A53 ANALYSES OF ER'FRASEASONAL APPLE FRiCE MQVEMEIN‘TS Thesis fat 1‘59 Degree ef Pia. D. M§CHE<3AN ESTATE UNEVERSITY Ewes? C. Pasour, Jr. $63 THESIS ____:. 11111111111111111111111111111111 11111111111111 3 1293 10699 8671 This is to certify that the thesis entitled AN ANALYSIS OF INTRASEASONAL APPLE PRICE MOVEMENTS presented by Ernest C. Pasour, Jr. has been accepted towards fulfillment of the requirements for Mdegree inJELiQQllural Economics 11/1 flflrWo/J £71179 V2/ 1 Major professor ML higan State University ' " '0'-' 'v u- can [14” LIBRARY 3 3 3%! MSU LIBRARIES “ RETURNING MATERIALS: .\ » 5'1" ll | ; Place in book drop to remove this checkout from your record. FINES wi11 be charged if book is returned after the date stamped below. 1 t. . , m3v+fivf§ AN ANALYSIS OF INTRASEASONAL APPLE PRICE MOVEMENTS BY Ernest C. Pasour. Jr. AN ABSTRACT OF A THESIS Submitted to Nfichigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1963 ABSTRACT AN ANALYSIS OF INTRASEASONAL APPLE PRICE MOVEMENTS by Ernest C. Pasour. Jr. Fresh apple prices at the farm level varied widely both between years and within a given marketing year during the postwar period. During this period, apple storage was profitable only in certain years. In addition to the variation in fresh apple prices, processing apple prices varied widely from year to year. The purpose of this study was to isolate and measure the effects of factors associated with within-year movements of United States apple prices at the farm level. An economic model was formulated after studying the economic behavior of the apple industry. This model consisted of fresh and processing apple demand functions, allocation and storage functions, and an identity. Total apple production in any year was assumed to be predetermined. The apple marketing year was divided into three periods to facilitate economic analysis. Period I coincides with Ernest C. Pasour, Jr. the harvest period, July - November. Periods II and III included the months December - March and April - June. respectively. All relationships of the model did not hold in each period, but there were as many equations as current endogenous variables in each period. Major data sources were publications of: (l) the U.S. Department of Agriculture, (2) International Apple Association, and (3) National Canners Association. All production and quantity variables were put on a per capita basis to adjust for changes in population. Farm prices were deflated by the Wholesale Price Index. After formulating the model and collecting the necessary data, the various relationships were estimated by single equation and two—stage least squares procedures. In general, relationships estimated by the two methods were quite similar. A satisfactory estimated demand function for processing apples could not be obtained. The model was reformulated by replacing the processing demand function with a demand relationship for all apples sold during the harvest period. In this relationship. a blend fresh and processing price was considered dependent and combined sales of fresh and processing apples and carryover stocks of processed apples were explanatory variables. Ernest C. Pasour, Jr. The demand for all apples sold in period I was inelastic. Demand for fresh apples during this period appeared slightly more inelastic than the demand for all apples sold. The findings mildly suggest that demand for fresh apples is slightly more inelastic than the demand for processing apples during the harvest period. Fresh apple sales, lagged fresh price. sales of competing fruits. and income accounted for 92 and 84 percent of the fresh price variation in periods II and III, respectively. Demand was slightly inelastic in period II but elastic in period III. In the allocation function of period I, the ratio of processing to period I fresh price, Eastern apple production, and other apple production explained more than 90 percent of the variation in sales to apple processors during the postwar period. The same factors explained about 80 percent of the variation in December 1 storage holdings. Beginning stocks explained more than 90 percent of the variation in storage movement during period II. The results of this and other studies were used to evaluate the feasibility of several apple supply control programs. The conclusion was that there are formidable theoretical and practical problems in instituting a Ernest C. Pasour, Jr. diversion or quantity control program. The large number of apple grades and varieties and the large geographical area of production intensify these problems. A predictive equation for canning and freezing pro— cessing apple prices was estimated which explained about 90 percent of the year—to-year variation in season average farm prices of canning and freezing apples. Predictive equations were also estimated for fresh apple prices in each period. Storage Vrules? were then developed for periods I and II to illustrate the possibility of improving storage decisions through application of the price prediction equations. AN ANALYSIS OF INTRASEASONAL APPLE PRICE MOVEMENTS BY 1' Ernest Cf Pasour. Jr. A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1963 ACKNOWLEDGMENTS The author is grateful to the large number of individuals who contributed toward the completion of this thesis. At Michigan State University, thanks are due the author's guidance committee: Robert L. Gustafson (Chairman), John R. Brake, Abba P. Lerner, Lester V. Manderscheid. and James H. Stapleton. Dr. Gustafson pro- vided direction and assistance during all phases of the study. With the exception of Lerner (who is currently on leave). all committee members contributed toward the final draft. The author also benefitted from discussions with Dennis L. Oldenstadt, a fellow graduate student. Thanks are also expressed to Mrs. Laura Flanders and Mrs. Karma Beal for their care in supervising the computing work and to Mrs. Kathy west who typed a preliminary draft of the manuscript. A number of individuals outside the university also provided assistance. Anthony S. Rojko, of the U.S. Department of Agriculture, analyzed the preliminary results and suggested a number of improvements. Dana G. Dalrymple. a former student at Michigan State University now with the ii U.S. Department of Agriculture, provided much of the basic data used in the analysis. Finally, the author appreciates the joint efforts of L. L. Boger and Loyd C. Martin who were instrumental in developing the research project, of which this thesis is a part. as a co—operative arrangement between Michigan State University and the U.S. Department of Agriculture. iii Chapter I. II. III. TABLE OF CONTENTS INTRODUCTION . . . . . . . . . . . The Problem Objectives Procedure Models Estimated Major Data Sources Prices Production Apple Storage Holdings Adjusting for Exports Processed Apple Stocks — Data Adjustments THE ECONOMIC BEHAVIOR.OF THE APPLE INDUSTRY Data Limitations U.S. APPLE EXPORT SITUATION . U.S. Exports U.S. Imports Trade Policies of the EEC External and Internal Tariffs Apple Production Canada and the U.K. Commonwealth Preferential Trading Arrangements Summary Apple Production Harvest Period iv Page l—‘ \INKOQOJ P‘H 18 18 l9 19 20 21 23 23 25 26 26 28 29 3O 32 34 34 36 Chapter Page Apple Storage 37 Types of Storage 37 The Apple Processing Industry 39 Location 39 Processing-Apple Utilization 41 Substitution Between Fresh and Processed Apple Products 42 Time Periods 43 Period I 43 Fresh Sales 43 Storage 43 Processing 44 Period II 44 Period III 45 Production-Stocks Identity 45 Apple Supply Predetermined 47 IV. THE ECONOMIC MODEL . . . . . . . . . . . . . . 49 Demand for Fresh Apples 51 Fresh Sales 53 Fresh Price 54 Lagged Fresh Price 54 Income 55 Permanent Income 56 Permanent Consumption Expenditure 58 Competing Fruits 59 Processing Apple Price 60 Demand for Processing Apples 61 Processing Price 62 Carryover Stocks 62 Chapter Processing Costs Income Fresh Price in Period I Crop Estimate Competing Fruits Lagged Processing Price The Processing Apple Allocation Function Processing-Fresh Apple Price Ratio Regional Apple Production The Storage Functions Period I Processing—Fresh Apple Price Ratio Regional Apple Production Period II Fresh Price Storage Considerations Price Increase in Previous Year Storage Heldings at the Beginning of Period II Competing Fruits Stocks During Same Period for Preceding Years Simplified Storage Functions Summary of Relationships in Mbdel Estimation Procedures and Assumptions Other Estimation Problems Single Equation Two-Stage Least-Squares Identification Standard Errors of Regression Coefficients Choice of Functional Form vi Page 62 63 64 65 65 67 67 68 69 69 7O 7O 71 71 72 73 74 74 75 75 75 79 81 86 86 86 87 88 89 Chapter V. THE ESTIMATED RELATIONSHIPS . . . . . . . General Procedure Testing the Regression Coefficients Partial Correlation Coefficients Coefficient of Multiple Determination Standard Deviation of the Residuals Demand for Fresh and Processing Apples Demand for All Apples Sold in Period I Fresh and Processing Sales Canned Carryover Stocks Demand for Fresh Apples Period I Price Trend Period II and III Lagged Fresh Price Competing Fruits Income Fresh Sales Seasonal Changes in Elasticity of Demand Allocation Functions A11 Processing Apples Price Ratio Eastern Production Other Production Canning and Freezing Apples Price Ratio Eastern Production Other Production vii Page 91 91 91 93 93 93 94 99 100 101 102 102 103 104 104 105 107 107 108 111 118 118 120 120 121 122 122 123 123 Chapter Storage Functions Period I Price Ratio Production Period II Storage Holdings at the Beginning of the Period CA Storage VI. IMPLICATIONS OF RESULTS . . . . . . . . . General Problems Determining Appropriate Elasticities Changes in Elasticity Foreign Competition Production Response Apple Marketing Diversion Quantity Limitation Product Promotion Bargaining Predicting Processing Apple Prices July Crop Estimates July Stocks July Price of Fresh Apples Predicting Fresh Apple Prices Period I PeriodsII and III Storage Optimum Allocation Over Time Storage Rules viii Page 124 125 126 126 126 127 127 130 131 132 133 134 134 135 135 140 142 143 143 146 146 146 147 147 148 149 150 152 Chapter Application of Storage Rules VII. BIBLIOGRAPHY APPENDICES . SUMMARY Storage Rule of Period II Storage Rule of Period I ix Page 154 155 157 163 179 185 Table LIST OF TABLES Page U.S. fresh apple prices at farm level. beginning and end of marketing year. 1947—1961 . . . . . . . . . . . . . . . . . 6 Per capita consumption of fresh. canned and frozen. and dried apple products. fresh equivalent basis. 1947—1961 . . . . . . . . . . . . . . 11 Production and utilization of U.S. apples, 1947-1961. thousands of bushels . . . . . . 35 Estimated fresh apple demand relationships. periods II and III . . . . . . . . . . . . . 106 Estimated allocation functions for canning and freezing and for all processing apples . . . 119 Appendix A Estimated fresh apple demand relationships by period . . . . . . . . . . . . . . . . . 188 Estimated processing apple demand relationships 190 Estimated demand relationships for all apples sold in Period I. alt + f1t . . . . . . . . 191 Estimated fresh apple demand relationships (OLS) by period. data transformed to logs . 192 Estimated allocation and storage functions (OLS) data transformed to logs . . . . . . . . . . 193 Estimated fresh apple demand relationships (OLS) by period. consumer disposable income variable replaced by personal consumption expenditures . . . . . . . . . . . . . . . . 194 Estimated preliminary storage functions for periods I and II . . . . . . . . . . . . . . 195 Table 10. 11. Appendix B U.S. production and sales of apples by period. 1947-1961. thousands of bushels . . . . . . . . . . . . . . . . . . . Per capita U.S. farm sales of fresh and processing apples by period. 1947-1961. in pounds . . U.S. fresh apple storage stodks at end of period. 1947 to 1961. thousands of bushels and end of July canner stocks of canned and frozen apple slices and apple sauce in fresh apple equivalents . . U.S. per capita storage movement of fresh apples by period. 1947-1961. and U.S. per capita canner stocks of canned and frozen apple slices and sauce in fresh apple equivalents . . . . . . . . . . Average deflated farm price by period of fresh apples and season average U.S. farm price (deflated) of processing apples, 1947-1961 . . . . . . . . . . . . . . U.S. per capita sales of competing fruits by period. 1947-1961. in pounds . . September apple crop estimate. Eastern apple sales. other apple sales. 1947-1961, pounds per capita . . . . . . . . . . . . . . . . Percent of total apple holdings held in CA storage on December 1 and April]. 1947—1961. United States . . . U.S. storage holdings at end of similar periods in previous years and within—year price increase of apples in storage. 1947-1961 . . . . . . . . . . . . . . . . . U.S. population by period. 1947—1961 . . . . . . Consumer and Wholesale Price Indices. 1947—1961, by period . . . . . . . . . . . . . . . . . xi Page 198 199 200 202 203 204 205 206 207 208 209 Table Page 12. Per capita deflated Consumer Disposable Income. seasonally adjusted at annual rates. by periods. United States. 1947- 1961 . . . . . . . . . . . . . . . . . . . . 210 13. Per capita deflated Personal Consumption Expen- ditures.seasonally adjusted at annual rates. by period. United States. 1947- 1961 . . . . . . . . . . . . . . . . . . . . 211 14. Indices of processing costs included in the processing demand relationship . . . . . . . 212 15. Fresh apples. exports and imports by period. 1947-1961. thousands of bushels . . . . . . 213 16. Processing apples. undeflated and deflated season average farm price. 1947-1961, dollars per ton . . . . . . . . . . . . . . 214 137. Fresh apples. average price per bushel (undeflated) per month. 1946-1961 . . . . . 215 113. U.S. per capita sales of fresh oranges by period. 1947—1961. in pounds . . . . . . . . 216 xii Appendix A. B. LIST OF APPENDICES STATISTICAL RESULTS . . . DATA USED IN ANALYSIS . xiii Page 185 197 CHAPTER I INTRODUCTION Price analysis. in general. is concerned with iso- lating and measuring the effects of the most important factors associated with price movements. Such analyses serve the goal of providing more accurate information to producers. marketing firms. and consumers. More accurate information should decrease uncertainty to all participants in the marketing process and thereby increase production and marketing efficiency. Price changes are associated with changes in supply and/or demand. Thus. in analyzing price variations. we must study the conditions affecting supply and demand. There are. however. innumerable forces affecting the level of demand and supply (and hence price) for any product. As a result. we must select and try to measure the influence of the most important factors associated with price movements. There are two categories of factors which need not be studied explicitly in short run price analysis. One category includes factors which have a negligible influence on price. In this category are prices and quantities of products which have a negligible effect on the price being studied. Another category contains factors which are important but which change slowly over time. The institutional framework. legal system. and consumer tastes often fall into this category. Information concerning the factors associated with price can be especially helpful to all segments of an industry which experiences wide price movements either between or within seasons. Apple prices at the farm level vary widely both between seasons and within a given season. Information pertaining to demand elasticities of fresh and processing apples is useful to producers or producer groups who wish to develop a marketing pattern that will maximize producer returns. Commodity groups are becoming more interested in the results of price analysis to answer practical problems.1 In apple marketing. information is needed during various parts of the marketing season. The elasticity of demand is likely to vary during the year since the avail- ability of substitutes varies. Also. weather or apple lShepherd points out that empirical work showing the demand for turkeys to be elastic (-1.4) was recently used as a basis for recommending to turkey producers that they not seek to reduce turkey production. G. S. Shepherd. Agricultural Price Analysis (Ames. Iowa: Iowa State University Press; fifth edition. 1963). p. 4. quality may cause a change in consumer tastes and affect the demand for apples. This study was addressed to an analysis of U.S. apple prices at the farm level. The primary emphasis was placed upon determining and measuring the effects of factors associated with changes in apple prices during various periods of the apple marketing season. Previous work in this area has been quite limited. Mbst past analyses of apple prices have dealt with changes in the season average farm price instead of focusing on within-year or intraseasonal price changes.1 The need for an analysis which considers changes during the marketing year is presented in the follow- ing section. The Problem Income from any agricultural commodity is determined by price as well as volume. The rate of marketing for com— modities with wide within-year price changes is likely to significantly affect producer returns.2 For apples. a major U.S. fruit crop. the potential effect of the rate of Season average farm price. as used in this study, refers to the average price during the marketing season. The apple marketing season (or marketing year) begins in July and ends the following June. It should be recognized that maximizing net returns may not stabilize prices. .._———— Ml__* _____ . 1.. .H‘F‘l u marketing on producer returns is quite large. In determining the most profitable marketing pattern for a commodity. we are not only interested in the average yearly price of the commodity over a period of years: we also need to know the price pattern which is likely to occur within a particular year. That is. an important problem in this area centers around seasonal fluctuations in demand and supply. Apples at the time of harvest may be sold for fresh use. for processing. or they may be stored and marketed later in the marketing year. Different prices are obtained for apples going into various end uses. The demand for processing apples relative to the demand for fresh apples at harvest varies from year to year for many reasons including changes in carryover stock of processed apple products. changes in government purchases. and changes in consumer tastes and preferences. Similarly. the pattern of within-year changes in demand for fresh apples may vary from year to year. Under Similar supply conditions. the price change during one marketing season may differ from the price change in another marketing season. Production and prices of crampeting fruits during various stages of the marketing Season and changes in consumer income are among the factors which might be expected to result in larger seasonal in- creases in apple prices in some years than in other years. The quantity of apples to store and the rate of sale from storage present major problems to the apple producer in each marketing year. Storage since World War II has been generally profitable only in certain years. Apple prices were lower at the end of the marketing year than at the time of storage during four of the fifteen postwar years (Table 1).1 In at least two of the remaining 11 years. the increase in price during the marketing year was not sufficient to cover storage costs. The decision as to whether to store apples must be made at harvest. The apple producer is likely to secure a greater return by varying his initial storage holdings from year to year. The rate of sale from storage presents other problems. After the initial storage decision has been made the producer is likely to increase the profitability of his Many varieties and grades of apples are sold in the fresh market. The fresh price (reported monthly by the ’ U.S. Department of Agriculture) is a blend price covering all varieties and grades. There is an additional problem in comparing apple prices at the beginning and end of the marketing season since the percentage of various grades and varieties marketed varies during the season. In general. however. the higher priced apples are placed in storage. so that the change in reported blend price may understate the actual per bushel gross return to storage. Table l. U.S. fresh apple prices at farm level. beginning and end of marketing year. 1947-1961. Fresh apple price . Crop At en 0 Change in price year At harvesta marketing yearb during marketing yearC -- Dollarspper bu. -- 1947 2.00 1.42 -0.58 1948 2.06 2.08 +0.02 1949 1.27 1.99 +0.72 1950 1.77 1.23 -0.54 1951 1.79 2.70 +0.91 1952 2.46 2.93 +0.47 1953 2.61 2.63 +0.02 1954 2.38 2.61 +0.23 1955 2.09 2.01 -0.08 1956 2.47 3.03 +0.56 1957 1.93 2.16 +0.23 1958 1.81 1.65 -0.16 1959 2.11 2.68 +0.57 1960 2.58 3.38 +0.80 1961 2.30 2.99 +0.69 aAverage fresh apple price during September. October and November. bAverage fresh apple price during April. May. and June. cThere has been a large increase in the quantity of apples placed in Controlled Atmosphere storage since 1955. We should expect this trend to be associated with an increase in the average within—year price movement. Source: Computed from U.S. Department of Agriculture Crop Reporting Board statistics. . “_._.._— ‘.__.. . storage operation from year-to—year by varying his monthly sales from storage. In determining the most profitable pattern of storage holdings. information is needed concerning the factors which influence apple prices during various stages of the marketing season. At the same time the apple producer is making the storage decision. supplies are also being allocated to the fresh and processing markets.1 These decisions are inter- related and will be determined by existing and expected prices in the various markets. There are substitution possibilities both on the supply and demand side. On the supply side. approximately one-third of U.S. apples are classified asffiual purpose? varieties.2 These apples are about equally suitable for use in either a fresh or processed form. In addition. some varieties classified as Ffresh? are also often used in processing outlets. Producers wish to allocate their crops between fresh and processing forms of utilization in such a way that net 1 . Apple processors are concentrated in the Eastern and Central states. Growers in some areas do not have an attractive alternative to selling in the fresh market. 2Dana G. Dalrymple. NEconomic Aspects of Apple Marketing in the United States.? (unpublished Ph.D. dissertation. Michigan State university. Department of Agricultural Economics. 1962). p. 16. returns are maximized. A large part of all apples produced are storable--at least for some period of time. In addition to allocating his crop between fresh and processing outlets. the producer desires to move his crop during the apple marketing season at the most profitable rate. On the demand side. empirical evidence suggests that consumers consider fresh and processed apple products to be substitutes.l That is. a high price for processed apple products relative to fresh apples tends to increase fresh apple purchases. Substitution possibilities on both the supply and demand sides result in a high degree of inter- dependence among apple markets at the farm level. Objectives The major problem of this study was to develop and fit an economic model which included the major behavioral relationships of the U.S. apple market. These estimated relationships should provide needed information about the factors associated with apple prices during various parts of the apple marketing season to apple producers. processors. and other apple buyers. From this model. equations were derived where feasible to predict apple prices in various periods of the apple marketing season. —._ 1This subject is discussed more fully in Chapter III. Providing accurate information of this nature to apple producers and buyers should increase the efficiency of the price mechanism in the allocation of resources and products within both the production and marketing sectors. Specifically. an attempt was made to provide information concerning the most profitable allocation of the apple crop for different sizes of crops and under alternative economic conditions. This information should assist apple producers in determining the quantity to store and the rate of sale from storage. In summary. the objectives of the study were: 1. To construct an economic model relating appropriate variables to fresh and processing apple prices during various periods of the marketing season. 2. To estimate the parameters of the model. 3. To relate findings of the study to apple marketing policy. Procedure A major objective of this study was to formulate an economic model of the U.S. apple industry that will explain short term fluctuations in apple prices at the farm level during the postwar period. The construction of such a model necessitated a study of the behavior of the apple industry. 10 The Cromarty-Boger model was reformulated in View of structural changes in the U.S. apple industry since World War II.1 Consumption of processed apple products has been increasing relative to fresh consumption (Table 2). In addition. there have been important changes in the product mix of processed apples. In view of the increasing importance of canned and frozen apple slices and sauce. this portion of the processing apple industry was given special attention in the processing sector of the model employed in this study. U.S. apple exports and imports have been low since World War II. After studying the apple export situation. a decision was made to adjust U.S. production data for exports and imports rather than formulate an export function (to explain changes in apple exports) as part of the over-all model. The rationale for assuming that U.S. apple exports will continue to be negligible is presented in Chapter II. For reasons of practicality. since research resources are not unlimited. the analysis presented here is based on 1W. A. Cromarty. VAn Experiment in Designing an Econometric Model to Explain Short-Term Demand Fluctuations for Apples.? (unpublished M.S. thesis. Michigan State University. Department of Agricultural Economics. July. 1953). and L. L. Boger and W. A. Cromarty. FA Model to Explain the Short—Term Demand for Apples.? paper presented at Econometric Society Meeting. Washington. D.C.. December 28. 1953. ' Table 11 Per capita consumption of fresh. canned and frozen. and dried apple products. fresh equivalent basis. 1947-1961. Per Capita Consumption . . Total Processed (Fresh Equivalent BaSis) Fresh Canned and Cal- and Canned Total Pro- endar Fresh Frozena Juice Dried Processed cessed Year (lbs.) (lbs.) (lbs.) (lbs.) (lbs.) (lbs.) 1947 25.4 3.0 4 1.3 4.7 30.1 1948 26.3 3.4 0 3 1.3 5.0 31.3 1949 24.7 3.4 7 1.1 5.2 29.9 1950 22.7 4.0 .9 1.3 6.2 28.9 1951 25.7 3.8 .8 1.2 5.8 31.5 1952 21.6 4.5 .8 1.0 6.3 27.9 1953 20.9 3.9 .8 .9 5.6 26.5 1954 20.0 4.1 1.1 .9 6.1 26.1 1955 19.6 4.8 .8 9 6.5 26.1 1956 18.9 5.3 1.0 8 7.1 26.0 1957 19.3 5.0 1.0 .7 6.7 26.0 1958 22.6 5.4 1.2 7 7.3 29.9 1959 23.0 5.2 1.5 .8 7.5 30.5 1960 20.1 5.6 1.4 .7 7.7 27.8 1961 18.6 5.7 1.4 7 7.8 26.4 aExcludes quantities consumed as baby food. These data include only canned. frozen. and dried apples. There are more than a dozen apple products on the market. Minor quantities of apples are used for jam. butter. jelly. wine. vinegar. brandy. etc. Source: C O 0 Preliminary U.S. Department of Agriculture. The Fruit Situation. No. 144. August. 1962. p. 28. 12 aggregation of the data into three within-year time periods or Fseasons.?l Thus. the study deals with the broad overall pattern of within-year price movements. rather than day-to—day or even month-to-month movements. Selection of the specific periods used was based primarily on the economic and technical or physical characteristics of the apple industry, but was partly influenced by practical data limitations. The quantities of apples channeled into the various outlets (fresh. processing. or storage) were considered as current endogenous variables during periods of the year when farmers have a choice of apple outlets. Fresh and processing apple prices were also considered endogenous variables. Models Estimated.--The initial model formulated in this study had one function relating fresh apple prices at the farm level. consumer income. production of competing fruits. and other variables to changes in movements of fresh apples during various periods of the apple marketing year. In another relationship. the quantity of apples pro- cessed was a function of processing apple price. processing costs. carryover stocks. and other relevant variables. In Some preliminary experimentation was also conducted ‘with a four period model. 13 addition to the demand relationship for fresh and processing apples. the model contained a fresh apple storage function. a processing allocation equation and a production-stocks identity. One formulation of the initial model included a processing demand relationship for all processing apples. The price indicator for this relationship was a blend price for all processing apples. A second formulation of the initial model excluded all apples utilized for processing purposes except canning and freezing apples. Most other apples processed may be considered as residual forms of utilization. In this way. attention was focused on the most important economic relationship. In each case. single- equation least squares estimates of the parameters were made prior to making two—stage least-squares estimates.l Satisfactory results could not be obtained for either of the processing demand relationships. Consequently. a revised model was adopted which contained a demand function :fbr all apples sold (fresh and processing) during the harvest period .2 —.__ . For a discussion of two-stage least-squares JTEBgression procedures. see J. Johnston. Econometric Methods (New York: McGraw—Hill Book Company. Inc.. 1963). pp. 258-260. 2This model is explained in detail in a later chapter. 14 After the relationships of the model were estimated by period. a different model was constructed for fresh apples. This model assumed no change in demand for apples between periods——allowing no shift in either the level or slope of the demand function. Then the model was adjusted to allow for shifts in the level of demand for fresh apples between periods while holding the slope of the demand function constant. In using time series data to explain the closely related processes in the apple market. more accurate estimates should be obtained by considering the dependent variables jointly. As indicated above. a number of structural equations are necessary in a model to describe the behavior of the U.S. apple economy. Any single equation selected from all the relationships comprising the economic model is just a part of the economic interaction in the apple market. The estimation of such relationships individually. ignoring closely related processes. may result in parameter estimates ‘Mhich are seriously biased. Thus. single-equation least- Eflquares estimating procedures under such conditions are lhikely to give biased estimates since each equation is C=<>nsidered singly and potential simultaneity is ignored.1 lShepherd. op. cit.. pp. 153-173. 15 In this study. an attempt was made to develop a behavioral model for the U.S. apple market. Each structural equation of the model contained variables having immediate logical connections with the behavior of the marketing sector which that equation purports to represent. In such a model. we are interested in estimating structural coefficients. A knowledge of structural coefficients is helpful even though our major purpose may be prediction. If a change in structure is expected. one needs to take into account experience collected under the old structure. Any attempt to predict the outcome of alternative decisions under the new structure with— out consideration of past experience under the old structure is Neither so lacking in precision or so wasteful of time 1 as to be useless.? Marschak indicates that a more promising lJ. Marschak. NEconomic Measurement for Policy and Prediction.” W. C. Hood and T. C. Koopmans (eds.). Studies in_Egpppmetric Method (New York: Wiley. 1953). p. 17. A. S. Rojko of the U.S. Department of Agriculture has pointed out to this writer that Marschak's statement con- cerning the unique power of the simultaneous equations approach is misleading. His argument follows. The example Marschak used was a tax problem in which one knows the change in structure. In practically all other situations. laowever. we cannot predict change in structure. In such asituations. the unique power or advantage of the simultaneous €2quations approach is lost. A similar view apparently is Sihared by F. V. waugh. See F. V. Waugh. ”The Place of Least Squares in Econometrics," Econometrica. Vol. 29. No. 3. (:3uly. 1961). pp. 386-396. R. J. Foote has accumulated a <2(Insiderable amount of empirical evidence indicating that Simultaneous equations methods lead to better predictions. even when there is no change in structure. See R. J. Foote. 16 approach is to base the decision upon an estimate of the old structure and on the knowledge of its expected change.1 In the behavioral model of the apple market. quantities of apples stored. processed. and sold on the fresh market are determined simultaneously and vary according to con- ditions of supply and demand in the various markets. As a result. a simultaneous equations method of estimating the relationships comprising the economic model becomes logi- cally appropriate during certain periods of the apple marketing year. During the final period of the marketing year. all remaining apples move into consumption as fresh. and the total quantity is predetermined. During this period. price is the only current endogenous variable. and the least— squares single-equation method of estimation becomes a valid application of the simultaneous equations theory.2 After formulating the economic relationships. collecting W. A. Cromarty. and W. R. Sparks. TEmpirical Results from .Alternative Methods of Fitting Systems of Simultaneous iEquations.? (unpublished paper presented by Foote at Midwest Quantitative Economic Symposium held at Michigan State (kniversity. February 4-6. 1963). lIbid. 2M. Ezekiel and K. A. Fox. Methods of Correlation and .lgfiigression Analysis (New York: John Wiley and Sons. Inc.; flflird edition. 1959). p. 432. 17 the necessary data. and fitting the final revision to the model. the findings of this study and other studies were related to apple marketing policy. Storage Nrules" were developed to illustrate the possibility of improving storage decisions through the application of price prediction equations. Major Data Sources A large part of the basic data was obtained from a previous study.1 In view of major differences in the U.S. apple industry before and after World War II. only postwar data. 1947—1961. were used in the study. Some of the more important variables and data sources are presented at this point. Prices.--Fresh apple prices at the farm level are reported monthly by the U.S. Department of Agriculture.2 A simple average of U.S. monthly farm prices in each of the three periods was used in the analysis. Processing apple prices at the farm level are reported ion a season average basis by the Department. Prices are -_k lDalrymple. op. cit. U.S. Department of Agriculture. Agricultural Prices. 3A weighted average would presumably have been 1>€3tter than a simple average since movement varies by month “Viuthin each period. However. movement data were not available for the fall months. 18 reported for apples to be (a) processed into canned and frozen slices and sauce. (b) dried. and (c) processed into other forms. In addition. a blend price is reported for all apples processed. This blend price was used in the pro- cessing demand relationship in one model fitted. Another model considered only canning and freezing apples in the processing demand relationship. In this model. the price of canning and freezing apples was used as the price variable. Production.--U.S. apple production is estimated by the U.S. Department of Agriculture.1 A small portion of apples produced is not sold. These apples are used in producer's homes or are not sold due to economic conditions. Economic abandonment includes apples not harvested and excess cullage of harvested apples. A function to explain that part of the crop not sold was not included in the model. As apple production has become more highly commerciaL- ized. the extent of economic abandonment has become negligible. IFor the purposes of this study. production refers to total apple sales . ‘Apple Storage Holdings.--Data from the International Estimates are made monthly during apple harvest from July-December and appear in Crop Production. 19 Apple Association were used in determining apple storage holdings by periods. Total apple holdings in each period were adjusted to eliminate processor holdings. This was done to get a more accurate record of the volume available for fresh use. Adjusting for Exports.——Fresh apple exports and imports on a monthly basis were obtained from U.S. Departments of Agriculture and Commerce publications.1 Apple exports and imports were aggregated by time period. Net apple exports were determined for each of the three within—year periods. and apple sales were adjusted in each period. Exports and imports of processed apple products were of minor importance during the postwar period and no data adjustments were made for them. Processedfiépple Stocks.--Large carryover stocks of jprocessed apple products were assumed to affect the demand for processing apples adversely. August 1 packer stocks <>f canned and frozen apple slices and sauce were used as an :indicator of total carryover stocks in the demand relation- esliip for processing apples. These data were obtained from the National Canners Association and the U.S. Department of T' lU.S. Department of Commerce. Foreigp Trade Reports and U- S. Department of Agriculture. Monthly Foreign Agricultural JTade of the United States. ' 20 Agriculture.1 Canned stocks are reported in cases of.various size cans. Frozen apple products are reported in pounds. Canned and frozen stocks were converted to a raw product basis in order to combine these stocks into a single indicator variable. The conversion factors used are presented in Appendix B. Table 3. Other variables and data sources of the analysis are presented at the time the model is presented (Chapter IV). Data Adjustments Fresh and processing apple prices were deflated by the Wholesale Price Index to remove changes over time in apple prices caused by changesin dollar purchasing power. Deflation in this manner assumes that a change in price level has no effect on consumption. VThis seems a reasonable assumption with respect to most perishable items . . ."2 The Wholesale Price Index was chosen as the deflator since ‘this study deals with apple prices at the farm or wholesale level . lCanned stocks appear in NCA monthly reports and frozen stocks appear in U.S. Department of Agriculture. <2<>ld Storage Reports. 2U.S. Department of Agriculture. Analytical Tools 3§S>Jr Studyinngemand and Price Structures. Agriculture Handbook No- 146. 1958. p. 27. 21 Population in the U.S. increased from about 143 million in 1947 to approximately 185 million in 1962. Increases in population shift the demand function. assuming other factors remain unchanged. In order to adjust for these changes. all production. consumption. and stocks data were placed on a per capita basis. Data Limitations Data problems exist in all empirical work. In apple price analysis, however. data problems are especially pronounced and this fact has been recognized by previous workers. Drew. in a recent study concerned with analyzing demand and spatial equilibrium models for U.S. fresh apples. made the following observation. VBy far the most important problem encountered concerns the basic data._"2 In addition to the usual limitations and shortcomings with respect to the accuracy and representativeness of available data. there is a dearth of price data by grade. variety. and origin of production in the apple industry. ‘ lPopulation estimates and the Wholesale Price Index were (Dhmained from U.S. Department of Commerce. Survey of Current Business. and Economic Statistics Bureau of Washington.D.C.. frflae Handbook of Basic Economic Statistics. 2W. H; DrewufDemand and Spatial Equilibrium Models 15<>r Fresh Apples in the United States? (unpublished Ph.D. Ciii-Ssertation. Vanderbilt University. Department of Economics. CTEiIIuary. 1961). p. 140. 22 A blend price was used in this study for both fresh and processing apples. Changes in this blend price over time may or may not be highly correlated with price changes for a specific variety or grade. The individual apple producer needs information on demand and supply conditions for his particular varieties and grades of apples. At present. data limitations preclude apple price analyses for particular grades and/or varieties on either a regional or a national basis. Changes in apple prices resulting from a changing varietal composition is difficult to distinguish from changes in demand when only a blend price is available. In recent years. there has been a shift in apple plantings to varieties best suited for the fresh market. At the same time. consumption of processed apple products has been increasing relative to consumption of fresh apples. Apple price information on a grade and variety basis would be helpful in adjusting production to changes in consumer tastes and preferences. CHAPTER II THE U.S. APPLE EXPORT SITUATION In this chapter. both the postwar export situation and potential increases in movement of U.S. apples in world markets are considered. U.S. Expgrts Prior to World War II. the export market (largely European) provided a significant outlet for U.S. apples. From 1934-1938. U.S. fresh apple exports averaged ten million bushels per year. During this period. the U.S. was the world's leading apple exporter. and exports averaged 10-15 percent of total production.1 Today. the U.S. ranks fifth in apple exports after Italy. Argentina. the Netherlands. and Australia. During World War II. apple exports of the U.S. shrank to one-tenth of the level prevailing before the war. .Following the war. most European countries prohibited or l . . . U.S. Department of Agriculture. Foreign Agricultural Service. Information Relating to World Production and Trade iJl Deciduous Fruits. Nbvember. 1961. 2The Produce News. February 9. 1963. p. 18. 23 24 severely restricted imports of United States apples and other fruit. This was done in order to preserve their limited dollar exchange for more essential goods. Such actions tended to increase the price of fruit and encourage the expansion of European orchards. A vested interest was established which has firmly resisted the reduction or removal of these restrictions. Since World War II. United States apple exports have been primarily to Canada. the United Kingdom. and countries of the European Economic Community (hereafter called EEC).l Exports during this period have varied between one and six percent of total United States' production with an annual average of about 3 percent. About 75 percent of all United States' apple exports were in the fresh form.2 Today. import restrictions on United States' apples are much less onerous in Canada and the United Kingdom relative to countries of the EEC. Although not barring U.S. exports. most of the EEC members (except Italy and the Netherlands) admit U.S. apples only when local stocks have been completely used. 1 . . . The Six member nations of the European Economic Community (EEC). often called the European Common Market. are France. Germany. Italy. Belgium. Holland. and Luxembourg. 2Exports and import data were computed from U.S. Ifiapartment of Commerce. ForeiquTrade Reports and from data snapplied by the Foreign Agricultural Service of the U.S. Department of Agriculture. W x _.._.—_r i 25 U.S..Imports Imports of apples into the United States historically have been quite small even though United States' import duties are low compared to those of most other countries. Since WOrld War II. imports of apples into the United States have averaged about 1.5 million bushels per year. repre— senting slightly less than 1.5 percent of total United Statesl apple production. More than 80 percent of all United States' apple imports during this period came from Canada. Approximately 80 percent of all apple imports were in the form of fresh apples. Summarizing the trade situation since World War II. U.S. exports and imports of apples and apple products have been quite low. In evaluating potential changes in U.S. apple exports and imports. attention is focused on countries likely to be most important as outlets for U.S. apples. Trade policies of Canada. the United Kingdom. and the EEC are likely to be crucial in determining whether U.S. apple exports and imports will continue to be of minor importance as they have been since world War II. A discussion follows Of the effect of alternative trade policies by these countries. 26 Trade Policies of the EEC Recent actions by the EEC indicate that a protection— ist policy for many agricultural products will be continued. The EEC official fruit policy. released early in 1962. in addition to continuing the existing high tariff rates. imposes a variety of import restrictions on nonmember countries in the form of quantitative controls. suspension of exports. and a compensatory tax. In addition. at the end of a transition period. nonmember countries will face a common external tariff (CXT) while tariffs between member countries will be eliminated. External and Internal Tariffs.—-The establishment of Vinternal? and Fexternal? tariff rates by Member States in 1962 was one step in the transition toward a common agri— cultural policy within the EEC. FInternalV rates are the rates applied by Member Countries to other Member States of lThe CXT to be applied after the transitional period on imports from nonmember countries is determined by taking the arithmetic mean of the tariff rates applied by member nations on January 1. 1957. However. the CXT determined in this way cannot be applied in all cases since some Member Countries are bound by treaty to respect tariff rates with nonmember countries. including countries operating under the General Agreement on Tariffs and Trade (GATT). These treaties ‘Will often contain a Fmost favored nation? clause. In such czases. GATT provides that the violation of the guarantee shall be compensated by the downward adjustment of another rate of comparable trade value. 27 the EEC during a transition period. while Vexternal? rates apply to nonmember countries such as the United States. The Finternal? rates represent the first of the gradual steps in the move toward ultimate elimination of duties between the Member States. while the Vexternal? rates represent a move toward the Common External Tariff of the EEC. The CXT is to be in effect by the end of a transition period for agriculture. At the end of this transition period. tariffs and quotas between member nations are scheduled to be abolished. The original time-table has been accelerated. Starting in July. 1962. 7—1/2 years were allowed for the move to a common agricultural policy. The common external tariff at the end of the transition period will likely be a greater obstacle to U.S. exporters than the previous duties even though it will approximate the average of the prior separate tariffs. The imposition of a CXT accompanied by the elimination of tariff barriers between member Countries. when contrasted with the present situation. will give producers within the Community an advantage relative to nonmember countries. In addition. if internal trade barriers are eliminated. apmfle production will tend to shift to those areas of the BBC in which apples have the best comparative advantage. Tfiiis factor in the long run will also tend to decrease the 28 competitiveness of U.S. apples with those produced within the EEC. Apple Production.--Although the EEC is currently a deficit area in apple production. apple plantings have been taking place within the area at an falarming rate."1 The relatively high proposed common external tariff along with other barriers of the official EEC fruit policy such as a compensatory tax. quantitative controls. and suspension of imports leave little doubt that EEC apple producers will receive preferred treatment. This is especially likely since farm producers in Western Europe have a strong political voice. Under such conditions. traditionally important factors in trade such as cost of production or transportation differentials will have little effect on the allocation of EEC apple markets. In recent years. import barriers by individual countries of the EEC have effectively restricted United States' apple exports into the area to a low level. In view of this fact. the Common Fruit Policy of the EEC is significant lInternational Fruit World. Autumn. 1959. p. 15. In May. 1962. a horticultural team of the National Farmers' ‘Union visited several countries of the EEC. Their con- (alusion was that the EEC faces the prospect of a possible cflnronic surplus of apples. Source: IAA Special Letter. July 20. 1962. 29 to the United States apple producer more as an instrument of continuing the past policy of restricting United States' apples into markets of the EEC rather than as a means of decreasing United States' exports to this area. The point is that though there will likely be reductions in United States' apple exports to the EEC. exports to this area have been low since World War II due. in part at least. to arbitrary restrictions on imports from the United States by volume quotas. time restrictions. etc. Canada and the United Kingdom Let us now consider the potential for U.S. apple exports in markets of the U.K. and Canada. both important importers of U.S. apples in the postwar period. Export policies of these countries toward U.S. apples is highly dependent upon future actions of the Common Market countries. The potential effects of the interdependence of Canada and the U;K. with the EEC will now be explored. A potentially important problem of the United States' apple industry is the admission of the United Kingdom into the EEC. At the time this is being written. entry of the ‘United Kingdom into the EEC as a full member seems unlikely irlthe near future. So far. the UzK. has taken an all or Inothing approach toward entry into the EEC. Even if the U.K. 30 does not join the EEC. she may enter an economic arrangement whereby special trade preferences are obtained.1 There are at least two facets to this problem (the entry of the U.K. into the EEC) which are important in considering the impact of the EEC on the United States' apple industry. At the present time. the United States competes for markets of the United Kingdom on the same basis as countries outside the Commonwealth. The tariff levels and other import barriers of the Uhited Kingdom are much less stringent relative to present or proposed barriers of the EEC. During the past few years. exports of united States'apples to the United Kingdom have been larger than those to the entire EEC. Entry of the United Kingdom into the EEC would mean a sharp increase in her import duties. which could have a severe impact on United States' apple exports to the area. Commonwealth Preferential Trading Arrangements.--The effect on U.S. exports of the entry of the United Kingdom 1During the past three years. ten nations have applied for membership into the EEC. The U.K.. Nbrway. Denmark. and Ireland have applied for full membership. Greece became an Associate Member on Nbvember l. 1962. Turkey and Spain have applied to become Associate Members prior to becoming full members. Austria. Sweden. and Switzerland have applied for Associate membership with a stipulation that they :maintain their neutral status. In addition. Portugal. Israel. .Iran. and Yugoslavia have indicated interest in some form of economic arrangement with the EEC such as a general Trade and Tariff agreement. U.S. Department of Agriculture. Fkareign Agricultural Trade of the United States. October. 1962. and Time Magazine. October 5. 1962. p. 23. 31 into the EEC is further complicated by the preferential trading arrangements which now exist between the United Kingdom and members of the British Commonwealth. If the United Kingdom is successful in securing preferential terms for Commonwealth exports in the United Kingdom market. United States' apple exporters will face both increased duties and increased preferencesin this market. H0wever. if the United Kingdom should secure preferential arrange- ments for Commonwealth exports in the entire EEC area. United States'apple exporters will face even greater dis— advantages. In the eventuality that the United Kingdom is not successful in negotiating the continuation of Commonwealth preferential trade arrangements. the Uhited States would likely face increased competition from the Commonwealth countries in her home markets. With respect to apples. the United States would face increased competition from Canada and Australia. Canada. in recent years. has been exporting between two and three million bushels of apples per year. Less than one-half of these have been exported to the United States. with a majority going to the United Kingdom. Australia has been exporting annually between four and five million bushels of apples to Europe. In addition. Argentina has been a heavy exporter of apples to Europe. The attainment 32 of the predicted chronic apple surplus within the EEC. or even a move toward self-sufficiency. along with the United Kingdom's entry into the EEC would likely serve to increase United States' imports from these countries. In summary. the entry of the united Kingdom into the EEC. with or without preferential trade arrangements for the Commonwealth countries. is likely to have an adverse effect on United States' apple exports and may have an effect on United States' apple imports. Though the future relationship of the U.K. to the EEC is not clear at this time. the probability seems quite high that the United Kingdom will be successful in negotiat— ing some form of trade agreement involving closer economic ties with the EEC. Under these circumstances. the U.S. would no longer be competing for markets of the U.K. on the same basis as countries of the EEC. Summary In View of increasing apple production in western Europe and present and proposed trade policies of the EEC. increases in exports of U.S. apples to Canada. the U.K.. or the EEC seem unlikely. Furthermore. exports of a signifi— cant nature to countries that have been unimportant as importers of U.S. apples seem unlikely in the foreseeable future. 33 In summary. apple exports were found to have a negligible influence in the U.S. apple economy since WOrld War II. A study of the proposed trade policies in countries that have historically been important importers of U.S. apples reveals that future increases in U.S. apple exports are unlikely. Consequently. the export demand for U.S. apples was not considered explicitly in this study. CHAPTER III ECONOMIC BEHAVIOR OF THE APPLE INDUSTRY Apple Production Apples are produced commercially in 34 states of the U.S.l Currently. the leading states in apple production are Washington. New Yerk. Michigan. Virginia. and California in that order. Considered together. these 5 states account for about 60 percent of U.S. apple production. During the postwar period. annual U.S. apple production varied from 86.9 to 134.3 million bushels (Table 3). Small. and progressively smaller. quantities of apples were used in farm households. Production having value during the period was about 97.7 percent of total production.2 Thus. an average of 2.3 percent of the commercial crop was not Commercial apple production. as used in this study. refers to the total apple crop in the commercial areas of these 34 states. 2f'Production having value" includes quantities sold and quantities used on the farm but excludes Feconomic abandonment.9 Economic abandonment includes fruit not harvested and excess cullage of harvested fruit. Cullage represents sorts and culls (from marketable apples) which are not moved in a lower value outlet. Excess cullage is a sub- jective measure and includes cullage in excess of some "normal" level. U.S. Department of Agriculture. Crop Reporting Board. Statistical Bulletin No. 292. August. 1961. p. 3. 34 a-a. '4- lie .pnmom msfluuomom mono or» so poemssnso mucosmsoasm Hogans some Hoosuoooa pom mama .Hoos .umsmsm .Nmm .OZ cflumaafim HMOHumHumum .mMm EOHM mmmalmnma Mom mpmn .omma .Hmflfimumwm .Nma .OZ 35 sfiuoaasm Hosaumflumum .mMm .musuasoflumm mo usofiuummon .m.D Eoum womanhvma mom mumn "mousom .ommaaso mmooxo masons“ umoH Ho ooumo>umn uos mmame.>h oas.oma Hmma ooa ooa.m oom.m mmm.oa mum.m mmm.m bh¢.ma Hmo.cm goa.os mam.moa coma hoo.a mom.m th.m www.ma wom.¢ bom.m Hma.ma moo.mv www.mh hem.oma mmma mom.m ovm.~ mvm.¢ 00¢.ma mam.m OHH.¢ mmm.ma mnm.ov hmm.mm mm¢.bma mmma mob.a moc.m Hmv.¢ wam.HH mmm.m mom.v mmn.ha www.mm mmm.mh www.maa hmma om omh.m mwh.m mmm.oa vao.m mmm.m omm.ma Hma.mm wo¢.mo mam.aoa omma mom.m mmo.m hm¢.m mHH.HH ago.~ 0mm.m www.ma omm.mm omw.ho mom.ooa mmma oom mma.m mm¢.m bam.ma mvm.m mm®.m omm.ma NHH.mm www.mm mum.HHH vmma o mvH.m mva.m mmm.m H¢¢.H Nh~.m Hgm.ma mam.>m mmo.mm www.mm mmma o 0mm.m 0mm.m mum.m mm¢.H mum.m vom.aa mam.¢m bmm.mm mmo.¢m Nmma mno.oa whm.¢ om¢.¢a sgm.aa mNN.H mm¢.m mmm.aa mma.mm mma.mm mmh.HHH amma mmh.m hm¢.¢ Nmm.m ovm.ma 0mm.a Hmm.o Nmo.ha mmm.o¢ wma.mh mos.mma omma mmm.ma bph.¢ moo.ba 0mm.ma Hmb.a hoo.v oga.¢a mam.>m mmo.om mem.¢ma mgma mmm mma.v mmm.¢ NmH.m mam vom.~ omh.h mm¢.ma www.cm 0mm.mm mgma on¢.¢ mgm.v mam.m mhm.aa mob mmm.v moo.m mom.om som.hh www.maa bead usossoosmn< omD moamm oafiosoom Enmm Hmuoa Honpo souonm omwun possmo Hmuoa Smoum soauosooum snow HMDOB Hmuoa mono poumxnmz uoz nudged msflmmoooum.mo moamm .mHoSmsn mo mpsmmsocu .ammalhgma .moammm .m.D mo coaumuflaeus pan GOHDUSponm .m manna 36 harvested or was lost through heavy cullage. Harvest Period.--Apple production is seasonal in nature. The harvest date depends upon the variety. geographical area. and weather conditions. Varieties are classified into three groups on the basis of harvest date and storage quality - FSummer.V Vfall.9 and Fwinter." The harvesting of summer varieties. which comprise roughly five percent of total production. begins in July and ends in September.1 The major portion of these apples are stored for a very short period to permit cooling and distribution to truckers and then move directly from packing sheds into the fresh apple market. A minor portion of the summer apples are sold to processors. The harvest period for fall and winter varieties begins in August and ends in November.2 These apples may move from packing sheds directly into fresh or processing apple markets or they may be stored and sold later in the apple marketing season. Thus. producers must make the economic decisions concerning most profitable rates of sales from storage as the marketing season advances. Most apples are 10.8. Department of Agriculture. Fruits and Tree Nuts. Bloom. Harvesting. and Marketing Dates. and Principal Producing Counties. Agriculture Handbodk No. 186. July. 1960. pp. 16-19. 21bid.. pp. 20-58. 37 stored in farmer owned facilities.l .Apple Storage Storage holdings tend to vary according to crop size with a larger quantity placed in storage when the crop is large. Since World war II. the percent of annual production of fall and winter varieties which was in storage on December 1 has varied between 34 and 45.2 Types of Storage.——There are three types of apple storage facilities. Common storage facilities are unre— frigerated. Such storage is for short duration and is frequently used by apple processors. The proportion of total apple holdings in common storage is not known. so these apples were considered as part of regular refrigerated storage. lSince World War II. apple producers have been shifting from public to private storage facilities. This change has been due to both physical and economic factors. Some of these factors are: l) apples are very sensitive to temperature and humidity conditions. Proper storage conditions for apples are not easily obtained in public warehouses which store other commodities. 2) Controlled Atmosphere storage is not available in public warehouses. 3) construction of storage facilities provides off- season employment for farm workers. 4) on farm storage facilities decrease marketing costs in terms of hauling costs and quality loss. Drew. op. cit.. p. 38. 2International Apple Association. VSpecial Letters.” ‘Various issues. 38 The bulk of all stored apples is placed in regular refrigerated storage. A.much smaller but rapidly increasing portion of apples is being held in Controlled Atmosphere (referred to as CA) storage. With this method of storage. a special atmosphere is maintained in a sealed storage room. The percentage of stored apples held in CA storage on December 1 increased from 0.2 percent in 1947 to 13.3 percent in 1961.1 Most of this increase has occurred since 1956. The proportion of stored apples in CA storage becomes progressively greater as the marketing year advances. In April. 1962. CA holdings represented 39 percent of all apple holdings.2 The increase in CA storage has had a strong effect on marketing patterns. Such storage has enabled apple varieties which do not store well for long periods. such as the MeIntosh and Jonathan. to be held in good condition for several additional months. There are at least two factors. however. which have tended to hold down storage in CA facilities. Average total storage costs under this system are approximately one and one-half times as high as for regular refrigerated 39 storage.1 The special facilities required in CA storage increase average fixed costs relative to regular refrigerated storage costs. Average variable costs are also higher since refrigeration materials cost more in CA storage. The producer's flexibility in marketing is also decreased when apples are stored in CA facilities. Apples placed in CA storage must be held in storage for a minimum of 90 days (to be sold as CA apples).2 Once the room is opened. the apples must be marketed within a relatively short time period to maintain quality. Apples not stored during the harvest season go directly into either the fresh or processing market. The_Apple Processing Industry Location.--The apple processing industry varies according to geographical location. In general. processors are concentrated in the Appalachian Area. (Pennsylvania. Maryland. West Virginia and Virginia). New Yerk and. to a lesser extent. Michigan and California. 1J. C. Thompson. Jr.. Apple Storage Costs in New YOrk State. A.E. Res. 87. Cornell University. Department of Agricultural Economics. Ithaca. New York. March. 1962. p. 56. 2This legal requirement is based on the fact that apples must be in storage for a considerable period of time to get the NCA effect.? i.e.. to be able to differentiate CA apples from other stored apples. 40 During the 10 years. 1951 to 1960. 85 percent of the canned apple slices and 78 percent of all canned sauce were packed in New York and the Appalachian Area.1 The pack of frozen apples. though small relative to canned apples. was more evenly distributed among areas. The pack of frozen apples by area during the same period was as follows: 36 percent in the Northeast. 33 percent in the Midwest. and 26 percent in the West.2 Dried apples were processed almost exclusively in California and Washington. Processing facilities are located in areas where sufficient quantities of apples suitable for processing are produced since it is not economically feasible to ship such apples over long distances. Consequently. the processing outlet is limited for producers in many areas of the U.S.3 However. fresh and processing markets are interrelated to a major extent in areas where canning and freezing outlets take substantial portions of the crop. Even in areas where processing utilizes low grade fruit deemed unmarketable as lNational Canners Association. ”Supply. Stocks and Shipments Canned Apples.” and ”Supply. Stocks and Shipments Canned Apple Sauce." monthly. 2Dalrymple. op. cit.. p. 132. Juice mills are found in every area. but apples pressed into juice are mainly sorts and culls from apples going into higher value outlets. 41 fresh fruit. price can influence to some extent the portion of the crop marketed in the fresh outlet. Processing:Apple Utilization.—-From 1947-1961. processing utilization averaged about 30 percent of total apple production.l Approximately 20 percent of all apples produced were canned. frozen. or dried. Other apples processed were used for lower value products such as vinegar. juice. and cider. In recent years. the proportion of apples processed as slices or sauce has been increasing while the proportion going into the fresh market has been decreasing. The increase in pack of apple sauce has been especially pronounced. These trends in apple utilization are reflected in the consumption data of Table 2. During the 15 year period from 1947-1961 per capita consumption both of canned and frozen apples and of apple juice increased quite sharply. Although dried apple consumption decreased. there was a net increase of consumption of processed apple products. During the same period. per capita fresh apple consumption trended downward. On balance. considering both fresh and processed l . . . U.S. Department of Agriculture. Fruits NonCitrus py,States. 1949—1959. Production. USe. Value. Statistical Bulletin No. 292. August. 1961. and annual issues with similar title dated July. 1962. 42 apple products. per capita apple consumption changed little in the postwar era. Substitution Between Fresh and Processed Apple Products Empirical evidence indicates that consumers. especial- ly institutional users. consider fresh and processed apple products as substitutes.l There is also a high degree of substitution on the supply side. Many apples are suitable for use in either a fresh or processed form. and the quantity of apples supplied by producers to processors is strongly influenced by the relative prices of processing and fresh apples.2 Although apple processingtakes various forms. the total quantity of apples purchased for each end use is in- fluenced by the prices at which apples are available. Thus. crop utilization and apple prices are jointly determined in the market. 1Drew. op. cit.. pp. 213—214. At the retail level. Drew obtained a positive cross elasticity coefficient of .32 between fresh apple purchases and price of canned apples (the price elasticity of demand for fresh apples was —l.10). A positive cross elasticity coefficient of .67 was obtained between canned apple purchases and prices of fresh apples (the price elasticity of demand for processed apples was -0.73). See also Homer C. Evans. The Nature of Compgtition Among .Apple Processors in the Appalachian Area. West Virginia University. Agricultural Experiment Station. Bul. No. 405. June. 1957. p. 56. 2Evans found that apple growers in the Appalachian Area consider fresh and processor buyers as highly substi- tutable. Evans. op. cit.. p. 88. 43 Time Periods In studying demand or price fluctuations. aggregation of data according to definite time periods facilitates economic analysis. In this study. the apple marketing year. July through June. was divided into three within—year periods or ”seasons.” Period I.--The first period is the beginning of the apple marketing season and includes the months of July- Nbvember. Almost all apples are harvested during this period. Production during period I was assumed equal to total annual sales of summer. fall. and winter apple varieties. Fresh Sales.--During period I. large quantities of apples are moved in the fresh market. In addition. both apple processing and storage are important during this period. The following characteristics relating to apple storage and processing activities provide a major part of the rationale for including the months July-November in period I. Storage.--The International Apple Association (hereafter referred to as the IAA) estimates apples in storage on a monthly basis. These estimates in each marketing year begin with a November 1 estimate and end with the June 1 estimate of storage holdings. The December 1 estimate seems to be considered the most significant of all 44 the storage estimates.l By this time in the marketing year. such factors as apple size. grade. and condition along with the general reactions of buyers are pretty well sized up. In this study. December 1 holdings were assumed equal to the quantity of apples stored during period I. Processipg.-—Apple processing is limited during July and August and is heavily concentrated during September. October. and November. In the period 1951-1960. 74 percent of the canned apple pack and 82 percent of the canned sauce pack was processed prior to December. Apples processed as canned apple slices and sauce are mainly tree-run and are sold totfluaprocessor at harvest. Consequently. most apples to be processed in these forms would be owned by processors or in their hands by the end of November (end of period I). Small quantities of apples are pressed into juice after period I. However. these are mainly apples graded out of fresh operations. In this study. all apples to be processed were assumed to be sold to processors in period I. Period II.—-The second period includes the months of December. January. February. and March. During this lDalrymple. op. cit.. p. 85. 2 . . . . National Canners Assoc1ation. op. Cit. 45 period. apples move out of storage to meet the demand in the fresh apple market. A small quantity of apples are processed in period II; most of these are sorts and culls from stored fresh apples or are fresh apple stocks held by processors. Apple processing which occurs after period I was ignored in this study because it is minor and these apples are mainly utilized in lower value outlets such as juice and cider. Period III.-—The third period includes the months of April. May. and June. The economic relationships of period II and III are similar. When contrasted with period II. however. a much larger proportion of the apples sold in period III are CA apples. Apples continue to move from storage and storage stocks reach a minimum before the next crop harvest begins in July. In this study. all apples stored in any marketing year were assumed to be sold prior to July 1 since quantities sold after this date are very minor. Thus. in each year at the end of period III (or. at the beginningof period I) there were assumed to be no storage stocks of fresh apples. Production-Stocks Identity The physical supply available during each of the four periods is equal to the quantity of apples in storage at the beginning of the period plus the quantity harvested during that period. Apples may remain in storage or be sold in the 46 fresh and/or processing markets. Storage and processing activities are. however. restricted to certain periods. A production stocks identity may be written (1) + f + a + = s S(m-l)t qmt mt mt mt m = l. 2. 3; t = 1947. 1948. . . .. 1961. In this identity. small letters represent flows and capital letters represent stocks. The subscripts p and t indicate. respectively. the period and year being considered. The identity states that for any period of any year. the supply of apples at the beginning of the period. S(m—l)t' plus the quantity harvested during the period. qmt' con- stitute the total supply. This supply is equal to the quantity of apples stored at the end of the period. Smt' plus the quantities used during the period in the fresh form. fmt' and in the processed form. amt' The identity holds for all periods. but in some periods storage and processing activities are at the zero level. For example. production takes place only in period I. Therefore. q2t = O and q3t = 0. There are no storage stocks at the beginning of period I. Hence. = 0. S3(t-1) Apples were assumed processed only in period I. So. a2t = 0 and a3t = 0. The quantity of apples moved in the fresh form. fmt' however. is positive during each of the 47 three periods. In the storage function which is developed in the next chapter. (2) Smt = Smt - S(m-l)t In this relationship. smt represents a flow during the mth period. In determining s = 0. Therefore. lt' S3(t-1) slt = Slt' In period I. 511: is poSitive representing movement into storage. In periods II and III. smt is negative indicating the rate of movement out of storage during the two periods. Total Apple Supply_Predetermined Apple supply is largely predetermined in any given year. Small quantities of apples. as previously indicated. may be left unharvested or culled during the marketing year because of price or price expectations. Hewever. only to this very small extent can the season's supply of apples . 2 . be conSidered endogneous. Orchards are becoming larger Slt represents stocks at the end of period I for any year t. S(m-l)t for period I and year t representsthe stocks at the beginning of this period which is equivalent to the stocks at the end of period IIIcf the previous crop year (t-l). 2A. H. Harrington. ”Demand for Fresh Market Apples" (unpublished Ph.D. dissertation. University of Illinois. JDepartment of Agricultural Economics. May. 1962). p. 84. 48 and apple production is increasingly a more specialized operation. The trend toward a fewer number of larger producing units has permitted economies of scale in apple production. The typical apple producer has mechanical Sprayers. pruners. and harvesting equipment which has de- creased the proportion of apples not suitable for market and reduced average total harvesting costs. The result has been a sharp decline in apples not sold for economic reasons. In this study. the quantity of apples sold was assumed to equal production and. consequently. was considered pre- determined in any crop year. lDrew. op. cit.. p. 12. CHAPTER IV THE ECONOMIC MODEL A complete economic model for apples at the farm level was formulated for each of the three periods of the marketing season.1 In period I. there is a demand for fresh apples and for processing apples at the farm level.2 In addition. apples may be stored during this period by the grower and moved into the fresh market later in the marketing year. Two demand relationships. a storage function. an allocation function. and an identity comprise the economic model. The rationale for including a processing apple 1The model was complete in the sense that there were as many equations as current endogenous variables in each period. The model initially formulated is presented in this chapter. The revised model for period I is presented in the next chapter. 2In this study. the quantity of apples sold was related to farm or wholesale prices along with a group of consumer ”demand shifters” such as income and sales of com- peting fruits. Hence. the demand relationships of this study are not behavior relations in the strict sense but are ipartially reduced form” equations. Hildreth and Jarrett Rake the following observation concerning partially reduced form equations: ”In a certain fundamental sense. all equations ‘we are likely to deal with may be regarded as partially reduced form relations. It is always possible to imagine a Inore fundamental explanation of the phenomena that we observe. :involving more equations and more endogenous variables.” Cl- Hildreth and F. G. Jarrett. A Statistical Study of Live- Stkbck Production and Marketing. Cowles Commission Monograph NO- 15. 1955. p. 108. 50 allocation function in the model in period I is presented later in this chapter. No processing occurs in period II. Hence. the fresh apple demand function. the storage function. and the identity comprise the economic model. In period III. storage move- ment is predetermined (movement equals stocks at beginning of period) and there is no processing. Thus. the fresh apple demand relationship and the identity comprise the economic model in this period. The existence of differentgrices at the farm level implies that fresh and processing apples are different commodities to producers and buyers. From the producer's standpoint. production costs are lower in producing apples for processing outlets.l Pruning and thinning may be done more lightly with a consequent increase in yield per tree. In addition. color. size. and shape need not be as uniform as for apples going into the fresh market. Minor skin blemishes can be peeled off and less care is needed in assembling fruit to be processed. The result is lower harvesting and hauling costs. Growers selling on the fresh market must also supply 1D. R. Papera. ”The Rise and Decline of the California .Apple Industry” (unpublished Ph.D. thesis. Stanford University. Food Research Institute. 1958). P. 114. 51 the containers whereas growers selling to processors usually get their containers back. Fresh growers. as an additional marketing cost. generally must pay a sales fee which is not required by growers selling apples to processors.1 Evans found that grower costs in the Appalachian Area were from $0.96 to $1.28 more per bushel in selling on the fresh market.2 The demand at the farm for fresh or processing apples is a derived demand based on consumer demand for fresh and processed apple products. A shift in the demand for fresh relative to the demand for processing apples may be brought about by changes in tastes. prices of competing fruits. income level. etc. The various relationships of the model and the sources of data used in estimating the parameters of the model follow. Demand for Fresh Apples The demand relationship for fresh apples is applicable during each of the three periods of the marketing year. This structural equation adapted from the Cromarty-Boger model lDalrymple. op. cit.. p. 59. The sales fee may be brdkerage or commission. This fee is not required for the grower selling directly to the processor. 2Evans. op. cit.. p. 47. 52 took the form:1 (1) fm where fmt f pmt p(m-l)t mt mt plt mt In period III. f = f( f f c a' u t pmt' p(m-l)t' ymt' mt' plt' mt per capita sales (in pounds) of fresh apples in period m and year t on a monthly basis. deflated farm price in cents per pound of fre31 apples in period m and year t. deflated farm price in cents per pound of fresh apples in the previous period. deflated per capita consumer disposable income in period m and year t in hundred dollar units. on an annual basis. per capita marketings (in pounds) of competing fruits in period m and year t on a monthly basis. deflated season average farm price in cents per pound of canning and freezing processing apples. This variable was included only in period I. an error term. mt can be considered as predetermined since there is no processing or storage (the movement out of 1Cromarty. opi_git.. p. 27. To simplify notation in this chapter. the dependent variable (Y) in each relationship discussed is expressed as a function of a group of explanatory variables (X1, X2. 9 o o , ka 1.1) as Y = f(Xl. XZ) o o o 1 In some cases. a parameter will refer to a coefficient . u). :1 a variable in a linear expansion of the function. In other cases. a parameter is the coefficient of the log of a variable when the relationship is linear in logs. Assumptions made concerning the disturbance term u in the estimation procedures of this study are presented in a later section of this chapter. 53 storage in period III is always equal to beginning stocks). Consequently. pit is the only endogenous variable in the relationship. Thus. in estimating the parameters of the fresh apple demand relationship during the final period of the apple marketing year. least-squares single-equation methods can yield unbiased parameter estimates. In periods I and II. however. the quantity of fresh apples sold is jointly determined with the quantities stored or sold to processors and prices. The structural equations in these periods must be estimated by a simultaneous equations method to obtain (asymptotically) unbiased estimates of the parameters. Fresh Sales.--Data on sales of fresh apples in period m and year t. f were obtained using the production mt' storage-stocks identity: + = + + qmt S(m-l)t Smt fmt amt Storage stocks information from the International Apple Association provided the necessary data to compute Smt l . . and S(m-l)t° Quantities produced and processed. qmt and a are estimated by the Crop Reporting Board.2 Hence, mt' 1IAA. op. cit. 2 . . . U.S. Department of Agriculture. Fruits NonCitrus by States 1949-1959. Statistical Bulletin No. 292. August. 1961. and annual supplements. 54 fresh sales were found by solving the relationship for fmt' = + - " fmt S(m—l)t qmt Smt amt Fresh Price.--The U.S. average farm price of fresh apples (in any period). Pf mt' was used as the price indicator. Monthly prices were averaged to get the price indicator in each of the three periods. Fresh apple price is an endogenous variable in relationship (1) during each period. In accordance with traditional demand theory. the coefficient of price was expected to have a negative sign. Legged Fresh Price.——The rationale for including f fresh price during the preceding period. P(m-l)t' as a predetermined variable was as follows. It was hypothesized that consumption now and consumption next period are sub- stitutes. Thus. a high price in the present period is expected to be assOCiated with smaller purchases in the current period and larger purchases in the next period. That «is. an increase in p(: is expected to be associated with -l)t an increase in fmt' Or. viewed differently. large purchases in the previous period due to an abnormally low price are expected to be associated with a decrease in sales of the present period. fmt' This result might be caused by either the partial satisfaction of consumer desires or the partial filling of storage facilities within retail outlets or house— holds . 55 Income.--Consumer disposable income was used as the income indicator variable in the analysis. Income was assumed to be predetermined although changes in apple prices have a small influence on disposable income. Income data are reported on a quarterly basis and do not coincide with the three time periods used in this analysis. Income during period I. was a weighted average of consumer disposable Ylt' income during the third and fourth quarters. A weighted average of consumer disposable income during the fourth quarter of year t and the first quarter of year (t+l) was constructed to get Y2t° In period III. equals consumer Y3t disposable income in the second quarter. Fruits are generally considered to be ”normal” goods. That is. an increase in income is expected to be associated with an increase in sales. Brandow estimated the retail income elasticity of fruits to be +.40 during the period 1955-57.1 For apples. the empirical evidence presents a mixed picture. Drew estimated an income elasticity coefficient of +.35 for fresh apples at the retail level based on data for the period 1934-1956.2 Harrington analyzed annual retail 1G. E. Brandow. Interrelations among Demands for Farm .Productsygnd Implications for Control of Market Supply. Penn. State Univ.. AES Bul. No. 680. Aug.. 1961. p. 17. 2Drew. op. cit.. p. 213. 56 fresh apple prices for the period 1934-1959 and concluded that the income effect was positive through 1954 but has not exerted a measurable influence since that time.1 Permanent Income.--Brandow. Drew. and Harrington in apple price analyses used consumer disposable income as the income indicator. Other measures of consumer income were tried in preliminary stages of the present analysis. One of these was a measure of ”permanent income.”2 The permanent income hypothesis suggests that consumer demand depends on the expected normal level of income. The following formulation permits an application of this hypothesis without constructing a permanent income series. A slightly simplified form of the fresh apple demand function was assumed. f * = + + + (2) fmt loo blpmt bZCmt b3ymt + vmt where f f and c r 3 def' d ' l d mt' pmt' mt a e a ine preVious y. an * ymt = expected or normal income in period m of year t. v = an error term mt An expectational equation of the following form was lHarrington. op. cit.. p. 171. 2M. Friedman. A Theory of the Consumption Function (Princeton. New Jersey: National Bureau of Economic Research. 1957). 57 assumed. * * * ) (3) ymt - Y(m-l)t - OL(Ym-l)t - Y(m-l)t where * o ymt is as defined above. and ymt = consumer disposable income in period m of year t. This function assumes that the change in expected income between the previous and the present period is a constant proportion of the difference between expected and realized income in the previous period. After making the necessary substitutions to express * (2) in terms of ymt rather than ymt. we have: b b f- .53.}. _ f __2_ (4) pmt _ a b + b fmt + (l Oop(m-l)t cmt 1 1 1 b b 2 l-a 3 +-—— -a -—— b (l )c( 1)t b f(m-1)t a b Y(m-l)t 1 1 1 + mt where l (1 - a) = --—- + umt bl Vmt bl V(m-l)t In this formulation. all variables other than income 1M. Nerlove. Distributed Lags and Demand Analysis for Agpicultural and Other Commodities. Agriculture Handbook No. 141. AMS. U.S. Department of Agriculture. June. 1958. p. 111. 58 enter as current and lagged variables. Income enters only as a lagged variable. In view of the large number of variables arising out of this approach and the limited number of observations available. this method was not pursued. This approach does provide another basis. however. for including p(:—1)t as an explanatory variable in the fresh apple demand relationship and for expecting its coefficient to be positive. Personal Consumption Expenditures.--Consumer disposable income less personal savings equals personal consumption expenditures. Measured consumer income is viewed as consisting of ”permanent” and ”transitory" components in the permanent income hypothesis. The transitory components show up mainly in measured consumer savings. These components do not affect consumption except as they are translated into effects lasting beyond the consumer's ”horizon.”l Hence. under Friedman's hypothesis. we might expect the correlation between personal consumption expendi— tures and permanent income to be higher than the correlation between disposable and permanent income. Exploratory results revealed that consumer disposable income and personal consumption expenditures were highly 1M. Friedman. op. cit.. p. 221. 59 correlated during the period of analysis. Preliminary results obtained were virtually the same when consumption expenditures were substituted for disposable income as the income indi- cator in the fresh apple demand relationship.l Consequently. the consumption eXpenditures variable was not given further consideration. and consumer disposable income was included as an income variable in the fresh and processing demand relationships. This variable was deflated by the consumer price index. Competing_Fruits.--Sales of competing fruits. Cmt' was included as an exogenous variable. Sales rather than prices were used because it was felt that sales are more nearly predetermined. Oranges are often considered to be competitive with apples in consumption. work by Harrington and Dalrymple. however. indicates that the relationship of oranges and fresh apples during the postwar period is one of independence rather than substitution.3 In the present study. sales of peaches. pears. and California table grapes by period were included in the index of competing fruits. The method of estimating 1These results are presented in Appendix A. Table 6. 2 U.S. Department of Commerce. Survsygof Current Business. 3Dalrymple. op. cit.. p. 176 and Harrington. op. cit.. p. 170. 60 sales of each of these fruits by period is presented in Appendix B. Table 6. ProcessingyApple Price.-—Empirical evidence shows that fresh and processed apple products are substitutes at the retail level.1 Hence. if increases in the farm price of processing apples cause increases in the retail price of processed apples. they should. other things equal. be associated with increases in fresh apple purchases. The price of canning and freezing apples. p:;. was included as the processing price variable since processing apples other than canning and freezing are of lower quality and are not as competitive with fresh apples. This variable was included as an explanatory variable in the fresh apple demand . . . . f . relationship only in period I. plt and pit are highly intercorrelated (r = +.84). and satisfactory results could not be obtained in the fresh apple demand function by I including pit.2 Consequently. this variable was dropped from further consideration in the fresh apple demand function. lDrew. op. cit.. pp. 213-214. 2 ' . . . When pl was included as an explanatory variable in the fresh apple demand relationship with price dependent. the coefficient of fresh sales was positive. a 61 Demand for ProcessingyApples Apple sales to processors were assumed to be made only in period I. Both price and quantity in the processing demand relationship were considered current endogneous variables. The quantity. a and price. pit. of apples lt' processed are determined jointly with fresh price. fresh sales. and apple storage in period I. The processing demand function was of the form: d c a u lt' lt' p1(t-1)’ mt ) e a f (5) a ’ f(plt' A lt' ylt' plt' lt lt' where f . . ylt' plt' and umt are as preViously defined and a1t = quantity of apples (in pounds) utilized by all apple processors on a per capita basis. pit = deflated season U.S. average farm price in cents per pound of all processing apples. A1t = per capita carryover stocks (in pounds) of processed apple products in canners hands at the beginning of period I. d1t = an index of processing costs. e1t = August apple crop estimate in pounds per capita. I c1t = production of competing fruits in pounds per capita. pI(t-l) = deflated season U.S. average farm price in cents per pound of all processing apples in the previous year. 62 Processing Price.—-Lower processing apple price (pit). other factors equal. was expected to result in a larger quantity of apples processed. Carpyover Stocks.--An increase in carryover stocks of processed apple products. A lt' was expected to decrease the demand by processors for apples in the current marketing year. Processed stocks data on a monthly basis are avail- able only for canned and frozen apple slices and sauce. These stocks constitute a large part of carryover and were assumed to be representative of carryover stocks of all processed apple products during the period of analysis. Apple processing begins in July but few apples are processed before August. Opening dates for apple processing vary from year to year depending upon crop conditions. End of July stocks data were used as the carryover indicator variable since stocks on hand at this time would include almost entirely products carried over from the previous apple marketing year. Processing Costs.--An increase in processing costs. d would decrease the processor demand for apples if lt' other factors remain unchanged. Processing costs for the postwar period are not available. Consequently. an index was constructed to estimate changes in processing costs during the period of analysis. 63 Labor and cans were selected as items to represent all processing costs. These items represent approximately 75 percent of total processing costs - a figure which has been quite constant in the postwar years. In constructing d the labor component was rep- lt' resented by average hourly earnings in the canning and freezing industries.2 Can prices were obtained from The Almanac of the Canning. Freezingy and Preserving Industries.3 Can costs were weighted twice as heavily as labor costs. The index was then deflated by the Wholesale Price Index. In 1962. an index of the prices of intermediate goods and services used in marketing farm products was constructed for the postwar period by the U.S. Department of Agriculture.4 This index and the constructed index were highly correlated (these indices are presented in Appendix B. Table 14). Income.--Drew estimated an income elasticity of 1 . V. F. Kaufman. ”Costs and Methods for Pie-Stock Apples.” Food Engineering. December. 1951. Other data used were supplied through correspondence with an accounting firm. 2U.S. Department of Labor. Bureau of Labor Statistics. Monthly Labor Review. various issues. A simple average for September. October. Nevember and December was used. 3 . . E. E. Judge. The Almanac of the CanningL FreeZing. and Preservipg Industries. No. 9. Court Street. westminister. Maryland. 1962. p. 308. 4U.S. Department of Agriculture. The Marketing and Transportation Situation. May. 1962. 64 +.53 for pnacessed apple products at the retail level.1 If this estimate is approximately accurate. an increase in income would likely be associated with an increase in demand at the farm level. other things equal. Preliminary investigation revealed that y1t and d 1t were highly intercorrelated (r = .94) and d explained very lt little of the price variation in initial analyses of the processing demand relationship. Consequently. the processing cost index. dlt' was dropped from the analysis. If there is a negative relationship between a1t and d . omitting d lt would likely cause a downward bias in the 1t estimated coefficient of ylt' As the estimates turned out. however. the coefficient of y1t was significantly positive. and indicated an unreasonably high (rather than unreasonably low) income elasticity (about 4). Fresh Price in Period I.-—Fresh apples appear to be substitutes in consumption for processed apple products.2 That is. an increase in fresh price increases consumer demand for processed products. Fresh apple prices in period I are positively correlated with fresh prices during the re— mainder of the apple marketing season. For these reasons. lDrew. op.cit.. pp. 213-214. 2Ibid. 65 a high fresh price during period I might indicate to the processor that the demand for processed apples will be high. Uhder these conditions. the coefficient of fresh price was expected to have a positive sign. Fresh and processing apple prices are highly correlated as indicated previously. Satisfactory results could not be obtained by including fresh price in the processing apple demand relationships.l Consequently. this variable was dropped from further consideration in the processing demand function. Cr9p_Estimate.--The September crop estimate. elt' made by the U.S. Department of Agriculture. is available to all segments of the apple industry. A large crop estimate is associated with lower fresh apple prices both at harvest and later in the marketing season. under such conditions. processors may expect the demand for processed products to be adversely affected during the ensuing marketing year due to the competitive relationship between fresh and processed apple products. If this is the case. a large crop estimate will adversely affect processor demand for apples. Competing Fruits.—-Another variable included in the 1 . . . When pit was included as an explanatory variable in e the processing mand relationship with price dependent. the coefficient of processing sales was positive. 66 processing demand relationship was an index of production of fruits that are competitive with processing apples. C1t° cit differs from c1t since different fruits are competitive with fresh apples than with processing apples (or processed apple products). A change in price of competing fruits might affect processor demand for apples in two ways. Many apple processors also process other fruits. Under given demand conditions for processed products. relatively lower prices of competing fruits would tend to make apple processing a less profitable operation at any given cost for apples. There is also substitution in consumption for pro- cessed apple products and canned peaches. pears. cherries. etc. An increase in production of competing fruits would tend to result in lower prices and hence result in a decrease in demand for processed apple products. Fruits included in cit were felt to be closely competitive with sliced apples (used mainly for pie stock) or apple sauce. Production of sour cherries. Washington. California. and Oregon Bartlett pears. California peaches. and California. Washington. and Utah apricots were included in cit. These fruits are primarily used for processing purposes. Preliminary results indicated that changes in this variable were not associated with changes in alt 67 and cit was dropped from the analysis. Lagged Processing Price.--Because processed apples can be stored for long periods. one might expect processors to buy larger quantities of apples in years when prices are low. That is. there is likely to be substitution in apple purchases between years on the part of apple processors. If this hypothesis is true. an increase in pI(t-1)' other factors equal. would be associated with an increase in alt' The Processigg Apple Allocation Function The total quantity of apples produced in any year was considered predetermined in this study. In period I. pro- ducers sell apples for fresh use. f and for processing. lt' alt' Apples produced and not moved in fresh or processing outlets at harvest are stored and sold at a later time in the fresh market. Although the total quantity of apples produced was considered predetermined. the quantity sold in the fresh or processing markets or the quantity stored cannot be con- sidered as predetermined. Two prices. pit and pit, are determined simultaneously with the allocation by producers of apples into fresh or processing markets or into storage. In this study. functions were estimated to explain changes in quantities of apples which producers wish 68 (l) to store (slt) and (2) to sell to processors (alt). The quantity producers sell fresh was treated as a residual. This choice of treating the quantity of fresh apples sold as a residual was arbitrary. With production predetermined. functions explaining changes in any two of the three quantities (flt' a Slt) may be estimated and the third lt' treated as a residual. The allocation equation formulated in this study to explain the quantity of apples sold for processing in period I was: a _ P (6) alt f( it: mt: ntl umt) plt where a a f and u have the same me ni as in lt' plt' pit mt a “9 the processing demand relationship. In t per capita Eastern apple sales (in pounds) in year t. n per capita apple sales (in pounds) in other t parts of the U.S. in year t. Processinngresthpple Price Ratio.--An increase in the processing-fresh price ratio would tend to result in more apples being allocated to the processing sector. The equilibrium price ratio in any season is determined simul- taneously with the allocation of apples to fresh and 69 processing markets. Regional Apple Production.--The processing apple industry is concentrated in the East. Therefore. the location of production may have an important effect upon the fresh and processing apple supply functions. A large crop in the East. m relative to production in other parts t! of the U.S.. n would likely mean that a larger portion ti of all apples produced would be processed.1 For these reasons. production was divided into ”Eastern production" and ”other production.”2 The Storage Functions Each producer makes his allocation among processing. fresh. and storage outlets more or less simultaneously. These decisions concerning the quantities to sell in each market and the quantity to store must be made at harvest. Since these decisions are interdependent. we might expect the same explanatory variables to be appropriate in 1G. E. Brandow. A Statistical Analysis of Apple Supply and Demand. A.E. & R.S. No. 2. Pennsylvania State University. Dept. of Ag. Econ. and Rural Sociology. University Park. Pennsylvania. January. 1956. p. 10. 2Eastern production is labeled as such by the Crop Reporting Service. Production of 14 Eastern states from Maine to N. Carolina is included. ”Other production” equals total production less Eastern production. 70 the storage function (of period I) and in the processing allocation function. A storage function including these explanatory variables was adopted for period I after experi- menting with a storage function of the type described below for period II. Storage occurs in period I and apples move from storage in periods II and III.1 The storage function is positive in period I and negative in periods II and III. In period III. movement from storage always equals beginning stocks so that s is predetermined. 3t Period I.—-The storage function of period I was: a (7) slt - f(plt' mt. nt. umt) f plt where a e plt' plt' mt. nt. and umt have the same meaning as in the processing allocation function. S1t = Slt ' S3(t-1) ProcessingeFresh Apple Price Ratio.--An increase in the price ratio is a reflection of an increase in processor demand relative to fresh demand. A relative increase in l . . A small quantity of apples moves in and out of storage in period I. but the extent of this movement is not known. 71 processing price will be reflected in a larger percent of the apples being allocated to the processing sector. It seems likely that part of the decrease in fresh sales would be in sales of periods II and III and. hence. would be reflected by a decrease in initial storage. The decrease in fresh sales. however. could be entirely at the expense of period I fresh sales. RegionalgApple Production.-—As indicated pre- viously. the apple processing industry is concentrated in the Eastern states although large quantities of apples are stored in these states. Apple production in other states is mainly for fresh use. An increase in Int or nt is likely to be associated with an increase in storage. but a given increase in n is likely to have a larger effect on s t 1t than the same increase in mt. Period II.--The storage function of period II. as initially formulated. was: f * (8) sZt 7 f(92t' k2t’ g(t-l)' Slt' c2t' SZt' umt) where f . . p2t. c2t. and umt have the same meaning as in the fresh apple demand relationship. and S21:: SZt ' Slt 72 k1t = the percent of stored apples in CA storage on December 1. g(t—l) = the price increase in dollars per bushel in the previous year from period I to period III. S = the per capita quantity (in pounds) of apples on hand at the beginning of period II. S = the average quantity (pounds per capita) of apples on hand at the end of period II during the three preceding years. Fresh Price.--The effect of current price. pit. upon movement from storage is not clear. Pubols found that current stocks and prices tend to move in the same direction.1 Lower prices. however. might be associated with decreases in movement from storage due to expectations of higher future prices. Expected future price less current price is the relevant consideration. in any period. in determining the quantitybo store and the rate of sale from storage. The difference between the expected price of period III and f f f . p2t' (Ep3t - p2t). could not be included as a variable in the storage function of period II since the expected price of l B. H. Pubols. ”Factors Affecting Prices of Apples." Agricultural Economics Research. Vol. VI. No. 3 (July. 1954). pp. 77-84. 73 period III was not known. However. three variables (klt. g(t-l)' and c2t) in the equation were included because of their possible relevance to the formulation of price expecta- tions. and given Epgt. an increase in pit should cause a decrease in quantity stored. Storage Cost Considerations.--Storage costs influence storage decisions by influencing expected profits. Apples will. in general. be stored and remain in storage as long as the expected price at a later date exceeds the current price plus storage costs (allowing for risk. spoilage. etc.). A large portion of apples are stored in producer owned facilities. and a large part of total storage cost consists of fixed cost. In the short run. apples will be stored as long as the expected priceincrease is greater than variable storage costs. Available data for years prior to 1951 and for years since 1957 indicate that regular storage rates varied little during the postwar period.1 This was made possible by economies resulting from increased storage capacity and increased efficiency and technology in storing apples. Average storage costs in recent years. however. have been 1Cromarty. op. cit.. p. 42 and personal correspondence with J. C. Thompson. Jr.. Research Associate. Department of Physical Biology. Cornell University. Oct. 30. 1962. 74 increasing due to the increase in CA storage. Controlled Atmosphere storage costs are approximately one and one-half times as high as costs of regular refrigerated storage. This increase in costs. however. is more than compensated for by the price premium realized for CA apples.l Under these conditions. we might expect an increase in CA storage to be associated with an increase in period III price and a decrease in movement from storage in period II. Price Increase in Previous Year.——The variable g(t-l) was included on the grounds that an increase in the within year movement of apple prices during the preceding year would adversely affect the movement of apples out of storage in the current year. In the storage relationship of period II. g(t-l) represented the price increase from period II to period III of the previous apple marketing season. Storagngoldings at the Beginningyof Period II.-- Storage holdings are published monthly by the IAA and are expected to influence decisions of apple producers concerning rates of sale from storage. An increase in storage holdings lThompson. op. cit.. p. 56. Thompson found total annual storage costs in New York were $0.23 per box for regular and $0.37 per box for CA storage. The average price premium for CA apples was $0.86 per box. 75 is likely to adversely affect the producer's expectations concerning future prices. Competinngruits.—-Sales of competing fruits. C2t' will influence the movement of apples from storage. The expectation of sharp decreases in supplies of competing fruits would lead apple producers to expect more favorable prices. Information pertaining to current and expected production and prices of competing fruits is published in the widely distributed Newsletter published by the IAA. Stocks During Same Period for Preceding_Years.—- Apples in storage at the end of period II during the three preceding years. $2t' may influence storage decisions due to past habits or experience. This variable may reflect either commitments or past experience by producers with apple buyers.1 A three year moving average was used to give * = S2(t-1) + S2(t-2) + S2(t-3) SZt 3 Simplified Storagg_Function Preliminary results showed that the storage function 1Evans. op. cit.. pp. 63-64. Evans found that apple processors take a long-range View toward maximizing returns and place a great deal of emphasis upon maintaining good relations with growers. The same situation may well prevail in the fresh apple market. 76 in period II could be greatly simplified.1 Beginning stocks. Slt' and the percent of stored apples in CA storage at the beginning of period II. k explained about lt' 90 percent of the variation in the storage movement during the period. Hence. the simplified function (9) SZt = f(Slt' k1t' umt) was substituted for the more involved storage function (8). Gustafson has shown that under certain conditions ” . the behavior of private inventory holders in aggregate operating in a competitive market. can be represented by a fairly simple functional relationship between the aggregate quantity of the commodity which is stored (carried over) at the end of a period and the total supply of the commodity which is available during the period (quantity carried in from the preceding period plus quantity produced during the period).”2 In the case of a three period model. with all production occurring in period I (and predetermined) and storage stocks at the end of period III equal to zero. the 1Results of the preliminary storage functions are presented in Appendix A. Table 7. 2R. L. Gustafson. ”Storage of Pork” (unpublished manuscript. Dept. of Ag. Economics. Michigan State University. February. 1959). p. 41. 77 essential conditions. in their simplest form can be stated as follows. First consider period II. and postulate that a) price in period II is a decreasing function of quantity sold in period II. i.e.. _ _ I . b) price in period III is a decreasing function of quantity sold in period III. i.e.. = 3 . c) the marginal cost of storage is the same for all storers and is equal to ' I 12(32)‘ Wlth 12 > 0. Then in competitive equilibrium. (1) v2(s2) = p3(52) - p2(sl —s2) which if solved for 82 as a function of S1 gives. say. S2 = 92(81). Differentiating (1) with reSpect to S1. we obtain ds2 p2(Sl - $2) I I 1 p2‘31 ’ $2) + 93(52) ‘ v;(52) Hence. 0 < 9; < 1 Next consider period I and postulate additionally that d) price in period I is a decreasing function of quantity sold in period I. 78 s < 0 where Q is production: e) the marginal cost of storage is the same for all storers and is equal to yl(Sl). with y; > 0. Then in competitive equilibrium 11151) = 92(81 - s2) - pl(Q - Si) or (2) “Y1(Sl) = pztsl - 92(sl)] - plm - 51) which if solved for S1 as a function of Q gives. say. S1 = 91(0). Differentiating (2) with respect to Q. we obtain as p;(Q - sl) pita - s1) + pgtsl - eztsln [1 - 95131” - 11(31’ Hence. 0 < 6; < l. The conditions can be generalized without changing the essential nature of the results by. for example. introducing random components to represent other factors influencing demand. and then setting marginal cost equal to expected change in price.1 This type of argument can be used to rationalize simplified storage functions such as (7) or (9). 1See. for example. R. L. Gustafson. Carrypver Levels for Grains. U.S. Department of Agriculture Technical Bulletin 1178. 1958. 79 In period I. mt and nt represent the total supply available during the period since S = 0. In period II. there is 3(t—l) no production and initial storage holdings. Slt' constitute the total available supply during the period. Summary of Relationships in Model The economic model of the apple industry constructed in this study consists of fresh and processing demand relationships. an allocation function. a storage function. and an identity.1 In the formulation which follows. the jointly dependent or current endogenous variables appear first in each relationship and are separated from predeter- mined variables by a semicolon. The period(s) in which each equation of the model holds is indicated by an X to the right of the equation. Variables excluded from the analysis after the preliminary stages (for reasons explained previously) are not included. Period f fl I II III (1) fmt' pmt ; p(m-l)t' ymt' Cmt X X X a a (2) alt' plt . Alt. elt' pl(t-1) X pa 1t (3) alt: f I mt. nt X plt lThe assumed functional form of the model and the assumed distribution of the error term are presented in sections following this summary of the relationships comprising the model. 80 Period I II III a (4) a s '35: ' m n X ° lt' f ’ t’ t p t b. SZt 7 klt: 811: X (5) s + a + s x )c x (m-1)t + qmt E fmt mt mt A review of the economic activities during each period revealsthat the model is complete. i.e.. the number of current endogenous variables in any period is equal to the number of equations in that period. In period I. the model has both fresh and processing demands and an allocation equation for apples at the farm level. In addition. a storage function is included to explain changes in quantity of apples stored for later sale in the fresh market. Current f lt' pit’ and pit. Each of the four relationships (1). (2). (3). and endogenous variables in period I are f a . s lt' lt (4a) and the identity hold in period I. After period I. apples move from storage into the fresh market. This movement is at a variable rate depending upon present and expected future prices. In period II. th. p2t. and SZt are current endogenous variables and (1). (4b). and (5) are the relevant relationships. It was assumed that no fresh apples are carried over to the next marketing year (S3t = 0). Consequently. s = S 3t 2t 81 That is. the movement from storage in period III is always equal to the quantity of apples stored at the beginning of the period. so a storage function is not needed during the final period of the apple marketing year. There is one current . f . . endogenous variable. 9 . and the relevant relationships are 3t (1) and (5) .1 Estimation Procedures and Assumppions The assumptions of the ordinary least squares (OLS) and two-stage least-squares (TSLS) estimation procedures (and statistical tests) used in this study are listed at this point. The data are then examined in an attempt to determine if there were serious deviations from the basic assumptions upon which the analysis was based. In matrix notation. the standard model employed in the OLS procedure is of the form: (6) Y = X y + U Txl TXK le TXl where: (a) U is a vector of unobserved random disturbances . 2 . . . With N(0.o I) distribution (b) X is a set of fixed numbers (measured without error) 1There is really just one equation since the identity in period III reduces to SZt 5 f3t and f3t is a predetermined variable in (l). (c) 82 X has rank K < T. The standard simultaneous equations model is of the form: (7) where: (a) (b) (c) (d) (e) (f) Y .8 = x ‘1' + U TxGGxG TxKKxG TXG Y is a matrix of T observations on G jointly dependent variables X is a matrix of T observations on K predetermined variables All variables (Y's and X's) are measured without error 6 is nonsingular ( 6 + 0) Ut(t = l. 2. . . . . T) has N(0. Z ) with Ut le GxG independent of Us. Elements of a given row of U may be correlated. Some elements of 6 and of F are assumed identically equal to zero; in the TSLS procedure one element in each column of B is assumed identically equal to one. under the assumptions of (6). the OLS estimate of y is consistent and best linear unbiased. In addition. the standard significance tests of the regression coefficients are valid. In time-series analyses. however. the data often do not conform to these specifications. If the 83 predetermined variables are not independent of the error term. if the disturbances are serially correlated. or if lagged endogenous variables are among the predetermined variables. the estimators no longer have all the character- istics noted above. The two-stage least-squares (TSLS) procedure used in this study is one procedure for estimating the parameters of a simultaneous equations model and under the assumptions listed under (7). yields estimates which are consistent and asymptotically as efficient as any obtainable using the same amount of information. Where the number of observations is small. as in this study. however. a simultaneous equations estimation approach may not estimate the parameters more accurately than the OLS single equation procedure. The model used for period II in this study was a linear simultaneous equations model in standard form. with G = 3. The model used for period I was not quite standard. since the ratio of two of the current endogenous variables appears in two of the six equations. No attempt was made to investigate the asymptotic properties of the TSLS estimates when a ratio is included in the model; intuitively it seems that they should still be at least consistent. The relationships of this study estimated by TSLS. in general. seemed somewhat closer to a priori expectations 84 than did the OLS estimates (although differences were negligible in several cases). Other investigators have also found this to be true for small samples. Foote found that TSLS procedures for small samples fairly regularly gave more accurate predicted values outside the period of fit than OLS methods.1 The problem of serial correlation in the disturbances in some cases has also been found to be serious in practice. This problem is especially likely to occur in time series analysis. Two or more successive disturbances may be influenced by the same factor rather than by the independent or random influences. In such cases. the result may be serious errors in the analysis. An attempt was made to test for serial correlation of the disturbances in this study. The Durbin—Watson test. the published tabulations for which extend to only five independent variables. was extrapolated linearly. where necessary. to include six variables. In this test. the following statistic was computed:3 1R. J. Foote. W. A. Cromarty. and W. R. Sparks. ”Empirical Results from Alternative Methods of Fitting Systems of Simultaneous Equations.” 2Clifford Hildreth and J. Y. Lu. Demand Relations with Autocorrelated Disturbances. Tech. Bul. No. 276. Dept. of Ag. Econ.. MSU. November. 1960. 3Joan Friedman. and R. J. Foote. Computational Methods for Handling Systems of Simultaneous Equations. AMS. U.S. Department of Agriculture Handbook No. 94. Revised May. 1957. pp. 77—78. 85 T 2 2 (dt dt-l) . t=2 d _ T 2 2 dt t=l where dt = the unexplained residual for observation t. The values d' and 4-d' were computed for the estimated relationships of the study and compared with the upper and lower limits of the test statistics. The three possible outcomes of the test are rejection of the null hypothesis (that is. no serial correlation exists among the residuals). non-rejection of the null hypothesis and indeterminancy. The indeterminate result is very common (this is especially true when the number of observations is small) which is a serious drawback in applying the Durbin—Watson test. At the 5 percent level of significance. the test was incon— clusive for each of the relationships estimated in this study. The presence of lagged endogenous variables also affects the properties of the estimators. Each of the fresh and processing demand relationships contained a lagged endogenous variable. If the disturbances in these relation- ships are normal and independent with zero means and a common variance. the estimators would be consistent but would 86 not be unbiased.1 Other Estimation Problems Single Equation.—-The demand. storage. and allocation functions. except in period III. have at least two jointly dependent variables. When estimating structural equations with single-equation least—squares regression procedures. the choice of which of the current endogenous variables to consider dependent is open to question. Hildreth and Jarrett suggest that ”least-squares bias might be minimized by treating as independent those current endogenous variables that are most strongly influenced by predetermined variables not appearing in the equation being estimated."2 Though this criterion does provide a guide. the grounds for making a choice remain quite uncertain. Consequently. alternative estimates were obtained taking price and quantity as dependent in the demand relationships. The estimated relationships not presented and discussed in the following chapter are presented in Appendix A. Two-Stage Least Squares.--In two—stage least-squares procedures. the jointly dependent variable to consider 1Clifford Hildreth. class notes taken in ABC 876. Statistical Inference in Economics. July. 1961. 2C. Hildreth and F. G. Jarrett. op. cit.. p. 71. 87 dependentin the second stage may be influenced by economic considerations but is still. at least to some extent. partly arbitrary. Thus. in estimating a demand relationship. quantity may be more appropriate than price as the dependent variable. In this study. alternative estimates were obtained with price and quantity taken as dependent in the second stage in the fresh and processing demand relation- ships. Quantity was selected as dependent (in the second stage) in both the allocation and the storage functions. Identification.--Each equation in Periods I and II satisfies the necessary condition for over—identification in the standard linear simultaneous equations model. namely the number of predetermined variables in the system less the number of predetermined variables in each equation is greater than the number of current endogenous variables in that equation minus one. No attempt was made to investigate the effect on identifiability of including. in two of the equations in period I. the ratio of two of the current endogenous variables. Intuitively it seems that using the variables in ratio form should. if anything. increase. rather than decrease. identifiability. Also. when the TSLS pro- cedure is used. if an equation is under-identified. that fact will tend to be revealed in the computations (at least when using the standard linear model). as one of the matrices 88 which has to be inverted turns out to be singular (except for rounding error). Standard Errors of Regression Coefficients.—-The procedure for computing standard errors of regression co— efficients in two-stage least squares is not asettled matter.1 In this study. standard errors of the b's from the second 2 stage were derived by use of the formula: r 1 2k Y _ Y 2 1/2 8* = c ( k k) b. ii df i 2 L d where s; i the ”correct” standard errors of the coefficients i at the second stage. cii = elements of the inverse matrix at the second stage. at 2 . . Zk(Yk - Yk) = the sumcf squared reSiduals uSing the observed Y's. df2 = the degrees of freedom in the second stage. i.e.. the number of observations minus the number of pre- determined variables in the second stage (including the vector of 1's since a constant term was included). lAll TSLS standard error formulas are asymptotic. Consequently. tests are valid. strictly speaking. only asymptotically. 2L. V. Manderscheid and W. Ruble. Estimation of Two- Stage Least Squares with Special Reference to Mistic Facilities. MOSOUOI A.E. 868' May, 1962' p. 5 (reVised) o 89 Some statistical investigators define S using b. 1 different degrees of freedom. Among the other degrees of freedom measures used are (l) the number of observations and (2) degrees of freedom in the first stage.1 The former would give a smaller standard error while the latter would give a larger standard error thantflmaprocedure followed in this study. Choice of Functional Form.--Inspection of the data did not point strongly toward any particular functional form. Estimates were first obtained by ordinary least squares assuming the underlying structure was linear. The relation- ships were then re-estimated with the data in log form. If the relationships among the variables are proportion- al rather than absolute. transforming all data to logs should give a relationship which better fits the data. That is. if the underlying structure. which we are trying to approximate. is more nearly represented by constant percentage changes than by constant absolute changes. a log form would be appropriate. The estimated relationships were quite similar in log and non-log form. However. the fits. based on R2. tended to be somewhat better when the data were not transformed 1Ibid.. p. 6. 90 to logs. Consequently. in most cases the results of the model in log form are not discussed (but are summarized in Appendix A). CHAPTER V THE ESTIMATED RELATIONSHIPS In this chapter. the estimated relationships are presented. The first section is a brief discussion of the various statistics which accompany each of the estimated relationships. General Procedure Testing_the Regression Coefficients.-—In the analysis. t values appear just below the regression coefficients in the relationships estimated by ordinary least squares and by two-stage least squares. A one-tailed t test was used in testing whether each partial regression coefficient was significantly different from zero since a priori information indicates the direction of the effect of each predetermined variable upon the dependent variable. In testing H6:Bl g_ 0 in a one-tailed t test. we do not reject if bi happens to be negative. Consequently. Xi can have a significant effect in this case only if bi > O. In testing whether a partial regression coefficient is significantly different from zero. it is useful to consider 91 92 the consequence of making a type I or type II error. Since we cannot simultaneously minimize both types of errors (except by increasing the number of observations) we must consider in any test which error would have the more serious conse- quences. very often in empirical work the a level is chosen at .01 or .05 without any real consideration of just how serious rejection of a true null hypothesis would be when contrasted with the error involved in accepting the null hypothesis when the alternative hypothesis is true. In this study. as in much econometric work. fairly strong a priori beliefs are held about the directions of the effects of the various explanatory variables upon the dependent variable. Thus. for example. it is felt with a high degree of confidence that Bi < 0 where Si is the parameter for carryover stocks in the processing demand relationship. The strength of this belief is such that it probably should not be questioned unless an estimate of 61 is obtained for which the probability of occurrence. given HO : Bi 3.0 is true. is quite high. A similar situation holds for most of the other explanatory variables. Conse- quently. in the results presented below. the .05. .10. and .20 levels of significance are all considered relevant. and are designated by ***. **. and *. respectively. 93 Partial Correlation Coefficients.--The coefficient of partial correlation (partial r/y) measures the importance of each of the independent variables taken separately while allowing at the same time for the variation associated with the other independent variables. Or. stated differently. the coefficient of partial correlation is a measure of the extent to which that part of the variation in the dependent variable not explained by the other predetermined variables can be explained by the addition of a specific predetermined variable.1 (The partial correlation coefficients appear just below the t values of the regression coefficients. Coefficient of Multiple Determination.--R? measures the percentage of the variation in the dependent variable which is explained by or associated with changes in the predetermined variables. 1R2 denotes an R? which has been adjusted for degrees of freedom.2 In this study. R2 is presented instead of R2 due to the small number of observations. Standard deviation of the residuals.--This statistic. often called the standard error of estimate. is denoted by 1Ezekiel and Fox. op. cit.. pp. 192—196. 2 _. 2R2 = l-(l-R ) (¥:%) where T is the number of observations and K is the number of predetermined variables including a vector of 1's. 94 Sy-x' It is a measure of how well the regression hyper- plane fits the data. i.e.. how closely the estimated values of the dependent variable approximate the observed values.1 Demand For Fresh and Processing Apples The estimation of fresh and processing demand relation- ships presented special problems in period I. Consequently. the model as summarized at the end of Chapter IV was sub- stantially revised. Results from the model as formulated in Chapter IV will first be presented and briefly analyzed. The revised model for period I will then be presented. In period I. the demand relationships for fresh and processing apples were estimated using both single- equation least—squares (OLS) and two—stage least-squares (TSLS) procedures. During this period. neither fresh sales (flt) nor processing sales (alt) can be considered pre- determined. In period I. the producer may either. (1) sell in the fresh market. (2) sell in the processing market. or (3) store and sell on the fresh market later in the marketing season. l . In two-stage least-squares regreSSion procedures. all current endogenous variables in the equation (to be estimated) except the variable considered dependent in the second stage are replaced by a linear combination of all the predetermined variables in the system. S -x and'Rz values presented in conjunction with relationships estimated by two- stage least-squares were based on estimated instead of observed values of all endogenous variables except the variable which is dependent in the second stage. 95 Both the fresh and processing demand relationships were based on 15 observations. Since the periods of the analysis were of unequal length. quantity variables were put on a monthly or yearly basis to facilitate the com- parison of coefficients for any given variable in different periods. The variables included in the fresh and processing apple demand relationshipsare presented and defined again at this point for ease of reference. fmt = per capita sales (in pounds) of fresh apples in period m and year t on a monthly basis. Pit = deflated farm price in cents per pound of fresh apples in period m and year t. y = deflated per capita consumer disposable income in mt . . . period m and year t (on an annual baSis) in hundred dollar units. cmt = per capita sales (in pounds) of competing fruits in period m and year t on a monthly basis. I pit = deflated season average farm price in cents per pound of canning and freezing apples in year t. alt = per capita farm sales of canning and freezing apples (in pounds) in period I and year t on a monthly basis. e1t = September apple crop estimate of year t in pounds per capita. Alt = August 1 per capita carryover canner stodk (in pounds) of processed apple products in year t. The following fresh and processing demand relationships with quantity dependent were estimated by TSLS.1 lOLS estimates of these relationships were quite similar to TSLS estimates and are presented in Apprndix A. 9 96 Demand for fresh apples: (1) Elt = 2.40 - .04pft - .08p§(t_l) + .34c1t - .oeylt tb .39 1.60 2.25 1.12 Partial r/y -12 -.44 +.57 -.33 s = .16. E? — .63 Demand for canning and freezing apples: I _ a _ a _ (2) alt — 5.93 + .26p1t '05pl(t-l) + .32y1t .lOA1t + .06elt tb 1.15 .85 4.24*** .63 2.07 Partial r/y +.39 -.30 +.84 -23 +.6l s = .13.}?2 = .72 y-x Coefficients of income (ylt). competing fruits (c ). and lagged fresh price (p3(t-l)) have ”wrong” signs in 1t (1). Downward trends in flt and clt and an upward trend in y1t during the period of analysis may provide an explanation of the perverse signs of C11: and ylt' The regression coefficient of fresh price. pit. has the right sign in (l). but the effect of fresh price on sales is not significantly different from zero. When c1t and y1t were replaced by a trend variable and lagged price was eliminated.“the estimated fresh apple demand relationship became more consistent with conventional demand theory. and this function was retained in the revised model of period I (presented later in this chapter). 97 In the demand relationship for canning and freezing I I apples. price (pit). lagged price (PI(t-l))' and crop estimate (e t) have ”wrong” signs. The effect of income on 1 canning and freezing apple sales was highly significant. However. there has been a sharp upward trend both in income and utilization of apples for canning and freezing purposes. Thus. income is likely acting as a proxy variable for a large number of factors which have caused the upward trend in processing utilization. The sign of the coefficient of processing price in (2) is especially disturbing. Similar results were obtained when this relationship was estimated with price as the dependent variable. In this case too. a change in sales appeared to have no effect on price.1 The results from this model are not consistent with conventional demand theory which holds that a change in sales. other factors equal. is associated with a change in price in the opposite direction. The model for period I was then reformulated to incorporate a demand function for total apple sales (fresh plus processing) of period I. The inclusion of this relationship means that only a fresh or processing demand 1Similar results were obtained when a processing demand relationship was estimated for all processing apples. These estimated relationships (mentioned but not presented in the text) are presented in Appendix A. 98 relationship (but not both) is needed to complete the model in period I. Various possible processing demand relation- ships were investigated. but an acceptable demand function for processing apples could not be formulated. A simplified demand function for fresh apples based on (1) (previously mentioned) was chosen to complete the model. although it appears to be less satisfactory than the other relation— ships of the model. The revised model of period I was: (3) pIt = Yipift + Yzpit (4) alt + flt = f(pIt' Ait’ ult) f (5) f = f opp umooxo moHQMHHm> moosomOpCm x.>uCoHHso Ham Mom mosam> om>nomno mo pmoumCfl poumsflumo Co comma mum oouComoum mosam> m pCm m .Eoummm ecu CH meanneum> omCHEHouoponm ecu Ham mo COHLMCHQEOU nausea m >9 omumammm.0nm ommum pCooom oCu CH uCooComop monopHmCoo oaflmaum> on» umooxo Aooumfiaumo on ouv sowumsoo ecu CH m0aflmaum> moosomoosm usmuuso Ham .mousomooum Coemmoummu moumsomlummoa ommumlosu CH9 .mosam> u men 30Hon mum muCoHonmooo Casumaounoo Hmauumm .mammm menu CUHCB on uCoaonmooo on“ BoHoQ push Cowman mUCmHUHmmmoo Coemmmnmou on» mo mosam> um mm. + He. + 66. + on. u Hm. ae.a *esmh.m seemm.m um am. we. mo. + HN.H+ me. + mo.~- mo.m mim.mv m moo “HHH possum mm. I oo. 1 as. + um. I NH.N essmm.m «eemm.m rssmm.m pm smo. emu. ma. . mH.H- He. + hm.~- 66.6 mmio~.mv mums mm. . mo. . so. + em. . oa.m sssom.m sesmm.m «ssmm.m um mm. em. ma. 1 6H.H- me. + em.~n em.o maim.mv mqo “HH ooaumm m x.mm us» use uAHIEwm uEm Enos onsooooum ml. - unmumeoo coaumeaumm paw mmuCoHowmmooO Coflumawuuoo Hoopumm w .mwsHm> u .mquflowmmooo Coemmoummm oaflmeum> uCopCome .HHH oCm HH uncauom .mmHCmCoaumaon osmsop cameo Cmoum ooumfiflumm .¢ OHQMB 107 correlated. However. similar results were obtained when quantity was considered dependent (Appendix A. Table 1). Thus. consumption appears to be substitutable between periods. at least to some extent. Competing Fruits.—-The sign of the coefficient for competing fruits. cmt' agrees with a priori reasoning in period II but is not consistent in period III. In period II. an increase of one pound per capita in sales of competing fruits resulted in a decrease in fresh price of $0.55 per bushel (1.15 cents per pound). The reason for the positive sign of c is not clear. While it is possible that 3t apples and the fruits included in c are complementary in 3t period III. c3t is more likely acting as a proxy variable for factors not included in the analysis. Income.--The income coefficient had the ”wrong" sign in period II. In period III. the income coefficient had a positive sign as expected indicating that apples are a normal good. The coefficient. however. was less than its standard error and the effect of y3t was not significant at an acceptable level. It is likely that the effect of income is being_ masked by the effect of other variables. Measuring the effect of income upon apple demand during the postwar period presents difficult problems arising out of trend considerations. 108 There has been a strong downward trend in per capita fresh apple sales accompanied by a strong upward trend in per capita income. The fresh apple demand relationships for periods II and III were re-estimated substituting a trend variable for cmt and Ymt' In period II. the trend coefficient was negative (significant at the .05 level) and R2 = .90. The trend coefficient was positive in period III (significant at the.20 level) and-R2 = .83. Thus. the fits were about the same in both cases when a trend variable was substituted for cmt and ymt (Appendix A. Table 1). Apple sales (on a per capita basis) have been decreasing during all portions of the marketing season but have decreased less in period III. This trend toward moving a higher percent of apples late in the marketing season and the upward trend in price in period III. probably are related to improvements in storage facilities and techniques which permit late marketings of higher quality products. CA storage is an important example of an improvement in storage technology which enables apples formerly of limited storage life to be stored for a considerable period of time. Fresh Sales.-—Changes in sales explained a large part of the price variation in periods II and III. In period II. an increase of one pound per capita (3.9 million 109 bushels at the 1961 population level) in fresh sales (monthly) in period II was associated with a price decrease of $1.14 per bushel (see [5.2a]). At the mean value of sales and price. demand was inelastic for fresh apples in period II (—0.78).1 Thus. demand for fresh apples appeared to be more elastic in period II than in period I. In period III. at the mean values of fresh sales and price. the elasticity of demand is -l.85--apparently higher than the elasticities of periods I and II. However. the average quantity of sales was much less in period III. Consequently. the increased elasticity could represent a move along a stable demand function rather than a shift in the function between periods. If the relationships among the variables are proportional. it is appropriate to estimate a relationship in log form. In this case. the elasticity of demand would be constant. When the data were transformed to logs. the elasticity of demand was -l.33 and R? = .86 which was a slightly better fit than was obtained in the linear relationship ((5.3) Table 4). Thus. it appears that demand is. in fact. more elastic late in the marketing season. The reason for a more elastic demand late in the 1When the fresh apple demand relationship was re- estimated g'th the data in logs. elasticity of demand = -0.75 and R = .92. 110 marketing season is not clear. However. it is likely to be connected with apple quality. Elasticity of demand provides a measure of the degree of substitutability between the product in question and competing products. A product with a highly elastic demand has close substitutes. The problem of poor apple quality (especially at the retail level) late in the marketing season has not been solved. Consumers are likely to substitute other fresh or processed foods more readily as apple quality deteriorates late in the marketing year. The weather is another factor which may be involved. Many people probably think of fresh apples as a cold weather food. The increase in ice cream and cold beverage consumption in warm weather is likely to be. at least to some extent. at the expense of apples. The difficulties in optimizing the marketing pattern for fresh apples posed by the apparent change in elasticity during the marketing season will be discussed in the following chapter. At this point. general problems in measuring elasticity of demand are discussed. and the results of an attempt to determine whether the level of demand for fresh apples shifts during the marketing season are presented. 111 Seasonal Changes in Elasticity of Demand.--Elasticity of demand for most commodities is likely to vary depending upon the length of time involved. There are two opposing forces affecting the elasticity of demand. Short-time elasticities (e.g.. week or month) are likely to be greater than longer time elasticities (e.g.. year) since a large part of the short-term fluctuations in supplies can be absorbed by storage operations.l Annual fluctuations in supplies of a semi-perishable commodity. such as fresh apples. cannot be absorbed in this manner. The ease of substitution is another force affecting elasticity of demand. The more time allowed for adjustment to a price change. the greater the adjustment is likely to be. Thus. in the long run. we expect elasticities to be greater than on an annual basis. Within short periods of time. the substitution effect on elasticity is likely to be more than offset by the opposite effect of storage. The lowest elasticity of demand is thus likely to be that based on data for a period just a little longer than the storage life of the good.2 Most elasticity estimates for farm products are based on annual data. For semi—perishable commodities. such lShepherd. op. cit.. p. 64. 21bid.. p. 65. 112 as apples. elasticities based on annual data are likely to represent minimum elasticities. Recent studies indicate that demand for fresh apples is inelastic when based on annual data.1 On the basis of the above argument. we would expect demand to be less inelastic when using data for shorter periods. In addition to problems with respect to the time period involved. the demand function may shift during the season. A limited amount of empirical work has been con— cerned with intraseasonal shifting of demand for fruits and vegetables. In demonstrating that intra-seasonal shifts in demand occur. it must be shown that intra-seasonal price changes cannot be explained by changes in quantity placed on the market. Mehren and Erdman found that the elasticity of demand for strawberries. computed from weekly data. in- creased as the season advanced.2 Foytik found that the demand function for plums shifted upward during the first few weeks of the marketing season and then began to drift downward.3 lBrandow. op. cit.. p. 20 and Bartter. L. M. Effects ongpple Supply_Management Programs in New York State. A.E. Res. 62. Cornell University. Dept. of Agricultural Economics. N.Y.. April. 1961. p. 3. 2G. L. Mehren. and H. E. Erdman. ”An Approach to the Determination of Intraseasonal Shifting of Demand.” Journal of Farm Economics. May. 1946. p. 595. 3J. Foytik. Characteristics of Demand for California Plums. Hilgardia. University of California. April. 1951. p. 487. 113 The estimated fresh apple demand relationships of this study indicate that apple prices at the farm level are more responsive to changes in sales in period I than in periods II or III. If these coefficients are correct. demand is least elastic in period I and most elastic in period III. If the elasticity of demand for apples varies between periods. it could be the result of a change in slope or level (or. some combination of the two) or a move along the demand curve. The less steep the slope at a given level. the more elastic is demand. Similarly. the higher the level with a given slope. the more elastic is demand. Hence. in comparing elasticities between markets. an increase in slope may be offset by an increase in level. so that the elasticity of demand remains unchanged. or even increases. In computing elasticities in periodsII and III. average prices and quantities were used. At these values. the ratio pit/ffit was equal to 1.87 and 4.86 in periods II and III. respectively. Thus. even though the slope (regression cpefficient of fmt) was greater in period III than in period II (Table 4). the increase in the ratio of average price to average quantity between periods II and III was enough to offset the change in slope so that demand was more elastic in period III. 114 In an effort to gain additional knowledge about intraseasonal shifts in demand. a more restricted fresh apple demand relationship was formulated and estimated. This model assumed no change in demand for fresh apples be- tween periods. allowing no shift either in the slope or level of the demand function between periods. The estimated relationship (by OLS) below for the period studied (1947-1961) had 45 observations and 40 degrees of freedom.1 of f =. —. . -. +. (9) pmt l 08 29f.mt + 53p(m_l)t 03 cmt 02ymt tb 3.46*** 4.84*** .61 .58 Partial r w/y - .48 + .61 - .10 +.09 s =.30.§2=.50 y.x All signs were ”correct” in (9). but the effects of cmt and ymt on price were not significant. Only half the variation in the dependent variable was explained by the four explanatory variables. This model was then adjusted to allow shifts by period in the intercept of the demand relationship. Three 0. l (dummy) variables (Qlt. Q 2t' and Q3t) were used. In any period m of year t. th has a value of 1 while the other In relationship (9). all variables are as defined previously except that price is in dollars per bushel. 115 two shift variables assume a zero value during this period. These shift variables allow changes in the level of demand by period while holding the slopes (regression coefficients) constant. The function to be estimated is of the form: f f = + (10) pmt O‘1‘211; + 01292‘: + 013931; aifmt + f329(m-1)t + §3Cmt + E34ymt In estimating this relationship. an overall constant term was included in the regression and Q1t was omitted.1 The equation to be estimated was then of the form f _ — a + (a2 — 0L1)Q2t + (a3 — 0L1)Q3t + 6 f (10a) pmt l 1 mt f + + 62p(m-l)t 53Cmt + B4Ymt In this formulation. o is the coefficient of Q1 1 t and is the intercept in period I. In (10a). the regression coefficients obtained for Q21: and Q3t are estimates of the difference between the intercept of the first and the second and third periods. respectively.2 The estimated demand function in this case had 45 observations and 38 degrees of 11f one of the dummy variables were not omitted. these variables and the vector of 1's for the constant term would be linearly dependent and a solution could not be obtained. 2R. L. Gustafson. ”The Use and Interpretation of 'Dummy Variables' in Regressions.” Michigan State University. Department of Agricultural Economics mimeo. January 30. 1962. 116 freedom. The OLS estimate of (10a) was: ~f f (10b) pmt - 3.08 + 1.05021: - .29Q3t - 1.23fmt + .26p(m-1)t tb 3.66***2.72*** .84 6.67*** 2.69*** Partial r w/y +.40 -.14 -.73 +.40 2.03 .4 tb 4 Partial r w/y +.3l -.07 s = .23, 3:52 = .70 y.x In (10b). coefficients of both income and competing fruits had incorrect signs. The results in (10b) indicate that the intercept in period II was significantly higher than the intercept in period I. That is. the coefficient of Q ( 2t a2 - o1) was positive and significantly different from zero. This was the expected result since demand from (5.1) and (5.2a) appeared to be more elastic in period II. With equal slopes. the more elastic demand would have a higher intercept. When slopes are. in fact. unequal. however. a model such as (10b) is not reliable in indicating the direction of change in the elasticity of demand between periods. As previously indicated. a change in level may more than be offset by a change in slope. Thus. results from (10b) cannot be used to make inferences about the relative elasticities of demand for fresh apples in periods I. II. and III. 117 One might view (9) as the most restricted demand relationship for fresh apples estimated in this study since it allows no change in either slope or level of demand between periods. Similarly. (10b) is less restrictive than (9) because it allows a change in level between periods but not in slope. Relationships (5.1). (5.2). and (5.3) are least restrictive. allowing changes between periods both in level and slope. In summarizing the results of the estimated relation- ships for fresh and processing apples. demand appears to be inelastic for total sales of apples in period I. The evidence mildly suggests that the demand for fresh apples is more inelastic than the demand for processing apples during the harvest period (period I).‘ Demand for fresh apples appears to become less inelastic as the marketing season advances and becomes elastic near the end of the marketing season. The implications of the apparent difference in demand of fresh and processing apples and the change in demand for fresh apples during the apple marketing season will be discussed in the next chapter. Estimated allocation and storage functions are now pre- sented. 118 Allocation Functions Although total production was assumed predetermined in any given year. the quantities channeled into the various outlets (flt' a and s t) are jointly dependent in period lt' 1 I. In this study. relationships were estimated to explain changes in the quantity of apples allocated to processors and in the quantity stored. The reasons that fresh and processing apples are really different commodities from the producer's standpoint were presented in Chapter IV. Allocation or supply functions to explain the quantity of (1) all apples sold to processors. and (2) canning and freezing apples sold to processors are presented below. These functions include variables expected to influence the allocation of apples to processors within any given year. The definition of the variables included in the allocation function for all processing apples follow: a f . ’ . alt' plt' plt were defined preViously. mt = per capita sales (in pounds) of Eastern apples in year t. n = per capita sales (in pounds) of apples pro- duced in other parts of the U.S. in year t. All Processing Apples.—-Single and simultaneous equation parameter estimates were quite similar in the allocation function for all processing apples (Table 5). 119 Table 5. Estimated allocation functions for canning and freezing and for all processing apples. - “_’ Regression Coefficients t values. & Partial gziiggiztand Constant Correlation Coefficientsa Estimation Term a f '-2 plt/pltb mt nt Sy.x R All Processing Apples OLS (ll)alt -7.57 +5.56 + .84 + .19 .49 .93 2.83*** 12.40*** 3.03*** + .65 + .97 + .67 TSLS (lla)a1t —7.80 +5.92 + .84 + .19 .63C .92C 2.77*** 12.38*** 3.05*** + .64 + .97 + .67 Canning and Freezing Apples OLS (12)a'1t -0.56 +1.94 + .57 - .21 .63 .74 1.06* 6.29*** 2.76 + .30 + .88 - .64 TSLS (12a)ait -0.53 +1.89 + .58 - .21 .64C .73C .89* 6.09*** 2.69 + .26 + .88 — .63 at values of the regression coefficients appear just below the coefficient to which they apply. Partial correlation coefficients are below the t values. I bIn (12) and (12a). pit/pit was used instead of a f plt/plt° CIn two-stage least-squares regression procedures. all current endogenous variables in the equation (to be estimated) except the variable considered dependent in the second stage are replaced by a linear combinatiop of all the predetermined variables in the system. S and R values presented are based on estimated instead Y6? observed values for all current endogenous variables except the variable which is dependent in the second stage. 120 In each case, (11) and (11a), the three explanatory variables explained more than 90 percent of the year-to-year variation in sales of processing apples from 1947-1961. The discussion which follows pertains to (lla). Price Ratio.--A large part of total apple pro- duction consists of dual purpose varieties. These apples are suitable for use in either fresh or processing outlets. Under these circumStances. we expect the allocation of apples among alternative uses to be influenced by prices in fresh and processing apple markets. The ratio of processing to fresh price ranged from 0.32 to 0.57 during the period of analysis. In (11a), an increase in the price ratio of .l is associated with an increasein processing sales of .59 pounds per capita. This result is consistent with economic logic. We expect that for a given level of m and n . producers will sell t t more to processors if pit/pit is high than if this ratio is low. Eastern Production.--A.much higher part of the Eastern states' crop goes into processing uses than is true for production in other parts of the United States. Thus, it is not surprising that Eastern production was a more important explanatory variable (in the allocation function) than other production as evidenced by the higher partial 121 correlation coefficient. An increase in Eastern production of 3.8 million bushels (one pound per capita at 1961 popu- lation level) was associated with an increase in total apples processed of 3.2 million bushels. Other Production.--Apple production in non-Eastern states is channeled primarily into the fresh market, but apple processing has some importance in all areas. As production increases more of the apples in the non-Eastern states are processed. under these circumstances, we expect an increase in production to be associated with an increase in apples processed. In the estimated relationship, an increase of one pound per capita in non-Eastern apple pro— duction was associated with an increase in all apples processed of 0.19 pounds per capita. An alternative allocation function for all processing apples was also estimated. This relationship was: a pa m (11b) '—£E = -.06 + .10—LE + .74 ———£L-—' qlt pf mt + nt lt t 1.07* 4.49*** b Partial r/y + -29 + .79 Sy x = .03. P? = .61 where All variables are as defined previously. The proportion of production processed (alt/qlt) varied from 0.23 to 0.37 during the period of analysis. 122 An increase in the ratio of processing to fresh apple prices, as expected. was associated with an increase in the proportion of the total crop processed. An increase in the proportion of the crop produced in the East, where apple processing is concentrated, was also associated with an Aincrease in the proportion of the total crop processed. Although changes in both explanatory variables had the ”correct? effect upon changes in the dependent variable, the coefficient of multiple determination (adjusted). 5?, was much lower than in the previously estimated allocation function (see [11a] in Table 5). Canning_and FreezingJApples.--The allocation functions presented above were for all apples processed. An allocation function was also estimated for canning and freezing processing apples. This portion of apples processed is by far the most important part of all apples processed. Canning and freezing apple sales. a' include virtually all lt' of the apples processed which have the fresh market as an alternative outlet. Variables included in this allocation function have been defined previously in the analysis. The OLS and TSLS estimates of the allocation function for canning and freezing apples differed very little (Table 5). Price Ratio.--During the postwar period, the 123 ratio piL/pft varied between 0.42 and 0.73. The effect of a change in price ratio on quantity (of apples canned and frozen) was less than in the allocation equation for all processing apples. The canning and freezing processing industry is concentrated in the Eastern states to a greater extent than is true of the total processing industry. In addition, higher quality apples are required for canning and freezing purposes than in other processing outlets. under these conditions, it is not surprising that the allo- cation response to a change in price ratio should be less pronounced for canning and freezing apples than for all processing apples. Eastern production.--An increase of one pound per person in Eastern apple production was associated with an increase in sales of canning and freezing apples of 0.58 pounds per capita ([12a] Table 5). Apples in addition to those used in canning and freezing outlets are processed in the Eastern states. Since a' is included in a 1t lt' it follows that any given increase in Eastern production is likely to be associated with a larger change of a1t than of a' . 1t Other Production.--An increase in non-Eastern production was associated with a decrease in sales of canning 124 and freezing apples. The reason is not clear why the coefficient of "other production" is negative. Some apples are sold into canning and freezing outlets outside the Eastern states. Other factors equal, a portion of any increase in apple production in these areas would likely be sold to processors for canning and freezing. In general. the estimated allocation functions appear satisfactory. The three explanatory variables explain a large proportion of the annual variation in sales of pro- cessing apples. This is especially true of the allocation function for all processing apples. Storage Functions Apples not allocated by producers into fresh or processing outlets in period I are stored and sold later in the fresh market. Hence, the quantity of apples stored in period I is jointly determined with quantities moved into fresh and processing outlets. slt represents the quantity of apples stored in period I and is positive. In period II. the quantity of apples remaining in storage and fresh sales from storage. f2t' are jointly determined. In the storage function of period II, s2t is negative. This is true since 3 = S - S and S1t > 82 2t 2t 1t t (some apples always move out of storage in period II). 125 Since s2t is negative. an increase of a predetermined variable with a positive sign is associated with a decrease in apples moving from storage. All apples in storage at the beginning of period III are sold during the period. Consequently, storage movement in period III, s is predetermined. 3t' Period I.--The variables included in the storage function of period I follow: f a' . . plt' plt' mt. and nt are as defined preV1ously. Slt = Slt ' S3(t-1) Slt = the per capita quantity of apples in storage (in pounds) at the end of period I of year t. = the per capita quantity of apples in storage (in pounds) at the beginning of period I of year t (83(t-l) s 0). 83(t-l) The estimated (OLS) storage function for period I was 3 - pit (13) s1t = -3.71 + .18-37 + .25mt + .67nt plt tb .24 2.05*** 6.52*** Partial r/y +.07 +.53 +.89 Sy.x = .85, ‘E2 = .80 1The results were virtually the same when the function was estimated using TSLS regression procedures. In neither case did a change in the price ratio have a significant effect upon Slt' \rl 126 Price Ratio.--A change in the ratio of fresh to processing apple prices had no significant effect on the quantity stored in period I. This is not surprising in view of Gustafson's findings.l Production.--Increases in Eastern production, m and in other production, n , were associated with in- t' t creases in the quantity stored in period I. These two variables explained more than 80 percent of the annual variation in December 1 storage holdings from 1947-1961.2 An increase in Eastern production, however, had a smaller effect on initial storage than an increase in production in other areas. This seems reasonable since a larger proportion of ”other? production is moved in the fresh market. Period II.--The storage function of period II con- tained only one dependent variable and was estimated by single equation regression procedures. The estimated relationship was: A=—. -. +. (14) SZt 1 90 58$1t 04klt tb l4.67*** 1.70** Partial r/y ' -.97 +.46 S a .27.;2 = .95 y.x 1This point is discussed more fully following the estimated storage function of period II. 2 2When the price ratio was eliminated from the analysis, R = .81. ‘6 127 where S is as defined previously. Szt = Szt - Slt (I) II the per capita quantity of apples in storage (in pounds) at the end of period II of year t. “I II the percent of all stored apples in CA storage at the beginning of period II. Storage Holdings at the Beginning of the Period.—- An increase of 3.8 million bushels (one pound per capita at 1961 population level) in initial storage stocks was associated with an increase of 2.2 million bushels in the rate of movement from storage. This variable alone explained about 93 percent of year-to-year changes in storage stocks during period II from 1947-1961. Thus, a knowledge of storage in period I provides a good indication of the rate of movement from storage and, hence, price since changes in sales were found to explain a large part of the price variation of periods II and III. Predictive equations for fresh price in periods II and III using S as an explanatory 1t variable are presented in the following chapter. CA Storage.——The CA storage technology enables a higher quality product to be stored for a longer period of time. Some varieties of apples may be held in CA storage facilities until period III with little deterioration in quality. In recent years, an increasing percent of all 128 apples stored have been placed in CA storage and held until period III. In (14), an increase of one percent in CA holdings as a percent of all storage holdings was associated with a decrease of .04 pounds per capita in the rate of movement from storage in period II. At the 1961 population level, this is equivalent to 154,000 bushels. The preceding results indicate that the aggregate behavior of apple storage operators in periods I and II can be represented quite accurately by simple functional relation- ships of the type suggested by Gustafson.l Under the con— ditions specified by Gustafson, changes in aggregate quantity of the commodity stored or carried over during any period can be explained by changes in the total supply during the period. The total supply consists of the quantity carried in from the previous period plus the quantity produced during the period. There are no apple stocks at the beginning of period I. Thus, production, mt + nt, constitutes the total supply. These two variables were found to explain more than 80 percent of the variation in initial storage stocks. l R. L. Gustafson, ”Storage of Pork,” pp. 41—44. 129 In period II, there is no production. Consequently, initial storage holdings, Slt' constitute the total supply during period II. Changes in Slt were found to explain more than 90 percent of the variation in storage movement during period II. CHAPTER VI IMPLICATIONS OF RESULTS There is current interest in exploring alternative marketing policies for the apple industry. In this section, the economic implications of several methods of controlling supply are evaluated. In addition, predictive equations for fresh and processing apple prices are presented and illustrative apple Fstorage rules? are developed based on these price predictive equations. Before discussing apple programs as such, general methods and problems in controlling distri- bution are discussed. Theoretically, there are two major approaches which may be used by a monopolist in controlling the distribution of a commodity being sold in two or more markets.2 A diversion program may be instituted in which a portion of the Production controls have not been proposed in the apple industry and will not be discussed. 2For a monopolist to profitably practice price discrimination, three conditions are necessary: (1) the seller must be able to separate the market, (2) demands in the various separable parts of the market must be 9considerably different,9 and (3) the cost of separating the markets must not be too large. G. J. Stigler, The Theory of Price (Revised edition; New York: The Macmillan Co., 1952), pp. 215-216. 130 131 product is diverted from markets having lower elasticities into markets with higher elasticities until the marginal net revenues are equal in each market. In the diversion programs which have been adopted in agriculture, demand in the market yielding the highest price is more inelastic than in lower value uses. Hence, sales of the product are restricted in the high price market and channeled into lower value uses. The California lemon program is an example. Lemons are diverted from the inelastic fresh market into the more elastic juice market. Another approach in controlling distribution of a commodity is to restrict the total quantity marketed. Such a program may or may not be applied in conjunction with a diversion program. Demand conditions are also crucial in the operation of a program limiting the total quantity marketed. For simplicity, assume there is only one market for the product. The quantity marketed under such a program would be restricted to some specified level. Unless demand were inelastic, however, this program would not increase total returns. General Problems A number of theoretical and practical problems re- strict the usefulness of supply control programs of the types 132 described above. Some of the major problems are described at this point. Determining Appropriate Elasticities.--Elasticities vary according to the period of time involved. Due to data limitations, the elasticity of demand for agricultural commodities is most readily computed from annual data. waever, demand for a semi-perishable product computed in this manner is likely to give its minimum elasticity. For a commodity with alternative outlets, the appropriate elasticities in controlling distribution are those which prevail at the time the allocation decision must be made. Demand conditions at this time may differ greatly from the average demand based on annual data. For most agricultural commodities, which may or may not have a large number of grades, varieties, etc., the necessary data are not avail- able to compute within season elasticities. Under these conditions, a commodity which appears to have an inelastic demand based on annual data may have an elastic demand during that portion of the marketing season when the quantity marketed is to be restricted. A closely related problem centers around the question of whether farm or retail elasticities are to be chosen as the basis of action. Consider a commodity selling in two retail markets, say in fresh and in processed 133 form. The demand in the fresh market is likely to be less elastic than in the processed market due to the relative availability of substitutes for the two products. Assume this to be true. It is quite possible that the derived demand at the farm level would be less elastic for the product channeled into the processing market. In general, we expect marketing margins to be greater for products which are more highly processed. Hence, the derived demand for the processed product (relative to the fresh product) would be more inelastic at the farm if the difference in marketing margins was enough to offset the difference in elasticities at the retail level. Thus, a knowledge that elasticities differ at the retail level for a commodity being sold in different markets does not imply that the derived elasticities at the farm level would have the same ordering. Changes in Elasticity.--The fact that elasticities may change over time is another important consideration relating to supply control programs. A.marketing policy relying on either diversion or restricting the quantity of sales may itself bring about a change in the elasticity of demand. The California lemon industry provides a classic example of the problems arising out of an attempt to increase 134 producer income through a diversion program. In this Vprorate? program, growers have attempted to increase average returns by exploiting an assumed inelasticity of demand for fresh lemons. Both the effect on long-run market demand and on long-run production apparently have been disregarded. The program is steadily forcing fresh lemons out of the market by subsidizing processed lemon products. The result is that grower returns per carton in the long run have not been increased. Foreign Competition.--The world-trade situation is another important factor to consider in restricting supply. The maintenance of domestic price above world market prices for a semi—perishable or storable commodity requires permissive legislation in the form of import tariffs, quotas, etc. Such barriers must be implemented to prohibit the substitution of the cheaper import for the more expensive domestic good. In the absence of import controls, imports, to a great extent (for many products), could negate the effect of any policy of restricting supply. Production Response.--If returns increase above a normal level of profits, production will tend to increase. 1R. J. Smith, FThe Lemon Prorate in the Long Run,9 The Journal of Political Economy, December, 1961, p. 586. 135 Hence, if an industry is in equilibrium and the method employed in controlling distribution is effective in raising average price, there will be an appropriate adjustment in production. This problem has been evident in the acreage control and price support programs for agricultural products. Apple Marketing The previous discussion is relevant in considering marketing policy for any commodity. The following analysis is related specifically to apple marketing. In analyzing present and proposed apple marketing policies, we must recognize (l) differences in demand elasticities between fresh and processing apples at harvest and (2) changes in the elasticity of demand of fresh apples during the apple marketing season. The economic implications of proposed diversion or quantity control programs for apples will now be discussed. Diversion.--A diversion program for apples was recently discussed.1 This program consists of a utilization model which would control sales of fresh apples at: the farm level and allocate the surplus to various processing l . . . . W. S. Greig, Max1m121ng Total Dollar Sales oprpples and Apple Products by a Utilization Model, MSU, Ag. Econ. 889 August, 1962, p. 22. 136 outlets. The underlying premise of such a program is that the demand for fresh apples is more inelastic (at the farm level) than the demand for apples going to processors. Empirical evidence concerning the relative elasticities of demand for fresh and processing apples at the farm level is mixed. Tomek in a recent study covering the period 1947—1961 (using annual data) found fresh apples to have a slightly more inelastic demand than processing apples at the farm level.1 The quantity of apples sold in the fresh market, when con— trasted with the quantity sold to processors, is more stable from year to year. That is, a larger percent of apples are sold in the fresh market in small crop years and a smaller percent in large crop years. This fact supports the findings of Tomek that the demand for fresh apples is, in fact, more inelastic than the demand for processing apples. Assuming Tomek's results are true, let us consider the effect of diverting a bushel of applesiiom the fresh market to the processing market. Using a simultaneous equations approach, Tomek estimated elasticities of demand at -0.4 and -0.6 for fresh and processing apples, respectively. W. G. Tomek, VAn Analysis of the Utilization of Apples at the Farm Level in the United States? (unpublished manuscript, February, 1963). 137 Harvest prices for fresh and processing apples averaged $1.93 and $0.82 per bushel, respectively,during the postwar period. At these prices and using Tomekfs elasticity estimates, a bushel of apples diverted from fresh to processing would increase total revenue by about $2.35.1 Marginal costs are also higher for harvesting and selling fresh apples. Evans found that grower costs in the Appalachian Area were from $0.96 to $1.28 more per bushel when selling on the fresh market.2 Hence, diverting a bushel of apples from fresh to processing outlets would likely decrease total costs, although a diversion program would require increased costs of grading and sorting. Thus, a diversion program for apples theoreticallynight have a large effect on net revenue even when the elasticity coefficients are not much different for fresh and processing apples. Using MSU consumer panel data, Greig found that processed apple products relative to fresh apples were more lMarginal revenue fresh = 1.93 (l + l/—.4) = -2.89. Marginal revenue processing = 0.82 (l + l/-.6) = -0.55. 2Evans, op. cit., p. 47. 138 elastic at retail.1 This finding seems reasonable since we usually expect the processed form of an agricultural product to have a more elastic demand. Greig then assumed that the derived elasticities of demand at the farm level had the same ordering as at retail. If marketing margins (as a percent of retail price) were the same in each market, the elasticities of demand at wholesale would have the same ordering as at the retail level. However, dollar marketing margins tend to be in- flexible as the quantity marketed changes. Also, processing and distribution costs are likely to constitute a larger proportion of retail price for processed apples than for fresh apples.2 Under these circumstances, the elasticity of demand for processing apples could be lower at the farm level. lUsing annual data cited by Greig for the years 1953-1957, this writer estimated retail demand elasticities for fresh apples and apple sauce of -.34 and -3.4, respectively (these results agree with findings reported by Greig). The estimated relationship for fresh apples, was of the form Q = a + bP. The standard error of b was almost as large as b indicating that the effect of P was not significant. In this situation, changes in quantity were not closely associated with. changes in price and R = .09. Hence, the estimated elasticity of demand for fresh apples is not reliable. 2Dalrymple quotes estimates of marketing margins for fresh and processed apples of 66 and 79 percent (of retail price), respectively. Dalrymple. op. cit., p. 244. 139 Brandow and Bartter estimated the demand for fresh and processing apples at the farm level. The demand was inelastic for each, but processing apples had the more inelastic demand.1 However, these estimates were based on annual data and results from the previous chapter indicate that the elasticity of demand for fresh apples varies widely during the marketing season. If demand at harvest (when virtually all processing apples are moved) is more inelastic for processing apples than for fresh apples, the utilization control program discussed by Greig would decrease instead of increasing total returns to producers. In the present study, total apple sales (fresh plus processing) in period I were found to have an inelastic demand. A satisfactory demand function for processing apples was not obtained in this study. The evidence mildly indi- cated that fresh apples in period I had a more inelastic demand than the demand for total sales, implying that the demand was more elastic for processing apples. The analysis was not adequate, however, to conclude that there was, in fact, a difference in the elasticity of demand in processing and fresh apple markets. In view of the uncertainty and lBrandow, op. cit., p. 20 and Bartter, op. cit., p. 3. 140 conflicting empirical findings with respect to the relative elasticities of fresh and processing apples at the farm level, a diversion program for apples does not appear feasible to this writer. In addition to the theoretical problems, there are a large number of practical problems in setting up a diversion program for the apple industry. In the first place, data are not available for variousapple grades, varieties, etc. In addition to data problems, there are a host of adminis- trative problems. Any program of this type, if effective, would increase returns to producers of fresh apples at the expense of processing producers. Such a program would not likely be favored by producers of processing apples. The type of apples produced varies by region but there is a high degree of market interdependence between regions. Hence, any diversion program on a state or regional basis would be strongly tempered by imports from other areas. A diversion program which changed the relative prices between uses would also require policing to keep the markets separated. .Quantity Limitation.--A volume control program has also been discussed for the apple industry.1 Under this lBartter, op. cit., p. 1. 141 program, apples less than a given size would be prevented from entering the market. The restriction might be placed only on the sale of processing apples or on sales of both fresh and processing apples. Such a program is based on the assumption that apples have an inelastic demand (in the market[s] to be restricted) at the farm level. Even if this requirement is met, the problems described earlier would persist. These are: (l) demand becomes more elastic in the long run accentuated by the price increase; (2) foreign competition is increased; and (3) in the long run, production would tend to increase in response to higher prices. Even if the theoretical problems were resolved, a host of practical and administrative problems would remain as under a diversion program. The operation of this program requires a knowledge of demand conditions for apples of various sizes. This information is not available. The quantity to hold off the market and the method of doing so present formidable administrative problems. Some regions and some producers have a higher proportion of smaller apples. In a quantity limitation program based on size, these pro- ducers would, in effect, be subsidizing producers having fewer small apples. On the basis of the preceding discussion, it is far from certain that either a general diversion or a quantity 142 limitation program would be an effective means of increasing returns to the apple industry. At this point, a number of potential measures for increasing returns (in some cases involving qualitative controls) are mentioned. These measures may be subsumed under a general heading called product promotion. These measures are beyond the purview of this study and will not be evaluated. Product Promotion.--A wide range of activities may be included in policies of product promotion. Advertising is one method widely used in promoting the sellers' wares. A specific commodity may also be enhanced in the eyes of the buyer through various merchandising practices which recognize market preferences with respect to size, quality, packaging. etc. In general, the costs and returns from programs of product promotion are difficult to assess. In the apple market, a strong consumer preference for high color fruit has been recognized. The preferred type of retail pack for applesappears to vary by region. Observing and following market preferences such as these could increase grower returns if the cost of complying with market preferences does not more than offset the increase in returns. Such programs might entail a degree of supply control and require more care in holding lower quality apples off the fresh market. 143 Bargaining.--Currently, there is interest on the part of apple producers in bargaining activities with apple processors. Available evidence indicates that competitive pressure is strong among processors and that net returns are equal from processing and fresh apple sales.1 In the event that processors are not making excess profits, bargaining efforts could be expected to have little effect on price in the absence of supply restrictions. If apple processors are not realizing monopoly gain as a result of their oligopolistic position, bargaining in conjunction with a program of controlled distribution on the part of producers would be subject to the same theoretical and practical limitations discussed previously. As in the previous case, theoretical and practical obstacles would be formidable in developing and administering such a program. Predicting Processing Apple Prices A high proportion of apple production consists of dual purpose varieties. Growers of these varieties have the choice at harvest of immediately selling their apples in the fresh or processing market or of storing part, or all of them, in anticipation of later fresh price advances. 1Evans, op. cit., p. 90 and Bartter, op. cit., p. 6. 144 This decision requires that judgments be made about seasonal price movements for fresh apples and about the price of processing apples. Farm prices of canning and freezing apples have varied widely from year to year during the postwar period. Widely varying prices mean more attention must be given to questions of when and where to market the apples pro- duced. Producers and processors need information prior to harvest in making plans for the ensuing apple marketing season. A knowledge of the market clearing price for canning and freezing apples should be of value to producers in determining quantities to sell (in various outlets) and store at harvest. This information would also assist processors and food manufacturers in planning their operations. Results from a recent study indicate that the U.S. season average farm price of canning and freezing apples can be estimated quite accurately by using data that are . . l . available early in the marketing season. Information 1E. C. Pasour and D. L. Oldenstadt, Farm Prices of .Apples for Canning and FreezinngUnited States 1951-61, Agricultural Economics Report No. 35, Marketing Economics Division, ERS, U.S. Department of Agriculture in cooperation with Michigan AES, MSU, June, 1963, p. 14. 145 on the economic factors, July crop estimate, July processed canner stocks, and July farm price of fresh apples explained almost 90 percent of the year—to-year variation in deflated farm prices of processing apples from 1951 to 1961. Data concerning these three economic factors are available early in the marketing season. The estimated predictive equation for farm price of canning and freezing apples follows.1 «a' _ f (1) plt — 130.68 112.04ejt 21.33A1t + 6.49pjt tb 2.88*** 3.69*** 1.11* Partial r/y -.79 -.86 +.44 w n in ." (D u 5.53 where p1t = deflated U.S. season average farm price of canning and freezing apples in dollars per ton in year t. — U.S. Department of Agriculture July apple crop estimate (for the U.S.) in bushels per capita in year t. ejt Alt = July canner stocks of canned and frozen apple slices and sauce on a pound per capita fresh equivalent basis in year t. The relationship which appears in the publication cited contained a trend variable which did not have a signifi- cant effect. This variable was eliminated and the other coefficients re-estimated to obtain the relationship presented. 146 f P jt = deflated U.S. average July farm price of fresh apples in dollars per bushel in year t. All signs in (l) are as hypothesized. Increases in both July apple crop estimate and in carryover canner stocks were associated with decreases in the season average farm price of canning and freezing apples. An increase in July fresh price, however, was associated with an increase in I pit. The interpretation of the three regression coefficients in (1) follows. Ju1y_Crop Estimate.--An increase of 0.1 bushel per capita (18.4 million bushels at the 1961 production level) was associated with a decrease of $11.20 per ton in the deflated season average farm price of canning and freezing apples. The July crop estimate was between 89 and 124 million bushels during the period of the estimated relationship. July Stocks.--July canner stocks of canned and frozen apples and apple sauce ranged from 0.345 to 1.622 pounds per capita, on a fresh equivalent basis, during the period 1951-1961. An increase of 0.1 pound per capita was associated with a decrease of $2.13 per ton in piL. July Price of Fresh Apples.--During the period 1951- 1961, July fresh apple price (deflated) was between $1.11 and $2.48 per bushel. An increase of $0.10 per bushel in 147 I July fresh price was associated with an increase in pit of $0.65 per ton. The results presented above indicate that canning and freezing apple prices can be estimated quite accurately early in the season so long as the factors in (1) associated with processing apple prices continue to have the relationship of the estimated period. Predicting Fresh Apple Prices Period I.--Fresh apple price, relative to processing price, is more difficult to predict early in the marketing season. A predictive relationship for fresh price in period I (July-November) was estimated in this study. In this relationship, the explanatory variables were July fresh price and the July U.S. Department of Agriculture apple crop estimate.1 Information concerning these variables is available at the beginning of the marketing season. This estimated relationship based on data for the period 1947-1961 was: lLagged fresh price, was initially included P l 3(t-l) as an explanatory variable in this relationship. The effect of lagged fresh price, however, was not significant at the .10 level and it was dropped from the equation. 148 (2) 8ft = 2.33 + .3919)?t - 1.76ejt tb 1.73** 3.49*** Partial r/y +.46 -.72 Sy.x = .14, R? = .67 where pfit and ejt are as defined in the predictive equation for canning and freezing apple prices and pit = deflated U.S. average farm price per bushel (in dollars) of fresh apples in period I of year t. Changes in period I fresh price were highly associated with changes in total production or forecast.l Taken to- gether, July fresh price and apple crop estimate explained almost 70 percent of the variationin period I fresh prices from 1947-61. Periods II and III.--After period I, fresh prices vary inversely with the quantity of apples in storage at the end of period I. During the postwar period, changes in the quantity of apples in storage at the beginning of period II, Slt' explained about 85 and 75 percent of the annual variation in fresh price in periods II and III, respectively. These relationships estimated by OLS are: The July apple crop estimate during the postwar period has been quite accurate as an indicator of total production. 149 45f _ (3) p2t — 4.36 .21Slt tb 8.25 s - .18, 82 = .83 y.x (4) ‘f - 4 93 - 24s p3t ‘ ' 1t —2 t 6.31 S = .27, R = .75 b y.x where Pit = deflated U.S. average farm price per bushel (in dollars) of fresh apples in period m and year t. Slt = the per capita quantity (in pounds) of apples in storage at the end of period I in year t. After period I, there is no production, and storage stocks constitute the total supply of apples. All of the apples in storage at the end of period I are moved by the end of period III. Under these conditions, it is not surpris- ing that the quantity initially stored has a highly signifi- cant effect upon price in both period II and period III. In the following section, apple storage problems are discussed and storage rules are formulated which appear to reduce the year-to-year variability in seasonal price move- ments. Storage In earlier sections of this chapter, marketing policies arising out of possible differences in elasticities 150 31 ifnresh and processing apple markets were evaluated. Another Prtihilem revolves around the question of how to optimally 315L<3cate fresh apples during the marketing season. That is, i1I‘view of the apparent shifts in demand during the marketing Sfiaason and the uncertain seasonal price movements, what is the 11flarketing pattern for fresh apples that would maximize net Ireturns to the apple industry. Optimum Allocation Over Time.--Theoretically, returns can be maximized by allocating a commodity over time in the same way as between different markets in any given point in time. Net returns would be maximized when the marginal revenues were equal in each time period assuming marginal costs were equal. In this situation, sales would be increased in periods of more elastic demand at the expense of periods of less elastic or inelastic demands. When a difference in time is involved, there is usually a difference in total costs due to storage costs and, hence, in marginal costs. The allocation principle remains the same, however, when marginal costs differ in different time periods. In such cases, net returns would be maximized by equating marginal net revenue in each time period, where marginal net revenue is defined as the difference between marginal revenue and marginal cost in any market. 151 In the case of apples, net returns would be maximized over time by equating properly discounted marginal net revenues in fresh and processing markets for periods I, II, and III. Information relating to storage costs and demand conditions in various periods of the apple marketing season is necessary to determine the most profitable marketing pattern. The attempt to determine Separate demand functions for fresh and processing apples during the harvest period in this study was not successful enough, it was felt, to warrant using the estimated functions as the basis for constructing marginal revenue functions. Estimated price prediction equations, on the other hand, seem relatively satisfactory. In the following section, to illustrate the possibility of storage decisions being improved by use of the price prediction equations, storage Frules? are developed such that (a) the quantity in storage at the end of period m (for m = 1.2) is a specified function of variables observable in or before period m, and (b) the parameters of the function are determined so as to equalize the marginal cost of storage and the expected change in price. Equating marginal cost of storage and expected change in price does not maximize producers' or storers' expected revenue, but it does maximize the expected Fsocial value” of storing activity, provided one accepts market price 152 as the measure of the Fmarginal social value" of the commodity in utilization. 2 Storage Rules The average seasonal price increase during the period 1947-1961 was $0.26 per bushel. Storage costs are about $0.23 per bushel for regular storage and $0.37 per bushel for CA storage and most apples are stored in regular storage facilities.3 Hence, on an average, the seasonal price increase appears to have approximated the cost of storage. However, there has been wide variation from year to year in within—year price movement (Table 1, page 6). and ipgp fagpp large deviations in particular years from equality of price change with cost of storage. Storage costs used in the following analysis were taken from Thompson's study of apple storage costs in New York State.4 As indicated in Chapter IV, however, storage costs appear to be fairly constant over the U.S. Marginal l . See Gustafson, garryover Levels for Grains. 2The procedure followed in this section is similar to the method used in Gustafson, VStorage of Pork.9 3Thompson, op. cit., p. 56. 41bid., 153 costs of storage were assumed constant. After apples are stored, variable storage costs are quite low. Storage costs between periods I and II and between periods II and III were taken to be $0.22 and $0.04 per bushel, respectively.l Estimated price predictive relationships used in developing storage rules were adapted from relationships previously analyzed.2 These relationships for periods I, II, and III are: (2) pit = 2.33 + .39pft - 1°76ejt 'E? = .67 (5) figt = 5.21 - 1.47:52t - .0le 32 = .84 (6) {Sgt = 3.63 - 2.441th + .OlTl 132 = .73 where pit = deflated U.S. average farm price per bushel (in dollars) of fresh apples in period m of year t. pf = deflated July U.S. average farm price per bushel Jt (in dollars) of fresh apples in year t. e.t = July U.S. apple crop estimate of year t in pounds J per capita. fmt = per capita sales (in pounds) of fresh apples in period m and year t on a monthly basis. The cost of storage in each period was weighted by the average percent of apples in regular and CA storage facilities in that period. 2Lagged price was eliminated as a variable from (5.2) and (5.3) in Chapter V and the relationships were re-estimated replacing Cmt and Ymt with a trend variable. When lagged price is left in. the quantity to store in the storage rule for period I or II becomes a function of current price. 154 T1 = trend (1947 = l, 1948 = 2. . . . , 1961 = 15). Relationship (2) was used instead of the fresh apple demand relationship of period I estimated in the previous chapter. As a fresh price predictive relationship, (2) explained a higher percent of the period I price variation and contains explanatory variables estimated by the U.S. Department of Agriculture early in the apple marketing season. Storage Rule for Period II.—-In determining how many apples should be in storage at the end of period II, SZt' the expected price change between periods II and III is equated with marginal cost of storage between these periods. That is, the equation to be satisfied is (7) 5.21 - 1.47f2t - .02Tl = 3.63 - 2.44f3t + .01Tl - .04 where the left side is price in period II, the first three terms on the right are expected price in period III and the fourth term on the right is the (constant) marginal cost of storage between periods II and III. The quantity of sales during period II. f2t' is equivalent to the quantity in storage at the beginning of period II, Slt' less the quantity in storage at the end of the period, SZt' All apples in storage at the end of period II are moved during period III. Consequently, f31: = S2t° 155 Substituting (Slt — SZt) for f2t and S2t for f3t , we obtain S as a function of in (7) and solVing for S2t 2t Slt and T1' When these substitutions are made, the storage rule of period II is: = . + . + . (8) S2t 41 38S1t 01Tl where S t = the quantity of apples stored at the end of period m m in year t in pounds per capita. Thus, the quantity of apples in storage at the end of period II under rule (8) is a positive function of the quantity on hand at the beginning of period II and the trend variable.1 Storage Rule for Period I.--In period I, the equation to be satisfied is: (9) 2.33 + 39p:t - 1.76ejt = 5.21 — 1.47f2t - .02T1 - .22 where the left side is price in period I, the first three terms on the right are expected price in period II, and the last term on the right is the (constant) marginal cost of 1The storage rule for period II when net marginal revenues are equated in periods II and III (instead of equating the expected price change) follows. From (5) and (6) and the cost assumption, it follows that f f = 3.63f - 2.44f 2 + .OlT f TRIII = P3t 3t 3t 3t 1 3t 156 storage between periods I and II. Substituting (Slt - S ) 2t for f t and equation (8) for S gives the following storage 2 2t rule for period I: (10) s = 2.26 - .43p§t + 1.93e. - .OlT lt 3t 1 In this case, the quantity stored in period I is a function of July fresh price, July crop estimate and the trend variable. f 2 TRII = P2tf2t = 5.21f2t - 1.47f2t — .02Tlf2t TC = .04321: Then = . - . + MRIII 3 63 4 88f3t .OlTl MRII = 5.21 - 2.94f2t - .02Tl MC = .04 set... EEPStitfifilng fitM; Saadfiiliga a22.82t :0. f3t' 9 II III ' 9 2t. we obtain the storage rule " =-. . +. SZt 21 + 38S1t 004Tl which maximizes net returns in periods II and III. This rule is quite similar to (8). The coefficient of Slt (the slope) is the same in each case, while the level of S2t for a given quantity of Slt is lower in the case where net returns are maximized. Both the Fderived? storage rulesibr period II are very similar to the empirically estimated Vobserved? storage equation for that period which was A or (Since S2t = Slt + Sgt) 157 Applicationof Storage Rules After computing the storage rules ([8] and [10]), they were applied to the years 1947-1961 to see what dif- ference their application would have made in the variability of seasonal price changes. For each year 1947—1961, using equation (10), the quantity was computed that would have h been stored in period I applying the storage rule, Slt' Then substituting the quantities that would have been stored into (8), S was under the storage rule of period I. § 2t 1t’ computed for each year of the analysis. After computing glt and §2t from the storage rules, sales for period II and III under the storage rules were & a computed. In these computations. f2t = Slt - S2t and f3t = SZt' Then the demand functions estimated in this study were used to determine the price that would have occurred in periods I, II, and III had the storage rule been in effect. The observed price of each period was adjusted as follows:1 0 mt - bm(fm — f (11) pmt = p t mt) where The following procedure assumes that other factors affecting demand, e.g., competing fruits, income, etc. would not have been affected by the storage rule. 158 E t = the price which would have occurred in period m m of year t had the storage rule been in effect. pit = the observed price in period m of year t. b = the regression coefficient of sales in the fresh m . . apple demand function of period m. fmt = quantity of sales in period m of year t under the storage rule. fit = the actual quantity of sales in period m of year t. In period I. the difference in total apple sales due to the storage rule during the period 1947-1961 would be & So ), where S0 is the quantity actually stored in (Slt ‘ 1t lt * period I and S is the quantity that would have been stored lt under the rule (10). In computing filt, bl was the regression coefficient of sales in the estimated demand relationship (of period I) for fresh and processing apples presented in the previous chapter.1 The change in fresh sales in period II that would have occurred had the storage rules been applied was determined as follows. Since. in general. f S . mt = S(m-1)t — mt we have: 1A weighted price (weighted by flt and alt) was used as the price indicator in the demand relationship for combined fresh and procesSing sales. When this function was re—estimated with pft as the dependent variable, the coefficient of (alt + flt) changed very little (from -1.17 to -1.15). ~ 0 o - = — + ‘ - (12) f2t th S1t S1t b2t SZt where all quantities are as previously defined. In period III, f3t = Szt’ * * Therefore, f - f° = 8 ° 3t 3t 2t ’ Szt' After computing the prices which would have occurred in period m and year t under the storage rules. 5 . seasonal mt I I ~ 0 I price changes in pmt were compared With seasonal price changes in observed price. pat. This comparison follows. o _ o _ o o = o _ o o = o _ o Let D12 " p2t plt' D23 p3t p2t' D13 p3t plt and D12 = p2t ' plt' D23 = p3t ' p2t' D13 = p3t ” plt Dij is the observed price change between period i and j, and fiij is the price change between periods i and j which would have occurred under the application of the derived storage rules, (8) and (10). The variance of Dij and fiij were computed for the period 1947—1961. These results are summarized below. Periods of the Analysis I - II II - III I - III Variance of Dij 0.095 0.089 0.212 Variance of fiij 0.089 0.064 0.053 Ratio of variances (eStlmated) 0.937 0.719 0.250 observed Percent decrease in variance under the derived storage rule 6%. 28% 75% There was a large reduction in variability (under the storage rules) of the price change from period I to period 160 III, but the other two reductions were quite modest. The explanation for this outcome is not clear, but the computations at least suggest the possibility of improving storage decisions through the use of price prediction equations. The decrease in variability in the seasonal price change under the storage rules would in this case have bea1 accompanied by an increase in total revenue. In a comparison of sales and prices computed from the storage rules with actual prices and sales, total revenue was higher under the rules in 13 of the 15 years included in the analysis. The average annual increase in total revenue under the rules was about two percent. The application of the rules would have affected total costs very little since the average quantity stored under the rule was about the same as the actual average quantity stored. Hence, the percentage increase in net revenue would have been greater than the percentage increase in total revenue. The above computations are indicative of the possible magnitude of the effect of improved storage decisions. The rules, however, were only applied to the same data from which the rules were developed, so that the substantial reduction in variability of the price change from period I to III which was obtained is undoubtedly an fiupper limit? estimate of the_improvement which might be possible using 161 price prediction equations of the fairly simple type presented here. The computed storage rules are aggregate inventory functions. Such rules, however, could be of value to indi- vidual apple producers. Apple production occurs only in period I. Prices during the remainder of the season are greatly influenced by the quantity of applesjnitially stored and the rate of sale from storage. Apple storage is profitable if the increase in price is more than enough to cover the costs of storage. Hence, if it appears that aggregate apple holdings will be less than that called for by (10) for period I or (8) for period II, the individual producer might profitably increase the quantity stored in period I or defer sales from period II to period III. During the postwar period, changes in initial storage holdings in period I were explained quite well by the simple storage function of Chapter V. After harvest, more than 90 percent of the change in storage movement between periods II and III was explained by changes in initial storage holdings. The IAA also publishes monthly storage reports which indicate the level of aggregate storage holdings. The individual firm might use such data in conjunction with the storage rules to determine whether or not to change its own storage holdings. Such information could provide 162 a basis for more orderly marketing. One complicating factor in developing a storage policy for the apple industry is that all producers do not have the same costs and the same expected returns. For example. both costs and returns are higher under CA storage conditions. Also, there are numerous grades and varieties of apples. The individual producer needs information pertaining to his specific apples. However, a knowledge of total storage holdings and the probable price increase for all apples is useful since there is generally a high degree of substitution among varieties and grades of apples. CHAPTER VII SUMMARY Fresh apple prices at the farm level have varied widely both between seasons and within a given marketing season during the postwar period. During this period, apple storage has been profitable only in certain years. In addition to the within-year variation in fresh apple prices, processing apple prices have also varied widely from year to year during this period. In general, price analysis is more difficult both theoretically and practically when the commodity is being channeled into more than one end use. This is the situation with apples during certain periods of the apple marketing season in areas where processing outlets provide an attractive alternative to the fresh market. Apples are harvested from July-November, and the marketing season extends through the following June. At harvest, some apples are sold on the fresh market, some are sold to processors, and the remainder are stored for later sale in the fresh market. A large portion of the apple crop consists of dual purpose varieties which are suitable for fresh or processing uses. 163 164 Demand for apples is likely to change as the marketing season advances. Thus, in determining the most profitable marketing pattern for apples, information is needed con- cerning demand conditions for fresh and processing apples at harvest and for fresh apples throughout the marketing season. The primary objective of this study was to formulate and estimate an economic model of the U.S. apple industry for the postwar period relating relevant variables to fresh and processing apple prices at the farm level during various periods of the marketing season. The economic behavior of the U.S. apple industry (including the U.S. apple export situation) was studied prior to formulating an economic model. Total per capita apple consumption has changed little in the postwar period. However, there have been important changes in the forms of consumption. Consumption of processed apple products has been increasing at the expense of fresh apples. The increase in processed apple products has been especially pronounced for canned and frozen apple sauce and apple slices. Structural equations were initially formulated for the following relationships: (1) demand for fresh apples at the farm, (2) demand for processing apples at the farm. (3) storage function, and (4) allocation function. 165 A production—stocks identity completed the model. An export function was not included to explain changes in U.S. apple exports since preliminary investigation revealed that exports have been of minor importance since World War II. Total supply was assumed to be predetermined in any year. Hence, a functionxnas not included to explain the quantity of apples not harvested (which has been minor in recent years). The apple marketing season was divided into three periods to facilitate economic analysis. There were as many equations as currently endogenous variables in each period of the analysis. Thus, the model was complete. Period I included the months July-Nbvember. All apples are harvested during this period. It was assumed that all apple sales to processors take place in period I since it is not economically feasible to store processing apples. Small quantities are sold to processors after period I, but these are mainly sorts and culls from stored fresh apples. Apples not sold to processors are sold in the fresh market. Some of these are sold in period I, while the remainder are stored for sale later in the marketing season. The fresh and processing demand relationships, storage function, allocation function and identity comprised 166 the model as initially formulated in period I. Fresh sales, processing sales, the quantity stored, fresh price. and processing price were jointly dependent variables in this period. A satisfactory demand relationship for processing apples could not be formulated in this study. The model of period I was then revised to incorporate a demand function for combined fresh and processing apple sales. In this relationship, the price indicator was weighted by fresh and processing apple sales in period I. An allocation function is necessary to complete the model in the harvest period because apples move into fresh and processing outlets with a different price existing in each outlet. Processing and fresh apples are different commodities from the producer's standpoint since production costs are lower in producing apples for processing outlets. Period II included the months December—March. There is no production during this period, and apples move from storage into fresh market outlets. Under these conditions, the quantity moving out of storage, the quantity sold fresh, and fresh price are current endogenous variables. Hence. the storage function, the fresh apple demand relationship and the identity comprised the economic model in period II. The final period of the marketing season included the months April-June. All apples in storage from 167 the previous year's harvest move into fresh market outlets during this period. Thus, at the end of June, stocks are depleted and the new harvest begins. There is no processing and both storage movement and fresh sales are predetermined in the final period of the marketing season. Consequently, fresh price is the only current endogenous variable in period III. The demand function for fresh apples and the identity comprised the economic model in this period. Secondary data were used in the analysis. The major data sources were publications of (l) the U.S. Department of Agriculture, (2) the International Apple Association, and (3) the National Canners Association. All production and quantity data were put on a per capita basis to adjust for changes in population during the period of analysis. Since the periods of the analysis were of unequal length, quantity variables were put on a monthly or yearly basis to facilitate the comparison of coefficients for any given variable in different periods. Farm prices of apples were deflated by the Wholesale Price Index to adjust for changes in the purchasing power of the dollar. As implied above, there is simultaneity among the structural relations in period I. The same situation to a lesser extent is true in period II. A simultaneous equations 168 system of estimation might be expected to yield more accurate estimates of parameters for the structural equations even though the number of observations is small. Thus, the structural equations in periods I and II were estimated by two-stage least-squares procedures as well as by ordinary least squares. In period III, there was only one current endogenous variable, and the ordinary least-squares procedure is a valid application of the simultaneous equations theory. In general, the estimated relationships were more satisfactory for periods II and III than for period I. Fresh apple sales, lagged fresh price, sales of competing fruits, and income explained a high percent of the variation in fresh price in periods II and III. Demand was slightly inelastic in period II but elastic in period III. Fresh apple sales, sales of competing fruits, and income were intercorrelated due to a downward trend in the first two of these variables and an upward trend in income during the period of analysis. Possibly because of these conditions. income hadthe ”wrong" sign in period II and competing fruits had the fwrong" sign in period III. In both these periods, fresh sales and lagged fresh price were the most important explanatory variables. In period I, the demand for all apples sold (fresh 169 plus processing) was inelastic. The elasticity of demand (average prices and quantities were used in computing elasticities) varied from —0.46 with quantity dependent to -0.62 with price dependent. These values were almost the same when the relationships were re-estimated with the data in log form. Fresh apple price in period I appeared to be deter— mined more by total production or crop forecast than by fresh sales during the harvest period. A demand function with quantity dependent was estimated for fresh apples in period 1. although it was not as satisfactory as the estimated relationship for combined fresh and processing sales during this period. The coefficients of competing fruits and income had Vwrong? signs in the demand function of fresh apples in period I. These variables were dropped and replaced by a trend variable. On the basis of results from this estimated relationship, demand for fresh apples in period I was slightly more inelastic than the demand for total apple sales. This, if true, implies that the demand for fresh apples is more inelastic at harvest than the demand for processing apples. Thus, on the basis of the estimated demand functions in this study, the evidence mildly suggests that the demand for fresh apples is slightly more inelastic than the demand for processing apples. 170 In this study, the total quantity of apples produced in any year was considered predetermined. Hewever, the quantity moved in the fresh or processing markets or the quantity stored in period I cannot be considered pre— determined. Fresh and processing apple prices are determined simultaneously with the allocation of apples into fresh or processing markets or into storage. In this study, functions were estimated to explain changes in quantities stored or allocated to processors, while the quantity allocated to the fresh market in period I was treated as a residual. In the estimated allocation function for all processing apples, the ratio of processing to period I fresh apple price, Eastern apple production, and other apple production explained more than 90 percent of the variation in total sales to apple processors during the post- war period. The most important explanatory variable was Eastern apple production. This is understandable since a large part of Eastern apples are sold to processors. An allocation function was also estimated for canning and freezing apples using explanatory variables similar to those in the allocation function for all processing apples. The ratio of canning and freezing to period I fresh apple price. Eastern apple production, and 171 other apple production explained about 75 percent of the year-to-year variation in canning and freezing apple sales during the postwar period. Each producer allocates apples among processing, fresh, and storage outlets more or less simultaneously. Thus, we might expect the same factors to be significant in the allocation and storage function. The same explanatory variables used in the allocation function were included in the storage function of period I. This function explained year-to-year changes in the quantity of apples stored at harvest. The two factors, Eastern apple production and production in other areas of the U.S. explained more than 80 percent of the variation in December 1 storage holdings during the postwar period. The price ratio did not have a significant effect in this relationship. The storage function of period II explained changes in the rate of sale from storage. Beginning stocks and the percent of all stored apples in CA facilities explained about 95 percent of the variation in storage movement _during period II. Changes in the quantity of apples stored at the beginning of period II was by far the most important explanatory variable in this relationship--explaining more 172 than 90 percent of the variation in storage movement. The estimated storage functions of this study indi- cated that the aggregate behavior of apple storage operators in periodsI and II could be explained quite well by simple functional relationships of the type suggested by Gustafson. Under conditions specified by Gustafson, changes in the aggregate quantity of the commodity stored or carried over during any period can be explained by changes in the total supply during the period. After presenting and analyzing the relationships estimated in this study, the results of this study and other studies were used to evaluate the feasibility of proposed producer supply control programs for apples. TWo major types of programs were evaluated. In a program of the first type, processing apple sales are increased at the expense of fresh apples. This program assumes that fresh apples have a more inelastic demand at the farm level rela- tive to processing apples. A large number of theoretical and practical problems must be considered in evaluating a diversion program of this type. There are few empirical results available pertaining to elasticities of demand for fresh and processing apples. The data that are available relate to blend prices without considering various grades, sizes, varieties, etc. Price and quantity time series are available only on an 173 aggregative basis. Hence, data limitations prevent the estimation of demand at the farm level for apples of particular grades, varieties, etc. The total quantity of apples moved in the fresh market relative to the quantity processed is more stable from year to year. This suggests that the demand for fresh apples in general is more inelastic than the demand for processing apples at the farm level. Tomek found this to be the case. As indicated previously, results of the present study also mildly support this thesis. Fresh apples quite likely have a less elastic demand (relative to processed apple products) at the retail level due to the relative availability of substitutes for fresh and processed apple products. Elasticities com- puted from M.S.U. Consumer Panel data support this thesis. However, marketing margins appear to be greater for processed than for fresh apples. Hence, the ordering of elasticities may be reversed at the farm level. In at least two studies, researchers found iflua derived demand for processing apples to be more inelastic than the demand for fresh apples at the farm. Under these conditions, the policy of diverting apples from fresh to processing outlets would decrease net returns. 174 There is also a problem of the length of time involved in computing elasticities. The elasticity of demand for semi-perishable commodities, such as apples, when computed ’from annual data probably gives a lower limit elasticity. A policy of supply control might appear profitable based on an elasticity computed from annual data and unprofitable when elasticity is computed from data for shorter periods of time. In addition to the above problems there are a number of formidable administrative problems which must be faced in considering a supply control program for apples. Pro- ducers in different areas produce different varieties. In some areas mainly fresh apples are produced while a large proportion of total production consists of dual purpose and processing varieties in other areas. Any program of increasing processing sales at the expense of fresh sales (if both have inelastic demands) wouldsubsidize fresh producers at the expense of other producers. A quantity control program has also been considered for the apple industry. In this program, apples under a certain size would not be marketed. This program would face most of the same theoretical and practical problems enumerated above for the diversion program. 175 Producer and processor bargaining has also been discussed as a policy for the apple industry. Though the number of apples processors is limited, the price paid for processing apples appears to approach the competitive price. If apple processors are not realizing monopoly gain as a result of their oligopolistic position, bargaining on the part of producers with apple processors would likely have little effect on processing apple prices in the absence of supply controls. A predictive equation for canning and freezing apple prices was developed in this study using July fresh price, July canner stocks, and the U.S. Department of Agriculture July apple crop estimate. During the period 1951-1961, these three explanatory variables explained almost 90 percent of the year-to-year variation in season average prices of canning and freezing apples. If similar conditions prevail in the future, the price of canning and freezing processing apples can be estimated quite accurately early in the marketing season. Information available early in the marketing season concerning the probable price of processing apples can be used byproducers in developing an apple marketing pattern. Such information would also be useful to processors and food manufacturers in making plans for the ensuing apple marketing season. 176 Predictive equations were also estimated for fresh apple prices in each of the three periods of the analysis. In the period I relationship, July fresh price and July apple crop estimate explained about 70 percent of the year-to-year variation in fresh prices at harvest. After period I, fresh price is highly correlated with movement from storage. Storage movement in periods I and II was explained quite accurately by changes in total supply. Total supply after period I consists of the quantity stored since production occurs only in period I. Changes in the quantity stored in period I explained about 85 and 75 percent. respectively, of the year-to-year price changes in periods II and III. After estimating and presenting predictive equations for fresh and processing apple prices, apple storage rules were developed for periods I and II to illustrate the pos- sibility of improving storage decisions through application of the price prediction equations. In developing a storage rule for a given period, the expected price change between that period and the following period was equated with the marginal cost of storage between the two periods. The quantity to store under the rule developed for period I was a function of July crop estimate, July fresh price and a trend variable. Under the storage rule of period 11. the quantity stored at the end of the period was a function of the quantity stored in period I and a trend variable. 177 After the rules were developed, they were applied to the years 1947—1961 to see what difference their application would have made in the variability of seasonal price changes and in total revenue. There was a large reduction in varia— bility (under the storage rules) of the price change from period I to periodIII, and total revenue was higher in 13 of the 15 years included in the analysis. Thus, it appears at least possible that storage decisions based on the price pre- diction equations could decrease the year-to-year variability in seasonal price movements. The U. S. Department of Agriculture July estimates of apple production and fresh price provide the data needed to apply the storage rule of period I. Storage estimates of the IAA provide the necessary information to apply the storage rule of period II. This study has not considered the demand for specific grades, varieties, etc. of apples for different geographical locations (these data are not available). The individual producer is most interested in the demand for his specific varieties and sizes of apples rather than in some general average. Hewever, as has been indicated previously. there is a great deal of interdependence both among regions and among various varieties and grades of apples. Regional prices are highly correlated with U. S. prices. A knowledge 178 of the factors associated with changes in U. S. farm prices will enable producers and apple buyers to more accurately estimate the market clearing price for apples of various varieties, grades, etc. in different regions. BIBLIOGRAPHY Bain, M. B., and Hoos, S. Apples - Fresh and Processed - Economic and Marketing Statistics. Berkeley, California: California Agricultural Experiment Station, University of California, May 1959. Bartter, L. M. Effects of Apple Supply Management Progpams in New YOrk State. (Agricultural Economics Re- search Bulletin No. 62) Ithaca, New York: Cornell Agricultural Experiment Station, Cornell University. 1961. Boger, L. L. When Should Apples be Sold? (Agricultural Economics Special Bulletin No. 381) East Lansing, Michigan: Michigan Agricultural Experiment Station, Michigan State University, 1952. ., and Cromarty, W. A. "A Model to Explain the Short-term Demand for Apples." (Paper read before the Annual Winter Meeting of the Econometric Society at Washington, D. C., December 28, 1953.) Brandow, G. E. Interrelations amonngemands for Farm Pro— ducts and Implications for Control of Market Supply. (Agricultural Economics Station Bulletin No. 680) University Park, Pennsylvania: Pennsylvania Agri- cultural Experiment Station, Pennsylvania State University, 1961. ’ . A Statistical Analysis of Apple Supply and Demand. (Agricultural Economics and Rural Sociology Bulletin No. 2) University Park, Pennsylvania: Department of Agricultural Economics and Rural Sociology. Pennsylvania State University, 1956. Brennan, M. J. FThe Supply of Storage," The American Eco- nomic Review, XLVIII, (March 1958). PP. 50-72. Cromarty, W. A. ”An Experiment in Designing an Econometric Model to Explain Short-term Demand Fluctuations for Apples.? Unpublished Master's thesis, Department of Agricultural Economics, Michigan State University, 1953. 179 180 Dalrymple. Dana G. "Economic Aspects of Apple Marketing in the United States.” Unpublished Ph.D. dissertation, Michigan State University, 1962. Drew. W. H. VDemand and Spatial Equilibrium Models for Fresh Apples in the United States.9 Unpublished Ph.D. dissertation, Vanderbilt University, 1961. Economic Statistics Bureau of Washington, D.C. The Handbook of Basic Economic Statistics. Washington: Economic Statistics Bureau of Washington, 1963. Evans, Homer C. The Nature of Competition amopg Apple Processors in the Appalachian Area. (west Virginia Agricultural Experiment Station Bulletin No. 405) Morgantown, West Virginia: West Virginia University. 1957. Ezekiel, M., and Fox, K. A. Methods of Correlation and Regression Analysis. Third edition; New York: John Wiley and Sons, 1959. Foote, R. J. Analytical Tools for Studyinngemand and Price Structures. U.S. Department of Agriculture, Agriculture Handbook No. 146 (Washington: U. S. Government Printing Office. 1958). ., Cromarty. W. A., and Sparks, W. R. ”Empirical Results from Alternative Methods of Fitting Systems of Simultaneous Equations.? Paper presented to the Midwest Quantitative Economic Symposium held at .Michigan State University, February 4-6, 1963. Foytik. J. Characteristics of Demand for California Plums. (In Hilgardia. XX, No. 20, California Agricultural Experiment Station), Berkeley, California: University of California. 1951. French. B. C., Levin, J. H. and Gaston. H. P. VStorage Holdings and Movement of Apples in Michigan and the United States,? Quarterly Bulletin, Vol. 36. No. 4, Agricultural Experiment Station, East Lansing, Michigan: Michigan State University. 1954. 181 Friedman, J and Foote. R. J. Computational Methods for Handling Systems of Simultaneous Eqpations. U.S. Department of Agriculture, Agriculture Handbook No. 94, revised (Washington, D.C.: U.S. Government Printing Office, 1957). Friedman. M. A Theory of the Consumption Function. (National Bureau of Economic Research. No. 63, General Series), Princeton. New Jersey: Princeton University Press, 1957. Greig, W. S. Maximizing_Total Dollar Sales oprpples and Apple Products by a Utilization Model. (Agricultural Economics mimeo. No. 889), East Lansing, Michigan: Agricultural Economics Department. Michigan State University, 1962. Gustafson, R. L. Carryover Levels for Grains, U.S. Department of Agriculture Technical Bulletin 1178. 1958. . VStorage of Pork.? Unpublished manuscript. Department of Agricultural Economics. Michigan State University, 1959. . FThe Use and Interpretation of 'Dummy Variables' in Regressions.” East Lansing,.Michigan: Department of Agricultural Economics. Michigan State University, January, 1962. (Mimeographed.) Harrington, A. H. FDemand for Fresh Market Apples." Unpublished Ph.D. dissertation, University of Illinois, 1952. Hildreth. C., and Jarrett. F. G. A Statistical Study of Livestock Production and Marketing. (Cowles Commission Monograph No. 15). New York: John Wiley and Sons. 1955. .. and Lu, J. Y. Demand Relapions with Autocorrelated Disturbances. (Technical Bulletin No. 276), East Lansing. Michigan: .Michigan Agricultural Experiment Station, Michigan State University, 1960. International Apple Association. FSpecial Letter.” Washington, D.C.: International Apple Association. 1947-1961. 182 ‘lnternational Fruit World, autumn, 1959. Judge, E. E. The Almanac of the Canning. Freezing and Preservinngndustries. Westminister, Maryland: E. E. Judge, 1962. Johnston, J. Econometric Methods. New York: McGraw-Hill BoOk Co., 1963. Kaufman, V. F. FCosts and Methods for Pie—Stock Apples." Food Engineering, XXIII (December, 1951). PP. 97-105. Manderscheid, L. V. and Ruble, W. Estimation of Two-Stage Least Squares with Special Reference to Mistic Facilities. (Agricultural Economics Mimeograph Series No. 868, revised, 1963). East Lansing, Michigan: Department of Agricultural Economics. Michigan State University, 1962. Marschak, J. Economic Measurementgfpr Poligy and Prediction in Studies in Econometric Method. Edited by W. C. Hood and T. C. Koopmans. (Cowles Commission for Research in Economics, Monograph No. 14), New YOrk: John Wiley and Sons, 1953. Mehren, G. L., and Erdman, H. E. VAn Approach to the Determination of Intraseasonal Shifting of Demand,9 Journal of Farm Economics, XXVIII (May, 1946). pp. 587—596. National Canners Association. Canned Food Pack Statistics. Washington: National Canners Association, 1962. . PSupply, Stocks and Shipments.? Monthly reports for canned apples and apple sauce, 1951-1961. Washington, D.C.: National Canners Association. Nerlove. M. Distributed gags and Demand Analysis for Agricultural apd Other Commogities. U.S. Department of Agriculture. Agriculture Handbook No. 141 (Washington: U.S. Government Printing Office, 1958. Papera. D. R. FThe Rise and Decline of the California Apple Industry.? Unpublished Ph.D. dissertation, Stanford University, 1958. 183 Pasour, E. C., and Oldenstadt, D. L. Farm Prices of Apples for Canning and Freezing in the United States, 1951-1961. U.S. Economic Research Service. Agricultural Economic Report No. 35 (Washington: U.S. Government Printing Office, 1963). Pubols, B. H. VFactors Affecting the Price of Apples," Agricultural Economics Research, VI (July. 1954), pp. 77-84. Shepherd, G. S. Agricultural Price Analysis. Fifth edition; Ames. Iowa: Iowa State University Press. 1963. Smith. R. J. VThe Lemon Prorate in the Long Run." The Journal of Political Economy, LXIX (December, 1961), pp. 573-586. Stigler, G. J. The Theory_of Price. Revised edition; New Yerk: Macmillan, 1952. Thompson, J. C., Jr. Apple Storage Costs in New York State. (Agricultural Economics Research Bulletin No. 87), Ithaca. New York: Department of Agricultural Economics, Cornell University, 1962. Time Magazine, October 5. 1962, p. 23. Tomek, W. G. FAn Analysis of the Utilization of Apples at the Farm Level in the United States.? Unpublished manuscript, Department of Agricultural Economics, Cornell University, 1963. ”Uncle Sam Big Exporter of Apples . . .?P The Produce News (February 9. 1963). U.S. Department of Agriculture. Agricultural Statistics, annual. . Fruits and Tree NutstBloom. Harvesting and Marketinngates. and Principal Producing Counties. Agriculture Handbook No. 186, 1960. . Fruits NonCitruslpy States, 1949-1959, Pnaduction Use. Value. Statistical Bulletin No. 292. 1962 and 1962 supplement. 184 . Fruits (NonCitrus), Production. Farm Disposition, Value, and Utilization of Sales, 1944-1949. Revised estimates. In Statistical Bulletin No. 114. . Prices Received by_Farmers for Apples, 1934-56 and Pears. 1919-56. Statistical Bulletin No. 253, 1959. . Agricultural Marketing Service. Marketing California Grapes. Raisins. Wine: Annual summaries. . Economic Research Service. The Fruit Situation. No. 144, 1962. . Economic Research Service. The Marketing and Transportation Situation. No. 145. 1962. . Foreign Agricultural Service. Foreign Agricultural Trade of the United States, monthly. . Foreign Agricultural Service. Information relating to World Production and Trade in Deciduous Fruits. November, 1961. . Statistical Reporting Service. Agricultural Prices. monthly and supplement No. 2, July, 1961. . Statistical Reporting Service. Cold Storage Reports. . Statistical Reporting Service. Crop Production, Monthly release. U.S. Department of Commerce. Business Statistics. Biennial edition. A supplement to the Survey of Current Business. . Foreign Trade Reports. Sprvey of Current Business. U.S. Bureau of Labor Statistics. Monthlprabor Review. LXV-LXXXIV, 1947-61. Waugh, F. V. FThe Place of Least Squares in Econometrics,” Econometrica. XXIX (July, 1961), pp. 386-396. APPENDIX A STATISTICAL RESULTS DEF INITION OF VARIABLES per capita sales (in pounds) of fresh apples in period m and year t on a monthly basis. deflated farm price in cents per pound of fresh apples in period m and year t. deflated per capita consumer disposable income in period m and year t (on an annual basis) in hundred dollar units. deflated personal consumption expenditures in period m and year t (on an annual basis) in hundred dollar units. per capita sales (in pounds) of competing fruits in period m and year t on a monthly basis. deflated season average farm price in cents (per pound) of canning and freezing apples in year t. per capita farm sales of canning and freezing apples (in pounds) in period I and year t on a monthly basis. deflated season average farm price in cents per pound of all processing apples in year t. per capita farm sales of all processing apples (in pounds) in period I and year t on a monthly basis. September apple crop estimate of year t in pounds per capita. August 1 per capita carryover canner stocks (in pounds) of processed apple products. per capita sales (in pounds) of Eastern apples in year t. per capita sales (in pounds) of apples produced in other parts of the U.S. in year t. 186 187 the average price in cents per pound of total apple sales of period I weighted by sales of fresh (flt) and processing (alt) apples. the average quantity of apples on hand at the end of similar periods during the three preceding years in pounds per capita. the percent of all stored apples in CA storage at the end of period m. trend (1947 = 1, 1948 = 2, . . . , 1961 = 15). 188 H6. Hm. . mm. + em. I m¢.N retmw.a ssxom.a satwm.m um mm. ca. co. mm. . me. + em. I I- mo.e also who "HH coaumm am. am. + mm. . cm. I ea.a m~.~ mm.a .oo.a us 66. ca. co. mm. + co. . oa. u u- mm.m name mqo mo. me. + mm. + as. . om. ca. .om.a mm. 0H OH. om. co. so. + Hm. + :1 cs. . 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H6.oH mHHV mAO “H poau0m m x.>m p»mx »E OAHI»vm »E 3»AHIEvm »E EH09 0nso0oonm NI. * m »30»0300 308»0EH»0H 6 0H30Hnm> mm»30H0Hmm0oo 30H»0H0HM00 HMH»umm . . . . . . »30o30m0n 030 005H0> » 0»30H0Hmm0oo 30amm0nm0m .HH 030 H moOHn0m How 030fl»035m 0mmuo»m >H03HEHH0HQ o0»0EH»0m .9 0H309 196 .H UOHHQQ MO COHHUCSM OGMHOUm mflu. CH UOQDHUGH HOG WM?» GHQMflHMb. HEM @390 .HHH uoHH0m 0» HH 00Hn0m Eoum “00> 050H>0Hm 03» 3H 0000H03H 00HHQ 03» 003 AHI»Vm .HH GOHH0Q new 30H»03:m 0m0uo»0 03» 3H .HHH UOHH0Q o» H powu0m Eoum u00> 050H>0Hm 03» 3» H03053 H0Q 0H0HHOU 3H 0000303» 00HHQ 03» 003 AHI»vm .H 00HH0Q 3H0 .HAHIEVm CGUMHQOH .uam.0umfifiumm QOHO H03E0»m0m .H ooan0m 3H .H poau0m mo msflccflm03 03» »0 0300»0 03 0H0 0H039n .00DH0>» 03» 30H03 0H0 0»30H09mm000 30H»0H0uuoo H0H»H0m .0»30H09mm000 30H000Hm0u 03» 3OH0£ »05h H00mm0 005H0> »0 APPENDIX B DATA USED IN ANALYSIS Table l. U.S. production and sale of apples by period. 1947-1961. thousands of bushels. Sales of Processing Sales of Fresh Apples2 Apples (period I) Productionl Period Crop Period Period Canning Year Period I I II III & Freezing All 1947 103.576 33.280 30.202 12.100 9,765 26,369 1948 84.342 36.358 22.452 6,580 8.709 19,455 1949 117.300 37.506 32.518 8.928 15.871 37.218 1950 115,537 26.151 34.214 13.771 18.782 40.353 1951 97.349 34.212 25.633 6.774 13.154 28.196 1952 90.505 33.731 24.790 7.601 12,860 24,918 1953 92.635 30.752 26.369 7.963 14.782 27.612 1954 108.389 31.118 27,972 9.226 21.602 39.112 1955 100.766 26.449 31.321 9.417 17.925 32.930 1956 98.569 29.141 26.405 6.913 21.234 35,161 1957 114.827 31.209 34.297 8.614 19.951 36.274 1958 122,639 35.542 31.829 13.687 22.772 40.342 1959 122.875 36.908 31.120 8.724 23.399 43.003 1960 106.255 33.597 26.261 8,525 22.350 36.091 1961 123,207 32,832 31,081 9,766 26.608 45.502 lOnly apples sold were included in ”production” as used in this study. Consequently. production in this study represents total production less apples for home use and apples not sold for economic reasons (i.e.. apples not harvested and excess cullage). 2Sales were adjusted for exports and imports. Con- sequently. total fresh sales plus all processing sales does not equal production (total sales). Sources: Production statistics and sales of processing apples are published by the Crop Reporting Board, SRS, U.S. Department of Agriculture. Sales of fresh apples by period were determined from the production stocks identity. 198 199 Table 2. Per capita U S. farm sales of fresh and processing apples by period, 1947-1961, in pounds. ProcesSIng Apple Fresh Apple Sales Sales Crop Year Period I Period II Period III Canning & All Freezing I flt f2t f3t alt alt 1947 11.05 9.96 3.97 8.76 3.24 1948 11.86 7.28 2.12 6.35 2.84 1949 12.03 10.36 2.83 11.93 5.09 1950 8.25 10.72 4.30 12.73 5.92 1951 10.60 7.89 2.08 8.74 4.08 1952 10.28 7.51 2.29 7.59 3.92 1953 9.21 7.85 2.36 8.27 4.43 1954 '9.16 8.18 2.69 11.52 6.36 1955 7.66 9.01 2.70 9.53 5.19 1956 8.29 7.46 1.94 10.00 6.04 1957 8.72 9.53 2.38 10.14 5.58 1958 9.77 8.69 3.72 11.09 6.26 1959 9.94 8.32 2.32 11.58 6.30 1960 8.90 6.91 2.23 9.56 5.92 1961 8.56 8.05 2.52 11.86 6.93 In estimating the demand relationships. the quantities presented below were converted to a monthly basis to facilitate the comparison of regression coefficients of fmt in different periods. Source: Computed from Tables 1 and 10. 200 Table 3. U.S. fresh apple storage stocks at end of period. 1947 to 1961. thousands of bushels and end of July canner stocks of canned and frozen apple slices and apple sauce in fresh apple equivalents. Fresh Apples-Storage StOCkS Canned and Frozen Crop Year Period I Period II Slices and Saucel (1000 bu.) (1000 lbs.) 1947 42.645 12.100 136.583 1948 29.124 6.580 144.616 1949 41.436 8.928 29.121 1950 48.100 13,771 188,756 1951 32.631 6.774 278,242 1952 32.578 7.601 152.329 1953 34.557 7.963 33.682 1954 37,462 9,226 43,047 1955 41.077 9.417 177.111 1956 33.255 6.913 155.918 1957 43,370 8.614 235.279 1958 45.705 13.687 211.993 1959 40,180 8,724 152,228 1960 34.948 8,525 233,182 1961 41,097 9,766 243,846 l . ConverSion factors used were: Apple Slices (cans per case/can size) Fresh Apple Equivalent/ Case (lbs.) 24/2 1/2's = 67.200 24/2'8 = 46.345 6/10's = 61.639 Apple Sauce (cans per case/can size) 24/2'8 = 39.724 24/303'8 = 29.396 48/8 oz. = 33.368 6/10's = 52.833 Misc. sizes = 55.000 Frozen apples were converted to a fresh apple basis using a conversion ratio of 1.25, i.e.. one pound of frozen apples equals 1.25 pounds of fresh apples. Table.3. 201 Continued. Sources: Conversion factors for canned apples were taken from U.S. Department of Agriculture, Agricultural Statistics. 1961. and National Canners Association. Canned Food Pack Statistics 1961. June. 1962. The conversion factor forfrozen apples was taken from Kaufman. V. F., ”Costs and Methods for Pie-stock Apples.” Food Engineering. December, 1951. (a) Information concerning fresh apple storage stocks were obtained from the International Apple Association. ' (b) Carryover stocks of canned apple slices and sauce were obtained from the National Canners Association, and M. B. Bain, and S. Hoos, Apples - Fresh and Processed — Economic and Marketing Statistics, Cal. AES, May, 1959. For the period 1947-1950 June Stocks were available but July stocks were not. June stocks were converted to a July basis by determining the average relationship between June and July stocks during the period 1951-1955. Stocks of frozen apple slices were obtained from Cold Storage Reports of the USDA. 202 Table 4. U.S. per capita storage movement of fresh apples by period, 1947-1961. and U.S. per capita canner stocks of canned and frozen apple slices and sauce in fresh apple equivalents. 1 August 1 Year Storage Movement of Apples Processed Stocks Slt szt S3t Alt --- pounds per capita —-- 1947 14.53 - 9.96 -3.97 0.947 1948 9.41 — 7.28 —2.12 0.986 1949 13.60 -10.36 -2.83 0.195 1950 15.44 -10.72 -4.30 1.244 1951 10.57 — 7.89 -2.08 1.801 1952 9.79 - 7.51 -2.29 0.970 1953 10.32 - 7.85 -2.36 0.211 1954 11.19 — 8.18 —2.69 0.265 1955 11.94 - 9.01 -2.70 1.071 1956 9.64 — 7.46 -l.94 0.926 1957 12.94 - 9.53 -2.38 1.373 1958 12.73 - 8.69 -3.72 1.217 1959 11.36 - 8.32 -2.32 0.858 1960 9.53 - 6.91 —2.23 1.290 1961 11.35 - 8.05 -2.52 1.327 1 8mt _ mt - S(m-1)t' Source: Computed from Tables 3 and 10. 203 Table 5. Average deflated farm price by period of fresh apples and season average U.S. farm price (deflated) of processing apples, 1947-1961.1 Fresh Apples Processing Apples Period I Period II Period III All Canning & Crop Year f f f a Freezing plt p2t p31: p11: plt —-- dollars/bushel --- 1947 1.94 1.43 1.35 0.72 1.29 1948 1.91 2.39 2.09 0.71 1.04 1949 1.51 1.42 2.01 0.55 0.86 1950 1.82 1.29 1.06 0.76 1.12 1951 1.61 1.86 2.42 0.51 0.68 1952 2.19 2.51 2.67 0.94 1.24 1953 2.40 2.38 2.38 1.36 1.75 1954 2.17 2.24 2.37 1.13 1.50 1955 1.99 1.75 1.76 0.74 0.95 1956 2.12 2.29 2.59 1.12 1.39 1957 1.83 1.29 1.81 0.70 0.90 1958 1.68. 1.57 1.38 0.59 0.72 1959 1.62 1.89 2.24 0.69 0.86" 1960 2.13 2.32 2.84 0.98 1.15 1961 2.05 2.04 2.51 0.78 0.89 1All prices were deflated by the Wholesale Price Index. In estimating the demand relationships. all prices were in cents per pound. Source: Apple prices by period are simple monthly averages and were computed from Crop Reporting Board statistics. 204 Table 6. U.S. per capita sales of competing fruits by period. 1947-1961. in pounds. Period I Period II Period III Crop Year c c' c c 1t 1t 2t 3t 1947 19.46 21.80 2.03 1.53 1948 14.20 19.88 1.40 1.14 1949 15.53 21.82 1.53 1.26 1950 11.78 19.66 1.50 0.83 1951 13.26 21.09 1.57 1.00 1952 14.81 18.81 1.46 1.15 1953 13.25 19.56 1.20 1.23 1954 13.71 18.34 1.18 0.82 1955 10.73 20.86 1.41 0.31 1956 12.95 20.59 1.08, 0.94 1957 12.15 19.47 2.70 1.03 1958 13.30 16.47 ‘1.18 1.45 1959 12.36 20.09 0.99 1.77 1960 11.87 18.65 1.06 1.57 1961 11.03 19.21 0.96 2.05 l . ' . . . . The three fresh fruits included in Cmt were California table grapes. U.S. peaches and U.S. pears. Four fruits were included in C1t- These Were Utah. Washington. and California apricots, Washington. California, and Oregon Bartlett pears, California peaches and U.S. sour cherries. In estimating the demand relationships. the quantities below were con- verted to a monthly basis to facilitate the comparison of regression coefficientscf cmt in different periods.r Source: Annual sales are reportedin U.S. Department of Agriculture, Crop Reporting Board statistics. Un— published data giving monthly sales as a percent of total sales for peaches and pears were furnished by the U.S.D.A. Sales of grapes by period were estimated on the basis of interstate truck and rail movement of California table grapes. Data pertaining to movement of California table grapes were obtained from various issues of. U.S. Department of Agriculture. Marketing California Grapes. 205 Table 7. September apple crop estimate, eastern apple sales. other apple sales. 1947-61, pounds per capita. Crop Estimate Eastern Sales Other Sales Crop Year e m n 1t t t --- pounds per capita --— 1947 37.56 12.17 21.42 1948 32.79 11.11 15.51 1949 41.50 15.76 21.85 1950 37.55 16.64 19.80 1951 37.15 14.17 16.00 1952 29.88 11.90 15.68 1953 29.85 11.95 15.81 1954 30.13 16.30 15.62 1955 31.32 13.35 15.82 1956 26.58 13.01 15.04 1957 31.13 14.02 18.08 1958 34.86 16.23 17.49 1959 31.86 16.61 16.49 1960 28.93 13.77 14.38 1961 32.61 16.69 15.42 Sources: (a) Crop estimates were taken from Crop Production. published monthly by the Crop Reporting Board of the U.S. Department of Agriculture. (b) Apple sales by region are published by the Crop Reporting Board. Statistical Reporting Service, U.S. Department of Agriculture. 206 Table 8. Percent of total apple holdings held in CA storage on December 1 and April 1. 1947-1961, United States. Crop Year December 1 April 1 k1t k2t --- percent --- 1947 0.19 0.57 1948 0.29 0.87 1949 0.22 0.66 1950 0.21 0.63 1951 0.57 1.71 1952 0.90 2.70 1953 1.06 2.89 1954 1.23 4.40 1955 1.81 6.32 1956 2.44 8.84 1957 3.43 13.30 1958 6.31 18.70 1959 8.45 22.80 1960 11.40 26.20 1961 13.30 39.00 Source: International Apple Association. 207 Table 9. U.S. storage holdings at end of similar periods in previous years1 and within-year price increase of apples in storage, 1947—1961. Storage Holdings Price Increase in PreVious Year . Period I- Period II- Cr°p Year December 1 April 1 Period III2 Period III * S * Slt 2t g(t-1) g(t-l) pounds per capita dollars per bushel 1947 12.99 2.86 -0.58 -0.07 1948 13.76 3.48 +0.02 -0.36 1949 12.31 3.04 +0.72 +0.61 1950 12.51 3.03 -0.54 -0.25 1951 12.82 3.12 +0.91 +0.60 1952 13.20 3.11 +0.47 +0.17 1953 11.93 2.95 +0.02 0.00 1954 10.23 2.32 +0.23 +0.15 1955 10.43 2.53 -0.08 +0.05 1956 11.15 2.68 +0.56 +0.36 1957 10.92 2.51 +0.23 +0.62 1958 11.51 2.42 -0.16 -0.22 1959 11.77 2.75 +0.57 +0.42 1960 12.34 2.91 +0.80 +0.60 1961 11.21 2.83 +0.69 +0.55 18* = Sm(t-l) + Sm(t-2) + Sm(t-3) mt 3 2 . The average farm price for September. October. and November was used to represent prices in period I since storage would occur only in the latter part of period I. Sources: Tables 3, 10, and 17. 208 ' 1 Table 10. U.S. population by period, 1947-1961. 4———‘ Crop Year Period I Period II Period III --- millions --— 1947 144.5 145.5 146.2 1948 147.1 148.1 148.8 1949 149.7 150.7 151.3 1950 152.2 153.2 153.9 1951 154.9 155.9 156.6 1952 157.5 158.5 159.3 1953 160.2 161.2 162.0 1954 163.0 164.1 164.8 1955 165.8 166.9 167.7 1956 168.7 169.9 170.7 1957 171.7 172.8 173.6 1958 174.6 175.8 176.7 1959 178.2 179.5 180.2 1960 181.2 182.4 183.2 1961 184.2 185.3 186.1 lPopulation estimates are published monthly. A simple monthly average was computed to obtain the population estimate in each period. Source: Economic Statistics Bureau of Washington. D.C., The Hapdbook of Basic Economic Stgtistics, monthly. 209 Table 11. Consumer and Wholesale Price Indices, 1947-1961. by period.1 Consumer Price Index Wholesale Price Index Crop Year Period Period Period Period Period Period I II III I II III 1947-1949 100 1947 97.0 100.2 102.0 99.6 103.9 104.9 1948 103.9 101.8 101.4 106.8 102.0 99.4 1949 101.0 99.9 100.6 97.5 97.1 99.2 1950 104.0 108.9. 110.7 107.2 115.0 115.8 1951 111.7 112.8 113.1 113.7 112.8 111.5 1952 114.2 113.8 114.1 111.5 109.8 109.6 1953 115.1 115.0 114.9 110.5 110.5 110.6 1954* 114.8 114.3 114.3 110.1 110.0 110.2 1955 114.8 114.6 115.5 111.2 112.1 114.1 1956 117.3 118.4 119.7 115.1 116.8 117.2 1957 121.1 122.4 123.6 118.1 119.0 119.3 1958 123.8 123.7 124.1 119.1 119.4 119.9 1959 125.2 125.6 126.3 119.3 119.4 119.7 1960 126.9 127.5 127.5 119.5 119.8 118.8 1961 128.2 128.4 129.1 118.8 119.5 119.0 1Consumer and wholesale price indices are reported on a monthly basis. A simple monthly average was computed to obtain the index for each period. Source: U.S. Department of Commerce, Survgy of Current Business and Business Stapistics. 210 Table 12. Per capita deflated Consumer Disposable Income. seasonally adjusted at annual rates, by period, United States, 1947-1961.1 Period I Period II 'Period III Crop Year ylt y2t y3t --- dollars -—— 1947 1.239 1.227 1.259 1948 1.262 1,257 1.237 1949 1.225 1.300 1.316 1950 1,335 1.307 1.320 1951 1,329 1.312 1.319 1952 1.340 1.368 1.381 1953 1,363 1.359 1.356 1954 1,369 1.399 1.444 1955 1.470 1.486 1.503 1956 ‘1.502 1,503 1,511 1957 1,501 1,472 1,464 1958 1.495 1.510 1.542 1959 1,524 1.524 1.536 1960 1,531 1,522 1.545 1961 1.562 1.575 1.589 1Consumer Disposable Income (reported on a quarterly basis) was deflated by the Consumer Price Index (1947-49 = 100). Consumer Disposable Income in period I, Ylt' is a weighted average of income in the third and fourth quarters of year t. Y2t is a weighted average of income in the fourth quarter of year t and the first quarter of year t + 1. Source: U.S. Department of Commerce, Survey of Current Business and Business Statistics. 211 Table 13. Per capita deflated Personal Consumption Expenditures, seasonally adjusted at annual rates, by period, United States. 1947-1961. C Period I Period II Period III rop Year I l ylt yzt Y3t 1947 1,206 1,191 1.187 1948 1.173 1.185 1,194 1949 1.200 1.225 1.244 1950 1.275 1.245 1.200 1951 1.202 1.215 1.229 1952 1.237 1.275 1.284 1953 1,266 1.259 1.270 1954 1,285 1.321 1,350 1955 1.376 1.385 1.385 1956 1,377 1.387 1.387 1957 1.388 1.360 1.356 1958 1.372 1,399 1.427 1959 1.423 1.431 1.450 1960 1,435 1.441 1.436 1961 1,451 1.468 1.477 lPersonal consumption expenditures (reported on a quarterly basis) were deflated by the Consumer Price Index, 1947-49 = 100. Personal Consumption Expenditures in period I, Ylt' is a weighted average of Personal Consumption Expenditures for the third and fourth quarter of any year t. Y2t is a weighted average of Personal Consumption Expenditures in the fourth quarter of year t and the first quarter of year t + 1. Source: U.S. Department of Commerce, Survey of Current Business and Business Stgtistics. 212 Table 14. Indices of processing costs included in the processing demand relationship. based on labor and can costs. Crop Year Constructed Indexl Intermediate Goods &'Serv1ces d1t d1t 1947-1949 = 100 1947 91.2 94 1948 94.5 103 1949 110.7 103 1950 101.5 106 1951 106.5 116 1952 109.2 116 1953 114.6 119 1954 117.2 120 1955 117.8 121 1956 122.8 126 1957 126.6 132 1958 128.1 134 1959 123.8 136 1960 126.0 138 1961 129.5 138 See Chapter IV for method of construction. Sources: (a) The Constructed index of processing costs was Labor costs were taken from. U.S. Department of Labor. Monthly Labor Review. The Almanac of the Canning. Industries. Freezing. Can costs were obtained from Preserving (b) The Index of Intermediate Goods and Services was taken from the U.S. Department of Agriculture. The Marketing and Transportation Situation. May. 1962. .>H£uc05 .mmumum pmufiab may no momma HMHSUHDUHHmd Gmwmuom .musuasoflum4 mo ucmfiuummmn .m.D paw mofi>nmm Hmnsuasoflumd smfimuom .conH>HQ manmummm> 213 0cm ufisnm .cocmnm mammamcd mquOEEOU mmflso .xooo coucHHU .¢ suHB mocmpcommouuoo "moonsom 0mm ova omv hvd.m mmw 0mm.m mmm.H Hon 0mm.H Hmmd NQH mma hwm ONO.H oav ®m¢.H mmm wmm mmm coma mmm hm mmg moo.N mmm mmm.m awn mum moa.H mmma mma 0mm mgw mmm gmm Oha.a cog mmm mmm mmma mmw Nb Hmm mom.N omm ¢m¢.m mmo.H ohm N¢¢.H hmmH mm I Nam mvm mmo Hmm 0mm hmm Vfim HMh omma mmm mma mpg aha Nmm HHH.H Hma mom @mo mmma vow waa mum 5mm mmm mmo.a oma hmv ham vmma mmm mom «mg moaI man mam mmHI one hww mmma hma hma cmm ngI How ogg Howl mmb mum mmma flmm HOH mNm Nhfl.a 0mm mmm.H wmm Hum mmm.a Hmma mHH mow wam Hhm mow mh®.H No 0mm mvb omma OH I fimm fimm Ham Nmm mwm.a mwa mmm mmn mvma mm mma 0mm omNI hNo.H hwh mHMI hmh wa mvma mgm m mwm hmo.H Hom mmm.a mma mfim ¢¢H.H hwma m H00 muuomEH manomxm mmma 5 H00 m H00 muHOQEH muuomxm mmma g Hoo N H00 manomEH manomxm Hum» mono mama a H00 Amman I .Hgmv HHH coauom A.Hm2 I .omnv HH cofluwm A.>oz I hasbv H noflumm A3 2: AS Go A3 A3 73 AS Ad .mamzmsn mo mocmmsonu .HmmHIhme .poflumm ma muuomfifl 0cm manomxw .mmammm smoum .ma magma 214 Table 16. Processing apples. undeflated and deflated season average farm price. 1947-1961. dollars per ton. Canning and All Canning and A11 Crop Year Freezing Processing Freezing Processing dollars/ton dollars/bushel (undeflated) (deflated) 1947 53.50 29.90 1.29 0.72 1948 46.30 31.80 1.04 0.71 1949 35.10 22.40 0.86 0.55 1950 50.20 33.80 1.12 0.76 1951 32.00 24.20 0.68 0.51 1952 57.70 43.80. 1.24 0.94 1953 80.80 62.70 1.75 1.36 1954 68.90 52.00 1.50 1.13 1955 44.20 34.50 0.95 0.74 1956 66.60 53.60 1.39 1.12 1957 44.50 34.50 0.90 0.70 1958 35.80 29.40 0.72 0.59 1959 42.80 34.10 0.86 0.69 1960 57.40 48.90 1.15 0.98 1961 44.20 38.70 0.89 0.78 Source: Prices published by U.S. Department of Agriculture. Crop Reporting Board. SRS. Wholesale Price Index Taken from Table 11. 215 .Homauooma you manucoa .mmoflnm amusuHsUHumm new .mmmaumwma mumms you .Hmma .masb .mmuanm .m« m .02 .mmsm .memaumvma mom .mmma .ocsu .mmm .oz cflumaasm HMUflpmflpmum .moflumfiumum unmom mCfluuomwm mono ousuasoflumm mo uswfiuummmn .m.D «mousom Ho.m ho.m mm.m mm.N m¢.~ mm.m mm.m hm.m ma.m m¢.N om.m on.m Hood b¢.m am.m no.m mm.m mm.N mn.m m©.m oo.m om.m mm.m hm.m ¢¢.N coma ww.m mh.m mm.m mm.N mm.m ¢~.N ha.m mo.m Ho.N mm.~ mm.~ mm.H mmma ov.a hm.a mm.a mm.H mm.a vw.a mm.H gm.a Hm.a mo.m ma.m mm.~ wmma hm.m mo.m mo.m m¢.H N¢.H mm.H mo.a mh.a mm.a ha.m H¢.N hm.m hmma mm.m No.m ¢>.N on.m no.m om.~ co.m Hm.~ ¢¢.N o¢.N mm.~ mm.m omma no.m mo.N hm.a bb.a mm.a mo.~. mo.~ no.m mm.H mm.m o¢.N hm.m mmma NF.N om.m om.m mm.N av.m m¢.N mm.m mm.m mm.m mm.m o¢.N H¢.~ vmma mh.m mm.m mm.m mm.~ mo.m No.m mm.m mm.m om.~ om.m Nb.m mh.m mmma mm.~ Ho.m mm.~ mm.m mo.~ mh.N wh.m mm.m m¢.~ mm.m mm.m hv.m Nmma hm.m hm.m mm.m om.~ mo.m NH.N Ho.m mm.a mm.a om.a mm.a mm.a Hmmal mm.H mo.a mo.a ¢~.H m¢.H om.a on.a oo.a hm.a mo.m oo.m av.m omma av.m hm.H mm.a m¢.H av.a hm.H bN.H hH.H ¢H.a om.a mo.a mm.a mwma mm.m H>.H mH.N ¢¢.m mv.m om.~ Hm.m ¢H.N oo.m mo.m mo.m Ho.m mvma mo.a H¢.H hH.H mN.H o¢.H m¢.a Hm.a om.a Hm.H mH.m gm.a mm.a bgma om.m mm.~ om.~ go.m m¢.~ mm.m mm.m hm.m om.~ mm.m Hm.m ¢O.m ovma w:5b mm: .umd .nmz .Qmm .GMb .Uon .>oz .uoo .ummm .ms¢ >H5b Hmow .HmmHIova .spcofi Mom Apmumammocsv Honmsn mom mUHum mmmum>m .mmammm nmmnm .ba magma 216 Table 18. U.S. per capita sales of fresh oranges by period. 1947-1961. in pounds. Crop Year. Period I Period II Period III 1947 13.75 16.11 10.95 1948 11.56 14.96 8.60 1949 9.54 12.05 7.90 1950 8.65 13.43 9.23 1951 9.50 13.60 9.45 1952 8.22 13.87 8.99 1953 9.31 13.07 7.63 1954 7.94 13.23 7.44 1955 7.33 12.85 7.89 1956 6.92 11.54 7.15 1957 6.91 9.89 4.05 1958 4.64 10.49 5.77 1959 6.13 11.62 5.36 1960 3.82 9.33 4.65 1961 4.07 8.89 4.69 Sources: Annual sales of fresh oranges are estimated by the Crop Reporting Board. unpublished data from the U.S. Department of Agriculture were used in estimating sales by period. ‘ , .qfl’fi. 7‘ oi“! / 9'. “um...“l . 3-..- , av." '7 a . *— ECUM U SE OMY "‘11111111111ES