between the grades, it is assumed that in each color classification the average price differential for the pooling period between Extra Choice and Choice was $0.82 a packed box and between Extra Choice and Standard $1.45 a packed box. 50 Once the adjusted net returns from shipments to each grade are deter- mined, the rates of payments by sizes or size groups within each of the grades can readily be calculated by the method outlined in Appendix B. Calculations of the distribution of the adjusted volume of by-products credited to each color classification among the several grades may at times be somewhat complex as shown in the case of yellow lemons (table 67). The methods employed are explained in the footnotes to the tables. 50 Calculated on the basis of a simple average of price differentials in the same markets on corresponding days as explained in Appendix B, Bul. 619] Maintenance of Equity in Pooling of Lemons 115 TABLE 60 Computation of Price Bates and Payments by Grades for Dark-Green Lemons, Pool No. 1 Grade Price differential from Extra Choice Volume grade-out Col. 1 X col. 2 Price rate Total payments 1 S 3 4 5 Extra Choice dollars per box 0.00 -0.82 -1.45 boxes* 564 320 181 dollars 0.00 -262.40 -262.45 dollars per box 1.937700 1.117700 0.487700 dollars 1,092.86 Choice. . 357.66 Standard 88.28 Total 1,065 -524.85 1,538.80 * Equivalent packed boxes. Sources of data : Col. 1: From table 40. Col. 2: From table 57, col. 1. Col. 3: Figures in col. 2 multiplied by corresponding figures in col. 1. Col. 4: Price rate of Extra Choice calculated from following equation: 1.065Z - $524.85 = $1,538.80 Transposing: 1.065Z = $1,538.80 + $524.85 Solving: X = %2 '?™f = $1.937700 l,Uoo Price rates of Choice and Standard obtained by adding to the price rate of Extra Choice the price differentials between Extra Choice and Choice and between Extra Choice and Standard shown in col . 1 . Col. 5: Figures in col. 2 multiplied by corresponding figures in col. 4. TABLE 61 Division of Merchantable By-Products between Grades for Dark-Green Lemons, Pool No. 1 Volume grade-out By-products Grade 1 2 3 Extra Choice boxes* 564 320 181 per cent 53 30 17 boxes* 92 Choice 52 Standard 30 Total 1,065 100 174 * Equivalent packed boxes. Sources of data: Col. 1: From table 57, col. 1. Col. 2: Figures in col. 1 divided by 1,065 and the quotients multiplied by 100. Col. 3: Figures in col. 2 multiplied by 174 and the products divided by 100. Total from table 59, col. 8. 116 University of California — Experiment Station TABLE 62 Computation of Price Kates and Payments by Grades for Light-Green Lemons, Pool No. 1 Grade Price differential from Extra Choice Volume grade-out Col. 1 X col. 2 Price rate Total payments i * S 4 5 Extra Choice dollars per box 00 -0.82 -1.45 boxes* 2,859 1,618 917 dollars 00 -1,326.76 -1,329.65 dollars per box 1.7292747 0.972747 0.342747 dollars 5,125 46 Choice 1,573.91 Standard 314.30 Total 5,394 -2,656.41 7,013.67 * Equivalent packed boxes. Sources of data: Col. 1: From table 40. Col. 2: From table 57, col. 1. Col. 3: Figures in col. 2 multiplied by corresponding figures in col. 1. Col. 4: Price rate of Extra Choice calculated from following equation: 5,394X - $2,656.41 = $7,013.67 Transposing: 5.394X = Solving: $7,013.67 + $2,656.41 Price rates of Choice and Standard obtained by adding to the price rate of Extra Choice the price differentials between Extra Choice and Choice and between Extra Choice and Standard shown in col. 1. Col. 5: Figures in col. 2 multiplied by corresponding figures in col. 4. TABLE 63 Division of Merchantable By-Products between Grades for Light-Green Lemons, Pool No. 1 Volume grade-out By-products 1 2 S Extra Choice boxes* 2,859 1,618 917 per cent 53 30 17 boxes* 898 Choice 508 Standard 288 Total 5,394 100 1,694 * Equivalent packed boxes. Sources of data: Col. 1: From table 57, col. 1. Col. 2: Figures in col. 1 divided by 5,394 and the quotients multiplied by 100. Col. 3: Figures in col. 2 multiplied by 1,694 and the products divided by 100. Total from table 59, col. 8. Bul. 619] Maintenance of Equity in Pooling of Lemons 117 TABLE 64 Computation of Price Rates and Payments by Grades for Silver Lemons, Pool No. 1 Grade Price differential from Extra Choice Volume grade-out Col. 1 X col. 2 Price rate Total payments 1 S 3 4 5 Extra Choice Choice Standard dollars per box 0.00 -0.82 -1.45 boxes* 12,081 6,838 3,875 dollars 0.00 -5,607.16 -5,618.75 dollars per box 1.485219 0.665219 0,035219 dollars 17,942.93 4,548.77 136.48 Total 22,794 -11,225.91 22,628.18 * Equivalent packed boxes. Sources of data: Col. 1: From table 40. Col. 2: From table 57, col. 1. Col. 3: Figures in col. 2 multiplied by corresponding figures in col. 1. Col. 4: Price rate of Extra Choice calculated from following equation: 22.794X - $11,225.91 = $22,628.18 Transposing: 22.794X = $22,628.18 + 111,225.91 a i • y S33.854.09 t1 Solving: X = 22 ?Q4 = $1.485219 Price rates of Choice and Standard obtained by adding to the price rate of Extra Choice the price differentials between Extra Choice and Choice and between Extra Choice and Standard shown in col. 1 . Col. 5: Figures in col. 2 multiplied by corresponding figures in col. 4. TABLE 65 Division of Merchantable By-Products between Grades for Silver Lemons, Pool No. 1 By-products Grade Volume grade-out Minimum quantity to Standard Prorated quantity Total 1 2 3 4 5 Extra Choice boxes* 12,081 6,838 3,875 per cent 53 30 17 boxes* 3,420 boxes* 4,352 2,463 1,396 boxes* 4,352 Choice Standard 2,463 4,816 Total 22,794 100 3,420 8,211 11,631 * Equivalent packed boxes. Sources of data: Col. 1: From table 57, col. 1. Col. 2: Figures in col. 1 divided by 22,794 and the quotients multiplied by 100. Col. 3: If the returns from by-products are assumed to be $0.30 a box, the minimum return to Standard should be 3, 875X$0.30=$1, 162.50. Standards, however, received $136.48 from shipments (table 64) which subtracted from $1,162.50 leaves $1,026.02 as the minimum return to Standard from by-products; $1,026.02 divided by 30 cents per box = 3,420 boxes, the minimum number of boxes to be credited to Standard. Col. 4: Total of 8,211 boxes obtained by subtracting total of 3,420 boxes in col. 3 from total of 11,631 boxes in col. 5. The other figures in col. 4 obtained by multiplying 8,211 by the figures in col. 2 and dividing the products by 100. Col. 5: Figures in col. 4 plus corresponding figures in col. 3. Total from table 59, col. 8. 118 University of California — Experiment Station The distribution of the adjusted volume of by-products credited to a given color classification among the several grades would be even more complex than that shown for yellow lemons in the event that the particu- lar color classification was entitled to an upward adjustment on by- products (rather than a downward one, such as is indicated in the pre- TABLE 66 Computation of Price Rates and Payments by Grades for Yellow Lemons, Pool No. 1 Price differen- tial from Extra Choice Volume grade- out Col. 1 X col. 2 Price rate Total payment Final adjustment Grade Price rate Total payment 1 * 3 4 5 6 7 Extra Choice Choice dollars per box 00 -0.82 -1.45 boxes* 1,740 2,436 2,784 6,960 dollars 0.00 -1,997.52 -4,036.80 dollars per box 1.153444 0.333444 -0.296556 dollars 2,006.99 812.27 -825.61 dollars per box 0.955740 0.135740 0.000000 dollars 1,662.99 330 66 Standard 00 Total -6,034.32 1,993.65 1,993.65 * Equivalent packed boxes. Sources of data: Col. 1: From table 40. Col. 2: From table 57, col. 1. Col. 3: Figures in col. 2 multiplied by corresponding figures in col. 1. Col. 4: Price rate of Extra Choice calculated from the following equation: 6.960X - $6,034.32 = $1,993.65 Transposing: 6.960X = $1,993.65 + $6,034.32 Solving: X = $8,027.97 = $1.153444 6,960 Price rates of Choice and Standard obtained by adding to the price rate of Extra Choice the price differentials between Extra Choice and Choice and between Extra Choice and Standard shown in col. 1. Col. 5: Figures in col. 2 multiplied by corresponding figures in col. 4. Col. 6: Since the total payment to Standard in col. 5 is a minus quantity, the total payments to Extra Choice and Choice combined must be reduced by the amount of that minus quantity. Price rate of Extra Choice calculated from the following equation in which the figures for the left side of the equation are the totals of cols. 2 and 3 less the figures in cols. 2 and 3 for Standard, and the fig- ure for the right side of the equation is the total of col. 5: 4.176X - $1,997.52 = $1,993.65 Transposing: 4.176X = $1,993.65 + $1,997.52 Solving: X = $3,991.17 = $0.955740 4,176 Price rate of Choice obtained by adding to the price rate of Extra Choice the price differential between Extra Choice and Choice shown in col. 1. Col. 7: Figures in col. 2 multiplied by corresponding figures in col. 6. ceding illustration) and at the same time one or more of the grades would have brought less than the by-products return if they had been shipped. Suppose, for example, that the price rate on Standard silver lemons, instead of being a positive number as shown in table 64, column 4, was a negative number and that the calculated total payment to Standard silver was a minus $210.00. In that event the following proce- dure would be required : First, the 7,305 boxes of silver to by-products (table 59, col. 2) would be distributed among the three grades. Since Standard received no return Bul. 619] Maintenance of Equity in Pooling of Lemons 119 from shipments, it would be entitled to 3,875 boxes of the 7,305 boxes. The remainder would then be prorated between Extra Choice and Choice, according to their respective grade-outs as given in table 64, column 2. Second, the 4,326 boxes which silver is entitled to receive from adjust- ments (table 59, col. 4 plus col. 6) would be distributed among the three TABLE 67 Division of Merchantable By-Products between Grades for Yellow Lemons, Pool No. 1 Grade Volume grade-out By-products 1 2 3 Extra Choice boxes* 1,740 2,436 2,784 per cent 25 35 40 boxes* 332 Choice 1,799 Standard 2,784 Total 6,960 100 4,915 * Equivalent packed boxes. Sources of data: Col. 1: From table 57, col. 1. Col. 2: Figures in col. 1 divided by 6,960 and the quotients multiplied by 100. Col. 3: Total from table 59, col. 8. Of the adjusted volume to by-products of 4,915 boxes, 2,784 boxes are credited to Standard since this grade received no returns from shipments; 4,915—2,784 = 2,131, which is the volume to be divided between Extra Choice and Choice. Before this division can be made, however, it is necessary to de- termine the net returns from by-products. If the returns from by-products are assumed to be $0.30 a box, the minimum return to Choice should be 2,436Xf0.30=$730.80. Choice, however, received $330.66 from shipments, which subtracted from $730.80 leaves $400.14 as the minimum return to Choice from by-products; $400.14 divided by $0.30 a box equals 1,334 boxes, the minimum number of boxes to by-products to be credited to Choice. 2,131 boxes— 1,334 boxes = 797 boxes available for distribution between Extra Choice and Choice. Prorating the 797 boxes on the basis of their respective grade-outs (col. 2) gives Extra Choice 332 boxes and Choice 465 boxes. Standard is entitled to none of the 797 boxes, since it was worth nothing from the standpoint of shipments (see table 66, col. 5). grades. Before this can be done, however, the average net return per box from by-products must be known. For purposes of illustration, we shall assume it to be $0.30. If the calculated total payment to silver Standards from shipments was a minus $210.00, and consequently, the total pay- ment to Extra Choice and Choice combined was reduced by an equivalent amount, then the first step is to calculate the number of boxes which would have a value of $210.00 for by-product purposes. This number is obtained by dividing the $210.00 by $0.30, which equals 700. The 700 boxes are prorated between Extra Choice and Choice on the basis of their respective grade-outs. The remainder (4,326 — 700 = 3,626) is then pro- rated between the three grades on the basis of their respective grade- outs. 120 University of California — Experiment Station APPENDIX G DATA ON VARIATION BETWEEN GROWERS IN PROPORTIONS OF THE SEVERAL BRANDS, SIZES, AND GRADES CONTRIBUTED TABLE 68 Yearly Variations between Lemon Growers in the Proportions of Excellent Brand Contributed; Santa Paula Citrus Fruit Association; 1925-26 to 1934-35 Mean Average deviation Range Year November-October Low High 1 * S 4 1925-26 per cent 32.8 30.7 61.2 51.3 68.7 48.7 35.5 45.7 55.6 23.6 per cent 4.99 4.82 6.31 5.90 5.58 8.62 7.27 5.96 6.38 8.54 per cent 15.9 16.1 45.8 37 3 50.6 19.5 11.3 25.9 16.0 8.5 per cent 47.3 1926-27 44.7 1927-28 78.4 1928-29 68.6 1929-30 85.3 1930-31 65.8 1931-32 63.6 1932-33 64.3 1933-34 72.6 1934-35 49.6 TABLE 69 Variations between Lemon Growers in the Proportions of the Several Brands Contributed; Santa Paula Citrus Fruit Association; Average 1925-26 to 1934-35 Mean Average deviation Range Brand Low High 1 8 S 4 Excellent per cent 45.4 15.7 17.5 17.3 3.6 per cent 4.39 3.46 3.03 3.07 1.01 per cent 29.9 5.9 12.1 11.2 1.7 per cent 56.8 ElMerito 25.8 Sunside Superba 28.8 27.4 Wave 80 Bul. 619] Maintenance of Equity in Pooling of Lemons 121 TABLE 70 Variation between Growers in the Proportions of the Several Sizes of Extra Choice Lemons Contributed to a Given Time Pool in 1933-34; Association D Mean Average deviation Range Size Low High 1 2 3 4 210's per cent 0.1 5 2.2 26.6 36.4 17.2 9.7 5.3 2.0 per cent 1.6 0.6 2.5 7.9 5.3 4.1 3.5 2.7 2.0 per cent 0.2 0.0 6.3 16.2 5.8 1.2 0.0 0.0 per cent 1.8 240's 3.7 270*s 32.4 300's 45.9 360's 47.1 432's 26.5 490's 19.7 540's 17.3 588's 18.0 122 University of California — Experiment Station o CO m Oi O rH K <*> O £ fc o o <*> 03 Oi B 53 o "^ B " O H O B « O Ph £ 1— 1 W ° t^ S 9 H h-H 1 « Xfl .« a o> oo to fed o» K >-H o o CO fed a a is o l-H 1 ^■"OOt^lOOOO o*)Oi-HCO^ o <; t3 O »N M CO tD * (O o "5 G k «!0 CO O ft N O l-H CD o» l-H § »o -a fed w 00 ~Oo5 * ^ •* W * •f cd ■«*< bO a & ^•m N M OO N CO ^ O*>00i— iftlOOCO CM O h-1 t- «5 CO l-H o o CO S3 ®-S a JL c« cp V3 (, •" C3 CO * O ft « 6 » ■* rt CO ft N N >c — i CN »-i CO a fee w l-H £ ^•u lO ft N N o e q.!»CMi-iOOCMO iO fed 03 O eo l-H d CO © S3 »-S c •JJ c3 cu 43 «« ^■"C3S05rt<-^<(N«0 % H CO CO W CO N CM CM c c« o >-< O.!»0t>-'CCO»0»0 U5 s t, 0) .fl O -^ o mO S CD fed o 03 > c O -l N CO ■* lO CD > CO CO CO CO CO CO «*j O O H N CO ^ CM CO CO CO CO CO Cj CTj 03 Oi 03 Oj 1— 1 T-H l-H l-H 1— ( 1— 1 Bul. 619] Maintenance of Equity in Pooling of Lemons 123 < Eh in Z © % w >o J CO 1 Q Tt< g CO OS o rH & (") 3 H H CZ2 o CO fe 1 O OS Ol (/J o» fc rH O i— i h O fc H< o o l-H <*! 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