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Lena. v fun-i 0r 94 ] mm 4‘ This is to certify that the dissertation entitled PRICING FLUID MILK WITHIN FEDERAL MILK MARKETING ORDERS: A SPATIAL ECONOMIC ANALYSIS presented by James Edward Pratt has been accepted towards fulfillment of the requirements for Doctor of Philosophy degreein Agricultural Economics Major prof or Date {/97/K4 / / MS U is an Affirmative Action/Equal Opportunity Institution 0- 12771 RETURNING MATERIALS: bViESI_J Place in book drop to remove this checkout from LIBRARIES m your record. FINES will be charged if book is returned after the date stamped below. 99R? ’39” (r 6’5 59 m i 5 9213 05')? ,“ 7 i" 5 g; f8 it, Vii!‘ MAY 21997 E595 car 1 51999 PRICING FLUID MILK WITHIN FEDERAL MILK MARKETING ORDERS: A SPATIAL ECONOMIC ANALYSIS BY James Edward Pratt A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1986 VkflEBEG ABSTRACT PRICING FLUID MILK WITHIN FEDERAL MILK MARKETING ORDERS: A SPATIAL ECONOMIC ANALYSIS By JAMES EDWARD PRATT Processors who purchase milk and process and distribute fluid milk products are characterized by much larger scales of operation than the producers who provide them with milk inputs. As such, the bargaining power wielded by a processor, relative to individual producers, is immense. Combined with the perishability of milk, the seasonal and counterseasonal patterns of milk supply and consumption, as well as the strong weekly pattern of retail sales relative to a nearly constant weekly supply of milk, increase the potential for market disorder. This situation and the general plight of depression era farmers lead to enactment of the Agricultural Marketing Agreement Act of 1937, which formed the basis and established the authority for federal milk marketing orders (FMMO's). Location adjustments, the major focus of this study, are used in nearly all FMMO's to provide for downward adjustment of prices paid by Class I processors located at increasing distances from the major consuming centers. These adjustments are intended to enhance the competitive environment among handlers and to provide an incentive for producers to deliver milk to plants located at or near market centers. A spatial microeconomic model of the firm is used to demonstrate that costly transportation can lead to monopolistic/monopsonistic behavior, which includes price discrimination and freight absorption. Using NEDSS, a network model of the spatial organization of the northeastern U.S. dairy industry, four theoretical spatial pricing systems for pricing Class I milk supplies are analyzed: discriminatory, uniform mill, uniform delivered, and cost-minimization. For each of three storability classes, the impacts of spatial pricing on optimal plant locations and milk and milk product movements are investigated. Results indicate that optimal Class I and Class III processing locations are relatively insensitive to the type of spatial pricing system which is used. Class II processing locations, hOwever, are sensitive. Although Class I assembly costs increase under each spatial pricing scenario, there are partially compensating cost effects which can occur in the costs of product distribution in all classes and in Class II milk assembly. To Thomas Alvin Whitby and all the other young people who have been asked to give so much, on faith. iv ACKNOWLEDGEMENTS The following is but a partial list of some of those individuals who have assisted me in the preparation of this dissertation and throughout my academic and nonacademic careers. Stan Thompson, my major professor, and Ken Boyer and Larry Hamm, members of my dissertation committee, gave me their valuable advice and guidance during my graduate study and dissertation preparation at Michigan State University. Andy Novakovic, my ex officio chairman, and Bob Story gave me problem-orienting direction as well as valuable encouragement. The support, over the years, of Emerson Babb, Charles French, and Cal Conner in my academic pursuits is also acknowledged. In this dissertation, I benefitted greatly from the substantial mathematical and programming skills of David Jensen. Wendy Barrett, as always, provided me with first class assistance in the preparation of the final document and Joe Baldwin preformed his usually clean work on the figures. The NE-126 Regional Research Committe, provided a forum to discuss the issues addressed in this analysis. The New York Department of Agriculture and Markets, Division of Dairy Industry Services has provided valuable support for parts of this research and for much of my research effort at Cornell. A special word of thanks goes to my associates in dairy marketing at Cornell, who have made my work interesting and rewarding. To my parents, Charles and Thelma Pratt, C. A., Helen, and Sonya, I express my thanks for years of support and encouragement. Also, I thank my many friends and associates at Kalamazoo College, Purdue, VPI, Michigan State, and Cornell for providing the personal exchanges which V make university education enjoyable. My many fishing buddies, especially Dale, have made my life much more enjoyable, particularly during those times when things haven't been going well. Finally, I would like to thank Mildred Warner, who's encouragement and advice finally conviced me to make the effort to complete this dissertation. vi BIOGRAPHICAL SKETCH James Edward Pratt was born August 13, 1947 in Kalamazoo, Michigan. He was raised in Comstock Township, Kalamazoo County, where he graduated from Comstock High School in 1965. From 1966 to 1970, he served with the U.S. Air Force as a weapons maintenance mechanic and crew chief of weapons loading crews. He was stationed in the U.S., Thailand, and Vietnam. In January of 1970, James entered Kalamazoo College where he majored in economics and minored in religion/philosophy. He graduated in June of 1972 and then entered the master's program in the Department of Agricultural Economics at Purdue University, where his M.S. thesis work involved a study of low-income rural residents in southern Indiana. After graduating from Purdue in May of 1974, James worked as a Research Associate at VPI & SU, returning to Purdue as a Research Associate in the area of dairy marketing in 1976. In 1978, James entered the PhD program in Agricultural Economics at Michigan State where he concentrated on spatial economics, transportation and logistics. After completing his coursework and preliminary examinations in June of 1980, he accepted a Research Associate position in dairy marketing in the Agricultural Economics department at Cornell, where his work has emphasized transportation, logistics, and spatial economics as they relate to issues in dairy marketing. vii TABLE OF CONTENTS DEDICATION ........................................................ iv ACKNOWLEDGEMENTS .................................................. v BIOGRAPHICAL SKETCH ............................................... vii TABLE OF CONTENTS ................................................. viii LIST OF TABLES .................................................... x LIST OF FIGURES ................................................... xiii I. INTRODUCTION ................................................ 1 1.1 Overview ................................................ 1 1.2 Purpose of the Study .................................... 6 1.3 Outline of the Study .................................... 8 II. THE DAIRY INDUSTRY AND FEDERAL MILK MARKETING ORDERS ........ 9 2.1 Production .............................................. 9 2.2 Consumption ............................................. 11 2.3 Marketing ............................................... 15 2.4 Instability in Milk Markets ............................. 19 2.5 Federal Milk Marketing Orders ........................... 22 Establishing or Amending an FMMO ................... 24 Handlers ........................................... 24 Classified Pricing ................................. 26 Pooling ............................................ 27 Other FMMO Provisions .............................. 27 Pricing Differentials .............................. 28 III. THE ELEMENTS 0F SPATIAL ECONOMICS ........................... 32 3.1 Introduction ............................................ 32 3.2 The Evolution of Theories of Spatial Economics .......... 36 Von Thunen ......................................... 36 Weber .............................................. 36 Hoover ............................................. 37 Losch .............................................. 37 Locational Interdependence ......................... 38 3.3 A Simple Model of Spatial Demand ........................ 38 3.4 Three Spatial Pricing Systems ........................... 43 Discriminatory Spatial Pricing .................... 44 viii Uniform Mill Pricing (f.o.b. or simple monopoly pricing) ...................................... 49 Uniform Delivered Pricing (c.i.f.) .................. 52 Summary ............................................. 53 3.5 Competition Over Space ............................... 54 3.6 The Spatial Model and Economic Performance ........... 66 3.7 Summary .............................................. 74 IV. THE ANALYTICAL MODEL ......................................... 76 4.1 Introduction ......................................... 76 4.2 The Northeast Dairy Sector Simulator ................. 77 Transshipment Formulation ........................... 80 Supply .............................................. 83 Consumption ......................................... 85 Marketing Costs ..................................... 96 Assembly of Raw Milk ........................... 96 Distribution of Finished Products .............. 97 Processing ..................................... 99 Numerical Implementation ............................ 102 The Minimum Transportation Cost Scenario ............ 112 4.3 The Proposed Analysis ................................ 113 4.4 Summary .............................................. 114 V. ECONOMETRIC ANALYSIS AND RESULTS ............................. 116 5.1 Introduction ......................................... 116 5.2 Base ................................................. 117 5.3 Discriminatory Pricing ............................... 122 5.4 Uniform Mill Pricing (f.o.b.) ........................ 133 5.5 Uniform Delivered Pricing (c.i.f.) ................... 143 5.6 Summary .............................................. 151 VI. SUMMARY AND CONCLUSIONS ...................................... 155 APPENDIX A. MONOPSONISTIC SPATIAL PRICING ......................... 163 Monopsonistic Discriminatory Pricing ................. 164 Monopsonistic Uniform Mill Pricing ................... 165 Monopsonistic Uniform Delivered Pricing .............. 166 APPENDIX B. PLANT LOCATION AND ASSEMBLY AND DISTRIBUTION MOVEMENTS FOR EACH SPATIAL PRICING SYSTEM ............. 167 BIBLIOGRAPHY ....................................................... 192 ix .10 LIST OF TABLES Coefficient of Localization, Selected Groupings of Manufacturing Industries, 1980 ........................... Typical Milk Composition ..................................... Use of Market Supply of Milk, 1983 and 1980 .................. Lowfat and Skim Sales as a Percent of Total Fluid Sales in FMMO's ................................................... Measures of Growth in Federal Milk Order Markets, Selected Years, 1947 to 1984 ...................................... Estimated 1980 Milk Marketings in the NEDSS Study Area, by State ................................................. Products Included in NEDSS Demand Categories ................ Percent Butterfat and Solids-Not-Fat in Each Product Category ................................................. Calculations of Component Structures for Selected Product Categories ............................................... Estimated Per Capita Consumption for Each Product Category, 1980 ..................................................... Equivalent Per Capita Consumption for Each Product Category, 1980 ..................................................... Per Capita Consumption for Each Product Class, Converted to Raw Milk Equivalents in Hundredweights ................... Per Capita Consumption of Product Catetgories, Adjusted for Class I-Class II Butterfat Transfers (cwts raw milk/capita /year) ................................................... Total Marketings and Consumption Estimates for the NEDSS Study Area ............................................... Average Cost of Processing Raw Milk Into Fluid, Soft, and Hard Manufactured Products, 1980 .............................. 3 10 12 87 88 89 90 91 92 93 94 95 .10 .11 .12 .13 .14 .15 .16 .17 Summary Characteristics of Milk Assembly for Each Product Class: Base Solution ..................................... 118 Summary Characteristics of Processing for Each Product Class: Base Solution ..................................... 118 Summary Characteristics of Product Distribution for Each Product Class: Base Solution ............................. 119 Class I Summary Characteristics: Discriminatory Pricing Solutions ................................................ 123 Class II Summary Characteristics: Discriminatory Pricing Solutions ................................................ 124 Class III Summary Characteristics: Discriminatory Pricing Solutions ................................................ 125 Total Marketing Cost Summary: Discriminatory Pricing Solutions ................................................ 126 Summary Characteristics of Milk Assembly for Each Product Class: Discriminatory Pricing, 30% Freight Absorption .... 128 Summary Characteristics of Processing for Each Product Class: Discriminatory Pricing, 30% Freight Absorption .... 128 Summary Characteristics of Product Distribution for Each Product Class: Discriminatory Pricing, 30% Freight Absorption ............................................... 129 Class I Summary Characteristics: Uniform Mill Pricing Solutions ................................................ 134 Class II Summary Characteristics: Uniform Mill Pricing Solutions ................................................ 135 Class III Summary Characteristics: Uniform Mill Pricing Solutions ................................................ 136 Total Marketing Cost Summary: Uniform Mill Pricing Solutions ................................................ 137 Summary Characteristics of Milk Assembly for Each Product Class: Uniform Mill, +129¢ ............................... 138 Summary Characteristics of Processing for Each Product Class: Uniform Mill, +129¢ ............................... 138 Summary Characteristics of Product Distribution for Each Product Class: Uniform Mill, +129¢ ....................... 139 xi .18 .19 .20 .21 .22 .23 .24 .25 Class I Summary Characteristics: Uniform Delivered Pricing Solutions ................................................ Class II Summary Characteristics: Uniform Delivered Pricing Solutions ................................................ Class III Summary Characteristics: Uniform Delivered Pricing Solutions ................................................ Total Marketing Cost Summary: Uniform Delivered Pricing Solutions ................................................ Summary Characteristics of Milk Assembly for Each Product Class: Uniform Delivered, -60¢ ........................... Summary Characteristics of Processing for Each Product Class: Uniform Delivered, -60¢ ........................... Summary Characteristics of Product Distribution for Each Product Class: Uniform Delivered, -60¢ ................... Total Marketing Cost Comparison: Three Spatial Pricing Scenarios ................................................ xii 148 148 149 .10 LIST OF FIGURES Individual Gross and Net Demand and Changing Elasticity; X-l ...................................................... 42 Individual Gross and Net Demand and Changing Elasticity; X— - 1/2 ................................................. 42 Individual Net Demands and Marginal Revenues ................. 46 Aggregated Net Demand, Simple Monopolist's Marginal Revenue, and Discriminating Monopolist's Marginal Revenue ......... 46 Hotelling's Extension of Cournot's Competitive Model ......... 56 Price Reactions Under Three Types of Spatial Competition ..... 59 Profit Switching Point Under GO Competition .................. 62 The Basing-Point Pricing System .............................. 65 Zero Profit Equilibrium and Market-Wide Marginal Cost Pricing .................................................. 73 Counties and States in the NEDSS Study Area .................. 79 Example Transshipment Network ................................ 81 Supply Points Used in NEDSS .................................. 84 Consumption Points Used in NEDSS ............................. 86 Actual Locations of Fluid Product Processing Plants .......... 103 Locations of 80 Aggregated Fluid Product Processing Centers Estimated for the NEDSS Study Area ........................... 104 Actual Locations of Soft Dairy Product Processing Plants ..... 105 Locations of 10 Aggregated Soft Dairy Product Processing Centers Estimated for the NEDSS Study Area ................... 106 Actual Locations of Hard Dairy Product Processing Plants ..... 107 Locations of 17 Aggregated Hard Dairy Product Processing Centers Estimated for the NEDSS Study Area ................... 108 xiii .11 .10 .11 .12 .13 .14 .15 Network Representation of NEDSS .............................. 109 Price Surface for Class I Milk Supplies: Base ................ 121 Price Surface for Class I Milk Supplies: Discriminatory Pricing, 30% Freight Absorption .............................. 132 Price Surface for Class I Milk Supplies: Uniform Mill Pricing, +129¢ Location Adjustment ........................... 142 Price Surface for Class I Milk Supplies: Uniform Delivered Pricing, -60¢ Location Adjustment ............................ 152 Class I Assembly Movements: Base ............................. 168 Class I Distribution Movements: Base ......................... 169 Class II Assembly Movements: Base ....................... ‘ ..... 170 Class II Distribution Movements: Base ........................ 171 Class III Assembly Movements: Base ........................... 172 Class III Distribution Movements: Base ....................... 173 Class I Assembly Movements: Discriminatory Pricing 30% Absorption ........................................... 174 Class I Distribution Movements: Discriminatory Pricing, 30% Absorption ........................................... 175 Class II Assembly Movements: Discriminatory Pricing, 30% Absorption ............................................ 176 Class II Distribution Movements: Discriminatory Pricing, 30% Absorption ........................................... 177 Class III Assembly Movements: Discriminatory Pricing, 30% Absorption ........................................... 178 Class III Distribution Movements: Discriminatory Pricing, 30% Absorption ........................................... 179 Class I Assembly Movements: Uniform Mill Pricing, +129¢ .................................................... 180 Class I Distribution Movements: Uniform Mill Pricing, +129¢ .................................................... 181 Class II Assembly Movements: Uniform Mill Pricing, +129¢ .................................................... 182 xiv .16 .17 .18 .19 .20 .21 .22 .23 .24 Class II Distribution Movements: Uniform Mill Pricing, +129¢ .................................................... 183 Class III Assembly Movements: Uniform Mill Pricing, +129¢ .................................................... 184 Class III Distribution Movements: Uniform Mill Pricing, +129¢ .................................................... 185 Class I Assembly Movements: Uniform Delivered Pricing, -60¢ ..................................................... 186 Class I Distribution Movements: Uniform Delivered Pricing, ~60¢ ..................................................... 187 Class II Assembly Movements: Uniform Delivered Pricing, ~60¢ ..................................................... 188 Class II Distribution Movements: Uniform Delivered Pricing, -60¢ ..................................................... 189 Class III Assembly Movements: Uniform Delivered Pricing, -60¢ ..................................................... 190 Class III Distribution Movements: Uniform Delivered Pricing, -60¢ ..................................................... 191 CHAPTER I INTRODUCTION 1.1 warm "...The earth is often in astronomical calculations considered as a point, and with substantially accurate results. But the precession of equinoxes becomes explicable only when account is taken of the ellipsoidal bulge of the earth. So in the theory of value a market is usually considered as a point in which only one price can obtain; but for some purposes it is better to consider a market as an extended region."1 We've all uttered or encountered the phrase 'time is money' at some point. Yet, except in the cases of personal travel and mail services, the thoughts that 'space is money' or 'distance is money' are less frequently entertained by most of us. The reality of economic life, however, is that all movements across geographic space are costly. Microeconomic theory has not generally embraced costly, or 'economic', space. Undoubtedly, some economic problems do not warrant the treatment of markets as extended regions, where multiple prices for a single commodity may exist contemporaneously. However, there are some economic problems which do warrent such treatment and in these cases, the typical use of the traditional microeconomic model does not serve well. lHotelling, H. "Stability in Competition." The Economic Journal 39 41-57. 1929, p.45. Early attempts to analyze the location of economic activity by Von Thunen, Losch, Weber, and Hoover faced this issue squarely, but were never fully integrated into generally received theory. Subsequent theoretical work by Smithies, Chamberlin, Hotelling, and Robinson and the antitrust analyses of Machlup, Stocking, and Loescher were treated as special cases. More recently, work by Greenhut, Ohta, Benson, and others has focused on the maturation of a general spatial microeconomic model. The need for a general spatial microeconomic model for the study of spatial pricing and market organization becomes more important for economic sectors which are relatively localized and high in transporta- tion intensity. In such sectors, the potential for spatial monopolistic or monopsonistic behavior is high and price surfaces which depart from the transportation cost gradient can be expected. Using data from the U.S. Bureau of the Census, coefficients of localization, measuring the geographic distribution of production relative to markets, can be calcu- lated for manufacturing sectors [Nourse]. In Table 1.1, a value of zero for the coefficient indicates that production, measured by employment, is distributed exactly as the market size, measured by personal income. A value of one would arise if all production took place in one region which had little or no income. The food and kindred products sector shows a relatively high degree of localization across states. Printing and publishing and electric equipment are equally localized. Tobacco product manufacturing, textile products, and leather goods have among the lowest degrees of localization. Table 1.1 Coefficient of Localization, Selected Groupings of Manu- facturing Industries, 1980. SIC Industry Coefficient* Code 20 Food and kindred products .15 21 Tobacco products .83 22 Textile mill products .65 23 Apparel and other textile products .34 24 Lumber and wood products .37 25 Furniture and fixtures .33 26 Paper and allied products .23 27 Printing and publishing .15 28 Chemicals, allied products .24 29 Petroleum and coal products .40 30 Rubber and miscellaneous plastic products .27 31 Leather and leather products .49 32 Stone, clay, and glass products .30 33 Primary metal industries .34 34 Fabricated metal products .21 35 Machinery, except electric .20 36 Electric and electronic equipment .16 37 Transportation equipment .32 38 Instruments and related products .31 39 Miscellaneous manufacturing industry .30 *Calculation done on the basis of individual states. Source: U.S. Bureau of the Census, Annual Survey of Manufacturing 1981 and t t st ca b t ct o the Uni ed States 1986. In 1984, intercity rail and truck transportation activities ac- counted for approximately 7% of the total farm-to-consumer food marketing bill.2 Indications are that for dairy products, this may fall 2United States Department of Agriculture. 1984 Handbook of A r c tur Cha ts. Agricultural Handbook No. 637. more in the 20% to 40% range [Aplin and Hoffman, Agribusiness Associ- ates, and Lee et. a1.]. Due to its highly perishable nature, continu- ous, biological production system, and widely-dispersed farm production sites, raw milk (approximately 87% water) must be picked up from farms daily, or every-other-day, and routinely transported to processing centers which may be a few or several hundred miles away. Processed products must then be re-transferred through spatially dispersed market- ing channels for ultimate distribution to consumers. Improvements in refrigeration and transportation technologies, public investments in road networks, and innovations in dairy product processing, which have introduced significant economies of size, have all tended to maintain or increase the geographic size of market areas for milk inputs and for dairy product sales. These circumstances, combined with increasing specialization of milk production on larger farms in more concentrated areas, which tend to be distant from dairy product consumption centers, have maintained the transportation activity involved in marketing milk and dairy products. From the inception of specialized processing facilities, vs. on-farm processing, the retail markets for dairy products have been highly competitive, with numerous occurrences of 'price wars' initiated by processors to capture wholesale market segments, often geographic areas, from rival processors, or initiated by retailers in order to attract new consumers. Given the market characteristics of raw milk, these price wars often led to instability in producer prices and market opportunities. Counter seasonal patterns in fluid milk consumption, compared to raw milk production, also led to highly variable prices and to sudden changes in producer marketing opportunities. Producers, finding themselves in relatively weak bargaining positions, have formed bargaining agencies to counter the processors' market power. A major institutional goal of such agencies is a desire to achieve equity among members. This manifests itself in efforts to ensure that all producers share in the high-valued returns from sales to fluid processors and are paid on some type of equal basis. These two goals historically resulted in 1) 'pooling' schemes where groups of producers pooled their receipts from processors and then redistributed them, and 2) the quotation of a 'base' price paid to all producers which is adjusted to reflect the distance of each producer's milk from the processing plant, and conse- quently its value. Likewise, before the rigorous interpretation of antitrust statutes and legislation enabling the establishment of federal milk marketing orders (FMMO's), localized fluid milk processors formed committees, associations, and other organizations for the purpose of administratively determining the prices which all members would then offer for milk received at their plants. Space is an important consideration in the pricing of milk within the area of a market's supply and has been recognized in the pricing systems, whether negotiated or administered, which have evolved since the time when the processing of dairy products became specialized. The consideration of a milk marketing area as a point may well serve the study of interregional trade and competition, however, it is a premise of this study that a single milk marketing area is characterized by a constellation of prices, because of the presence of costly, economic space within the marketing area. Therefore, the analysis of the prices of a single milk market must explicitly recognize its spatial character, in the same manner as the actual shape of the earth is important to studying the movement of the equinoctial points. 1.2 Purpose of the Study With passage of the Agricultural Marketing Agreement Act of 1937, FMMO's, as they are known today, were authorized. FMMO's were intended to redress some of the marketing conditions which contributed to exces- sive market risks placed on milk producers. FMMO's have developed, through the administrative, legislative, and judicial processes, a highly complex variety of tools used to establish the system of marketing rules and formulas under which the participants in a regulated market must operate. One of these tools is the enforce- ment of minimum prices which processors must pay for milk received in their plant; an administered pricing system. This administered pricing is only one of many aspects of FMMO's. Under the assumption that producers pay the cost of transporting their milk, FMMO-administered pricing systems typically take the form of a uniform f.o.b. basing-point price, where a market center is specified and used as the basing-point. Prices throughout the administrative area are then specified as the base-point price minus an estimate of transportation costs. This spatial price adjustment is intended to 1) provide an incentive to producers to ship their milk to consumption centers and 2) to equalize raw product costs to comparably located, competing processors. In a theory of spatial microeconomics, where monopoly/monopsony power occurs naturally and price discrimination results, the absorption of some freight charges by the monopolist/monopsonist would be warranted by profit maximization. Additionally, administered prices which perfectly reflect transportation costs give no incentives for producers to ship their milk in the most efficient, market cost minimizing, pattern nor for processors to obtain their milk inputs or to locate in total market cost-minimizing locations. To encourage efficient move- ments of milk and efficient processing locations, administered milk prices, over space, must depart from the perfect values dictated by transportation costs. The objective of this study is to analyze the use of transportation costs to spatially adjust the administratively determined milk prices received by producers and paid by processors who are regulated under FMMO's. While price location adjustments can be used to encourage efficient (i.e., marketing cost-minimizing) market performance, criteria other than full transportation costs may be appropriate to use in such location adjustments. An empirical investigation to measure the impacts of alternative location adjustments on efficient market performance is carried-out using a spatial network model of the northeastern U.S. dairy industry. The specific objectives of this analysis are to: 1) Describe the general system of spatial pricing currently used in most FMMO's; 2) Define and describe several spatial pricing systems in the context of a general spatial microeconomic model; 3) Evaluate the potential market performance impacts of alterna- tive price location adjustments, using a mathematical program- ming model of the northeastern U.S. dairy industry; and 4) Identify the implications for public policy suggested by the results. 1.3 Outline of the Study In the following chapters, the dairy industry and federal milk marketing orders are described, a general microeconomic model of the spatial economy is presented, and a mathematical programming model of the northeastern U.S. is developed to analyze the impacts of using several alternative spatial pricing systems to specify administered prices for milk used in fluid products. Chapter II describes the characteristics of the dairy industry which resulted in the promulgation of FMMO's and the general operational tools of FMMO's, including the spatial aspects of FMMO administered pricing. Chapter III presents the elements of a general model of spatial microeconomics. Three spatial pricing systems are defined and described using this model. In addition, the issues of competition over space and competitive equilibrium and efficiency are addressed. In Chapter IV, a mathematical programming model of the dairy industry in the northeastern U.S. is presented. While retreating to the position of specifying points in geographic space, the high degree of spatial disaggregation of the mathematical programming model is intended to closely approximate characteristics of the spatial microeconomic model. Chapter V presents an analysis of spatial pricing systems using the mathematical programming model, and Chapter VI discusses these results and their implications for public policy. CHAPTER II THE DAIRY INDUSTRY AND FEDERAL MILK MARKETING ORDERS The production, consumption, processing, and marketing of milk and dairy products has undergone some very significant changes in the last century. New biotechnology innovations and processing techniques, which will maintain the pace of change, loom on the horizon. With all these past and current technological advances, however, milk still is and will likely remain a relatively perishable, transportation intensive product. 2.1 Production Although the composition of milk varies slightly with breeds of cows, geographic location, season of the year, and management practices [Grippen], water remains the predominant component. The remaining components, especially the butterfat, can be separated from the water and used in the processing of various.dairy products. The approximate average composition of a hundred pounds of milk is given in Table 2.1. Milk is produced by means of a continuous, biological process. Cows are usually milked two (and occasionally three) times per day and the normal lactation period is about 300 days. It takes approximately 27 months for a newborn calf to mature enough to enter the milking herd, thus, short-run expansion of the milk supply is severely constrained biologically, even though some expansion can be obtained by altering feed composition and feeding rates, by more frequent milking, and by less culling of cows in operations which are not constrained by facility capacities. CHAPTER II THE DAIRY INDUSTRY AND FEDERAL MILK MARKETING ORDERS The production, consumption, processing, and marketing of milk and dairy products has undergone some very significant changes in the last century. New biotechnology innovations and processing techniques, which will maintain the pace of change, loom on the horizon. With all these past and current technological advances, however, milk still is and will likely remain a relatively perishable, transportation intensive product. 2.1 Production Although the composition of milk varies slightly with breeds of cows, geographic location, season of the year, and management practices [Grippen], water remains the predominant component. The remaining components, especially the butterfat, can be separated from the water and used in the processing of various dairy products. The approximate average composition of a hundred pounds of milk is given in Table 2.1. Milk is produced by means of a continuous, biological process. Cows are usually milked two (and occasionally three) times per day and the normal lactation period is about 300 days. It takes approximately 27 months for a newborn calf to mature enough to enter the milking herd, thus, short-run expansion of the milk supply is severely constrained biologically, even though some expansion can be obtained by altering feed composition and feeding rates, by more frequent milking, and by less culling of cows in operations which are not constrained by facility capacities. 10 Table 2.1 Typical Milk Composition Me an LeugL. Water 87.5% Lactose 4.9 (4.4-5.3) Butterfat 3.7 (2.7-5.9) Casein 2.7 (2.9-4.3) Albumin (whey proteins) .5 Others (ash, minerals, vitamins) .7 100.0 Sources: Alexander, Grippen. Farm milk is an excellent medium for the development of bacteria and consequently, very perishable in nature. It is essential to cool milk to about 38°F as quickly as possible after milking in order to retard the growth of bacteria. Improvements in storage and cooling facilities on farms as well as refrigerated transportation have made it currently possible to collect milk every-other-day instead of the everyday pick-up typical before the 19605. New farm processes, which are on the technological horizon, may eventually extend this time period as well as reduce the amount of water which must be transported by a factor of 1.5 to 2.0 [Mortara]. Dairy production is characterized by specialized inputs; milk cows, milking machines, bulk tanks, coolers, piping and pumps, specially designed buildings, and skilled dairy farm management which are all resources with little or no value in alternative enterprises. The ll relatively high level of fixed costs associated with many of these specialized inputs retards both the rate of entry, when industry expan- sion is warranted, and the rate of exit for contraction. Milk production is highly seasonal. May and June, with high quality pasture and fresh forages and early spring calving, are the peak months and November, with the end of summer pasture and drying-off of cows, is the low month. Dairying has become a specialized farm enterprise with nine-tenths of all milk coming from farms which received at least half of their receipts from milk sales in 1978. It is also becoming specialized geographically. While all states produce milk, Wisconsin, California, New York, Minnesota, and Pennsylvania accounted for one half of the total production in 1983. In summary, farm milk is a highly perishable, complex multi- attribute commodity whose image as a 'homogeneous' product is very misleading. The specialized, biologically based production technology makes short-term adjustments in quantity produced relatively unrespon- sive to price changes. 2.2 Consumption The use of farm milk in consumer products consists primarily of fluid milk, cheeses, butter, and nonfat dry milk. These and other dairy products can be grouped by their storability, fluid products being the least storable and manufactured products, such as cheese, nonfat dry milk, and butter, being the most storable. 12 Table 2.2 Use of Market Supply of Milk, 1983 and 1980 Product Billion Pounds Percent of Total (milk eguivalent)* 1983 1980 1983 1980 Fluid 49.7 50.9 36 40 Butter 25.8 22.8 19 19 Cheeses (including cottage) 41.9 35.0 31 27 Other dried, evaporated and frozen products 16.3 15.5 12 12 Miscellaneous 3,9 2,1 __2 __2 137.6 26.3 100 100 *Fat basis. Source: Dairy Situation and Outlook. DS-401, July 1985. Among the above classes, the greatest seasonal variation in consumption is found in fluid milk products, for which consumption is highest in the fall and winter months and lowest in the spring and summer. Seasonality in fluid milk consumption is met by planning for large enough milk supplies to meet the needs during the peak consumption months. The resulting excess supplies in the low fluid milk consumption months is used in storable manufactured products. Population demographic charac- teristics such as age, race, and geographic area, as well as incomes and prices, play a significant role in determining the product mix and the quantities of dairy product consumption [Boehm 1976, Boehm 1975, Jacobsen]. The aggregate consumption of fluid products nationwide has been on a long-term decline. During the 1970's, the passage of the post World War II 'baby boom' population from the peak fluid milk consumption years to lower consuming adults has accelerated this decline. Four important 13 changes in the consumption of fluid products have had and will continue to have strong impacts on the organization of fluid milk markets [Manchester]. i) Regulations which required the pasteurization of milk, imple- mented initially by local health authorities, were instituted between 1897 and 1924, by which time most large municipalities had such ordinances. These requirements effectively marked the end of milk product processing done on farms and farm-based retail sales, and marked the emergence of milk processors as powerful market participants. The emergence of recent innova- tions in relatively small—scale dairy processing technologies and the increasing size of farms may make it possible to move some part of the processing/marketing activity back to farms [Mortara]. ii) The system of daily or every-other-day home delivery of fluid milk products has been superseded by the dominance of supermar- kets, both independents and chains, during the 19608. Previ- ously, thousands of individual customers were served by systems of delivery routes in particular market areas. These home delivery routes have been replaced by wholesale routes to a relatively small number of retail outlets. In addition, super- market chains have integrated back into processing. It was estimated that 20% of the fluid milk sold in FMMO's in 1978 was processed by chain stores in their own plants. This estimate was 35% for California [North Central Project 117]. Store sales, in contrast to home deliveries, have introduced a sig- nificant level of daily variation in sales [Christensen et al.]. iii) iv) 14 In order to supply stores with milk at peak times during a week, plants require greater deliveries of farm milk on Tues- days and Wednesdays and much lower deliveries on Friday through Sunday. Consumer acceptance of innovations in the packaging of fluid milk products, such as the use of paper and plastic containers, and the use of larger container sizes, combined with improve- ments in refrigerated transportation and storage, have signifi- cantly expanded the geographic extent of fluid milk markets. Homogenization and the reduced need for the consumer to see the creamline paved the way for paper containers which reduced container weights by over 50% and eliminated the need for returnable bottles. The use of plastic containers which can be molded in the processing plant has reduced the cost of con- tainers. The gallon sized containers have also reduced bot- tling and handling costs. Lowfat fluid products have recently emerged as a growing proportion of total fluid sales [Table 2.3]. The recent concerns with cholesterol and calcium will undoubtedly contribute to an increased consumer awareness of the specific component composition of all dairy products. Table 2.3 Lowfat and Skim Sales as a Percent of Total Fluid Sales in FMMO's Yeas. Esteem; 1965 9 1975 29 1984 40 Source: [Federal Milk Order Market Statistics: Annual Summaries] 15 Fluid product consumption, like milk supply, is relatively un- responsive to short-term price changes [Boehm 1976]. Demographic characteristics and changing tastes and perceptions are the prime movers. Consumption of manufactured, storable, dairy products, such as cheese, butter, powdered milk, ice cream, etc., have had varying trends. Personal, at home, consumption of butter and nonfat dry milk has been steadily declining for a number of years and may have reached a stable, low level. Natural cheese consumption, especially that of American and Italian varieties, has shown significant growth. And, with increasing household incomes and changing tastes, the emergence of 'specialty' cheeses as a growth area may also prove to be significant. Ice cream and other frozen dessert consumption seems to be directly linked to population changes, while the consumption of other soft products, such as yogurt, have shown marked growth. The less perishable nature and the typical weight-reducing pro- cesses for the storable, manufactured products has differentiated their role in milk markets from that of fluid milk. Many of these products can compete in wholesale markets on a national basis and storage can be used as a means for evening-out seasonality. By contrast, even the largest wholesale and retail fluid market areas of today are, at most, regional in scope. 2.3 Marketing The characteristics of farm milk supply and dairy product consump— tion described above actually go a long way in determining the marketing characteristics present in the markets for farm milk. As noted above, l6 perishability and high moisture content are distinguishing features of fluid milk markets and are less pronounced in manufactured product markets. The reduction of seasonality in production and the almost counter-seasonality in fluid consumption, combined with the emerging dominance of store sales of fluid milk, at the demise of home delivery, have diminished the necessity for carrying seasonal fluid reserve sup- plies, but increased the need for maintaining daily and weekly reserves which are immediately accessible. Today's refrigeration and transportation equipment and facilities are impressive, yet even in the days before pasteurization and motor transport, milk in 40-quart cans moved significant distances to serve metropolitan fluid consumption. By 1916, the milkshed for the New York metropolitan area had expanded to a radius of 400 miles and more. "According to one well-informed writer, in 1879 milk trains ran regularly between New York and points more than 250 miles distant. He said that stations in Vermont located 210-250 miles out were shipping 400,000 gallons of milk a year to New York; also that milk held in a cooling tank for eight hours at Rutland, Vermont, 240 miles from New York, was being shipped at night and delivered to New York consumers by daybreak the next morning."[Spencer and Blanford, p.69] The intermeshing of technological innovations, consumer prefer- ences, and public interests have proven to be the catalysts for changes in the balance of market power in milk markets. Leland Spencer [Spencer and Blanford] has characterized the period of time before the federal government's role in milk marketing became forceful in 1933, as: 1) to 1880 - the era of small-scale competition, 2) 1880-1916 - the era of dealer pricing/dominance, and 3) 1916-1933 - the era of collective bargaining. 17 Subsequent to 1933, retailers, though not always directly involved in the bargaining of farm milk, emerged as an important market force. Each of these eras has seen the shifting of market power from one group to another and much of the public policy response, at least with respect to FMMO's, has been characterized by attempts to redress these market power shifts relative to some perception of a 'good' market situation. The pricing of milk by dealers was done on a 'flat-pricing' basis during much of the era of dealer pricing. Under this system, dealers paid a single price for all milk being used for fluid consumption. Dealer associations colluded to set a price which was not to be 'broken' to insure equal competition. Any changes which were desired in quantity were accomplished by adding or dropping producers. This single price was usually high enough above the prevailing manufacturing milk price to insure a ready reserve of producers. Base-excess pricing plans emerged as mechanisms to avoid the risky, unstable positions producers experienced under flat pricing. These plans were instituted by both dealers and producer groups. Under such plans, short-season bases were established and producers were paid the manufacturing price for production above the base. These plans were weak due to the lack of market responsiveness to long-run changes in demand conditions in the setting of bases and ineffective policing of dealer and producer behavior. Producer equity issues such as allocation and distribution of bases were also difficult to resolve. Classified pricing schemes, where milk was priced on the basis of its eventual use and proceeds were pooled among all producers, were instituted by milk marketing cooperatives in large metropolitan markets 18 between 1910 and 1930. Such systems were very dependent on producers presenting a united front in negotiations with dealers and, later, with processors, since access to uncommitted milk supplies provided a strong bargaining advantage for dealers. The development of the Babcock test for butterfat in 1890 brought about, albeit slowly [Spencer and Blanford, p.302], the system, still in effect today, of using butterfat differentials in pricing . Also, quality premiums, in the form of 'barn scores' based on farm inspections, were used by some dealers prior to 1920. There is also evidence of low-bacteria premiums being paid as early as 1910 [Spencer and Blanford, p.306]. Location and spatial pricing differentials, the focus of this study, also played a role in the early milk pricing systems. Prior to 1897, most producers were paid on the basis of the flat-pricing system. In addition, the railroads assessed the same freight charges throughout the milk-shipping area of the New York-New Jersey market. Producers' net prices were unaffected by their location respective to the markets for their milk. Producers located closer to the market, members of the Milk Producers Protective Association, complained to the Interstate Commerce Commission (ICC) that they were being exposed to unfair competition from more distant milk producers and in 1897, they won a judgment that the flat freight charge was indeed unfair [Spencer and Blanford, p.811]. The ICC established a four-zone rate system which stood until 1916 when nearby producers again petitioned the ICC to revise the rate system because of a significant expansion in the milkshed. The ICC issued a new rate schedule, based on 20-mile wide l9 freight zones, for Boston in 1916, and in 1917 issued a schedule based on lO-mile wide zones extending 400 miles from the market for New York. This lO-mile zone system in New York continued in effect through the 1920's, as dairy cooperatives gained bargaining strength, and it became the basis for negotiated pricing systems, even as motor transpor- tation began to emerge as competition to the railways [Spencer and Blanford, p.875]. This same basic transportation differential system, negotiated before 1921, with lO-mile zones and a base pricing zone of 201-210 miles, is today an integral part of the New York-New Jersey Federal Milk Marketing Order. 2.4 Ingtgbiligy in Milk Markets Milk production and fluid product demand are characterized by nearly perfectly counter-seasonal patterns. Combined with perish- ability, these seasonal patterns require the presence of seasonal reserves throughout much of the production cycle in order to meet the peak demands in the consumption cycle which occur during the trough in the production cycle. Because of higher farm standards for fluid grade milk, the cost of producing milk eligible for use in fluid products is higher than the cost for producing manufacturing grade milk. Thus, the cost of carrying these fluid reserves is higher than the average cost of all milk production. The market solutions resulting from how to deal with these reserves are at the heart of the issues of 'instability' and 'orderly marketing' in milk markets. Processors and dealers who purchase milk from producers and perform the functions necessary to prepare and distribute it to retailers or directly to consumers are characterized by much larger scales of 20 operation than the producers who provide them with milk inputs. As such, the bargaining power wielded by a processor/dealer in his nego- tiating position with respect to many individual producers is immense. In its extreme, as in the flat pricing scheme noted above, this bar- gaining power can result in a system whereby producers are faced with the absence of a purchase offer at an otherwise acceptable price. Processor/dealers simply added or dropped producers as their input needs dictated. Producers were often left in positions of trying to find markets for their highly perishable product on very short notice. Producers, in order to redress this seeming imbalance in negoti- ating power formed associations to present a unified, stronger position in their negotiations with processors/dealers. Specific issues ad- dressed by these associations included the equitable sharing of markets by all producers (the base-excess and classified pricing plans noted above) and assurance of markets for member milk (which eventually led to these associations running their own manufacturing plants as balancing operations). Cooperative associations representing dairy producers reached a zenith of negotiating strength in the New York metropolitan milkshed during the period 1916-1922, when Dairymen's League Inc. (which became the Dairymen's League Cooperative Association in 1919) represented two-thirds or more of all producers serving the New York City market. This was a formidable market force which successfully carried out a general milk strike in October of 1916 to bring about negotiated contracts with New York City milk dealers. While the strength of the Dairymens League waned soon after 1922, the strength of dairy coopera- tives in general has increased over time to the point where an average 21 of 92% of producers marketing milk in Federal Orders belonged to co- operative associations in 1977. The average share of producers belong- ing to the largest four cooperatives was 86% and the average share of producers belonging to the largest cooperative was 64% [Babb et a1. 1979]. Larger shares of producer membership in cooperative associations present opportunities for increased organizational efficiencies through centralized control and direction of milk movements. "...the movement of milk from the farm to market is generally directed by the management of the coopera- tive association which largely negates the action of individual producers in determining point of deliv- ery of their milk."1 Additionally, it is sometimes contended that dairy cooperative associ- ation market power has become equal to or even eclipsed that of the processors/dealers in milk price negotiations and that a situation of bilateral monopoly (a monopsonistic buyer vs. a monopolistic seller) best represents the conditions present in most milk markets today. Microeconomic theory [Henderson and Quandt] suggests four possible market outcomes in such a situation: 1) the seller dominates and forces the buyer to accept his price, 2) the buyer dominates and forces the seller to accept his price, 3) the buyer and seller collude to set quantities in order to maximize joint profits and then bargain with respect to sharing these profits, and 4) the market breaks down. 1Federal Register, Vol. 39, No. 137, Tuesday, July 16, 1974, p. 26035, 7 CFR. 22 "It is not possible for the seller to behave as a monopolist and the buyer to behave as a monopsonist at the same time " [Henderson and Quandt, p.244]. The levels of profits generated by the dominant side of the market in cases 1 and 2 above‘provide lower bounds for their negoti- ations in case 3. 2.5 W2 The continual struggle for associations to maintain sufficient membership to effectively bargain with processors/dealers [Spencer and Blanford, Chap.XXVI] and the highly competitive atmosphere in which the processors/dealers competed with each other resulted in a continual slipping of any negotiated pricing systems back toward the characteris- tics resulting from the flat-pricing system [Novakovic and Boynton]. This series of 'breakdowns' and the general plight of depression era farmers culminated in the Agricultural Adjustment Act of 1933, its amendments of 1935, and, finally, in the Agricultural Marketing Agree- .» ment Act of 1937, which formed the basis and established the authority for FMMO's as they are known today. FMMO's are perceived by their administrators3 as having four very general purposes: 1) promote orderly marketing in fluid milk markets, 2) stabilize milk prices and improve producer incomes, 2Much of this material is based upon [USDA 1981, Kaiser, Boynton and Novakovic]. 3See [Boynton and Novakovic]. 23 3) establish the terms of trade between producers and proces- sors/dealers, and 4) assure consumers of adequate supplies of fluid milk at reasonable prices. Obviously, these are very general guides and their implementation into specific policy actions has evolved through a long history of adminis- trative hearings and court cases. The term 'orderly marketing,’ and its contemporaneous interpretation, [Manchester, Chap.8] has embodied the intent of FMMO's. In the description which follows, many terms, which have precise legal definitions, will be used in a general manner. Since the focus of this study is the generic issue of location differentials, it is felt that the very detailed legal definitions, which are necessary for the administration of FMMO's, would be unnecessarily burdensome. Addition- ally, while the general provisions of FMMO's are common to most orders, the specific implementation of any provision may take several different forms. The following description of FMMO provisions is intended to be generic and, as such, will not match the entire set of specific provi- sions which have been implemented for any particular order. Even though the analytical model of Chapter IV is based on the northeastern U.S., the model and the analysis for which it is used in no way are intended to reflect the particular, specific administered pricing system now in Ieffect in this geographic area. This will be clearly evident to those familiar with the federal and state regulatory specifications which are actually in effect in this area. The analytic model is used to investi- gate the general issue of location differentials. 24 t n o e d FMMO's are legal instruments, authorized by the Federal government, to regulate the marketing of milk in specific geographic areas. They are initiated by the Secretary of Agriculture after milk producers in the specific geographic area approve, by a two-thirds margin, a referen- dum calling for the establishment of an order. Before a referendum is held, however, a public hearing is conducted and the Secretary must give a favorable recommendation for the formation of the specific FMMO. The Agricultural Marketing Service (AMS) issues written copies of specific rules and regulations which would govern the order. Producers must pass the entire set of rules and regulations and cannot vote on specific items. This also applies in the case of amendments to an FMMO. Establishing the boundaries of the marketing area is crucial to the effective operation of an FMMO, since regulated handlers (i.e., milk dealers and processors who sell fluid milk products within an FMMO area), must conform to order regulations for milk sold inside and outside of the market area. With the natural expansion of fluid milk marketing areas, FMMO's have correspondingly expanded both through addition of new areas and by mergers, Table 2.4. nd r Handlers are the focal point of most of the provisions which have been instituted under FMMO's. Handlers who deliver fluid milk products on routes to points within the specified market area of an FMMO are subject to the provisions of that FMMO whether or not their plant resides within the market area. Handlers are regulated on the basis of the location of their sales. 25 .umoz pom owmuo>< \m .%Ho>wuoommou .mszoo .m.D ome bad .onma .oomH .omoH ou wawbuooom «n-0mma .mm-an¢a .on-omaa .mm-mm¢~ A.o>wuooumo mamoon mconH>oum wGAOwum Loans Go oumov .umoh mo 6cm \M .umoh we cam \d .oHanwm>m was damn r Om Hm m.m¢ oam.~¢ mmm.~a omw.wHH mam ¢¢0.HNH ms swoa no on m.w¢ smo.Hq mm¢.mm oo¢.naa Hoo.a mom.¢oa we owoa mm mm m.mm woa.oq m¢m.mo www.mma mam.H ne¢.¢¢H mm whoa mm on m.Hw moo.o¢ «ca.mo HH¢.m¢H wwm.H awn.mua we onaa we on m.mo Hom.¢m «sq.¢m who.mmfi Hem.a Hmm.NOH mm mwaa me so N.qo www.mu maw.¢¢ oaw.¢wa mm~.~ mam.ww om coma mm Hm «.mo «mo.mH wea.m~ Hao.mma mme.H mom.ee no mmaa mm as m.wm ooo.HH owe.wa dmm.mna HOH.H * mm omma Hm % m.mo wom.m owm.¢H omm.mmH Hma a on mead. mmmmmmm mammmmm mecso coAHHAz mumamm more: mamas mmmama xHHa obmuw HH< madam H mmmHo \m \A \N mmoum \H muonob a“ com: H mmmHo mofiuo>waob mucosuoum muoabams wcuuoxuma muoxuca can madman mowuo>waob CH com: noospoum no mo Jada no use» ou caom xaaa “convene moauo>aaov Honasz Honadz Housman mo wonadz mo omeCoouma mo “doaboum cowumaaaom mm muaHoood omeCoouom ew-NSmH .mumow bouooaom .muoxumz Hobuo xHHz Hmuobom aw nusouo mo monummoz ¢.N canny 26 Other provisions also govern the regulatory status of handlers such as: a) the percent of total plant sales which are fluid sales in the marketing order, b) if the plant is a producer-dealer which sells almost ex- clusively its own milk, c) if the plant sells bulk milk to other regulated plants, and d) cooperative associations shipping directly to pool plants may qualify as handlers. C e c n FMMO's require that regulated handlers pay at least minimum prices for the milk which they purchase from producers, based on the product use to which they put the milk. In most orders there are three classes: Class I Perishable: Fluid products such as whole, lowfat, and skim milk, Class II Semi-perishable: Soft products such as fluid cream, cottage cheese, yogurt and ice cream, and Class III Storable: Hard products such as cheese, butter, and nonfat dry milk. Until 1962, the year of the maximum number of separate FMMO's, each FMMO was responsible for determining the schedule of classified prices which would ensure adequate fluid milk for its market area and maintain an 'orderly' market. Subsequent to 1962 and the 'Nourse' report [UDSA 1962], FMMO's began to switch to a system whereby local FMMO's based their minimum Class II and Class III prices on the Minnesota-Wisconsin 27 (M-W) price series“ for milk used in manufacturing, usually taking the M-W as Class III and the M-W plus 10 cents as Class II. At the same time, Class I prices in each FMMO were based on the M-W plus a transpor- tation differential determined to represent the transportation costs of shipping milk from the upper midwest (approximately centered on Eau Claire, Wisconsin) to the basing-point in each order. In this manner, all FMMO's were linked to a barometer of the national supply/demand situation. 2991193 Equity among producers shipping to regulated handlers is addressed through the practice of pooling the value of receipts from regulated handlers and redistributing these receipts to producers on the basis of their respective quantities shipped. Pooling has been done in the past on an individual handler basis, however, only one FMMO currently does this. Pooling on a marketwide basis is done in all other FMMO's. Other Ems} Ergvis isms In addition to setting minimum prices, FMMO's perform many other functions. These are administered by a market administrator, appointed by the Secretary of Agriculture, who executes the directives of the order. Assisted by a staff of auditors, statisticians, economists, and technicians, each administrator is responsible for making the calcula- tions necessary to determine monthly prices, auditing and verifying the 49ee [Babb 1990]. 28 monthly reports made by handlers, and preparing and disseminating market information. The administrator is also responsible for the verification of weights, samples, and butterfat tests of milk received from producers for whom such services are not being provided by a cooperative. As deemed appropriate, the market administrator and his staff perform other tasks, such as special market research and establishment of voluntary promotion programs funded through deductions made from payments for producer marketings. In 1983 six such programs were in effect with many similar programs in effect under state and federal authorizations. Qualifying cooperatives whose members market milk under FMMO's are entitled to special benefits and privileges under many FMMO's. These include bloc voting for members on proposed or amended orders, repooling of members’ receipts, exemption from some market services payments for verification of weights and tests which they may provide for their members, and special pricing provisions. P c n f en a1 Several sources of pricing differentials are used by FMMO's. Class prices paid by handlers and blend prices received by producers are adjusted by fixed schedules to reflect the butterfat content of producer milk. Some FMMO's have instituted seasonal pricing plans to provide economic incentives for producers to reduce the seasonality of produc- tion. Location, or transportation, differentials are adjustments made to the minimum order prices on the basis of geographic location. Location adjustments, the major focus of this study, are used in nearly every FMMO [USDA 1984, Table 14]. Location differentials are 29 applied to both Class I and blend prices and currently these differen- tials are the same for both prices in all FMMO's. Nearly all orders provide for downward adjustment of prices paid by plants at increasing distances from the major consuming centers. These adjustments are intended to enhance the competitive environment among handlers by equalizing raw product cost across geographic points in the market. They are also intended to provide an incentive for producers to deliver adequate quantities of milk to plants located at or near market centers. "The principle of location economics and that of providing substantially equal raw product costs to all competing handlers (both of which we accept as desirable criteria) requires that different prices for Class I milk be established for various locations within any milkshed." "In addition, we are concerned with maintaining as high a degree of efficiency as possible in the organization of the milkshed. This can only be achieved where the fluid milk requirements are obtained from areas immediately adjacent to the market, so that surpluses will be processed into the more concentrated manufactured dairy products in the outlying areas of the milkshed, thus minimizing total transportation costs" [USDA 1962, P.II-l-lS]. However, this is a very difficult task. If location differentials accurately reflect bulk milk shipping rates, then producers paying these transportation costs and receiving these perfectly adjusted prices have no incentive to deliver milk to the plants located closer, and pre- sumably more efficiently, to the market center. If the rates of proces- sor price adjustment over space are perfectly reflective of bulk milk shipping costs, the processors will be competing on the basis of pro- cessing and distribution costs and will have incentives to locate at points which minimize total costs of these two functions. However, such a system would tend to make processors indifferent to the location of milk suppliers. 30 Location differentials in most FMMO's are currently specified at fixed value rates in market order provisions and, as such, must go through the administrative process to be changed. These types of changes can be made when other order provisions are being amended, but the history has been that location differentials do not change with transportation costs [Gerhardt]. It is reasonable to suspect that changes in these differentials generally lag behind and are usually below transportation costs, a case which would make deliveries to plants nearer the market center more difficult to attract. Additionally, with fixed base points, geographic shifts in population and production can create situations where previously specified differentials do not encourage milk to move toward market centers or emerging multiple market centers. Two Federal court cases have established the precedent that loca- tion differentials applied to Class I handlers must also be applied to the blend price of pooled producers [Blair vs. Freeman] and that 'nearby differentials,’ i.e. differentials paid specifically to producers located close to the defined market base which cannot be justified on the basis of costs, are illegal [Zuber vs. Allen]. There is still some question as to whether the use of different rates of differentials for Class I and blend prices is illegal as well. Similarly, direct-delivery differentials, where processors located close to a market center pay an additional charge, intended to compensate for additional hauling costs due to traffic congestion near the market center, have not been tested through litigation. The preceeding description of milk markets, pricing mechanisms, and location adjustments under FMMO's has shown the physical, economic, and 31 historical importance of location adjustments in pricing fluid milk. The following chapter describes three spatial pricing systems in the context of a general microeconomic model. The issue of spatial competi- tion is also addressed. In the subsequent chapters, a mathematical model of the northeastern U.S. dairy industry is used to analyse the impacts of using each of these three spatial pricing systems to price fluid milk. CHAPTER III THE ELEMENTS OF SPATIAL ECONOMICS 3.1 Int oduc o The inclusion of space as an explicit variable in microeconomic theory, when distance is costly, will be referred to herein as 'spatial economics' or 'the spatial model'. The spatial model involves more than simply an added dimension which serves as a price linkage between distinct markets in the traditional Samuelson-Enke multi-market trading framework. In the spatial model, the location of the firm is not taken as fixed and invariant, but is treated as a decision variable. The economic agent who makes decisions for the firm is free to treat plant location in the same manner as input and output decisions are treated in the more traditional microeconomic analysis [Greenhut 1956]. The agent is also free to choose the pricing rule which will be used to achieve the economic goal. This choice would be based on 1) an assessment of the nature of demand over space, 2) the firm's production costs, 3) the cost of distance, and 4) the conjectural price variation, i.e. how the firm assumes that other spatial rivals, either actual or potential, will react to any changes made in price/output. The essential question involved in choosing a plant location in economic space, where distance is costly, and in choosing a pricing structure over this space, is to determine the optimal, feasible extent of the market which is served by the plant. Individual demands and the density of consumers play an important role in the spatial model [Greenhut 1956 Chap VI, Benson 1980a, Greenhut 32 33 et a1. 1975]. In spaceless microeconomics, individual demand functions can be summed to derive an aggregate market demand function. In the world of economic space, individual demands do not sum as directly to the market aggregate [Greenhut 1978]. Since the price paid by the spatial consumer does not equal the price received by the plant, due to transportation, the plant faces consumers having demand functions which are net of transportation costs [Benson 1980a]. The gain or loss of a distant customer has a different impact on the demand facing the firm vis-a-vis an otherwise identical nearby consumer. As such, the spatial market is a differentiated market in which spatial price discrimination becomes a naturally feasible occurrence, even if individual gross demands are identical [Hoover, Greenhut and Ohta 1972]. Using models of the spatial economy with various sets of reasonable assumptions (i.e. assumptions used in spaceless microeconomic theory), many 'counter-intuitive' results can be obtained, vis-a-vis the space- less microeconomic model of the firm. Among these are the following: 1) In the spatial model where consumers are located continuously on a line or plane from the plant's location,...price discrimination always yields greater output for the spatial monopolist than does simple f.o.b. pricing.[Greenhut and Ohta 1972, p. 713] The classical price discriminating monopolist operating in a spaceless economy, (Robinson, Henderson and Quandt, p.215] faced with two or more separate markets, will produce the same quantity of output under either f.o.b. or discriminatory pricing. The perfectly discriminating monopolist in the spaceless economy [Henderson and Quandt, p.217], on the other hand, will produce more output than 2) 3) 34 his nondiscriminatory counterparts and, from a maximum output perspective, discriminatory pricing might be preferred. For a firm pricing its output at the plant (f.o.b. or 'mill' pricing) (see Section 3.4), operating as a monopolist with respect to nearby customers, but facing competition from distant rivals for more distant customers, it can be shown that the monopolistic portion of its net aggregate demand function will be more elastic than the competitive portion [Greenhut et al. 1975, Salop 1977, Salop 1979]. In addition, if the competitive rivals react to price changes by the firm with equal price changes of their own which are designed to protect their market area (Loschian competition), the equilibrium mill price for the firm operating in competition may be higher than the price under a pure spatial monopoly [Greenhut et a1. 1975]. Under the same market conditions as in 2) above, with the added constraints that firms will enter a market area until there are zero profits for each firm, a decrease in unit transportation costs can increase the product price. Decreases in fixed production costs can increase the product price. And, decreases in marginal production costs can decrease or increase product prices [Capozza and Attaran]. The above results and other dissimilarities in comparative static results between the spatial and spaceless models often depend crucially on the shape of the individual demand curves [Benson 1980a, Greenhut et a1. 1975] and on the assumptions made about the firm's conjectural variations with respect to its rivals [Benson 1980b]. Actual spatial 35 price surfaces which do not conform to the predicted results of the point-trading spatial models, where prices between trading points which actually trade differ by transportation costs, can be predicted by the spatial microeconomic model. With its explicit treatment of spatially generated monopoly elements, the model naturally results in occurrences of discriminatory pricing and freight absorption. Given the highly dis- persed and perishable nature of milk production, processing, and con- sumption, and the subsequent intensive transportation activity, the advantages of using an economic model which explicitly provides for space in analyzing intra-market pricing in FMMO's is deemed to be necessary. In the sections which follow, a brief review of the evolution of spatial economics is given (3.2). An analytical model is then presented (3.3) to describe three forms of spatial pricing: discriminatory pricing, uniform mill pricing (f.o.b.), and uniform delivered pricing (c.i.f.) (3.4). Monopoly and several forms of competition in the spatial economy are presented (3.5) and issues of economic performance in the spatial economy are investigated (3.6). Throughout this chapter, spatial pricing systems are presented from a spatial monopolist's point of view. This is done to conform with generally accepted practise in spatial economic literature. Fluid milk processors, however, are monopsonistic with respect to milk producers. Appendix A presents the three spatial pricing systems in the form of monopsonistic pricing and demonstrates the equivalence of these two points of view with regard to freight absorption. 36 3.2 lbs Evolupipp pi Theopigs of Spatial Economigs1 The early theories of plant location, which were forerunners to the more general spatial model used in this thesis; were not well integrated into microeconomics. Their focus was usually socio-historical or economic-geographical in nature. The few early studies which did attempt to integrate location with a more general economic theory were mostly of German origin and emphasized costs. V u e Johann Heinrich Von Thunen's theory of the location of agricultural production2 used transportation costs and a derived rent surface to explain the type of farm produce which would be most advantageously cultivated on plots of land which were successively more distant from a central town. The result drawn from his model is the familiar concen- tric circles of land use around the central town, where those products capable of returning higher rents (i.e. the highest net value per acre) are produced in the areas closer to the town. Webe; Unlike Von Thunen's system, which was based primarily on trans- portation costs and which took the locations of economic activity as 1The content of this section draws heavily from [Greenhut 1956] and [Isard]. 2Johann Heinrich Von Thunen, Der Isolierte Stagt in Begiehppg guf Lapdwigtschafp ppd Napionalokppomig (3rd ed., Berlin, Schumacher- Zarchlin, 1875). 37 given, Weber's system3 allowed for the inclusion of additional cost considerations, i.e., labor and agglomeration costs, and focused on the optimum location as the objective criteria. Similar to Von Thunen's system, however, Weber treated demand as an exogenous variable. Hem: Edgar Hoover4 sharpened the cost considerations proposed by Von Thunen and Weber. He categorized the costs factors of location into transportation and production factors. The cost of distribution as well as the cost of procurement are included in Hoover's transportation factors. Like Weber, Hoover's analysis depended on substitution among costs to determine an optimum location. Unlike Weber, he drew much clearer and sharper distinctions between the cost elements involved by emphasizing their unique characteristics. As with Von Thunen and Weber, Hoover abstracted from demand in his system of least-cost location analysis. 1.9.9911 August Losch5 is the best known of the 'market area school'. The interest of this approach is in finding the optimum marketing area, 3Alfred Weber, Qpe; dgp Stppdpzp pg; Industgign, Par; 1, Reine eor ndo ts (Tubingen, 1909) and Theopy of Location, translation by C.J. Friedrich, Chicago University Press, 1928. “Edgar M. Hoover, chppiop pf Epppomig Agtivity, 1st ed., McGraw-Hill, New York, 1948. SAusust Losch. WWW- Gustav Fischer, Jena, 1944. 38 given that buyers are distributed over space. Under such a premise, the demand curve facing a firm is no longer presumed to be horizontal, since customers at a distance face a higher gross delivered price. Losch's model, unlike Von Thunen's and Weber's, places a heavy emphasis on demand. Firms locating in a spatial world, with costly transportation, realize that they face a downward sloping demand and that the presence of competitive rivals is a possibility. Locat n nterde endence In attempts to extend the market area type of analysis, several authors6 have suggested broadening its framework to include: 1) freely moveable locations or planned locations, and 2) more general forms of anticipated price reactions (conjectural variations) on the part of rival firms. These extensions are intended to stress the attraction or repulsion of a firm resulting from the presence (actual or potential) of a rival. 3.3 A Simple Modgl pf Spppigl Qemgpd To facilitate the exposition and analysis of the spatial pricing systems, the forms of spatial competition, and the measures of market 59ee [Greenhut et. a1. 1975], [Hotelling], and [Smithies 1941b] for examples. 39 performance, a simple model of spatial demand will be presented in this section.7 This model will be modified or extended as further topics warrant in following sections of this chapter. For simplicity, assume that: i) there is a homogeneous set of n buyers distributed along a line from a single firm, such that the first buyer is at the seller's location and each successive buyer is one additional unit of distance away from the seller, ii) all buyers have identical downward sloping demand curves; and iii) the freight rate per unit of distance is a constant, t, such that: p - a - bq a,b>0 (3-1) 9 - % (a-p) (3-2) .n I IH or b (a-(m+tD)), (3-3) where, m - the seller's mill price t - the constant freight rate per unit D - the buyer's distance from the firm p - the delivered price, (m+tD) q - the individual quantity demanded and a and b are positive constants. In a spaceless market, where t-O, individual demand becomes, q - % (a-m) (3'4) 7This section draws from [Greenhut and Ohta 1975], [Hsu], [Beckman], and [Greenhut 1978]. 40 and aggregate demand facing the seller is, Q - B (a-m). (3-5) b In a spatial market, where t > 0, the maximum sales distance, i.e., the distance beyond which no buyers are willing to purchase the product, Do, is given by setting q equal to O in equation (3-3), such that, no - m. (3-6) The aggregate market demand would then be, Do Q - X l (a-(m+tD)) (3-7) D-O b In the case of buyers evenly distributed along the line, with density V, aggregate market demand becomes, D Q - v f0 % [a-(m+tD)]dD (3-8) 0 _ V‘a-mlz. 2bt For a line extending in both directions from the firm, (3-8) becomes Q - Yia;mli. bt (3-8') For the case of buyers evenly distributed over a homogeneous plane, aggregate demand becomes, Do f (a-m-tD)D dD do (3-8") 0 3bt:2 Taking the first and second derivatives of (3-8') and (3-8") with respect to m, the seller's mill price, reveals that over the range of economically relevant prices, i.e., a>m and m>0, both exhibit the expected negative slopes and both are concave, sz/dm2>0. In fact, 41 regardless of the shape (convexity) of the identical individual demand curves, it can be shown that the aggregate demand curve facing a single firm over the relevant economic space will be convex [Greenhut 1978, p.23]. Since the elasticity of the aggregate demand curve at a price depends on the shape of the individual demand curves, this has strong implications for the comparative statics of various competitive spatial models [Benson 1980a]. For example, if (3-1) is redefined as, p - m+tD - a-h qx, (3'9) x then q - is (a-(m+tD))1/x. (3-10) For x>O, of which x-l is the special, linear demand case of Figure 3.1, at a price, p*, the elasticity of demand increases for each successively more distant buyer. These increases of elasticity, when aggregated, increase the elasticity of the aggregate demand curve. In Figure 3.1, the elasticity at point B on the individual gross demand curve is less than the elasticity at the same price at point A on the individual's net demand curve. The net demand curve is adjusted to a delivered price by tD. As distance, D, increases, the individual net demand curves become relatively more elastic. For -lwpam N.m ouswwm «2.6 a. mecca .a HIN ”muwouummam mawwcmno mam panama uoz can mmouu Hmdpu>wch H.m oudmwh no: manta «a vac 43 successively more distant buyer. These decreases reduce the elasticity of the aggregate demand curve and in contrast to Figure 3.1, Figure 3.2 depicts a situation such that, at price P*, the elasticity of the gross individual demand at C is higher than that of the net individual demand at D. In short, "anything which causes a spatial firm to lose or gain distant consumers, changes the elasticity of the aggregate demand faced by the firm."[Benson 1980a, p.1103] 3.4 Ihgee Spgpial Ppigipg Sysgems This section describes three spatial pricing systems which will be used in the analysis of intra-order milk pricing. These systems are hereafter referred to as 1) discriminatory pricing, 2) uniform mill pricing (f.o.b.), and 3) uniform delivered pricing (c.i.f.). In re- ality, firms could use modifications or mixtures of these systems. For example, a firm might price discriminatorily over a spatial range of customers and use f.o.b. pricing beyond that range, or a system of discriminatory freight zones might be used rather than individual discriminatory prices. For the purposes of this analysis, where the effects of each pricing system on market performance is desired, mix- tures or modifications of these pricing systems, for the most part, will not be analyzed. 44 W9 As was noted in section 3.1, a spatial market is characterized by differentiated individual demand curves. This provides a natural environment for the operation of a perfectly discriminating pricing system. Figures 3.1 and 3.2, however, indicate that, at a price, the elasticity of individual demand could be either increasing or decreasing with distance, depending on the shape of the individual demand curves. The optimal direction of price discrimination by a firm, i.e., against nearby buyers or against distant buyers, is determined by whether or not individual demand schedules vanish at some finite price and, if not, by the shape of the demand curve. If demand does vanish at a finite price, "spatial monopolists discriminate generally against nearer buyers regardless of the shape of the demand curve--concave, linear, convex, or some mixture of all" [Greenhut and Ohta 1975, p.77]. "Without vanishing demand, the monopolist will discriminate against distant buyers, to the extent possible due to resale possibilities, if the demand curve is more convex than a negative exponential, and will discriminate against nearby buyers if the demand curve is less convex than a negative exponential" [Greenhut and Ohta 1975, p.84]. In the absence of resale restrictions, discrimination against distant buyers is limited by the possibility of nearby buyers reselling the product to distant buyers. Distant buyers, however, taking delivery at their own locations will be unlikely to make up the double freight charge of reselling to nearby buyers.10 Thus, it 9This section draws from Hsu. 10Note, in this instance, if the distant buyer actually contracts (Footnote Continued) 45 is assumed in this study that discrimination against nearby buyers is the most likely possibility. Figures 3.3 and 3.4 depict the situation for a price discriminating spatial monopolist. In Figure 3.3, let the line segments p1q1, p2q2, and p3q3 represent the individual net demand curves for three identical spatial buyers, each successively more distant from the firm. The dashed lines emanating from p1, p2 and p3 represent the respective marginal revenues. In Figure 3.4, the line prsq is the horizontal summation of the average revenues and the discontinuous solid lines pb, cd, and ef represent the marginal revenue associated with prsq, i.e., the simple monopolist's marginal revenue, SMR. The continuous solid and dashed line pacgef is the summation of the individual marginal revenue curves, i.e., the discriminating monopolist's marginal revenue, DMR.11 If it is assumed that the monopolist has a constant marginal cost, MC, an intersection of MC with the line segment pa will produce the same results for the simple pricer as for the discriminator. In this case, only market 1 is served with the same quantity of output by each pricer. If MC intersects with ab above c, then the discriminator will produce more output than the simple pricer and he will serve both markets 1 and 2, while the simple pricer still serves only market 1. If MC intersects (Footnote Continued) the freight himself, he may be able to avoid the double hauling costs and would contract to have the product delivered to a nearby buyer instead. The characteristic of who actually contracts the freight service may be important with respect to enforcing a price discriminating system. 11Note that the aggregated average revenue has begun to take a convex shape and that as the number of buyers distributed evenly over space becomes larger, the DMR and SMR become more distinct with SMR lying below DMR at all points. 46 osco>om Hangman: m.umwaonocoz mafiumcwaauouwa use .o::o>om Hmawwumz m.umqaoaocoz onEHm .paoaoa uoz voudmouww< ¢.m ounwfih mosao>om Hosanna: was mucoaoo uoz Hmapa>wpca m.m ouswwm 47 ab below c, the discriminator and simple pricer will produce the same level of output, but it will be distributed differently between markets 1 and 2, with the discriminator reallocating output from market 1 to market 2. A similar succession of cases follows as MC is decreased. As the spatial division of buyers becomes finer, i.e., more individual demand curves are present, cases where the discriminator's output is greater than that of the simple pricer become more prevalent. Using the simple model presented in section 3.2, we can formulate the discriminatory spatial monopolist's pricing system such that: q - 1- (a-p) (3-2) b or q - % (a-(m+tD)) (3-3) where, m - the seller's mill price; t - the constant freight rate per unit; D - the buyer's distance from the seller; p - the delivered price; q - the individual quantity-demanded; and a and b are positive constants. In addition, total costs are T(Q) - CQ+F (3-11) where, Q - total quantity produced and sold; c - constant marginal production cost; and F - total fixed cost. 48 To make this section more complete,12 the buyer density, V in (3-8), will be defined by an arbitrary non-negative function over D, ¢(D), such that the market area has a physical boundary, R; ¢(D) if OR. Monopoly output can be expressed as, B Q - f q(D)¢(D)dD (3-13) 0 where BSR. Assuming the monopolist wishes to maximize profit, profit can be written as: Ed «a - f (ma-c) %(a-Pd) ¢(D) an - F (3-14) 0 where Bd - seller effective market area under spatial discrimination md - discriminatory mill prices; and Pd - md + tD. The seller chooses a function of md defined over D to maximize profit, n. Using calculus of variations [Hsu. p.53-54], this problem can be 12The question of quantity of output under discriminatory prices has been debated, with contrasting results [Greenhut and Ohta 1972, Greenhut and Ohta 1975, Beckman]. These differences can be partially attributed to the assumption made with respect to the monopolist's market area. If you assume that he will sell to the extent of his market in simple or discriminatory pricing, i.e., that his market area is fixed, then the two pricing systems yield identical output results. If you assume that he can expand his market area, discrimination may lead to increased output. Thus, in Figures 3.3 and 3.4, we are explicitly assuming that the spatial monopolist can expand his market area. 49 solved to show that the necessary condition that m3 be an optimal discriminatory price schedule requires m3 - a/2b +c/2 - cn/z. (3-15) Discriminatory prices for each buyer are a function of demand, cost of production, and cost of transportation, but are independent of buyer density. The extent of the market, Bd, however, does depend on the range of consumers since, D if D d0, (3-17) 0 Where BS is the extent of the uniform mill pricer's market, i.e. the distance beyond which no sales will be made, such that from 3-3, q - o - % <3-18) and B3 - a-ms t Marginal profit with respect to the uniform mill price, ms, is dug- Qs + (ms-c) 933 (3-19) 35; dms Applying integral differentiation,14 a-ms dQs - dS t 2 - l (a-ms-tB) ¢(Bs) as; dms b Bs + f - l ¢(D) dD (3-20) 0 b Since 0 - % (a-ms-tBs) from (3-18), (3-20) becomes 14 b If g(t) - f f(t,y)dy, and b - h(t), o b 921:1 - 99191 . f dD. (3-20) as; b o substituting (3-20) back into (3-19), Bs Qt. - g %(a'ms-tD)¢(D) dD dms 85 + (ms-a>(-l) f ¢ dn. b 0 Solving for mg, the optimum mill price, yields, at dn/dms - 0, mg - a/2 + c/2 - cfi/z (3-21) _ 38 where D - I Q ¢122 Q2. Bs f ¢dn 3:, the optimum extent of the uniform mill pricer's market is, a: - 9:9 + 5. (3-22) 2t The optimal uniform mill price, mg, is a function of demand, a, production costs, c, transportation costs, t, and the distribution of buyers, D - f(¢). The effect of transportation cost is dependent on the average distance, D, to buyers who are being served at the optimum mill price, "...where there is no attempt to differentiate among buyers, the seller treats his entire market as if it were at the same location" [Greenhut 1956, p.156]. As with discriminatory pricing, the monopolist finds it advantageous to absorb some freight costs. Under optimal uniform mill pricing and the specified functional form, he will absorb fifty percent of the freight to the average distance customer. 52 WW; (c.i.f.)15 To complete the possible theoretical extremes in spatial pricing, the uniform delivered pricing system is described here and used in the analysis reported in Chapter V. In a uniform delivered pricing system, the seller quotes an equal delivered price to all buyers within the extent of his market. Profit for the uniform delivered pricing monopo- list is, 30 «n - f (PD-tD-c)(fl;322 ¢(D) dD (3-23) 0 b Where B0 is the extent of the uniform delivered pricing monopolist's market, i.e. the distance beyond which he will not wish to make sales, that point where, FD - tBD - c - 0. (3-24) such that BD - PD-c t marginal profit with respect to the delivered price is, PD-c 3:9 - g( g ) . (PD-tBD-C)-(a-PD) ¢(D) dD dPD dPD b 31) _ + f a - 2P9 + tD + c ¢(D) dD (3-25) 0 b From (3~24), the first term of (3-25) becomes zero, such that _ ED 919 - Bo (a-ZPp+C) + p f D ¢(D) dD. dPD b b O 15This section draws from Hsu. 53 Solving for PD at 2:9 - O, 915 - a/2 + c/2 + co/z (3-26) Where D is the average distance to buyers over the market extent, and, BIS—3‘ ___ (3-27) 2t 0 «and: Under a uniform delivered pricing system, the spatial monopolist's price, PE, is a function of demand, production costs, transportation costs and the distribution of buyers over the space, ¢. Summary In each of the three spatial pricing systems described above, the monopolist finds it advantageous to quote prices, either mill or deliv- ered, which reflect his willingness to absorb some portion of the freight costs involved in delivering the output to his customers. The magnitude and particular form which the absorption takes will determine the way in which a price surface predicted by the spatial microeconomic model differs from one predicted by point-trading models which do not admit freight absorption. Given these general formulations of three pricing systems, section 3.6 attempts to investigate the implications of the spatial economic model on market performance and to draw some very general comparative welfare implications. Before moving to these topics, however, the topic of competition over space must be addressed. Section 3.4 assumed complete spatial monopoly behavior, a very strong assumption. In the following section, 3.5, several forms of spatial competition will be considered and impli- cations for spatial pricing systems discussed. 54 3.5 Compepipipp Qge; Spage In section 3.4, the three spatial pricing systems, discriminatory, uniform mill, and uniform delivered, were described in the context of a spatial monopoly, where the optimum market extent of the monopolist was assumed not to overlap with any actual or potential rivals. In many spatial markets this would be an unwarranted assumption. Beginning with this section, the term 'competitive' will be used to refer to any market which is not monopolistic. More specifically, two firms whose optimum monopolistic market areas would overlap will be referred to as being 'in competition' or operating in a 'competitive market'. In spaceless microeconomics, the entry of rival firms is assumed to occur at the same point as the existing monopolist, thus the emphasis of such models is on the splitting or sharing of a given aggregate space- less demand as the number of firms increases. Cournot's original analysis [Cournot, Greenhut and Ohta 1975, Chap. 7], culminates with the result that, ”assuming each seller behaves competitively and entry is open, an oligopoly approaches the competitive output and price as the number of sellers increases without limit" [Greenhut and Ohta 1975, p.109]. In the spatial model, however, rivals have more choice with respect to the place of entry. They might enter at the monopolist's point, Cournot's assumption, they might enter near, but not exactly at, the monopolist, or they may enter at some distance from the monopolist. However, if they entered at a distance so remote as to result in no market overlap at optimum, profit maximizing prices, then from the above definition, they would not be deemed to be in competition. Thus, entry at a distance, and its many consequences, is the essential difference 55 between competition in the spaceless and spatial economic worlds. Rivals will only enter a spatial market at a distance if the freight cost advantage of serving nearby buyers offsets production cost dis- advantages over a sufficient number of buyers to make the rival location feasible. Entry at a distance in the spatial model increases supply, but also increases net, observed demand, since more customers are served, and/or average transportation costs are lowered. The subsequent price effect of a firm's entry at a distance in the spatial model is indeterminate without specific knowledge of the supply and demand functions. ”Occur- rences which affect only supply or demand in the spaceless world affect both supply and demand in a spatial world” [Benson 1980b, p.62]. Harold Hotelling, in his classic 1929 article on spatial competi- tion, firmly established the foundation for most subsequent spatial competition work. He did so as an extension of Cournot's oligopoly model which was shown to be unstable, with radical all-or-nothing shifting of buyers between sellers with only slight price changes, whereas, reality suggests "...gradualness in the shifting of customers from one merchant to another as their prices vary independently..." [Hotelling, p.44]. In his analysis, Hotelling posits two firms located at positions A and B at a-4 and b-l distances from the end of a line market of length l, with uniformly distributed buyers who have completely in- elastic demands of 2 unit of quantity each (Figure 3.5). Both sellers' products or services are homogeneous and there is positive constant unit transportation cost. 56 (II, _\ [111:1]!!!llJlLllJLlllljllllllllll:J Far-JP 4 A '4 ATJ a x y b Figure 3.5 Hotelling's Extension of Cournot's Competitive Model A and B may charge different mill prices, but neither must let his mill price be higher than the other's plus transportation costs to his own location or he will have no buyers. The simultaneous profit maxi- mizing prices at A and B, acting independently, can be shown to be 36 and 34, respectively, with qa-l8 and qB-l7. Hotelling dismisses the possibility of collusion, explicitly or by concerted behavior, by assuming that such a relationship would be too "fragile" to endure. If B is free to choose his location, given A, he will seek to make b, his monopoly advantage market area, as large as possible. He will locate as close to A, without being at A, as he can (thus approaching Cournot's model). Small changes in price will result in large numbers of buyers shifting between sellers, an unstable position. In Hotelling's model, profits for each firm are directly related to transportation cost. Higher transportation costs increase the wedge separating the two firms, effectively stretching £ so that each firm's 57 monopoly position is enhanced.16 Under such a situation, it would be in each firm's best interest to "...make transportation as difficult as possible" [Hotelling, p.50]. A number of variations on Hotelling's basic model have been sug- gested. These usually differ with respect to their 'conjectural hypoth- eses,’ i.e. how the firm views its rival's reactions to changes it makes in price [Benson 1980a, Greenhut et a1. 1975, Capozza and Van Order 1978, Salop 1977, Salop 1979, Capozza and Van Order 1977, Ohta, Benson 1980b, Benson 1984]. Three assumptions about conjectural variations appear most often: 1) Loschian Competition (L) Each firm assumes that its market area is fixed, i.e. that any reduction in its mill price, which is intended to expand its market area, induces an immediate and equal change in the price of its rivals so as to leave its market area unchanged. The Loschian competitor is assumed to price like a monopolist within its market area. 2) Hotelling-Smithies Competition (HS) Each firm assumes that its rival's mill price is fixed. The firm may price monopolistically over its natural monopoly market area, but it must beat it's rivals delivered price in those areas where both can profitably sell. 3) Greenhut-Ohta Competition (GO) 16With completely inelastic demands, all customers on 1 are served. With more elastic demand, some buyers may not be served, limiting monopoly profits. 58 The firm's delivered price at its market boundary is taken as fixed, i.e. a delivered price ceiling for each firm is parametrically given. Figure 3.6 depicts graphically the price relations in each type of competition. Two competitive firms, one located at O and one at a distance of D from O compete for buyers located between them. Each firm's delivered price increases with constant transportation costs. The boundary between the two firms will occur at the intersection of the delivered prices, RL. At RL, buyers will be indifferent as from which firm they purchase . Also at RL, Po + ti - P5 + t(D-R1) where Po - mill price for firm A P5 mill price for firm B D Distance between firms R1 - the market radius for firm A and t - constant freight rate solving for R1, R1 - 1/21: (PB-Po+tD). (3-28) If firm A should lower its price by AP, then under Loschian compe- tition, the rival will lower his mill price by AP, to keep the market boundary the same, RL. Thus, under Loschian competition, the new boundary price would be at point B, and dPfi/dPo - l and, from (3-28) dR/dPo - 0. Under L competition, the firm is faced with a fixed marketing area over which to maximize its profits. Thus, Bd, B§(3-22), and BB(3-27) are 59 P-AP’ ~ Figure 3.6 Price Reactions Under Three Types of Spatial Competition 60 parameters rather than variables. Under such a situation, discrimina- tory pricing is the most profitable system [Beckman]. Under HS competition, the rival firm at D is expected to maintain its mill price in the face of changes in the mill price of A, such that, dPfi/dPo - 0 and the intersection of delivered prices occurs at C, with firm A having a new radius of RHS: and from (3-28), dR/dPo - -1/2t. Under GO competition, the border price is fixed so that if A drops its price by AP, then B will increase its price by AP such that, dPfi/dPo - -1 and the intersection of delivered prices occurs at D, with firm A having a new radius of RGO» and from (3-28), dR/dPo - -l/t. GO competition, with maximum or ceiling delivered prices, takes neither its own market area as fixed (L) nor the prices of its rivals as fixed (HS), but only takes the maximum delivered price it can charge as fixed. It is unlikely to engage in pricing behavior which could result in delivered price schedules such as POEB and PfiCB in Figure 3.6, which could occur with Loschian competition. Under GO competition, the firm is faced with pricing decisions such as those covered for monopolists in section 3.4, but with an added constraint: a maximum delivered price. By parametrically varying the maximum delivered price, it can be shown [Greenhut and Ohta 1975, Chap.8] that the profit maximizing firm will use uniform mill pricing up to a point and then switch to discriminatory pricing. The profit levels 61 for f.o.b. and discriminatory pricing cross, for example in Figures 3.7 A and B, at some level of the maximum delivered price. "As the degree of competition increases, a spatial seller increases his profits by switching from discriminatory to nondiscriminatory pricing. Moreover, the switching point (i.e., when to switch) can be determined unambiguously if the demand conditions are known" [Greenhut and Ohta 1975, p.139] This switching can be shown to occur and to be independent of the shape of demand. 1) Profits for the unconstrained discriminatory monopolist are greater than those for the unconstrained f.o.b. pricing monopolist, regardless of the shape of gross demand. 2) Over the monopolist's natural marketing area, profits must decrease monotonically with decreases in P' (increased competition), regardless of the shape of gross demand. 3) The minimum P' related to discriminatory profit is the mill price for the buyer located at the plant. This will be greater than marginal cost, while the minimum P' related to f.o.b. profit for the same buyer will be equal to marginal cost. Bressler argues elsewhere that the level of fixed costs plays no role in efficient plant location; however, it plays a decisive role in the determination of discriminatory vs. f.o.b. pricing under GO competi- tion. In Figure 3.7A, if the level of fixed cost is F2F2, the zero- profit competitive equilibrium will occur at P2 and the firm must use discriminatory pricing or suffer negative profits (assuming zero marginal costs). If fixed costs are F4F4, the zero profit equilibrium will occur at P4 and the firm must use f.o.b. pricing. In this section, three forms of spatial competition, each based on an alternative assumption about a rival firm's price reactions, were reviewed. In the introduction to Chapter III, section 3.1, a 62 (1 Discriminatory F.0.B. Os OUTPUT. Discriminatory F.0.B. (A) MAXIMUM DELIVERED PRICE Figure 3.7 Profit Switching Point Under GO Competition 63 "counter-intuitive" example of prices rising with the level of competi- tion was given. The basis of this example can now be seen. If we assume that positive profits will attract new entrants in a market and that these rivals are most likely to enter at a distance, then any change which increases demand and, subsequently, profits, will lead to an increased number of firms. All firms will then be operating over smaller marketing areas and can face decreased elasticity (see section 3.3) of demand. This would occur under demand circumstances where the more elastic buyers are lost, leading to less elastic aggre- gate demands facing each firm. This situation results in greater monopoly power, i.e. a larger difference between price and marginal revenue, which could then produce the result of increased mill prices accompanying greater numbers of firms. Under the above demand condition (increasing elasticity of more distant buyers), changes in any other parameters which affect market areas can similarly produce counter-intuitive results [Capozza and Attaran]. An increase in the density of buyers, a decrease in the freight rate, or a decrease in the level of fixed cost could all result in increased mill prices. Finally, it is appropriate at this point to review one final form of spatial competitive behavior which has received much attention in the past; basing-point pricing. Under a basing-point(s) system, all sellers, wherever they are located, quote identical delivered prices to buyers. These are typically made up of a base price plus transportation costs from a base mill(s) to the delivery destination. With the U.S. Supreme Court decision of 1948, which upheld the illegality, under antitrust laws, of the use of a basing-point system in the cement 64 industry, many studies of the basing-point pricing system and its consequences were done [Machlup, Loescher, Stocking]. Figure 3.8, which is essentially the same as Figure 3.6 with the market areas extending in both directions from each of two rival firms at O and D, graphically presents the essentials of a basing-point pricing system. Under Loschian competition, firm A, at O, and firm B, at D, will establish a mutual market boundary at RL, where A's delivered price, mill plus transportation costs, 'beats' B's from O to RL and to the left of O and even though B has a cost disadvantage, DP§>OPO, its delivered price 'beats' A's from D to RL and to the right of D, pre- sumably a large enough market to warrant the establishment of firm B. Under basing-point pricing, with A as the base mill, instead of estab- lishing its own mill price P5, B will take the delivered price schedule of A, PRL to P6, as its own and compete with A over the same market area. The difference between PDPRL or PfiPb and PRLPé being known as 'phantom freight'. A third firm located at X would, under a basing- point system with A as the base mill, also quote delivered prices of PoPé. Basing-point systems can emerge and persist in the absence of explicit collusive behavior on the part of participating firms. Once the base mill price is determined, or simply announced, known freight rate schedules can be applied to determine the delivered price for every buyer location. Such a system usually results in very stable, if not greatly enhanced, prices since one firm or agency is making all deci- sions of price changes. A slight variation on the single basing-point system is the multi- ple basing-point system where more than one base mill exists. If firms 65 \ .. N .1 r-P“"'“'"'" "‘ ,5: o x ’FIRM A‘ 7111111 1:" Tm Figure 3.8 The Basing-Point Pricing System 31d ‘ B 66 A and B were regarded as base mills in Figure 3.8, firm C, at X, would use A's delivered price schedule for any delivery point to the left of RL and B’s delivered price schedule for delivery points to the right of RL. Under conditions where the firm locating at a distance, B, has a cost advantage, DPfi < 0P0, "the firm locating at a distance would be foolish not to set its own net-mill f.o.b. price independently of other existing prices, and thereby gain full control over the distant segment of the market” [Greenhut 1956, p.78] However, if the distant rival has no cost advantage and is relatively small, it may fear a price war with plants located at O and conform to the basing-point price schedule. 3.6 at od conomic e f ce As was seen in section 3.3, the elasticity, at a price, of the aggregate net demand facing a firm, which operates in the spatial model, depends on the shape of the individual demands. The gain or loss of distant buyers due to production or transportation cost changes or due to the entry of rival firms at a distance (section 3.5), can have opposite effects on some basic measures of performance such as price and output, depending on individual demand conditions [Benson 1980a]. Without specific information about the shape of individual demand and the level of costs, no clearly unambiguous comparative statics results can be generated. There are, however, two topics of social welfare in the spatial model which can be addressed in a more general fashion: 1) In a competitive spatial model, there are "agglomerative tendencies" which result in firms tending to "cluster unduly", [Hotelling] pgpgpis ppzipps and 2) the spatial model, with costly transportation, ensures 67 that individual firms cannot have perfectly elastic demand and, conse- quently, any zero-profit equilibrium, where average revenues equal average costs, will necessarily result in a situation where price is higher than marginal cost. Hotelling (section 3.5) addresses the first topic. He assumed a line market of length 2 with firms located at points A and B, a and b units of distance from each end, respectively (Figure 3.5). There is a uniform distribution of buyers, each with an invariant one unit of demand. Given the fixed locations, total transportation costs can be minimized if X equals Y, i.e. if the firms charge the same mill price. Since a, the area in which A has a clear advantage, is larger than b, the area in which B has a clear advantage, A's price will be higher than 3'8 and, consequently, X will be less than Y. Some buyers closer to A will find it to their advantage to buy from B and total transportation costs will not be minimized. "If the stores were conducted for public service rather than for profit their prices would be identical in spite of the asymmetry of demand" [Hotelling, p.53]. With moveable locations, the least transportation cost locations would be at the quartiles of 3. However, even if A chose one of these locations, it would be in B's best interest to locate as close to A as possible on the side of A with maximum length so as to gain control over the largest market segment. Subsequent entrants will similarly gravi- tate toward prior locations, rather than disperse in an optimum manner. With greater than perfect inelasticity of individual demands, the incentive for B to locate as close to A as possible is diminished. B, however, would not move as far away as minimized transportation costs would require. 68 Benson addresses the second welfare issue. Free entry in spatial competition, prompted by positive profits for existing firms, combined with the necessarily downward-sloping demand facing each firm results in Chamberlinian tangencies between average revenue and average costs at points where both are downward sloping.17 This occurs when profits are driven to zero. This presents a situation where price is higher than marginal cost and where average cost is not at its lowest point. This situation, brought about by the spatial element, is pointed-out as prima facie evidence of the inherent inefficiency in spatial markets. Bressler states, "in short, competition is not and cannot be effective in bringing about low costs and the optimum organization of plants and facilities...it is clear that spatial monopoly creates an unstable situation and can be expected to result in an excessive number of plants and correspondingly higher-than-optimum costs" [Bressler, p.119]. An alternative view of this situation takes the position that the inevitable difference between price and marginal cost is actually a payment to cover a social cost. The under-allocation of resources is offset because of social benefits which are external to the firm. "The excess of f.o.b. mill price over site-specific marginal production cost is the additional marginal cost of output due to the existence of alternative sites" [Benson 1984, p.283]. To see this argument, start with the following spatial price relationship, P - Pm+tD (3-29) 17This section draws from [Benson 1984]. 69 where P - delivered price Pm mill price t - constant freight rate, and D - the buyer's distance from the firm. Individual net demand can then be represented as and in a linear market extending two directions from the plant, firm's aggregate demand becomes Do Q(Pm) - 2 f £(Pm + tD) dD 0 Do 5 f'1(02-Pm, Do 5 I t 2 where T - the physical maximum market length. Profit for the single firm becomes W ' Pm ° Q(Pm) - C(Q). where C(Q) - the firm's production cost function. Aggregate market demand, when there is more than one firm, 06 Q(Pm, N) - 2N f f(Pm+tD)dD 0 where N - number of firms. Presuming N evenly spaced firms throughout the market area, 95 s f'1(O)-Pm, 95 s 51 c N where D6 denotes the maximum extent of the market. If it is assumed that all potential buyers are served, i.e. D6-T/2N, then each firm's proportion of total sales, S-Q/N, is (3-30) a single (3-31) (3-32) (3-33) becomes (3-34) (3-35) 70 S - 2 2° f(Pm+tD)dD/N (3-36) ' 3(Pm1NiT) and marketwide demand can be stated as a function of the number of firms and the mill price, Q - N~S(Pm,N).18 (3-37) dQ/dN - S+N dS/dN - S - D6 - f(Pm+tD6). (3-38) As firms enter the market, the left term of (3-32) holds at an equality and entering firms can sell over their maximum potential market area without affecting the market areas of existing firms. In this situation, the entry of new firms should increase effective market demand by substantial amounts. Total aggregate demand continually increases, with entry, because more customers are served or because total transportation costs decline. However, at some point the left term of (3-35) holds at an inequality and all firms are unable to sell over their maximum potential market area and the increments to demand become smaller and smaller. 18 Do d(f f(Pm+tD)dD) dS/dN - o , 95 - T/2N - h(N). dN From footnote 14 in section 3.4, D6 dS/dN - dD6/dN - f(Pm+tD6) + f d(f(Pm+tD)) an o dN since dD6/dN - -T/2N2 and d(f(Pm+tD)) - 0, dN then dS/dN - -T/2N2 - f(Pm+tD6) - -D6/N - f(Pm+tD6). 71 Buyers' benefits which result from the entry of new firms are not reflected in the revenues of existing firms. Likewise, the costs of establishing new locations are not seen in the existing firms' cost functions.19 As such, N, the number of firms, does not enter as a decision variable in any firm's profit equation, but does exist as a cost for the market. A firm's total cost function, C, can be expressed as, TC - C(N,S(Pm,N)) (3-39) and each firm's profits will then be n - Pm - S(Pm,N,D6) - C(N,S(Pm,N,D6)), (3-40) where D6 appears in the cost and demand functions because competing firms will maximize their profits over their supply area of length D6. D6 depends on the firm's mill price relative to his rival's. Profit maximization requires, de arm dD6 3P; - 9. - 9S - 99 - 9S. - dDé - 0 (3-41) dS de dS dD' 3P; Pm - dC/dS - s 99 + 99. , dD6 . (3-42) Under Loschian competition, where, dD6 - 0, (3-42) becomes 31’; Pm - 99 - _§_. (3-43) dS gs de 191f the entry of new firms affects the costs of production, through competition for inputs, then part of entry costs may be borne directly by existing firms which have no decision control over N. 72 If it is assumed that 1) buyers have identical gross demand and are uniformly and continuously distributed over the market area, 2) firms face identical production costs, 3) firms are evenly dispersed, and 4) firms have identical conjectural price variations, they will all charge the same mill price, (3-43). Additionally, firms will enter the market until profits are driven to zero (necessitating the additional assumption of completely portable locations). The equilibrium occurs when firms perceive their Loschian demand, S(Pm,N,D6), as being tangent to site-specific average cost (C/S), the Chamberlinian tangency (Figure 3.9A). At this point, total revenue, Pm - S(Pm,N,D6), equals total cost, C. Market equilibrium, where market- wide total revenues equal marketwide total costs, can now be expressed as, N-Pm-S(Pm,N,D6) - N-C(N,S(Pm,N,Do)). (3-41) If there is a change in some exogenous variable, K, which alters Pm (such as the price of substitutes), then the impact on the market can be expressed as, N - (S(Pm,N,D6) + Pm - as + Pm - as - dD6) , am 5K de dD6 3?; 3K 9 -N-<99._ds +9q.__ds .th .de as de dS dD6 3?; 3K" + (C(N.S(Pm.N.Dé)) + N. 99 + N . 99 . Q) 911 . dK. (3-44) dN dS dN dK From (3-41), the two terms in (3-44) which are multiplied by de/dK can be seen to sum to zero, and 73 wcfioaum umoo Hangman: opH3-uome2 pcm adwunaawsvm uwmoum ouoN o.m oudwwm . m . .< .23 .31.... as: e As: A: - 2352. n 3582: u u — llllllll'nl 2.2 see mznd lull-I'IIIIII ll'llll'llllrllllllll lull 1m. 9 “moo us.— unaum mmamz ofiu you poumaaumm muoucoo wcummoooum uosvoum hufima umom woodwouwm< OH mo acowumooq w.q muswwm 107 mucmam wawmmoooum uosvoum huudo who: no mcowumood Hmauo< m.¢ unamHh 108 «my. boa—um mmamz on“. now voumawumm muousoo wcwmmmooum “.26on his cum: pouwmoumma. S no mcowumoog Cad 6.":me 44' 109 mmamz mo cowumucomounom xuosuoz HH.¢ madman HHHan l .mdo nmN HHHM HHHA I .QQU fl HHHM _ _ . SN: " 8“,: n 32.8: _ fine _ 3an n 938 "SS 83 u :3 u :3 _ . “ novoz _ moauaounmu _ . _ _ auu< “ nuvoz “ nuu< unoo . wsammuuoum " can auooo “ novoz “ uou< umoo " uuvoz " mou< panama .coauaaswaoo _ aowuanwuuman _ haasn . wcawmoooum .mcammououm _ aanfiumm< _ madaam .haaasm 110 top of each node or arc section in Figure 4.11 represents the actual number of nodes or arcs in each section in NEDSS. An outside supply node and an outside processing node for each product class are added to the number of nodes described earlier in the supply and processing sections. There are a total of 324,705 arcs and 2,370 nodes. This is a very large problem which requires substantial computing resources simply to generate, as well as to solve. The network solver used in NEDSS is an implementation of the primal simplex method for linear programs [Jensen]. The implementation takes advantage of: 1) the network structure of NEDSS. This is accomplished by implementing the revised simplex method and maintaining the basis and its inverse using list structures. The list struc- tures used are those developed by Grigoriadis and Hsu [Grigoriadis and Hsu, Grigoriadis] for RNET, a "minimum cost network flow" computer program written in FORTRAN at Rutgers University. The significance of using list structures to maintain the basis is that the pivot operations of the simplex method can be performed in a number of steps proportional to the number of nodes in the network. This is much faster than they can be performed by a general purpose simplex code. 2) the unique structure of this particular application. In Figure 4.11, it can be seen that there are actually four separate transportation problems embedded in the network: 1) production to processing, 2) Class I processing to Class I 111 consumption, 3) Class II processing to Class II consumption, and 4) Class III processing to Class III consumption. Each of these sections is "bipartite", i.e., the set of nodes can be partitioned into two subsets so that all arcs begin in one set and end in the other. This information may be used to store the endpoints, (FROM(i) and TO(i)), of an arc (i), as func- tions or subroutines with very efficient internal storage processes that are independent of the size of the problem. 3) the small percentage of arcs which are capacitated. From the problem description, the only arcs which are capacitated are the processing arcs. There are fewer of these arcs than there are nodes in the network. This observation is used to store the capacities as a function with internal storage equal to the number of processing nodes plus some amount independent of the problem size. The exploitation of these special properties (along with the implementa- tion of a program capability for using prior feasible solutions as initial, restart solutions for a subsequent problem) allows for the efficient solution of this very large problem. NEDSS can be operated in several different modes with respect to processing capacities and processing costs: 1) processing capacity at any potential location may be assumed to be unlimited and processing costs per unit can be assumed to be constant with respect to volume processed, 2) processing capacities at each potential processing loca- tion may be constrained to some amount and processing costs assumed 112 constant, 3) processing capacities can be unlimited with processing costs per unit assumed to decline with increased volume, and 4) process- ing capacities can be constrained and processing costs assumed to decline. When operated with variable processing costs. For all the results reported in Chapter V, NEDSS is not guaranteed to find the global optimum solution [King and Logan] due to the inclusion of nonlinear processing costs which are introduced by economies of scale in processing. An iterative heuristic procedure is used to find an approximate solution. The usual avenue of approach to analysis of intermarket trading problems is to specify production and consumption quantities or functions, marketing costs, and any applicable constraints and then to solve for approximate, cost minimizing flows and corresponding prices. For this analysis, it is proposed to start with this cost minimizing problem formulation and then to extend it by the use of pre-determined pricing systems, which will be imposed on processors as additional marketing costs. The pricing structure will be based on the three spatial pricing systems presented in Chapter III. The Minimum Transportation figs; §cgnagig For this problem, estimated 1980 supplies (Table 4.1), consumption (Tables 4.7 and 4.8), and bulk and processed product transportation costs (see earlier sections) are used. The processing of products is not constrained to occur at any particular locations. Processing of each class of product may take place at any of the 284 geographic points which are the union of the production points and consumption points (Figures 4.3 and 4.4). For these potential processing points, 113 capacities of each product processed at a particular location are not restricted. In addition, the processing costs of each location are made a function of the volume of milk processed at that location (Table 4.10). In this way, if the processing cost reductions due to increased volume processed at a particular location are larger than the increased assembly and distribution cost incurred by assembling and distributing over a larger area, NEDSS will increase the location's volume. This scenario is intended to represent NEDSS's "idealized" or "rationalized" organization of the processing and transportation of milk and milk products for 1980. 4.3 The Eroposed Analysis Typically, it is assumed that the markets which are being modelled in a spatial mathematical programming framework are ones in which competition prevails, i.e., that there is but one price in each market. Subject to the market clearing constraints, a solution to the transpor- tation cost minimization problem also solves the maximum valuation problem. If market coordination is directed toward minimizing transpor- tation costs, then producers will receive the largest possible net returns. As was seen in Chapter III, however, the spatial economy is distin- guished by a natural tendency toward monopolistic behavior, where price discrimination and freight absorption will be a natural element under various spatial pricing methods. Under conditions of spatial competition, where a firm may find that its market is bounded at some distance which is less than the optimum, it may still find absorption 114 advantageous. As such, market transportation cost minimization may be an inappropriate objective function. 4.4 Summary The specification of each spatial pricing system in NEDSS is accomplished by modifying the objective function values for bulk milk movements from supply points to Class I processors. These values can be considered as the actual differentials which processors face, rather than the total costs of transportation. Under discriminatory pricing, actual transportation costs are modified by reducing all possible transportation costs from supply to Class I processors to a proportion of their estimated values. The proportion represents the percent of freight absorption. For example, reducing all Class 1 supply costs to 30% of their estimated values, implies a 30% rate of freight absorption. At 100%, the discriminatory and base pricing scenarios are identical. Under uniform mill pricing, objective function values associated with movements of milk from supply to Class I processing are specified as a constant amount, limited to the actual transportation costs for each particular movement. As the constant is increased, that is, as the fixed rate of freight absorption increases to a level as high as the highest estimated transportation cost, the uniform mill prices and the base prices approach each other. Under uniform delivered pricing, objective function values associated with Class I supply movements are all reduced by a constant amount. These reduced values are limited to a level of 1¢ for each 75 115 miles. As the constant amount of reduction approaches zero, the uniform delivered prices approach the base prices. In Chapter V, the three spatial pricing systems described in Chapter III are specified and a variety of parametric solutions to NEDSS are obtained. Based upon estimated bulk milk transportation costs, the levels of FMMO location differentials, and on an implied rate of freight absorption, a single discriminatory pricing solution is selected for comparison to the base scenario. Particular uniform mill and uniform delivered pricing solutions are also chosen such that the total marketing costs of the chosen solutions nearly equal that of the chosen discriminatory solution. Plant locations, milk and milk product movements, and marketing costs for each of the chosen solutions are compared to the base solution. Chapter VI summarizes the results of the comparisons among spatial pricing solutions and draws conclusions based upon these results. CHAPTER V ECONOMETRIC ANALYSIS AND RESULTS 5.1 introduction Using NEDSS, a mathematical programming model of the spatial organization of the northeastern U.S. dairy industry, three spatial pricing systems for pricing Class I milk supplies are analyzed. For each class of milk product, the impacts of spatial pricing on optimal plant locations and milk and milk product movements are investigated. Each pricing system is characterized by freight absorption, whereby neither Class I milk processors nor producers pay the full amount of transportation costs, but each pays only a portion. In the mathematical model, where the locations and levels of milk supplies are given and fixed, prices specified under each of the three pricing systems determine the geographic price surface, or gradient, which, in turn, determines optimal plant locations and milk and milk product movements. A base, cost minimizing, solution of NEDSS is compared to a solution from each of the three spatial pricing systems described in Chapter III: discriminatory, uniform mill, and uniform delivered. A number of solutions for each pricing system are obtained and reported. However, only a single solution from each pricing system is chosen for comparison to the cost minimizing, base scenario. The solutions which are chosen for comparison are chosen such that each results in total marketing costs (assemble, processing, and distribution) which are nearly equal. 116 117 The specification of each pricing system is accomplished by modify- ing the objective function of NEDSS to reflect each particular pricing structure. For each analyzed structure, the cost of transporting bulk milk from supply points to Class I processing locations is modified. These costs are then considered as the actual differentials faced by Class I processors, rather than the marketwide bulk milk hauling costs. All other costs remain as specified in Chapter IV. In the sections which follow, the particular specification of each of the spatial pricing systems in NEDSS and the resulting solutions are described. Comparisons of physical characteristics as well as market- wide costs between the pricing systems are made. 5.2 Base To provide a standard of comparison, the parameters described in Chapter IV are specified and a solution to NEDSS is obtained which represents an idealized, total marketing cost minimizing solution. In this problem, the markets for all three storability classes are assumed to function in concert to minimize total marketing costs. Tables 5.1 to 5.3 and Appendix Figures B.1 to B.6 describe this cost-minimizing solution. As expected, fluid milk processing plants (indicated by triangles in Appendix Figures B.1 and B.2), locate at or near the consumption centers (indicated by squares) which they serve. These plants must then reach out from these consumption centers to obtain their required milk supplies (indicated by circles). The consumption orientation of Class I processing is apparent from the relatively large number of processing sites and distinct assembly movements and the much longer average 118 Table 5.1 Summary Characteristics of Milk Assembly for Each Product Class: Base Solution CLASS I II III Movements Number* 185 10 35 Distance (miles) Weighted Average** 62.4 15.0 10.1 Longest 220 81 73 Cost Total ($1,000) 7,782 584 1,972 Average (¢/cwt) 49.0 21.6 18.8 *Represents only those movements between two distinct geographic points. **Includes all movements. Table 5.2 Summary Characteristics Class: Base Solution of Processing for Each Product CLASS I II III Number of Locations 69 7 19 Pounds Processed (100,000) Total 5,509 Average 2,303 3,867 9,515 Largest 24,871 7,865 2,365 Smallest 253 1,298 Cost Total ($1,000) 40,106 5,892 9,522 Average (¢/cwt) 252.4 217.6 91.0 119 Table 5.3 Summary Characteristics of Product Distribution for Each Class: Base Solution CLASS I II III Movements Number* 74 144 158 Distance (miles) Weighted Average** 12.8 152.7 381.2 Longest 108 349 822 Cost Total ($1,000) 39,644 898 2,329 Average (¢/cwt) 249.4 33.2 13.6 *Represents only those movements between two distinct geographic points. **Includes all movements. 120 assembly distances as well as the much shorter average distribution movements. The large number of assembly movements are indicated in Appendix Figure B.1, while the relatively few distinct point-to-point distribution movements are indicated in Appendix Figure 8.2. Class II (Appendix Figures B.3 and B.4) and Class III (Appendix Figures 8.5 and B.6) plants locate at a distance from the major consuming areas, toward the major sources of milk supplies, minimizing the number and distance of relatively expensive assembly movements. This results in a relatively large number of distribution movements between points. As noted in Chapter IV [Table 4.9], a deficit in total milk supply is filled by the importation of Class III products from the midwestern U.S. through Sandusky, Ohio [Appendix Figure B.6]. The base solution also provides shadow prices, or imputed values, for milk delivered to processing plants. These shadow prices indicate the value of an additional hundred pounds of milk delivered to a plant. The shadow prices at the optimal Class I processing locations can then be used to map the optimum, market cost-minimizing Class I price gradi- ent for the study area. Figure 5.1 indicates these shadow prices (normalized to zero at Altoona, Pa.) and visually estimated positions of isovalue lines at 30-cent intervals. These imputed Class I values are highest in the New York-New Jersey-Connecticut-Boston area and fall as the distance from this population corridor increases. The highest differential is 149 cents on Long Island. Somewhat isolated population centers, closer to milk supplies, such as Buffalo, Pittsburgh, and Syracuse lay at much lower levels on the price surface. 121 swam ”moaannsm xHHz H mmmao now oommusm ooaum H.m shaman 50 «V v «v m a no as «a 6 av 3. 3 v n . 3 a. 2 av on v 0 an 3 9 «a on an «a on o. 3. 2. on 1 q '0 Q0? Q5 ON hp 0 N5 MN mm N? a n 2. 8 s 3.4“, 3 on a“ o ONw pN saw 000 . mm 0 00 00¢ 0' p? On 00 on a S n on wv or 122 5.3 121W To specify the discriminatory spatial pricing system in NEDSS, the objective function values for Class I bulk milk transportation costs are modified. Specifically, bulk milk transportation costs from every supply point to all potential Class I processing points are parametri- cally reduced to a percent of their initial values. The base solution serves as the point of departure for the discrim- inatory pricing systems and may be thought of as a discriminatory system where the Class I processors absorb 100% of the freight cost. This results in a uniform delivered price schedule (c.i.f.), where all pro- ducers would receive the same net price. As Class I bulk transportation costs burdens borne by the Class I processors are reduced to proportions of the actual hauling costs, both the mill and the delivered prices to producers at unequal distances from a given plant will not be uniform. Since the plants bear only a proportion of the costs, mill prices for supplies increase less rapidly at increasing distances from the plants as the percent levels of plant freight absorption are reduced. When the absorption proportion is zero, i.e., when Class I plants pay no part of the bulk milk transportation costs, a uniform mill pricing schedule (f.o.b.) results. Since transportation costs are the only criteria NEDSS has for assigning supplies to plants, a minimum Class I price gradient is specified. None of the stipulated pricing systems are allowed to push particular prices below this surface. This minimum surface is specified as l¢ per 75-mile zone, such that a 13¢ differen- tial would apply at 975 miles. At each percent reduction level, NEDSS is solved. 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Distance (miles) Weighted Average** 84.4 12.8 14.1 Longest 183 51 60 Cost Total ($1,000) 9,805 553 2,208 Average (¢/cwt) 61.7 20.4 21.1 *Represents only those movements between two distinct geographic points. **Inc1udes all movements. Table 5.23 Summary Characteristics of Processing for Each Product Class: Uniform Delivered Pricing, -60¢ CLASS I II III Number of Locations 74 7 17 Pounds Processed (100,000) Total 6,157 Average 2,148 3,867 11,792 Largest 21,571 6,710 2,607 Smallest 286 1,144 Cost Total ($1,000) 40,333 5,879 9,472 Average (¢/cwt) 253.8 217.2 90.5 149 Table 5.24 Summary Characteristics of Product Distribution for Each Class: Uniform Delivered Pricing, ~60¢ CLASS I II III Movements Number* 68 140 157 Distance (miles) Weighted Average** 7.7 136.0 337.7 Longest 108 302 822 Cost Total ($1,000) 39,104 803 2,312 Average (¢/cwt) 246.1 29.7 13.5 *Represents only those movements between two distinct geographic points. **Includes all movements. 150 and II processing costs are higher while Class III processing costs are lower. Distribution costs for Class I and II are lower and are higher for Class III. As in all the previous scenarios, Class I processors remain oriented to the consumption centers. Assembly movements closely resemble those of the discriminatory case, lacking the long-distance movements present under uniform mill pricing and lacking the compact assembly areas present in the base solution. Class I distribution movements in all four scenarios are similar, with discriminatory and uniform delivered pricing having slightly less movement. Class II processing center locations are similar in the base, uniform mill, and uniform delivered cases. Discriminatory pricing, however, departs from this pattern with Class II processing centers locating much closer to the major population centers. Assembly patterns for Class II are also quite similar in all cases with uniform mill pricing having slightly more compact assembly. Class II distribution movements show similarities in those cases with like plant locations, and relatively less movement in the discriminatory pricing case. Class III processing center locations are nearly the same in all three scenarios presented. The presence or lack of plants in central Pennsylvania and eastern Ohio being the only identifiable differences. Class III assembly patterns appear to be as compact under all four pricing schemes. Class III distribution movements are also quite similar in all four pricing scenarios. The magnitudes of price differentials under uniform delivered pricing with 60¢ absorption is similar to those in the discriminatory 151 scenario [figure 5.4]. The highest value is 84¢ at New York City and the lowest value point is at Plattsburgh, NY. Although the uniform delivered pricing scenario displays the same high-valued corridor as the other scenarios, there are differences in the shape of the gradient in other areas. The Cleveland to Pittsburgh area displays a constant level of approximately 20¢. Much of central Pennsylvania and the southern tier of New York also have a very flat price surface. 5.6 Summary A base, cost minimizing solution of NEDSS is compared to a solution from each of the three spatial pricing systems: discriminatory, uniform mill, and uniform delivered. The three particular scenarios chosen for comparison are chosen so that each results in nearly equal total marketing costs which are approximately 1 1/2% higher than the total marketing cost of the base, cost minimizing solution [Table 5.25]. While Class I assembly costs in each of the three scenarios show relatively large increases (18-32%), other components of the total dairy marketing bill, including processing costs, distribution costs, and assembly costs for Class I and Class II milk, reveal compensatory capabilities. As a group, these other components are able to maintain or even decrease their base solution levels. The locations of processing centers for all three product classes are very stable among pricing scenarios with the exception of Class II processors in the discriminatory pricing scenario analyzed. In this case, Class I processors in some large metropolitan areas find it advantageous to pass over nearby supplies in order to obtain more 152 ucoaumdfin< Gouuoooq vow- .wawouum cono>fiaoa anomfica ”moHHQQSm 3H“: H macaw you oocwusm mowum ¢.m wuswwm 153 0.909 m.wm m.mm mm o.wm o.H~H o.NHH mm o.mNH m.OOH m.om w.¢m c.00H Amman mo av moq.oaa mHN.N¢ «Hm.w mow coa.mm mom.ua wom.~ mmm mom.m cmo.mm Nm¢.o omw.m mmm.oq sac Mao m.HoH 9.mm 0.0m HOH m.om m.¢HH ¢.NHH cm 9.999 o.ooa 9.909 n.9o H.009 Amman mo av on.OHH o¢9.mq mm~.~ mom Noo.mm mmw.HH oHN.N mos wma.m mmm.mm mwm.m ~o9.m NmH.o¢ soma now m.HOH «.mm o.mm mm m.wm H.¢NH 9.00H 9m o.NmH ¢.ooa m.mo H.009 0.009 Amman mo av mmm.oHH ww9.H¢ mem.m mos Hmm.mm www.NH mmm.a mom m9~.oa mqm.mm mam.a mow.m mum.oq wen .mwo www.moa Hum.wc mmm.m mow «do.mm wmm.OH «no.9 «mm Nam.9 mam.mm Num.m Nam.m moH.o¢ ommm Aooo.9%v .2909 12909 999 99 9 .2909 999 99 9 49.909 9: 99 9 393 wcfiowum wommmHo mommmao mommmHo onHDmHmemHo >HQXMmm< oszmmoomm moHHmCoom wswowum Hmwumam mouse ”comwumaaoo umoo wcwuoxumz kuoh mm.m manna 154 distant supplies. Class II processors then find it possible to locate within these pockets of supply, close to the population centers. Milk assembly and milk product distribution movements generally follow the same patterns in each scenario with slight variations in the apparent compactness of the shipping areas, except for the case of Class I assembly in the uniform mill pricing scenario. In this solu- tion, the New York metropolitan area receives some Class I shipments from eastern Ohio and northern Virginia. Even with these long-range movements, Class I assembly costs in this scenario are lower than in the other two spatial pricing scenarios. At equal levels of total marketing costs, the three spatial pricing systems which were analyzed had very little impact on the optimal locations of Class I processing centers. These centers remain consump- tion center oriented. Class III processing center locations also remain supply center oriented in each scenario. The movements of milk to Class I processors and the location of Class II processors are among the most notable impacts of discriminatory pricing. CHAPTER VI SUMMARY AND CONCLUSIONS Federal milk marketing orders evolved, at least partially, in response to the presence of unequal bargaining power between dairy producers and processors. Among other things, FMMOs set minimum prices which regulated processors must pay to producers for milk supplies. On the basis of location theories and a desire to equalize the cost of raw milk supplies for Class I processors who are comparably located with respect to a defined market center, FMMOs have generally evolved systems of spatial price adjustments. In these systems, minimum Class I prices are adjusted to reflect the lower value of Class I milk supplies at greater distances from the market center. These adjustments are most often made through the implementation of a basing-point pricing system with constant adjustments per unit of distance. Redressing the imbalance in bargaining power between market participants has been one aim of FMMOs, however, the character of the imbalance has changed over time. Today, much of the milk marketed under FMMO regulation is represented by producer cooperative associations. Many bargaining situations for Class I milk supplies may be more aptly described as bilateral monopolies, rather than simple monopsonies. Theoretically, in such situations, one side must dominate in the setting of output levels and prices, then the two sides bargain for the resultant profits. It is one of the premises of this study that Class I milk processors dominate the output decisions and that at least part of the bargaining for profits between producers and processors takes place 155 156 in the form of FMMO hearings on the level and form of price location adjustments. The monopsonistic market position of fluid milk processors mani- fests itself in a particular form--that of a spatial monopsonist. Spatial pricing theory indicates that spatial monopolists/monopsonists have incentives to absorb freight and to practice spatial discriminatory pricing, where possible. Based upon this second premise, three spatial pricing systems for spatial monopoly pricing--discriminatory, uniform mill, and uniform delivered-~are described and their freight absorbing characteristics are demonstrated. Using NEDSS, a mathematical programming model of the spatial characteristics in the northeastern U.S. dairy industry, each of these spatial pricing systems is formulated by appropriately modifying the objective function for milk movements from supply points to Class I processing points. These problems are then solved at various levels of freight absorption and specific solutions are compared to a base, cost-minimizing solution. The particular discriminatory pricing solution which is chosen for comparison is one with a 30% rate of freight absorption. This rate is close to an implied rate based on current estimates of bulk milk hauling costs and rates of location adjustment used in many FMMO's. The solutions for the uniform mill pricing system and the uniform delivered pricing system which are chosen for comparisons are those solutions resulting in total marketing costs nearly equal to the total marketing costs which occur under the discriminatory pricing system with 30% freight absorption. The solution to the base, cost-minimizing scenario yields shadow prices, or imputed values, for milk supplies at the optimal Class I 157 processing locations. The geographic distribution of these values over the study area indicates a pattern which is very similar to what would be expected under a basing-point system with a base zone, or corridor, rather than a simple base point. This pattern results when Class I processors are assumed to have total marketing cost minimization as their objective. Producer blend prices are also adjusted for location under current FMMO rules. Individual producers cannot be expected to ship milk to more distant plants unless they are fully compensated for their share of any additional transportation cost burdens. With the emergence of dominant regional producer cooperative associations and their reblending authority, many individual producers are no longer directly faced with these alternatives. Decisions with respect to milk movements are made by means of a central coordinating mechanism. As such, producers may not directly feel the impacts of decisions concerning the destination of their milk. A third premise of this analysis is that the implied Class I price level is of sufficient magnitude to call forth the desired Class I milk supplies. Location differentials are viewed as signals used to direct otherwise willing supplies to Class I processors. Blend price differentials are not explicitly considered in this study. The repooling of receipts and the central coordination of shipments by producer associations preempt this individual producer decision. The results of the comparisons between the base solution and the chosen solution for each spatial pricing system indicate that optimal Class I processing locations are very similar among solutions to the three pricing systems which result in similar levels of total marketing costs. Class I product distribution costs dictate that the location of 158 Class I processing centers be at or near major or isolated population centers. Class III distribution costs also result in very similar processing locations among the three pricing scenarios studied. Class III processing centers locate at or near supply centers which are relatively long distances from the major population centers. These results conform to expectations which are consistent with the cost-based theories of location. In the base scenario and in both uniform pricing scenarios, Class II processing centers also conform to expectations in which they occupy spaces intermediate to those of Class I and Class III supply areas. However, in the discriminatory pricing scenario, which most closely resembles current FMMO pricing adjustment, some Class II processing centers find it advantageous to locate close to the major population centers, well inside the supply procurement areas of local Class I processors. Although accurate and complete information about actual assembly and ditribution movements for each product class were unavailable, actual plant locations and estimates of aggregated plant output were obtained. Actual locations of Class II and Class III processing centers do not match precisely the pattern which would be predicted by cost-based location theory or by the cost-minimizing solution of NEDSS. Most actual Class III processing takes place in the areas of concentrated supply which are distant from the major population centers, however, a small portion of Class III processing does take place at or near the major population centers. Class III processing is found near Boston, New York City, and Philadelphia. Similarly, significant actual Class II processing facilities are also found at or near these metropolitan areas. A cost-based theory of location, as well as the 159 base solution of NEDSS, however, predict that these processing centers would locate at intermediate positions relative to consumption-oriented Class I centers and distant, supply-oriented Class III centers. Assembly areas for the three product classes would be distinct with little or no overlapping. Many factors could account for the discrepancy between observed and predicted behavior. Agglomeration behavior generated by complimen— tarities in processing between classes, metropolitan sources of component by-products provided by the relative solids-not-fat intensity of Class I products, compared to the butterfat intensity of Classe II and III products, the availability of existing processing facilities formerly used for Class I products, or simple management misconceptions or mistakes could all result in the observed behavior. However, it is a major finding of this analysis that the monopsonistic character of Class I processing and the natural occurrence of discriminatory pricing and freight absorption can also reSult in the observed behavior. Seemingly by design, FMMO location adjustments generally do not represent the full cost of transporting milk from supply points to processing centers within a market area. As such, these adjustments represent price surfaces with less than 100% freight absorption. These location adjustments are generally specified as fixed rates per unit of distance, a method which results in a discriminatory price surface. The price of Class I supplies delivered to processors located at increasing distances from the market center decreases at a lower rate, with distance, than the total market costs of moving those supplies to the market center. 160 Voluntary or administered freight absorption and discriminatory pricing of milk supplies on the part of Class I processors results in total Class I milk assembly costs which are greater than the minimum achievable levels. Total marketing costs, however, do not increase by the total amount of increase in Class I assembly cost because changes in Class I assembly present opportunities for Class II and Class III processors to reduce their total assembly and distribution costs. The existence of compensating effects reduces the rate of marketing cost penalization for setting Class I differentials which increase Class I assembly costs and, similarly, reduce the rate of potential marketing cost gains for setting Class I differentials which decrease Class I assembly costs. Additionally, if the initially chosen location differ- entials result in processing center locations which differ from those in some subsequent set of differentials (such as in moving from the dis- criminatory price surface analyzed to the base solution), an additional cost of relocation of facilities is incurred. The presence of a downward sloping demand for milk supplies and the resultant Chamberlinian tangencies are often pointed to as prima facie evidence of market inefficiency relative to an idealized, perfectly competitive model. Reformulations of this situation, however, suggest that what appear to be economic profits could also be interpreted as returns to processors for the establishment of new plants at distances from the market center. Four FMMOs and at least three state-regulated orders operate within the geographic area covered by this study. The particular location differentials currently in place in these regulated areas are not studied. Location differentials which closely resemble the same freight 161 absorption level and discriminatory type as are currently specified in many FMMOs are studied. These differentials result in plant location patterns which do not conform to the patterns expected from cost-based location theory where Class II processing centers find it advantageous to locate inside the area of Class I milk supplies for the major metro- politan areas. If the goal of efficiency in total marketing cost is to be met by approximating the location patterns of the marketing cost minimizing solution, pricing mechanisms other than the discriminatory mechanism now in use might be considered. Uniform mill and uniform delivered pricing may provide alternative location adjustment mechanisms. However, if the use of rates of location adjustment which are equal to actual transportation costs would result in a total loss of incentives for Class I processors to pursue total marketing cost minimizing objectives, then discriminatory pricing, which does provide at least a partial incentive, may be appropriate. The losses in efficient Class I assembly which are induced by use of discriminatory adjustments, are partially offset by the optimizing behavior of Class II (and possibly Class III) processors. The presence of Class II processors at sites nearer to population centers than would be expected in a cost-minimizing organization, i.e. withing the assembly areas of market center Class I processors, is consistent with discriminatory pricing. Allowing location differentials to become, in effect, negotiating instruments for producer-processor price bargaining through the FMMO hearing process adds a degree of instability to optimal plant location decisions. The use of specific modifications to the differentials to 162 address individual competitive situations between Class I processors should also be avoided. The establishment of stable location adjust- ments, and the implied price surfaces, through the use of predictable rules should be a goal of the FMMO system. The choice of pricing mechanisms may be relatively broad. The results of this analysis indicate that at a chosen level of total marketing costs, uniform mill and uniform delivered pricing, two distinctly different systems, produce very similar market results with respect to plant locations and milk and milk product flows. The use of a basing-point system for establishing location adjust- ments may not be necessary, given the strong distribution orientation of Class I processing centers, which is demonstrated by the location of Class I processing at or near major or isolated population centers in each of the simulated pricing scenarios studied. In the presence of centralized coordination, differentials which encourage nearby procurements, regardless of the processor's location could have the same locational and total cost effects as those which attempt to direct milk toward a perceived market center. The use of adjustments which are based on the actual costs of moving supplies to each actual or potential center may be sufficient to ensure efficient plant locations and milk movements . APPENDICES APPENDIX A MONOPSONISTIC SPATIAL PRICING The three spatial pricing systems described in Chapter III are presented from a spatial monopolist's point of view. This appendix reformulates these systems in terms of spatial monosonistic pricing, which is more descriptive of fluid milk processors, and demonstrates the equivalence of the two approaches with respect to the presence of freight absorption. Assume that: i) there is a homogeneous set of sellers distributed over a plane by the density function ¢(D), ii) there is one buyer, iii) all sellers have identical supply curves, and iv) there is a constant freight rate, t, such that: Ps ' QS ' or 93 ' where, Ps ' QS ' Pb ' m + bqs - Pb - tD (Ps'a) (Pb-tD-a) dmd 019' the seller's local price; the seller's quantity; the monopsonist's mill purchase price; t - the constant freight rate per unit; D - the buyer's distance from the seller; and 163 164 a and b are positive constants. Monopsonistic Discriminatory Pricing Bd «d - f (r-pb) 1(pS-a) ¢(D) dD - F 0 b where Bd - monopsonist's effective market area pb - discriminatory mill prices; and Ps ‘ Pb ‘ tD; r - constant marginal revenue; and F - total fixed cost. The buyer wishes a function of pb, defined over D, which maximizes his total profit. Let, Pb - p* + w h(D) where h(D) is an arbitrary function of D. Bd 1rd - f (r-p*-w h(D)) %(p* + w h(D) -tD -a) ¢(D) dD - F o (dnd/dw)w.o - (dD/dW)w-0 d d[(r-p*-w h) ¢ db. 0 b d" - 'Qs + (r'Pb) 233 35% dpb PhLE dQs - §$_E__l - l (Pb‘tBs’a) ¢(Bs) HEB dpb b Bs + f l ¢(D) dB, 0 b Since 0 - % (pb-tBs-a), BS 98E - f l ¢ an dpb 0 b and, BS 95. - -£ 1(pb -tD -a) ¢(D) dD dpb b + (r-pb) IBS¢(D) dD. b 0 Solving for pg, pg - a/2 + r/2 + tD/Z As in the monopolistic case, the uniform mill pricing monopsonist will set a mill price which reflects absorbing one-half the freight to the average distance supplier. 166 M o o s c U i orm e1 v re cin 3d x _ f (r-ps-tD) -a ¢(D) dB 0 at Bd, r-ps-tD - 0, and Bd ‘ r'Ps 't" ELEs SI. ' _L__£__l . (r'Ps‘th) LPsLEl ¢(D) dD dPs dPs b Bd + f 1' ‘ZPLtD +8 M» an. 0 b Since r-ps-tD - 0, Bd d_7r_-f £22m 43(1)) dn, dps O b Solving for ps*, ps* - a/2 + r/2 - cB/z. APPENDIX B PLANT LOCATIONS AND ASSEMBLY AND DISTRIBUTION MOVEMENTS FOR EACH SPATIAL PRICING SYSTEM This appendix contains maps showing the plant locations and flows of milk and milk products between points in solutions to selected scenarios for each of the three spatial pricing systems analysed, as well as for the base, cost-minimizing scenario. Assembly and distribution maps for each product class for each scenario are included. 167 168 swam ”muaoao>oz hanaomm< H mmmao H.m unawam 169 ommn ”mucoao>oz noaudnfiuumfia H mmcao ~.m madman 170 omom ”masoao>oz manaomm< HH mmmao m.m shaman 171 Figure 5.4 Class II Distribution Movements 172 swam ”musoao>o=.zanammm< HHH mmmHo m.m oHSMHm 173 III Distribution Movements: Base Figure B.6 Class 174 cowunuomn< won .w:«owum huouwcwaauomaa ”mucoao>o= xanaomm< H mmwao n.m oudwflm 175 Gowumuomn< wen .wswoaum xuouwafiawuomaa ”mucoao>oz Coauapauumwa H mmmao m.m ouswwm 176 cowumuomn< men .wcwowum huoumcuauuomwo “mucoao>oz manaomm< HH mmmHu m.m oudwum 177 . coaumuomn< wen .wCHowum huouuCHEHuvmuo “mucoao>o= Gouusnwuumaa HH mdeU oa.m ousmfim 178 COHUQHOmn< men .wcflowum huoumcwawuomaa “muCoao>oz aanaommd HHH mmmHo Ha.m musmfim 179 III Distribution Movements: Discriminatory Pricing, 30% Absorption Figure B.12 Class 180 +mNH+ .wcaoaum HHHZ Enowwcb "muaoao>oz hanaomm< H mmmao m9.m musmua 181 +mNH+ .wcwoaum 9H9: EMOMHGD ”muaoao>oz cowuznwuumuo H mwuao ¢H.m ousmHm 182 32+ .wcaofium :92 393.25 ”3.92.962 hang—mamas HH mama mad 3de 183 II Distribution Movements: Uniform Mill Pricing, +129¢ Figure 3.16 Class 184 +mwa+ dwcwofium Haw: EMOMHGD ”mucoao>o= hanaomm< HHH mmmao ha.m ouswfim 185 III Distribution Movements: Uniform Mill Pricing, +129¢ Figure B.18 Class 186 -60¢ Figure 3.19 Class I Assembly Movements: Uniform Delivered Pricing, 187 sow- .wcHoHum wouo>HHon EuochD "mucoao>o= :oHudnHuumHa H mmcHo o~.m ouswwm 188 vow- .mcHoHum count/:09 3903.5 "3:99.262 thaomm< HH mmmHo Hmd ovum: 189 Uniform Delivered Pricing, -60¢ Figure 8.22 Class II Distribution Movements: 190 eoo- .wcHoHum pouo>HHoo auouHED ”muaofio>o= thaomm< HHH mmuHo mm.m ouswwm 191 3.... .wcHoHum vouo>HHoa anomHaa ”muaoao>oz :oHuanuumHo HHH mmuHo em.m oustm BI BLI OGRAPHY BIBLIOGRAPHY Agribusiness Associates, Inc. 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