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Marketing cooperatives and supply management Janmaat, Johannus Anthonius 1994

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MARKETING COOPERATIVES AND SUPPLY MANAGEMENT:THE CASE OF THE BRITISH COLUMBIA DAIRY INDUSTRYbyJOHANNUS ANThONTIJS JANMAATB.Sc., The University of British Columbia, 1992A THESIS SUBMITTED ]N PARTIAL FULFiLLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTERS OF SCIENCEinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF AGRICULTURAL ECONOMICSWe accept this thesis as conformingto the required standard.THE UNIVERSITY OF BRITISH COLUMBIAAugust, 94© Johannus Anthonious Janmaat, 1994In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(SignatureDepartment of /c5The University of British ColumbiaVancouver, CanadaDate //cIDE-6 (2)88)AbstractCooperatives are commonplace in the dairy sector throughout the developed world. Acooperative is an organization whose patrons are those who contribute the capital. Two features thatdistinguish a cooperative are: profits are distributed by member patronage, and member control isdemocratic. In theory, this organizational form cannot sustainably capture economic rents. Membersadjust their production until any captured rents are eliminated, restoring the competitive solution.In British Columbia, the dairy industry is regulated by supply management. Production quotascontrol output, while fanner returns are guaranteed by restricting imports and administering the price.All milk is pooled, and processors need not deal directly with dairy producers.A simple model of the BC dairy industry, with farm production or processor input as the onlyvariable, shows that the ‘competitive yardstick’ is not maintained. The industry wide milk pool decouplesthe cooperative from its membership. When this cooperative maximizes its patronage dividend, supplymanagement totally separates it from its members incentives. Given that the administrative price is notset to eliminate all processing rents, the positive patronage dividend is an incentive for all farmers to jointhe cooperative. Simultaneously, a competing IOF can capture rents because it is buying milk at the pooiprice and does not compete with the cooperative for its input needs.The financial statements of the Fraser Valley Milk Producers Cooperative Association lendsupport to the model. Based on performance ratios, this cooperative is behaving similar to other firms inthe dairy industry, and may be capturing rents on behalf of its members. The one area of discrepancy is inthe source of financing, and this can be largely explained by changing member investment preferences.Our model predicts that in B.C. the price of quota should be dependent on the return generatedby our theoretical cooperative. We find that the present perfonnance of the cooperative is not a usefulpredictor of the quota price. However, quota price appears to be closely linked to indicators of futureeconomic performance, and the sign of this linkage is consistent with our model.IITable of ContentsAbstract iiTable of Contents iiiList of Tables VList of Figures viAcknowledgments ViiiIntroduction 1Chapter 1: The Structure of a Cooperative 31.1) What is a Cooperative 31.2) Consequences for Cooperative Behavior 101.3) Summary 19Chapter 2: The British Columbia Dairy Industry 202.1) The History of the B.C. Dairy Industry 202.2) Goals of the System 262.2.1) The Federal Government 272.2.2) The British Columbia Government 292.2.3) The Farmer 332.3) Economic Consequences 362.4) Summary 39Chapter 3: The Unrestricted Problem 403.1) Background 403.2) The For Profit Processor 423.3) The Independent Farmer 443.4) The Unregulated Market with Independent Agents 463.5) The Cooperative Processor 493.6) The Cooperative Member Farmer 513.7) The Unregulated Market with a Cooperative 533.8) The Unregulated Market with One Cooperative and one For Profit Firm 563.9) Summary 64Chapter 4: A Quantity Restriction 664.1) The For Profit Processor 664.2) The Independent Farmer 694.3) The Supply Controlled Market with Independent Agents 714.4) The Cooperative Processor 724.5) The Cooperative Member Farmer 744.6) The Supply Controlled Market with a Cooperative and a For Profit Firm 754.7) The Quantity and Price Restricted Single Input Optimization Problem 81ill4.8)Sumniary.82Chapter 5: The Pooled Milk Supply 835.1) A Cooperative and an IOF in Competition with Naive Conjectures 835.2) A Cooperative and an IOF in Competition with Cournot Conjectures 915.3) A Cooperative and an IOF in Competition with Unrestricted Conjectures 935.4) Summary 98Chapter 6: The Milk Market with a Supply Restriction, a Pooled Milk Supply,and a Minimum Price 996.1) Problem Definition 996.2) Solution with Naive Conjectures 1016.3) Solution with Open Conjectures 1056.4) Summary 110Chapter 7: A Linear Example 1117.1) The Unregulated Market in Isolation 1117.2) Open Economy in an Importing Country 1157.3) Closed Economy with an Aggregate Volume Restriction 1177.4) Closed Economy with a Floor Price 1207.5) Closed Economy with an Import Price Pool 1227.6) Summary 125Chapter 8: The Financial Statements of the FVMPCA 1288.1) Return on Total Assets 1298.2) Current Ratio 1328.3) Debt to Equity Ratio 1348.4) Surplus Above Market Return 1398.5) Percent of Surplus Retained 1418.6) Summary 143Chapter 9: Econometric Analysis 1459.1) Theoretical Background 1459.2) Data 1469.3) Results 1549.4) Summary 158Conclusion 159References 163IvList of TablesChapter 1: The Structure of a Cooperative 31.1) Rochdale Cooperative Principles 51.2) Cooperative Principles, International Cooperative Alliance 61.3) Cooperative Behavioral Principles, by Staatz 8Chapter 2: The British Columbia Dairy Industry 202.1.1) Consequences of Supply Management 38Chapter 8: The Financial Statements of the FVMPCA 1288.1) Summary statistics for the return on assets comparison 1318.2) Summary statistics for the current ratio analysis 1338.3) Summary statistics for the debt to equity ratio analysis 1388.4) Sununary statistics for the surplus above market return 140Chapter 9: Econometric Analysis 1459.1.1) Summary statistics for quarterly series 1539.1.2) Summary statistics for annual series 1539.2.1) Quarterly regression results 1549.2.2) Annual regression results 1549.3.1) Quarterly data auxiliary regressions 1569.3.2) Annual data auxiliary regressions 1569.4.1) Quarterly regression corrected for serial correlation 1579.4.2) Annual regression corrected for serial correlation 157VList of FiguresChapter 1: The Structure of a Cooperative 31.1) Annual Transfers to the FVMPCA 91.2) Number of Plants and Average per Plant Production 121.3) Number of Producers and Average Production 151.4) Changes in the Method of Financing 18Chapter 2: The British Columbia Dairy Industry 202.1.1) Free Market Situation 372.1.2) Supply Managed Market 37Chapter 3: The Unrestricted Problem 403.1.1) Firm’s total revenue and total cost as a function of total milk received 443.1.2) Firm’s marginal value product as a function of total milk received 443.2.1) Farmer’s total revenue and total cost 453.2.2) Farmer’s marginal revenue and marginal cost 453.3) Supply and demand 473.4.1) Supply curve for raw milk 483.4.2) Monopolistic processor total 483.5.1) Cooperative total revenue 503.5.2) Cooperative marginal value product and average value product 503.6.1) Cooperative member total revenue and total cost 533.6.2) Cooperative member marginal revenue and marginal cost 533.7.1) Marginal and average value product against member supply 553.7.2) Aggregate marginal revenue and supply curves 553.8.1) IOF Oligopolist in imperfectly competitive market 603.8.2) Cooperative in imperfectly competitive market 603.8.3) Aggregate market supply curve 60Chapter 4: A Quantity Restriction 664.1) Marginal value product, free market price, and shadow value 684.2) Farmer’s marginal cost with and without supply management 704.3) Aggregate processor MVP and aggregate processor MC 724.4) Cooperative MVP, AVP, and adjusted AVP 744.5) Oligopolist’s marginal value products 774.6) Cooperative’s marginal value products 78Chapter 5: The Pooled Milk Supply 835.1) The rents of the cooperative when it has been decoupled from its membership 885.2) The supply effect of the patronage dividend 89Chapter 6: The Milk Market with a Supply Restriction, a Pooled Milk Supply,and a Minimum Price 996.1) Interaction between the decoupled cooperative and an IOF 1046.2) Patronage dividend effect on farmers 105viChapter 7: A Linear Example 1117.1) Unregulated competitive market 1127.2) Unregulated market with imperfect competition 1137.3) Unregulated competitive market in an open economy 1157.4) Oligopolist in an open economy for the final output 1177.5) Quantity restricted competitive market 1187.6) Competitive market with a floor price 1217.7) Pool price as a function of total milk brought to the pooi 125Chapter 8: The Financial Statements of the FVMPCA 1288.1) Return on assets comparison 1308.2) Current ratio comparison 1328.3) Composition of member funds in the FVMPCA 1358.4) Debt to equity comparison 1378.5) Percent surplus above market return 1398.6) Percent of surplus retained as a share of total surplus earned 142Chapter 9: Econometric Analysis 1459.1) Quota price with fresh fluid price and blend price 1479.2) Quota price and economic indicators 1489.3) Quota price against surplus earned and TSE 300 composite 150VIIAcknowledgmentsThis project grew out of what was initially intended to be a simple graduating essay, to becompeted over a four month summer. Clearly it has grown somewhat. Many people could beacknowledged for their involvement in the preparation of this document, and in providing me with theinformation that helped construct this analysis. In particular the Social Sciences and HumanitiesResearch Council and the University of British Columbia must be acknowledged for funding support.I am particularly grateful to the people at Agrifoods International Cooperative Limited, inparticular Carol Paulson and Cliff Denning, for the information they helped me gather, and the feedbackthey gave me on the pieces of the work as it progressed. I am also grateful to the members of thiscooperative, in particular my parents, for their opinions and comments which were invaluable for theinsights it provided into how the industry and the organization operates.I thank Mary Bohman, my supervisor and the initiator of this project, for her direction, insights,and encouragement. Lastly, I must thank my wife Suzie for her constant support, and Charolait andSkunkie, the cats, for their company while the project took shape.vi”IntroductionCooperatives are a prevalent feature in the dairy sector throughout the developed world. In almost allcountries one would consider, at least fifty percent of the milk produced is received first by a cooperative[Grant, 1991]. The behavior and success of these cooperatives varies between countries. In the UnitedStates dairy cooperatives tend to be first receivers of the milk. Many then sell it to processing plants, or ifthere is an excess, process it themselves. That portion processed by the cooperative often makes its way tothe stocks of the Commodity Credit Corporation. In the European Community cooperatives are moreinvolved in the direct marketing of the milk. In Britain, there is one dairy cooperative, which has alegislated monopoly on the receipt of milk. It is also the largest marketer of milk through its own‘DairyCrest’ label. A key factor that may determine what role cooperatives take in the marketing of milkis their interaction with the regulatory structure where they operate. This interaction has been littlestudied.In Canada, cooperatives are also directly involved in the marketing of milk. The degree of involvementvaries between provinces. In Ontario, they are not very prominent. In this province all milk is soldthrough the milk board, with rights determined in part by an auction system. No processor, cooperative orotherwise, has a direct claim any of the milk. Producers receive the same basic return, irrespective of theprocessor they first ship to, and so see little need for a cooperative. In BC the situation is a little different.Here the milk marketing board may require milk transfers between processors, but the receiving processorhas first option, given the same class of use. BC also had one of the most successful dairy cooperatives inCanada, the Fraser Valley Milk Producers Cooperative Association (FVMPCA).Before its merger with two other cooperatives, the FVMPCA was a successful dairy cooperative based inthe lower mainland region of BC. Interviews with industry participants indicate that it was an aggressivecompetitor, and an innovator in the industry. In 1992 the FVMPCA merged with two Alberta dairycooperatives, the Northern Alberta Dairy Pool (NADP) and the Central Alberta Dairy Pool (CADP),forming Agrifoods International Cooperative Association. The organization saw this merger as anessential move to maintain its ability to serve increasing demands from its clients.1In any industry, the behavior of the agent firms, be they cooperative or investor owned firms (IOFs), isgoverned by the interplay between the incentives facing the decision makers in the agent firm, and theconstraints imposed by the regulatory environment. Partly encouraged by the prominence of theFVMPCA, this work investigates how the regulatory structure in BC may have affected the evolution andsuccess of a cooperative.The first chapter will consist of a description of a cooperative, and some of the general implications of acooperative’s structure on its behavior. Chapter two describes supply management and summarizes thegeneral effects of this policy on the market. In chapters three through six we build a model of theinteraction between a cooperative, an investor owned firm, and the regulatory environment. Chapterseven explores a simple mathematical model of these results. Chapter eight presents information takenfrom the financial statements of the FVMPCA, and in the last chapter we look at the results of a simpleeconometric analysis of the price of dairy quota as a function of the cooperative’s expected returns. Weconclude the paper with a summary of our results.2Chapter 1, The Structure of a Cooperative.This chapter begins by presenting a definition of a cooperative. In the process we explore some of thehistory of the cooperative movement. The development of this movement has helped to identify some keyfeatures of a cooperative, as defined by an economist. We then show how these features appear in theFVMPCA.A cooperative’s structure has implications for its behavior. Following the definition of a cooperative, wepresent a summary of these implications. The structural implications produce characteristic patterns inthe cooperative’s organization and relation to its membership. The financial information provided in theannual reports of the FVMPCA, among other sources, shows how these implications may have affectedthe behavior of this cooperative.1.1) What is a Cooperative?A cooperative is a form of industrial organization where those that receive the services of the organizationare also the suppliers of the capital. In agriculture, cooperatives are a particularly common form oforganization. This is probably a function of the unique problems faced by farmers. The input supply andoutput purchasing markets are normally occupied by a small number of buyers and sellers. Farmers arecaught between these oligopsonistic and oligopolistic players with little market power, facing high inputprices and low prices for the products they produce. With such unfavourable market conditions, farmerscould clearly benefit from collective action. As with any situation of economic crisis, ideologies havebecome strongly interwoven in the cooperative movement. Fundamentally, through cooperative action,farmers can gain a degree of bargaining power, bringing more competition to the industry, and in sodoing improve their own welfare [Staatz, 1987a; Shaffer, 1987].This has generated two lines of thought in the literature on cooperative. One approach has been to modelthe cooperative in consideration of the behavioral consequences of its structure. Another is devoted topromoting the growth of the cooperative movement, and spreading the ideology and philosophy ofcooperation. For example, the International Labour Office defines a cooperative as follows:3A co-operative [...] is an association ofpersons who voluntarily joined together toachieve a common end through the formation ofa democratically controlledorganization, making equitable contributions to the capital required and accepting afair share of the risks and benefits of the undertaking in which the members activelyparticipate [ILO, 1988 p6].This definition embodies most of the essential features of the cooperative, but in a highly normative way.The ideas of a ‘common end,’ of ‘democratic control,’ and of ‘fairness’ have strong emotional appeal, butcontain few specifics and are of limited analytical value.To the people involved in cooperatives, this form of industrial organization is not only a way of counteringdisproportionate market power, but is also a way of living. Many authors have written and continue towrite on the importance of the normative side of cooperatives [Bogardus, 1952; Bailey, 1955; ILO 1988;...]. Cooperatives must therefore not be analyzed simply as economic institutions affecting the balancebetween demand and supply, but the analysis must be completed with an understanding of these subjectivevaluations. Cooperatives have been both an economic agent and an ideological movement for most oftheir existence.Most cooperatives are based on the famed Rochdale principals. These were laid down by a group ofrenegade weavers, the ‘Society for Equitable Pioneers’ in Rochdale, England in 1844. The Rochdalecooperative was not the first attempt at cooperative activity, but it was the first success, and the principlesthat the Rochdale Weavers adopted were chosen with an awareness of what had befallen previous attemptsat cooperative action. The Rochdale cooperatives were set up in response to perceived market failures,but these failures were seen as tied to a general societal malaise, and not to disproportionate market power[Bailey, 1955]. The goals of cooperation were set down both as an ideology and a practical attempt tochange the structures affecting the welfare of the people involved [Rhodes, 1987]. In this way, theycontributed to rearranging the balance of market power. The Rochdale principles are listed in table 1.4The Rochdale Cooperative Principles1. Open membership to all, regardless of sex, race, politics, or religious creed;2. One vote per member;3. Any capital needed should be provided by members, and should earn a limited rate of return;4. Any net margins should be returned to members in proportion to patronage.5. Cooperatives should allocate some funds for education in the principles and techniques ofcooperation;6. Market prices should always be charged, i.e., no price cutting to pass on cooperative savingsdirectly;7. Cash trading: no credit given or asked;8. Products should be accurately formulated and labeled;9. Full weight and measure should be given;10. Management should be under the control of elected officers and committees; and11. Accounting reports of financial health should be presented frequently to members.{reference: Cooperative Theory, Agricultural Cooperatives: A Unified Theory of Pricing, Finance, and Investment.Ronald W. Cotterill, ppl7l-258.}Table 1.1: Rochdale Cooperative PrinciplesThese are the foundation upon which the structure of the modern cooperative is based. Most moderncooperatives fundamentally adhere to the first five principles listed here. The ideas of open membershipto all, equal democratic power, little return on equity, surpluses distributed according to patronage, andallocating resources for education in cooperative ideals. The further Rochdale principles are more specificto the market that the Rochdale weavers faced. The charging of the market price and the use of cashtrading were instituted to prevent the financial crises that had confounded previous attempts atcooperation. The remaining principles represent the promise by the members to conduct businesshonestly and openly with each other, one of the main motivations for their union in the first place.Modern cooperatives have modified or discarded many of the more specific Rochdale principles. Todaythere are institutions in place to prevent corruption in the conduct of business affairs; ensuring ethical5The Rochdale Principles of Cooperation Established by the 1966Congress of the International Cooperative Alliance1. Membership of a cooperative society should be voluntary and available, without artificialrestriction or any social, political, racial, or religious discrimination, to all persons who can makeuse of its services and are willing to accept the responsibilities of membership.2. Cooperative societies are democratic organizations. Their affairs should be administered bypersons elected or appointed in a manner agreed by the members and accountable to them.Members of primary societies should enjoy equal rights of voting (one member/one vote) andparticipation in decisions affecting their societies. In other then primary societies theadministration should be conducted on a democratic basis in a suitable form.3. Share capital should only receive a strictly limited rate of interest.4. The economic results arising out of the operations of a society belonging to the members of thatsociety and should be distributed in such a manner as would avoid one member gaining at theexpense of others. This may be done by decision of the members as follows:(a) by provision for development of the business of the cooperative;(b) by provision of common services; or(c) by distribution among members in proportion to their transactions with the society.5. All cooperative societies should make provision for the education of their members, officers, andemployees and of the general public in the principles and techniques of cooperation, botheconomic and democratic.6. All cooperative organizations, in order to serve the interest of their members and theircommunities, should actively cooperate in every practical way with other cooperatives at local,national, and international levels.Cooperative Theory, Agricultural Cooperatives: A Unified Theory of Pricing, Finance, and Investment. Ronald W.Cotterill, ppl7l-258.Table 1.2: Cooperative principles, International Cooperative Alliance.behavior in the business dealings between members, suppliers, and customers is no longer a driving forcefor organization. However, market power is still a concern, as is the issue of alienation caused by largeinstitutions and distant decision making. The principles that today’s cooperatives adhere to reflect thismodern reality. The cooperative principles adopted by the International Cooperative Alliance (ICA) arelisted in table 2.6The first principle is a direct extension of the first Rochdale principle. The second ICA principle is amodification of the second Rochdale principle. It acknowledges the different structure of federatedcooperatives. In such cooperatives, the ‘primary’ or local cooperative is democratically structured.However, the federation is often administered based on the patronage of the member coops [Hyadu, 1988].The third principles are virtually identical. The fourth is an extension of the fourth Rochdale principle,which recognizes that cooperatives need not necessarily return all earnings to the membership directly,but may return earnings in the form of services or future returns. An example would be generalinformation or extension services provided by the cooperative, or investment for future sales growth. Thefifth principles are again virtually identical. The sixth ICA principle is not presented in the Rochdale list.It further recognizes and promotes federated cooperatives, along with a loyalty to the ideology.Economic analysts try to avoid normative criterion. They attempt to identify behavioral rules or lawsbased on the interaction of the stated principles and the theoretically predicted or actually observedbehavior of the actors involved. These “economist’s principals of cooperation” are meant to represent themain factors that determine a cooperative’s behavior, rather than those that determine its ideologicalposition. In this regard the values and principles embodied in the ideology of the cooperative are notignored. One attempts to explain behavior that at first seems to be economically irrational by putting it inthe context of an economic ‘value’ and using other measurable values as references.Many authors have compiled lists of cooperative behavioral principles. When these authors are dealingwith agriculture, they are usually similar those in table 3, presented by Staatz [198Th]: In the case of theFVMPCA, these principles have been embodied as follows. The service provided by the cooperative, theprocessing and marketing of milk, is available primarily to members. Some non-member milk would beprocessed. In BC the FVMPCA acted as a ‘processor of last resort,’ receiving all production when otherplants were closed. Further milk could be redirected according to processor demand. Between 1970 and1991, the largest net receipt of milk accounted for about 15% of production, with the average being lessthan 4.5% of member production [FVMPCA, Annual Reports]. Figure 1.1 shows the amounts of milkreceived by the cooperative. The peak in 1981 occurred immediately before the Fraser Valley Milk7Cooperative Behavioral Principles1. The stockholders, who are farmers, are the major users of the firm’s services.2. The benefits a stockholder receives from committing capital to a cooperative are tiedlargely to patronage. There are three reasons for this:(a) The business pays a strictly limited dividend on equity capital invested in theorganization.(b) Net margins are distributed among stockholders in proportion to theirpatronage with the business rather then in proportion to their equityownership in the firm.(c) Stock of cooperative firms does not appreciate because there is a very limitedor nonexistent secondary market for it. Therefore, capital gains are not amajor benefit of stock ownership in cooperatives, in contrast to IOFs.3. The formal governance of the business by the stockholders is structured“democratically” in the sense that:(a) Voting power is not proportional to equity investment. The limitation on“voting one’s equity” may be in the form of one-member/one-vote, or votingmay be proportional to patronage or stock ownership but subject to somelimit such as restricting any one member from having more than 5 percent ofthe total votes.(b) There are strict limitations on the number of non stockholders who mayserve on the board of directors.Table 1.3: Cooperative behavioral principles, by Staatz [198Th].Producers Association (FVMPA) merged with the Shushwap-Okanagan Dairy Industries CooperativeAssociation (SODICA) to form the FVMPCA. The peak could indicate market growth for the FVMPCA,some of which was likely at the expense of SODICA.The benefits of membership accrued as a ‘final payment’ on the milk production, not as a return onequity. The rules of the association stated that, “No member shall receive any dividend or interest on hisshares” [FVMPCA, 1983, p11]. This is consistent with the cooperative principle, “share capital shouldS50.045.04O03O025.0. 20.0U,15.0h..I— 10.0.5.00.0Figure 1.1: Annual transfers to the FVMPCA16.0%Transfers• Percent Transferred 14.0%lao% .010.0%0CD2.0%0.0%only receive a strictly limited rate of interest.” The board of directors decided how much of the receiptsfrom sales would be retained to coverlosses, costs, borrowing charges and expenses incurred by the Association in carryingon the business of its membership, and a reasonable allowance for depreciation on allplant and equipment. [FVMPCA, 1983,i2S]The association could deduct up to 5% of total sales from what remained for the purpose of investment inplant, equipment, or other activities. Investments that were larger than this 5% limit could not beproceeded upon without a special resolution of the membership. Capital invested was redeemed as abond, known as a ‘loan certificate,’ which paid a fixed rate of return. Loan certificates were paid out after15 years, and were freely tradable between members and others who did not patronize the cooperative.The interest rate was decided by the members in a vote at the annual meeting.Capital held as shares conferred voting rights only. A farmer who wanted to become a member of thecooperative had to buy a minimum number of shares. Before 1983, members could accumulate shares.The retained portion of the final payment was rolled into shares and loan certificates, normally 10% asshares, the remainder as loan certificates. The shares were redeemed at par when the last of the member’s— _ — — e e — — — — — — — — — — — —9loan certificates was paid out. However, following the merger in 1983, the rules were changed. Allvoting members would hold exactly five shares. Voting power was held by members, as distinct fromshippers. Family members who worked primarily on the farm of someone holding a shipping account,and shareholders who worked primarily in an incorporated farm business, could be voting members. Theboard of directors was chosen by vote among the members [FVMPCA, 1983].This organization shows most of the characteristics of the typical cooperative, as required by law. Theaccess to capital seems to have provided a high degree of flexibility on the financial side, providing thefirm with a strong competitive position. Simultaneously, the loan certificate system, multiplememberships, and the level of management and board accountability, added to or facilitated a high degreeof member participation in the governance of the organization.1.2) Consequences for Cooperative BehaviorIt is in light of the unique behavioral rules of a cooperative that one must evaluate the differences betweena cooperative and an investor owned firm (IOF). One should not consider a cooperative as guided by thesame objectives and constraints as a traditional IOF. In general the cooperative does not have the sameobjectives, a consequence of the democratic control by the member patrons. Some of these differencesmay put the cooperative at a competitive disadvantage, and others may give it an advantage.Multiple Objectives and Efficiency: The ‘broader scope for optimization’ [Staatz, 1987a] derives fromthe integration of the behavior of the cooperative and that of the member farms. Farmers may see thecooperative as ‘an extension of the farm.’ The cooperative members will promote decisions by thecooperative to support the objective of the farm, and the farmer will modify the decisions at the farm levelto integrate with the behavior of the cooperative [LeVay, 1983].This behavior may be disadvantageous from a competitive perspective. For example, in the case of anagricultural marketing cooperative with members dispersed over a wide geographic area, isolatedmembers will have an interest in keeping remote facilities operating. Such small facilities are likely lessefficient, due to from diseconomies associated with their size. Members are concerned about paying10higher transportation costs to get their production to the cooperative’s facilities. At the same time, thefarmer, as a member of the local community, is concerned about the community reaction if the plant isclosed. Farmers see their acceptance in the community as a positive ‘good’ and the effects of closing theplant as a ‘cost’ that is equivalent to a certain level of income. An IOF will look only at the profitabilityof the plant, and the effects of its closure on overall firm profits. The concerns of the individual shipper atthis isolated location will not be a factor in the decision, and would be ignored.As the cooperative becomes larger, and covers a large geographic area, some degree of subsidization ofthe less profitable plants by the more profitable plants will probably occur. This subsidization will distortthe decision that would have been made had the local cooperative been independent. It may have chosento close the local plant in isolation, and either dissolved the cooperative or simply pooled transportationcosts to a distant processor. With the possibility of being subsidized, and likely a history of havingreceived subsidization, there will be greater pressure to keep the plant open. If the cooperative has anumber of such isolated plants and producer members, there will be a large political lobby to keep all thesmall plants open. This political pressure may result in business decisions being compromised, and theprofitability of the cooperative being jeopardized. Producers who ship to more profitable plants have anincentive to leave the cooperative. They will remain until the difference between the price they canreceive from IOF buyers and that from the cooperative exceeds the value of the pro-competitive effect ofthe cooperative and the other non-market values such as “fairness” and “cooperation.”The history of the FVMPCA shows that this pressure may be affecting its behavior. It has the largestnumber of plants of any single processor in the British Columbia, and has been slower to rationalizeproduction than the industry as a whole. Figure 1.2 shows the number of FVMPCA plants and provincialprocessing licenses and the normalized average throughput per plant or license. The milk board requiresall processors to hold a license if they are actively processing milk. License numbers are not restricted,but a license does require an annual fee be paid to the board if it is not to be revoked. Throughput wasnormalized by indexing it to the relevant 1974 production level. A normalization was used to highlightchanges between FVMPCAs and non-FVMPCA throughput. The number of cooperatively owned plants1160 25050 200-I4IA[ii :11: J.LiiikuiIIIIIItIlIIth : I1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988FVMPCA’ ‘All Coops BC Totals —4—— FVMPCA —4— BC AverageFigure 1.2: Number of plants and average per plant productionhas remained relatively constant over the period considered. This contrasts with a generally downwardtrend in the total number of processing licenses. The high number of licenses in 1988 occurred while theprice of milk in BC was higher than in the rest of the country. The number of licenses issued may reflectan attempt by processors to enter and take advantage of the market opportunity.The constant number of cooperative plants, when compared to the total number of processors would beuninteresting if cooperative plant efficiency was keeping pace with the rest of the industry. The averagethroughput of the plants was calculated by dividing the total production in the FVMPCA and in theprovince as a whole by the respective number of plants. This number was then scaled by using 1974 as abase year, which allows both data sets to be shown on the same chart. The average throughput forFVMPCA plants in 1974 was 39.33 million litres per year, which was more than ten times the averageamong nou-FVMPCA processors of 2.92 million litres. By 1986, the FVMPCA throughput had increasedto 42.50 million litres per year, while the throughput of non-FVMPCA processors had increased to 7.11million litres per year. The total processing licenses in the province includes cottage industries, whichaccounts for the much lower level of production in total. Many of these small processors are highlyspecialized, which may endow them with unique avantages. Efficiency measurements based onI I12throughput need to be interpreted carefully. However, the rationalization that has occurred in the industryas a whole does not seem to have occurred in the FVMPCA.An interesting fact is the jump in the number of processing licenses in 1987 and 1988. At this time, therelative price for milk in BC was higher than the rest of the country. The jump in the number ofprocessing licenses issued may be a response by entrepreneurs to this opportunity. The increase in thenumber of licenses is primarily responsible for the drop in the throughput level.Historically, many of the cooperatives in the dairy industry arose specifically in response to therationalization taking place in the early part of the 20th century. The large companies that controlled theindustry were closing small, unprofitable plants in rural areas, leaving farmers with a supply of cream andno one to sell it to [Hazlett, 1992]. Because of fixed assets in the form of diary cattle and dedicatedequipment—more a factor in recent times as dairy farms specialize—the farmer had a high sunk cost inthe production of milk [Manchester, 1983]. The ability to market the milk and gather some return is abenefit to the farmer, even if the profit is not as high as an IOF would demand. The local farmers are infact better off ‘subsidizing’ their local cooperative processor by accepting lower returns on capital for theplant, since it maintains a higher return to the assets on the farm. A small local cooperative may have acompetitive advantage locally. The cooperative provides a marketing service where none would otherwiseexist [Sexton and Iskow, 1988].Democratic Control and OrganizationalDirection: The democratic principles that are the hallmark ofthe cooperative also present potential problems. In a cooperative where all members are the same size,and have uniform interests, the democratic method of making decisions generates the best decision for all.However, as presented above, producers at different locations may have different interests. Similarly,producers with different sizes may also have different interests. Larger producers often are more‘businesslike’ in their approach to agriculture. They have reduced their own costs and increased scale,and have reduced their cost to the cooperative by shipping a large volume of product at one time. Thesemembers benefit when shipping and inspection costs are allocated to individual producers. Smaller13producers prefer to pool these costs. Overall, large efficient producers and producers close to plantssubsidize those who are smaller, and those located farther away.In most industries there are more small firms than large ones, while large firms are together usuallyresponsible for the largest share of output. This is also the case within most cooperatives, where we findfar more small member producers than large ones, even though the large volume producers collectivelyaccount for the majority of the cooperative patronage. The democratic rules of a cooperative make itdifficult for the interests of the largest producers to be represented in accordance with their impact on thecooperative’s revenues.Figure 1.3 shows the average production of all producers in BC, of FVMPCA members, and of producerswho are not members. The most relevant comparison is between FVMPCA members and non members,since cooperative members are about 80% of the total number of producers. The average production ofmembers is lower, but not by all that much. Before 1980, the average production of the members of theFVMPA was almost the same as that of the rest of the producers in the province. In 1982 the FVMPAmerged with the SODICA to form the FVMPCA. Following the merger, a number of larger shippers(although actually non-members) began their own processing facility in response to an FVMPCA policy ofaccepting production from members only. The merger meant that the FVMPCA acquired more facilitiesand a number of smaller producers, causing average member production to fall. The FVMPCA respondedto the risk of loosing large producers by offering a volume discount. This move was made after a numberthreatened to leave [personal interview].The tendency for the interests of large producers to be ignored in a cooperative may be lessened by thesupply management system. Supply management makes it more difficult for producers to expand,reducing the size range of cooperative members. It also provides a more secure return to small producers,reducing their reliance on the cooperative’s patronage dividend. In 1977, it was estimated that theminimum efficient processor in North America would be supplied with the milk of between 10,000 and20,000 cows [Sexton and Iskow, 1988]. In the U.S., where there are no supply restrictions, herds close toor above these sizes do exist, and are often closely tied to a processing plant. In Canada, the rules of14600550500(0‘15-‘400 3-Uj::..:.:...iMPCAMembers______AllProducers___g• FVMPCA Producers 0• Non-FVMPCA Producers 250I —A——All Producers I—r —i- ---i —I 200m a a o c 0 o o o o o o o— — — — — — — — — — — _ — — — — — — — — — —1600140012000C).100028000600E4002000Figure 1.3: Number of producers and average productionsupply management often restrict the overall market share a singe producer may hold, keeping farm sizesmall.Another often cited effect of the democratic structure of the cooperative is the difficulty in bringingexpertise to the board of directors from outside the organization. It is felt that member farmers lack thebusiness skill required to run a large organization. It is also felt that management can take advantage ofthis possible confusion of the board of directors and pursue its own objectives. This is seen as being incontrast to IOFs, which are felt to be free to pursue profit maximization as the sole objective, with theboard of directors perfectly representing the interests of the stockholders. There is in fact no reason tosuppose that the objectives of the board of an IOF are that uniform [Rhodes, 1987].The board of directors of the FVMPCA has contained members with a diversity of experience to draw on.All are required to be producing dairy fanners, but board members have had backgrounds in banking andagricultural economics. This indicates that expertise has been available within the organization. InCanada an entrant into dairy production requires a large commitment of capital. New entrants who arenot coming into the industry by succession will often have had non-farming, and often white-collar,15experience before entering. This generates a pool of diverse skills which one would not expect if it waseasier to enter. Board membership has tended to remain fairly stable over time, suggesting that the boardmembers could become fairly well informed about how the processing industry operates. However, staticboard membership could mean that the management has successfully convinced the board and themembership of the complexity in the industry and the fact that ‘nonnal’ farmers could not run theorganization. Some members have expressed sentiments along these lines [personal interviews].Considering the high degree of member involvement during most of the life of the FVMPCA, memberapathy and/or domination of the board by management interests seems not to have occurred.Moral Hazard and Financing: Members have a tendency to under finance the cooperative, relative to theoptimal level of financing for an IOF [Lerman and Parliament, 1991; Parliament eta!, 1991;...]. Thistendency arises in part from member risk aversion. Farmer patrons have the choice to invest capital in thecooperative or in other opportunities. These farmers already have a lot of capital invested in this industryin their farms. To avoid risk, the farmer should diversify outside the industry.The inability of share capital to appreciate also reduces the incentive to invest. Since shares cannot besold, but are redeemed after the member retires, there is no vehicle to capture the future value of thecooperative. The benefits of investment in the cooperative accrues to members only during theirinvolvement with the cooperative. Members choose their optimal level of investment based in part on thisfinite discounted income stream.The level of investment members make is based on the individual’s perceived income risk should thecooperative fail. As the cooperative ages, becoming a more established player in the market, the portionof the membership that experienced the economic conditions at the time when the cooperative was formeddeclines. The perceived severity the cooperative’s dissolution becomes smaller, reducing the incentive formembers to invest.The free rider problem, where members seek to minimize their own investment relative to others whohave invested, will also lead to a tendency to under finance. New members and young members have an16inclination to try to minimize their investment, while the investment of older members remains in theorganization as the financing capital. They can have equal control through the democratic process, butlower the risk of their position.The FVMPCA has experienced a reduction in the level of member equity. Figure 1.4 shows how thedistribution of financing has been arranged in the cooperative. In 1970 over two percent of the surpluswas retained. The percent retained was calculated as the ratio of the retained earnings to the totalavailable for distribution. As the years passed, this ratio was reduced until in 1991 it was just below onepercent. As a consequence, the debt to equity ratio basically during this period. The debt to equity ratiowas calculated as the liabilities of the cooperative to the sum of loan certificate capital and share capital.The reduction in the share of the profit retained was seen as a positive step by younger producersinterested in expanding their own operations. They appear to be less concerned about the historical eventsthan older members. These older producers often speak against these changes, and also show a greaterphilosophical link to the cooperative principles that were seen as critical to breaking the monopsonisticpricing they faced in the past.Factors in Favour of Cooperative Organization: There also are some potential advantages that thecooperative has over the private firm. Unfortunately these differences are difficult to quantify and analyzein anything approaching an objective manner. Perhaps the greatest evidence that there are benefits tocooperative organization is the fact that they continue to exist in spite of clearly identifiable structuralshortcomings. The cooperative structure offers the opportunity for more communication betweenmanagement and the member patrons. Management is able to better respond to the concerns of themember patrons in how services are delivered. It also allows membership to be better informed of themarket conditions that determine the success of the cooperative, and may provide the member farms withthe information to more rapidly respond to these changes. The cooperative structure offers a potentiallyhighly effective mechanism for the dissemination of information on production techniques and industrydirection.172.50%.Um-I•2.00%(00• 1.50% 0U)0.50%00.0.00%Figure 1.4: Changes in the method of financingCooperatives, by their nature and history, embody a philosophy as well as a set of economic incentives.This philosophy often brings with it a sense of loyalty that goes beyond that associated with the risk of lossshould there be no cooperative in the industry. This fact can be a significant competitive advantage.Members are willing to accept losses at present to guarantee the long term success of the cooperative.Depending on the degree to which the ‘philosophy’ of cooperation is adhered to, this fact may partiallyoffset or even override the tendency to under finance the cooperative.The role that the agricultural cooperative plays is dependent on many factors. In the beginning,cooperatives were formed to address a wide range of perceived failures in the marketing system. Todaymany of these market failures have been contained by government authorities. Modern cooperatives areagencies that allow the farmer to vertically integrate into the marketing system, without havingthemselves to establish the scale for an efficient processing operation [Sexton, 1988]. Today’s farmers arealso managing much larger and more specialized operations, requiring operators that are muchtechnically skilled. The benefits of cooperation are different today. They allow farmers to specialize inproduction, while the cooperative takes care of marketing. The question is whether this organization stillI0 D F:0 Q O m— — — — — — — — — — — — _ _ — — — — — — — —18serves the best interests of the producer, or if the main interests being served are those of management,and personal goals of individuals on the board of directors.1.3) SummaryCooperatives are a unique form of industrial organization that is common in production agriculture. Acooperative is characterized by a number of features, including democratic control by the members of theorganization, return of profits to the members on the basis of patronage, and a limited return on equity, allof which is provided by the membership.This form of organization has a number of potential disadvantages, stenmiing primarily from theindividually opportunistic actions of members. Members do not fully internalize the cooperative objective,as a result, the organization as a whole is constrained in the actions it can take. The informationcontained in the financial statements of the FVMPCA indicates that some of these problems were makingthemselves evident.However, there are also some potential advantages to cooperative organization. These are hard toidentify, and even harder to quantify. Many stem from the interaction between economics and socialphilosophy which a cooperative represents. The very fact of their prevalence indicates that there must besome advantages to membership.Throughout the remainder of this work we explore the interactions of a cooperative with the regulations inthe B.C. dairy industry. In the next chapter we outline the development of the supply managementsystem, with a special focus on B.C. Following this we build a simplified model of a dairy marketingcooperative, and explore how the regulations might impact on its behavior. Our main concern will bewith the clearly identifiable costs and benefits of this form of organization, so we will largely ignore thewider range of features that characterizes a cooperative.19Chapter 2, The British Columbia Dairy IndustryThe dairy industry has a history of govenunent intervention that stretches back almost one hundred years.Many feel that the dairy industry faces unique challenges, such as specialized capital investment on thefarm which generates the opportunities for opportunistic behavior by the monopsonistic processors whopurchase the milk. Late last century dairying underwent a stressful transition from producing primarilycheese, butter, and cream to the production of fluid milk. The hardship faced by farmers eventually gavegovernment few politically acceptable options that did not involve extensive involvement in the dairysector.Canadian governments chose to enact a supply management system, which supports the fanner byguaranteeing that a specific amount of the farmer’s production will have access to the market at aguaranteed price. In return the farmer is required to accurately regulate production, and must pay for thedisposal of any surpluses. In B.C. the program is administered by the provincial milk board, whichallocates quotas for fluid milk production, and administers the federally allocated quota on industrialproducts.The supply management system accomplishes a number of objectives, in particular bringing stability tothe industry. However, this stability comes at a cost, which the entire economy pays. In this chapter wecharacterize the regulations that make up the supply management system.2.1) The History of the B. C. Dairy IndustryThe Canadian dairy industry, like that in most of the industrialized economies, has been heavily regulatedfor many decades. One objective of these regulations has been protection of farmers from what are seen tobe unpredictable and often devastating market forces. This attitude arose in the later part of thenineteenth century. The dairy industry was adjusting from producing primarily solid milk products, suchas cheese and butter, to one supplying fluid milk to urban centers. The large capital investment inprocessing technologies, the perishability of the product, and the strict sanitary regulations, generated a20highly asymmetric bargaining position between the farmer producing the milk and the processor who waspurchasing it.This bargaining relationship was further aggravated by the production technology. Solid milk productswere to this point made primarily on the farm, and were sold to the merchants in town on a per unit basis.If the fanner could not sell the day’s production on a particular day, it could be stored to the next day. Ontop of this, the farm was usually very diversified, and the skim milk that was a byproduct when the creamwas removed was usually fed to calves or hogs. The storable manufactured product was treated as a unitquantity, and the trading mechanisms were appropriate to this. However, fluid milk cannot be practicallystored, so that the farmer had to find a buyer for a certain quantity of milk every day, irrespective of themarket price that day. The problem now became one of properly managing and pricing a flow rather thanbuying a unit of milk, a problem to which the trading institutions of the day were unaccustomed. Thetraditional trading relationships relied on a per unit style of pricing, and was unable to properly price asituation where the short run marginal cost of production was almost zero [Manchester, 1983].The farmer received a significant premium for the milk that was sold for fluid consumption, but couldnever be certain that the milk produced would receive this price. Many farmers expanded production inresponse to the price, only to find themselves forced to sell milk at a loss. Processors often turned awaymilk during the spring and summer months, and were searching far afield during the low production falland winter. For many years as this adjustment proceeded, milk prices were highly volatile and generallytrending downwards. The continuing adjustment forced many farmers from their farms. As theshakedown continued, farmers in many areas organized into cooperatives and associations to gain somemarket power. They also aggressively lobbied their governments to provide some relief and impose somecontrol in the industry. The added hardship of the depression further aggravated the situation, and wheregovernments had not acted earlier, they intervened now.In British Columbia the situation was much like that elsewhere in the industrialized world. After manyyears of aggressive competition, governmental involvement began in 1929 with the passage of the PiiiProducts Sales Adjustment Act. This act created a board to equalize the returns between producers who21managed to ship milk to the fluid market and those who were shipping to the lower priced manufacturingmilk market. This was the first time that pooling had been seen in BC. Before this, severe competitionwas forcing down the price of milk, and heavily impacting on the livelihood of the dairy farmers [SSCA,1978, p’7].Two years later began the legal challenges, the traditional way that Canadians arrive at a stable division ofpower between the federal and provincial levels of government. The part of the Canadian constitutionaffecting this division of powers, derived from the British North America Act (BNA), does not clearlydelineate the level of authority. Parliament has the authority to regulate trade and commerce [BNA Act,91.2], but the provincial Legislature has authority over “... all Matters of a merely local or private Naturein the Province [BNA Act, 92.16].” Industrial milk is generally considered to fall under trade andcommerce, as industrial products can move across provincial borders. However, when the regulationswere introduced, inter-provincial trade of fluid milk was nonexistent making its regulation a matter of alocal nature. Traditionally the courts have been the mechanism through which the legally proper level ofauthority was identified [Jackson, 1990].In 1931 the Dairy Products Sales Adjustment Act was declared ultra-vires -- beyond the authority of—theprovincial government. In response the federal and provincial governments simultaneously introducedmarket control legislation. Shortly thereafter, the federal law was found to be ultra-vires the federalgovermnent. However, the provincial legislation survived until 1941, ten years more [SSCA 1978].During this period, the federal government introduced subsidies to assist the dairy industry. Initially thesewere put in place to alleviate the conditions farmers faced with the depression. Later, as the war began,subsidies were again introduced to encourage production in the face of wartime shortages [Barichello,1981].In 1941 the provincial board was found to be exercising powers beyond those provided by the enactinglegislation. Once again the industry was without regulation. However, in 1942 the marketing of milkcame under the control of the War Time Prices and Trade Board. All prices were controlled to preventinflation. Coupled with this a subsidy was provided to encourage production. These measures remained22in place until 1946. In 1947 the BC Milk Board was established by amending the provincial PublicUtilities Act. The board was empowered to set both retail and producer prices, and subsequently raisedthese prices to provide the producers with compensation for the wartime subsidy that had been lost [SSCA1978]. At the same time, the government began to support farm prices with deficiency payments andoffers to purchase. These were intended to be temporary measures to alleviate unusual hardships, but theyheralded the beginning of the active involvement by the Canadian government in the trading and storageof dairy products [Barichello, 1981].In response to lobbying efforts by Canada Safeway, consumer price controls were abandoned by the milkboard in 1953. This change lead to heavy competition between processors attempting to dominate themarket. At the same time, in a bid for market superiority, the Fraser Valley Milk Producers Association(FVMPA), a producer cooperative formed in 1913, followed a policy of aggressive pricing that loweredproducer returns. The FVMYA argued that as a cooperative it was not bound by the producer price thatthe board dictated. By 1955 another court case concluded with the finding that the board had no power tocontrol the price paid to producers [SSCA 1978].Subsequently a royal commission was struck to deal with the crisis. The findings lead to the passage ofthe Milk Industry Act in 1956. This act placed the control of production and marketing of milk under areestablished Milk Board. It gave the board the power to:1. license producers andprocessors;2. audit farm and dairy business record.s, and;3. set standards for the production, processing, distribution and sale offluid milkwithin the province [SSCA 1978, p9].It also established a quota system covering fluid milk production. The quota system gave the board theauthority to regulate the total amount of fluid milk produced, as well as control the farm level ofproduction. This was seen as a way of apportioning the returns from this market fairly between thefarmers.23Shortly after this, in 1958, the federal govermnent introduced the Agriculture Stabilization Act. This actdid not affect the dairy industry immediately, as the federal authorities continued to interact with theindustry on an ad hoc basis. In the early 1960s the dairy farmers, disturbed with this piecemeal approach,lobbied for a central authority to administer the federal dairy policy. In response, in 1967 the CanadianDairy Commission (CDC) began operation. The CDC was vested with a broad range of powers. It couldissue offers to purchase, provide for storage, for processing, and for disposition of product. It could applyimport controls, provide deficiency payments, conduct dairy product promotion, deduct levies fromindividual producers, and conduct investigations into production, processing, and marketing activities ofany dairy product. Participation by the provinces was voluntary. [Barichello, 1981].The CDC developed the federal Market Sharing Quota (MSQ) program. Under this program, all thefarmers in each participating province were allocated an annual quota guaranteeing them a share of themarket. This move brought the regulation of all of the production of industrial milk in Canada under oneconsistent set of rules. Farmers would receive a guaranteed price for the milk produced within the MSQamount, and paid a penalty levy on any excess amounts. The initial allocation of MSQ between theprovinces was based on the historic distribution of production. Provinces such as Ontario and Quebec,which had a long history of dairy production, received the largest shares of the MSQ.In 1973 the province of British Columbia joined the federal Comprehensive Milk Marketing Plan. At thetime, the provincial milk board was given the authority to administer the federal Market Sharing Quota(MSQ), and collect the levies that were due on overproduction [SSCA, 1978]. The Milk Board could notissue MSQ, and as the historically based allocation did not anticipate future population shifts, B.C. saw itsshare of the local market for industrial milk fall over time [SSCA 1979]. In an attempt to acquire moreMSQ, B.C. withdrew from the national scheme in 1982-83. The next year B.C. won an agreement onlevies and MSQ allocation, and reentered the system [Barichello, 1987]. The agreement, known as the‘65/35 agreement’ guaranteed B.C. a level of MSQ equal to 35 percent of the total milk produced in theprovince. Although this arrangement maintains industrial production at a level that is below the national24average, it has managed to insulate the B.C. dairy industry from changes in the level of consumption ofindustrial milk products.At present the industry is facing several important challenges. The first challenge comes as a result of theprice differential between the Canadian and American milk prices. Consumers have become aware ofhow large the price differential is, and as the global economy continues to sputter along, consumers arebecoming more and more conscious of where their income is going. The amount of cross border shoppingfor dairy products has become a significant issue over the last decade [Shelford, 1988a] and has beenestimated as up to five percent of the B.C. domestic market. If this cost gap does not close, either throughprice change or exchange rate movement, , imports will continue to reduce the domestic demand.A persistent case involving a number of milk shippers who have opted to produce milk without quota hasbeen an ongoing irritant to the B.C. Milk Board for almost a decade. In August 1993 the final courtdecision was handed down, and the ruling threatened the dairy industry throughout Canada. The rulinghanded down by Madam Justice Newburry held that the enabling legislation at the federal level definedmilk as the product that was regulated, and not dairy products [BCJ, 1993]. As such, any producer couldproduce any amount of milk, provided that the milk was processed into a further product while still in thelegal ownership of the producer. This ruling means that the grounds for the federal market sharingsystem are in question unless the enacting legislation is changed. As of 1988 there were over thirtyproducers who were producing without quota, and in the uncertainty that exists now, this number is boundto grow [Shelford, 1988b].The last challenge to the supply management system is a result of the General Agreement on Tariffs andTrade (GAiT). A GATT appeal decision ruled that ice cream and yogurt are not primary products, andthus cannot be given the same protection as primary dairy products. Under article eleven of the GATT,import restrictions were allowed if there was a domestic supply control program in place. This article hasbeen removed. .Tariffs must replace the import restrictions, relaxing the precise control government hadover import volumes. All indications are that the tariff levels will be very high, giving domestic producerssignificant protection. However, this change invariably limits the degree of control that the domestic25authorities have over the domestic consumption. Further, the system of levies to offset export losses isconsidered an export subsidy, and is also prohibited by the GATT. Supply management will have toundergo some significant restructuring to survive over the long term.2.2) Goals of the SystemThe goals of the Canadian Dairy programs follow from the turmoil that was present in the industry beforethe programs began. Following Barichello [1981], the federal policy objectives can be stated as:1. to ensure a reasonable degree ofself-sufficiency in processed daiiy productsupplies,2. to procure price stability for both producers and consumers,3. to ensure that efficient Canadian industrial milkproducers receive areasonable return on their resources,4. to provide Canadian consumers with adequate and continuous year-roundsupplies ofhigh quality processed dairy products at reasonable realpricelevels.For the most part, these goals apply at both the federal and provincial levels.These goals have been achieved, more or less, through the use of the supply management system. Selfsufficiency is ensured by default through the elimination of legal imports of dairy products. Stability isachieved through an administered price and supply management, limiting the opportunity for supply andprice shocks on both the consumer’s and producer’s side of the market relationship. A ‘reasonable’ returnis guaranteed by an administered price partly derived from a formula which suggests a price in accordancewith milk’s ‘cost of production.’ In fact, the rapid rate of technological advance in agriculture probablymeans that the administered price is higher than it ‘should’ be. And lastly the ‘adequate’ supply and high26quality is ensured through active regulation of how much must be produced, and under what conditionsthis production takes place.2.2.1) The Federal GovernmentThe Canadian Dairy CommissionThe federal Comprehensive Milk Marketing Plan is controlled by the Canadian Dairy Commission(CDC). The objective of this body, created under the Agricultural Stabilization Act of 1957-58 andamended in 1975, isto provide efficientproducers ofmilk and cream with the opportunity ofobtaining afair return for their labour and investment, and to provide consumers ofdairy productswith a continuous and adequate supply ofdairy products ofhigh quality [Barichello,1981, p19].To accomplish its goals, the CDC operates the Market Sharing Quota (MSQ) system. The MSQ ismeasured on the basis of a farmer’s butterfat production over the year. The amount of MSQ that isrequired is decided every year by a panel of representatives from each province that is part of the program.This quota is administered by the provincial Milk Board, along with the provincial fluid quota [SSCA,1979]. Thus, it is at the provincial level that one finds the regulations that govern the allocation andtransfer of quota between producers, and the regulations that govern processors.To make the supply management system effective, imports must be tightly controlled. The regulatorybody cannot accurately control how much milk is brought to the market if consumers and buyers are ableto import at will, and producers can sell outside the supply regulations. The Export and Import PermitsAct was used to establish import restrictions, which have been extended from only butter in 1951 to coveralmost all dairy products today. These regulations have been admissible in an era of growing free tradethrough the presence of the article eleven exemption for agriculture in the GATT.27Until 1988, the government calculated the milk price through a “Returns Adjustment Formula” (RAp)that tried to balance the farmers’ cost of living and the cost of production. On top of this there is still ahigh degree of ad hoc adjustment possible by the administrative authority. The RAF was established in1975, and was intended to be in effect for only a couple of years. However, it was not replaced until 1988.In 1988 a system was established to estimate production costs based on provincial surveys. However, thegovernment has continued to be actively involved in the price determination process, with significantopportunities for political involvement [McKinley, 1990]. This has meant that the price is still notreflective of the costs. In general it is believed that the price which is paid to the farmer is significantlyhigher than their cost of production. The fact that farmers are willing to pay substantial amounts ofmoney to purchase quota rights supports this idea.When a farm price has been decided upon, this value is then used in another formula to arrive at a pricethat reflects a fair return to the processor as well. The formula is based on a support price for butter andskim milk powder, and a guaranteed processing margin. At this price, the CDC buys any surplus thatexists, establishing a price floor. With the MSQ program the stocks are usually quite small; the CDCessentially stores the product for resale when supplies are short. This price floor then becomes the priceagainst which all other products are compared, and the returns generated by other dairy products will be atleast as great as that possible on butter and skim milk powder. Target prices are also established for otherprocessed dairy products, and have usually been slightly above those for butter and skim milk. A subsidyis added to the milk price that the farmer receives to make up any difference between the support pricefloor established for the processor, and the target return to the producer.From the price that must be paid to producers, a levy is deducted to cover the cost of disposal of thesurplus milk. This ‘within quota’ surplus is the result of the ‘sleeve’ that is built into the system to allowfor year to year fluctuations in price and demand [Barichello, 1981]. The disposal is usually accomplishedby exporting the milk products at a loss. This levy is distinct from the producers individual levy that mustbe paid on that part of the milk that is produced in excess of the quota amount.28The actual price that is paid to the farmer is determined at the provincial level, where the processor priceis set. On a practical administrative level, the dairy industry in each province is regulated by marketingboards that sit in those provinces. The federal legislation, the Agricultural Products Marketing Act,specifically authorizes the transfer of the federal regulatory power to the provincial board for the purposeof administration.The complicated nature of this system means the price paid to producers is almost totally unrelated to theconsumer’s demand in the market. The combination of the price control and the market size regulationensures that the milk price will maintain a roughly constant relationship with the cost of production andthe cost of living. The guaranteed market and the security of ‘sufficient’ returns accomplish the maingoals as seen from the farmers’ perspective.From the consumers’ perspective, one sees a stable price, and a constant supply of dairy products fromyear to year. Whether or not this is in the consumers’ interests depends on what alternative sources of theproduct exist, and at what cost these can be had. The pricing system does appear to be biased in thefarmer’s favour. The formula includes a profit margin that is meant to be ‘fair’ and price changes tend tolag behind the cost of production.22.2) The British Columbia GovernmentThe Marketing BoardsThe provincial authority in BC is derived from the British Columbia Natural Products Marketing Act,which provides for the delegation of a broad range of powers to the designated board, the BritishColumbia Milk Marketing Board (BCMMB).29the board is vested with thepower within the Province to promote, regulate, andcontrol in any and all respects theproduction, transportation, packing, storing, andmarketing, or in any of them, of a regulatedproduc4 including the prohibition ofproduction, transportation, packing, storing and marketing, or any of them, in whole orin par4One of the powers that is specifically designated to the board is the ability to establish production quotasand regulate their transfer. The act specifically prevents the board from assigning a value to the quota itissues, but there is nothing in this act that prevents producers from paying each other for the transfer ofthese rights.The crown appoints three people to the BCMMB, one of whom must not be involved in the dairy industry.Beyond one required annual meeting, they hold meetings whenever necessary to deal with any issues thatcome up. A small administrative staff handles the day to day responsibilities, which include:1. Licensing ofvendors andproducers;2. establishing the classification ofqualifying milk on a basis of utilization;3. establishing values at which vendors shall account to the Boardfor qualifyingmilk used in each class;4. establishing daily milk quotas for producers5. and other miscellaneous duties.The regulatory specific are contained in two ‘general’ board orders, General Order 31 and General Order133. General Order 133 covers the specifics of the regulation of the provincial fluid milk market.General Order 31 governs the way in which the federal powers are administered locally by the local board.The federal program is administered by dovetailing them with the fluid milk regulations, for the most30part. Until 1991 the quota that governed industrial milk was not even traded independently. It wastransferred in the same proportion to the total held as the holder transferred fluid quota.Several principal features of General Order 133 are the formula price, the pooling of the milk supply, andthe volume constraint on producer output. The BCMMB establishes a basic accounting value for all‘qualifying’ milk using a specific price formula. The formula is established in recognition of theadditional cost of producing a constant year-round supply. The producer price has beenestablished at a level which adequately compensates for the higher cost ofproducinga consistent year round supply, available when and where the consumer desires it[SSCA, 1978, p.32].The formula uses an average price for a ten year period beginning with the previous year. This base isadjusted by a weighed average of three general economic indices and four agriculture specific indices.This accounting value is used to generate a blended pool price according to the actual utilization of milkwithin the board’s administrative area.Milk is divided into seven different classes under the BCMMB orders. Class 1 milk is used in ‘fresh’fluid form in the local British Columbia market, and is allocated the full accounting value. Theremaining milk is divided into six classes covering different combinations of final use and final market.These classes are allocated a lower price than the class one price. The final price the farmer receives isthe sum of the milk prices weighted according to the share of the final use of all milk, the utilizationadjusted price.Processors must pay the utilization adjusted formula price to the farmer. The specifics of the utilization ofthe individual plant or processor are irrelevant from the farmer’s perspective. If a processor utilizes milkfor a lower average class value than it pays the farmers, the milk board makes up the difference. If it usesits milk in a higher class, it must pay the difference to the milk board. The result is that each processorpays the same price, ignoring administrative costs involved in the adjustments, for all the milk it usesfrom a particular class.31To make the program effective, the Milk Board must have a tight control on all aspects of the production,distribution, and utilization of the milk produced in and brought into the province. To accomplish this,the Milk Board collects extensive details from all ‘vendors’ of dairy products in the province. Thesedetails include all volumes of milk received, final utilizations of all milk, i.e., classes of product produced,and detailed financial information including statements of profit and loss [BCMMB, 1990]. With thesedetails, the board can determine if all the milk is going to its best use, and take punitive action if milk isbeing channeled inappropriately.The aggregate milk supply is regulated through the quota system. Each licensed producer is allocated ashare of the milk market that remains with the producer until a valid transfer takes place. The total quotain the province is determined by the milk board through a projection based on factors such as populationgrowth, demographic changes, demand shifts, etceteras. The quota amount is allocated to existing quotaholders on the basis of their current share of the total quota.The Milk Board ofFluid Quota is a daily production quota which is issued to producersby the BC Milk Board. The quota represents a producer’s share of the fluid milkmarket and is based upon his[sic] total daily production during the four month periodin which aggregate milkproduction in each Milk Board Region is at a minimum. Theaggregate allocation ofmilk quotas to each region, in any year, is equivalent to 120percent offluid milk sales during the quota earning period of the previous year.Because milk quotas are based upon daily production, this 20 percent margin providesfor seasonal and transitional fluctuations in production an4 also, for fluctuations inday-to-day demand [SSCA, 1978, p.32].Farmers who supply more than their quota allocation are charged a levy, and farmers who consistentlyship less than their quota allocation will have their allocation reduced. Reductions are distributed to thosewho are consistently overproducing. The combination of the overproduction levees and the threat of quotaloss through underproduction ensures that the total supply on the market remains very close to the amountspecified by the milk board.32The pooling of the milk is accomplished through the authorization of processors to request milk fromother processors. The BCMMB orders establish a priority of use for class one milk. If a processorrequests milk for class one use from another processor that would use it for a lower class, the milk must betransferred.The board may ... direct that excess quantities ofqualifying milk receive4 or to bereceived by a vendor shall be transferred by that vendor to another vendor requiringthe millç provided that Class 1 utilization has the “highestpriority”Below class one transfers, the hierarchy is based on the accounting value of the milk in that class. Mostprocessors generally regard supplying the fluid market as the highest value use for milk, so this provisiongenerates a situation much like an anonymous pool from which the individual processors draw milk.They are not specifically tied to any producer. The mitigating factor in the orders is that the receivingprocessor must compensate the supplying processor for the cost of handling and transporting the milk.2.2.3) The FarmerWhen the program was introduced, quota was assigned on the basis of the producers share of theaggregate production during that part of the year when the production level was the lowest. Since then,the quota that a farmer holds can change in two ways. Firstly, if the farmer is consistently below thequota level over two “quota months,” the amount of quota held can be reduced to the fanner’s averageproduction level during these periods. This has seldom happened, indicating that there is likely a shadowvalue associated with the supply restriction. In the second place, the farmer’s individual quota allocationcan be increased as a result of increases in the overall demand for the product [SSCA, 1978, p33]. Theoverall demand for milk in British Columbia has been growing steadily for almost as long as the programhas been in place. The main driver in this trend has been the continuing growth in the population of theprovince.33The benefit that accrues to the farmer from the system comes in several parts. Two general classes ofbenefit can be identified. The first class of benefits are those that arise from the difference between thesupply managed market and the unregulated market. These benefits include the security the systemgenerates and a price level that is higher than that which would prevail in a free market. Security isimportant to the farmer since the production level is planned at least one year in advance. The farmermust make the production decision in the face of market risk, and the greater this risk, the more resourcesare going to be devoted towards protecting against it. The higher price required as ‘adequatecompensation for year round production.’ guarantees the farmer a level of profitability from operations onthe farm. As far as the price is above the cost of production and the opportunity cost of the assetscommitted, the farmer will be receiving a benefit.The second class of benefits are those that accrue as a result of environmental and structural changeswhile the system is in place. These benefits include the growth in quota that accrues to existing dairyfarmers and the degree to which the price more than ‘adequately’ compensates the farmer for what isproduced. Quota growth comes from the increase in the volume of milk represented by the quota thatresults from growth in the market. This benefit accrues unequally across Canada. In regions such as theMaritimes and Saskatchewan which are facing a declining population, the farmers quota allocation will befalling as the market contracts. This compares to provinces like Alberta and B.C. that are experiencingpopulation growth. The extraordinary compensation results from factors such as the lethargy of the priceformula to reflect changes in cost structure, and the ability for political lobbying to generate and protecteconomic rents that are accruing to the farmers. These extraordinary rents are believed to be largelycapitalized into the price of the quota, and the high price which this scarce ‘input’ commands indicateshow large these rents might be.For those producers who have been in production for more than five years, the quota becomes a tradableasset. Subject to certain volume requirements, farmers can freely trade quota between themselves. In1978, any producer who was transferring Fluid Milk Quota also had to surrender an equal percentage of34MSQ to the Milk Board. There is no restriction on whether the quota is to be sold with cows, or with afarm.The province is split up into a number of quota regions, with quota being freely tradable within the region,but no transfers possible between regions. The increases in quota that accompany increases in demand arealso tied to the quota region within which the demand increases. This means that the benefit whichaccrues to the quota holder associated with increases in the demand is tied to the region where the quotaapplies.The fluid quota technically remains the property of the Milk Board, and as such the milk board does notrecognize the existence of a price for the quota. However, farmers are willing to pay each other to acquirethe right to ship milk that goes to the person who holds the quota. Quota is the most scarce resource inthe industry, there are no substitutes. We expect that with many potential buyers, much of the will becapitalized into the quota price. The size of this price will reflect the security benefit, the expecteddemand change, the expected difference between the cost of production and the amount of revenuegenerated by producing milk, and any benefits generated through the tax system. The forecast incomestream will be discounted at a rate that reflects the opportunity cost of placing capital in quota and the riskthat the program will collapse.Trading of quota is carried out either by direct trade between farmers, or through agents such as livestocktraders. The farmer is restricted to hold an amount no more than one percent of the total provincialproduction [Barichello, 1987]. At present there are no farms in the province even close to this size. In1991, the average dairy farm in BC was milking close to 80 cows. To have one percent of the provincialmilk production would imply a herd of more than 700 cows with the average per cow production. Thelargest herds in the province are only about half of this size. If we look to the US, we see herds of over1000 animals. The difference in herd size can be explained in part by different production conditions thatfavour large size. However, the presence of much larger operations in parts of the US that aregeographically similar to areas of Canada would indicate that there is also a policy effect.35Beyond brokerage costs, there is a tax of between 9.1 and 20 percent transfer assessment, dependent onthe nature of the transfer, which returns quota to the milk board. Through this process, the milk boardacquires a stock of quota which it uses in its ‘Building Program,’ providing fluid quota for farmersentering the industry. Because of the attractiveness of the industry, there is a long waiting list of peopledesiring to enter [Barichello, 1987].2.3) The Economic ConsequencesThe economics of supply management are quite straightforward. Figure 2-la shows the unregulatedmarket outcome. The quantity of milk is detennined by the intersection of the supply curve and thedemand curve. An amount qi of milk is produced and sold at a price p.Under supply management, the total quantity available is restricted by a central authority. In figure 2-lbthe supply has been restricted to q8. Consumers are willing to pay Pc for this quantity of milk, but it has amarginal cost to the producers of only Pp. In the absence of a program, producers would produce qf - qmore milk, all of which would be consumed at the market price of p. In terms of consumer surplus, thearea represented by A is transferred from the consumers to the producers. Areas C and D are deadweightloss.The quota price determined by the shadow value to the producer of another unit of production. In thediagram, the supply curve represents the industry average marginal cost to the producer of producingmilk. Consistent with controlled pricing, producers take the price as exogenous. At the margin, theproducer would receive the difference Pc-p, if another unit of output could be produced. Since anotherunit worth of quota would entitle the farmer to ship this unit of milk, the price of the quota is going tohave an upper limit given by the present value of this price difference.36Figure 2.1.1: Free market situationFollowing Barichello [1981, 1987] we can identify some further consequences. Table 2-1 presents a list ofthe positive and negative effects of the dairy industry regulation in Canada taken from Barichello [1987].Since the degree to which the programs have changed is minimal, these consequences are basicallyunchanged.A couple of subtle benefits can be included. The most obvious one is the fact that the supply managementprogram involves little direct burden on the government treasury. However, it has been argued that itwould be more efficient if government were to subsidize the farmers directly [Barichello, 1981; Grubel,1977]. It is also difficult to measure efficiency gains because when less resources are needed to protectagainst risk. The stability and predictability of the milk price has meant that the assorted insuranceprograms and periodic cash infusions which characterize other sectors of Canadian agriculture are absent.Further, since resources are not being devoted to risk reducing activities, the resources in place in theindustry are likely to be employed more efficiently.$ S $APC/NDPtPpq 0DQFigure 2.1.2: Supply managed market37SUMMARY OF POSITIVE AND NEGATIVE EFFECTS OF CANADIAN DAiRY REGULATION2. Size of dairy sector3. Stability4. Continuous, adequate supply ofmilk products at reasonableprices.5. Equitable across producers.B. Efficiency Effects1. Farm level welfare costs2. Processing, Distribution, RetailingSector.- production levels preservedcompared to free trade- more dairy products in Canada are“made in Canada” due to selfsufficiency policy for fluid milk andbutterfat- production and price patternscontinue to be stable- production and price patterns aremore predictable- supply is continuous- industrial milk program rules applyto all provinces- level of total milk productionslowly falling.- number of milk producerscontinuing to fall at a steady pace.- this stability may be only partly dueto the present regulation.- policy instability in early years ofthe program.- product choice narrowed.- consumer price not reasonablecompared to alternatives.- unfair to entering and expandingproducers- unfair to fluid milk producers- unfair to producers in moreefficient milk producing provinces.- inefficient, arbitrary allocation ofindustrial milk production acrossprovinces.- inefficient, arbitrary allocation ofindustrial milk production withinprovinces where MSQ is nottraded.- reduced future supply to dairyfarming of best entrepreneurialtalent.- biased genetic selection in dairycattle breeding.- institutional policy risk ofunexpected changes in policy rules.- inefficient milk allocation system toprocessing plants.- reduction in competition.- distorted advantage to butterproductionTable 2.1: Consequences of supply management.A: Program Goals1. Increased dairy farmer income - temporary income enhancement - smaller producers and recent- capital gains to established entrants share few of theseproducers, mostly to larger benefits.producers.382A) SummaryGovermuent involvement and regulation has been a constant feature of the dairy industry for almost onehundred years. Regulations were initially adopted to counteract the hardship that farmers were facing asthe industry shifted from producing solid milk products with only a limited perishability hazard to theproduction of fluid milk for the growing urban market. The experiences of this transition period are stillthe paradigms against which the industry participants struggle, although it is unclear whether they arestill true.Canada has adopted a supply management system to deal with the perceived problems of the dairyindustry. Supply management does provide stability, a continuous flow of safe, high quality product, adegree of self sufficiency, with little effect on the government treasury. These positive factors must beweighed against the costs, which include reduced total milk consumption, less efficient resourceallocation, stagnation against changes in demand and comparative advantage, and a loss ofentrepreneurship.At present, supply management faces a number of challenges. Consumers are unwilling to accept thehigh price that the program generates. Legal challenges have resulted in a vacuum in the legislation, andthe General Agreement on Tariffs and Trade has rendered several of the policy tools on which supplymanagement relies inappropriate. In light of these challenges, it is time that the supply managed sectorsreevaluate their goals, and consider various alternatives to accomplish them.Canadian dairy cooperatives developed within this policy environment, and it is under the presentregulations that they must operate. The subtle differences in competitive conditions and policyenvironments have lead to pronounced differences in the degree and competitive strength of dairycooperatives between the provinces in Canada. In Ontario we find a virtual absence of marketingcooperatives for dairy products, while in Quebec they hold by far the largest share of the market. In thefollowing chapters we will explore how these interactions are manifested.39Chapter 3: The Unrestricted ProblemIn this chapter we begin to develop a mathematical model of a cooperative. The principle objective of theanalysis is to see how supply management impacts on the relationship between a cooperative and itsmembership the interaction between a cooperative and an IOF competitor. Trade will be ignored for theduration of this analysis The impact of trade is only on the magnitude of the interactions we are exploringhere.This chapter begins by building the model without restrictions. We define the technology and theobjective functions of the economic actors, and see how they interact. In the next two chapters we explorethe effects of the volume restriction and the pool price in isolation. Chapter six pulls all the elements ofsupply management together.3.1) Background.The theoretical analysis of cooperatives first developed around the ‘Illyrian’ firm, a producer cooperative,the most quoted work being that of Ward [1958]. As reviewed by Bonin et a! [1993], the objective ofWard’s producer cooperative is to maximize the patronage dividend that can be returned to the labourinput. Ward finds that the equilibrium solution is not Pareto-efficient, with the market employing morelabour than competitive firms would. When the labour input is allowed to move between the producercooperative and its competitive rivals, this resource moves until it generates the same marginal returnwith all employers. The producer cooperative restores the competitive solution.If the producer cooperative is allowed to restrict membership, then the competitive yardstick result doesnot occur [Bonin et a!, 1993; Cotterill, 1987]. Restricting membership allows the cooperative to short themarket as an IOF would, generating a higher than average return for its membership. The membershipwill not allow new members to join, protecting their higher return. This form of cooperative behavesmuch like its IOF rivals.40The first analysis of marketing cooperatives to be widely quoted was that of Helmberger and Hoos [1962].Helmberger and Hoos modeled a cooperative that marketed a homogeneous product on behalf of itsmember finns. Their analysis also chose dividend maximization as the objective of the cooperative. Theydemonstrate that the optimal point of operation is consistent with the minimum cost point for those inputsnot supplied by the members. In the Helmberger-Hoos cooperative, the member firms choose their ownproduction, which they market collectively. The equilibrium outcome occurs where the marginalproduction cost of the members is equal to the net revenue—surplus per unit received—of the cooperative.A competitive yardstick result is generated analogous to the labour managed case.Hardie [1968] developed the analysis of the marketing cooperative to the multi-input and multi-productcase. He used a linear programming approach to show that the shadow value associated with each inputcan be thought of as an appropriate member return. Hardie’s model was developed from the single inputcase built by Helmberger and Hoos, showing that a shadow value can represent member returns in thesingle input case when the production level is taken as parametric.Imperfect competition between cooperatives and between cooperatives and IOFs is only beginning to beaddressed [Ireland 1987]. The majority of the research has dealt with the labour managed firm, inparticular as the former communist countries are liberalizing. Law and Stewart [1983] show that when alabour managed firm and a profit maximizing firm are in competition, the profit maximizing firm willassume the Stackleberg leader role, and the cooperative the follower role, and neither will want to changeposition. In general, an IOF prefers to have a cooperative as a rival in place of another IOF.Objectives different from dividend maximization have been proposed [Cotterill, 1987; Ireland, 1987;LeVay, 1983]. Principle among these alternative objectives is maximizing farmer welfare. Overallfarmer welfare is not maximized at the maximum dividend point. It is also not maximized at theintersection of the supply function of the member agents and the net revenue product of the cooperative.Typically the welfare maximizing point still involves some market shorting, and is unstable whilemembers are free to choose their own production level.41Sertel [1991] investigated the relationship between a workers enterprise and a profit maximizing firm inimperfect competition. Sertel’s model moves from a standard capital and labour technology to a labouronly production function by demonstrating that capital will be chosen optimally and can therefore beignored. Sertel then focuses on the labour input, which is supplied by the members. The labour managedfirm has a restricted membership by demanding compensation for workers who are replaced. This‘market’ for membership rights mimics a capital market, so that the behavior of the cooperative and theTOF become indistinguishable. The point where the membership rights have the largest value generatesthe same labour input level as an IOF with the same technology chooses.Our analysis follows a construction very similar to that of Helmberger and Hoos, and our conclusionsreflect for a marketing cooperative many of the results that Sertel finds for a worker enterprise. Weassume that there is only one homogeneous, undifferentiable product which the members deliver to theircooperative. All other inputs are ignored. The stochastic nature of member production, differencesbetween members, and variations in output price are also ignored. These factors are important, but wouldcomplicate the many features that are already part of this analysis. The objective of our model is toinvestigate the effects of the various features—price pooling, price control, and aggregate volumerestriction—on the interaction between a cooperative, its membership, and a competing IOF.3.2) The For Profit Processor.There is only one input in the processing sector, the raw milk. All processors have the same technology.For the investor owned firm (IOF) we write the profit function as:3.1In this equation, t is profit, the difference between revenues, the product of the output price p and theamount of output produced using the production process f (v,,), and the costs, the product of the rawinput price m and the amount of raw product used by the firm, V.42This is a somewhat atypical way of modeling the behavior of a firm. Normally one would minimize costsubject to a production constraint, and then optimize over the amount of output the firm chooses toproduce. We are modeling the input decision of the processor, and therefore ignore the output market. Itis easier to see the effect of the supply management restrictions on the input side. We are modeling thedemand behavior in the milk market, where our consumers are the raw milk processors, and their utility ismaximized by maximizing their profits.The firm controls the amount of input, v,, , used. The first derivative of the firm’s profit function is:3.2 Tht/öv =p(af/av)_mTo locate the profit maximizing input level, we set this equation equal to zero. As expected, we find thatthe profit maximizing solution is to set the marginal value product equal to the price of the input.3.3 p(af/avj=mWe assume that the production function is concave and decreasing over the relevant range, guaranteeing adiminishing marginal product. We assume the functions are smooth, monotonic, and continuous,ensuring only one solution Finally we assume that the second order conditions are satisfied, so that oursolution is a maximum.Figure 3.1.1 shows what the total revenue and total cost curves might look like with respect to the amountof milk the processor receives. We suppose that at low production levels, the plant would be runninginefficiently and little of the milk received would be transformed into the final product. Efficiency wouldincrease until some optimal level was reached, after which it might decline. Total revenue is a function ofboth the technical efficiency of the production process and the effect of the firm’s production on the outputprice. Our functional specification has so far contained a fixed output price. With a fixed output price,the shape of the revenue curve will be determined by the production technology alone. As the profit43$ $v, milkFigure 3.1.1: Total revenue and total cost as__________a function of total milk received.function has been defined, the total cost is going to be the product of the milk price and the amount ofmilk used, a straight line through the origin.The marginal value product for this relation is shown in figure 3.1.2. It is initially climbing, and crossesthe line representing the milk price once before reaching a peak. From its high point, it falls, crossing themilk price line once again. The milk price line is the marginal cost curve that corresponds to the totalcost curve in the first figure. There are two intersection points. The left point is an unstable equilibrium.At this point the last unit produced is finally breaking even, and no profits are being made. The rightpoint corresponds to the profit maximizing production level for the firm.3.3) The Independent FarmeiThe independent farmer’s profit is not linked to the processor’s profit. This farmer takes theoffered price as given. For this fanner, our model assumes a well behaved cost function, convex andincreasing in the amount of milk produced. It is probably not too unrealistic since there is generally felt tobe an optimal production level for most of the assets held by the farm, with increasing costs away fromthis point.TotalRevenueTotalCostMWmv, milkFigure 3.1.2: Marginal value product as afunction of total milk received.44$ $milkFigure 3.2.1: Total revenue and total cost as Figure 3.2.2: Marginal value product as aa function of total milk produced. function of total milk produced.Relying on these assumptions, we propose the following objective function:3.4 rtj’=mvf_c(vr)The profit t f is equal to the revenues mv[ generated by fanner i producing yr units of milk fordelivery to the plant, less the cost c(vf) of producing it. The first derivative of equation 3.4 is:3.5 mtr/ovr =m_ac(vf)/ovfSetting 3.5 equal to zero, we get the traditional relationship where marginal cost is equal to marginalrevenue, the price.3.6 m = ö c(vr )/ovrFigure 3.2.1 shows the total cost and total revenue curves for a hypothetical farm. On this diagram, thevertical distance between TR and TC is greatest at the production level given by v/’. Profit is representedby the distance between these two lines. In figure 3.2.2 we have the marginal conditions. The convex andyr milk vf45monotonically increasing marginal cost is consistent with the assumptions that it is well behaved. Theprice m which the fanner receives represents the marginal revenue. To locate the optimal productionlevel, we set the marginal revenue equal to the marginal cost, and reproduce the profit maximizing pointgiven by the pmduction level vI.3.4) The unregulated market with independent agents.Now that we have defined the objective functions for the actors in this market, we need to study theirinteraction. The objective functions for the JOF processor and the independent fanner shipping milk tothis processor are:3.1m (v ) — mv } IOF processor optimization problemmax{mv! — C(V )} Independent fanner’s objective function.vi,In this construction, v is the amount of milk the processor chooses to purchase. It is purchased at aprice of m, is processed using a technology represented by f(v), and the output is sold forp. Thefanner produces yr of output at a cost of c(vf), and sells it to the processing market for m. The modelhas been built under the assumptions of an unregulated competitive market. The agents treat the prices aspredetermined, and believe that their own actions have no effect on the actions of the other agents in themarket. The first order conditions we generated are:3.3 The for profit processor.p(af/av)= m3.6 The independent fanner.m = a c(Vf )/avf46$SupplyDemandQ milkFigure 3.3: Supply and demand derived from aggregate MW and MC curves.This result is precisely what we expect between atomistic agents in a competitive market. The IOFprocessor chooses ifs input level such that the marginal value product equals the marginal cost of theinput, the milk price. The farmer chooses to produce such that marginal cost equals marginal revenue,again the milk price.The market interactions between these agents balances their individual optimization problems to clear themarket. If we assume a large number of processors and a large number of farmers all actingindependently, then all will take the price as given, and we get the competitive outcome, the intersectionof the market supply and the market demand curves.Figure 3.3 shows the unregulated market when there are a large number of buyers and suppliers. Thedemand curve D is the aggregation of the marginal value products curves for all the processors buyingmilk. The supply curve S is the horizontal aggregation of the marginal cost curves for all the producers.The intersection of these two curves locates the competitive solution. At this point, total farmerproduction is Q, which is purchased by the processors for the price m. There are no economic rentsavailable to anyone.47$ $TC0mW’1Q milk Q1 Q0 milkFigure 3.4.1: Supply curve for raw milk. Figure 3.4.2: Monopolistic processor total cost andtotal revenues.If there are a small number of processors the competitive outcome is less likely. If we go to themonopolistic extreme with only one processor, then the processor has the power to set the price along theproducers’ supply curve. The total cost that the monopsonist must pay is equal to the product of the priceand the amount of milk purchased. In the competitive market the price is exogenous to any agentsdecision. With one purchaser, the price that needs to be paid to generate a particular level of output isgiven by the supply curve. At the margin, this means that the monopsonist faces an upward slopingmarginal input cost curve rather than the horizontal one that characterizes the competitive case.Graphically, the total cost that the processor pays, at any given level of output, is equal to the area of therectangle bounded by the output level on the right, the price line above, and the axes (figure 3.4.1). If theprice is taken as given, the area of thisrectangle increases only in response to increases in quantity. The top of the rectangle is fixed at themarket clearing price. For the monopolist, the area of the rectangle increases both as a response to therightward movement of the amount of milk purchased, and with the upward shift of the price line. ThisTC148upward shift occurs because for any particular level of milk purchased, the monopsonist need only coverthe marginal costs of the producer represented by the supply curve.When we construct the total cost curve, we see it starting at the origin, but initially increasing at a slowerrate than the linear total cost curve of the fixed input price (figure 3.4.2). The TC1 curve increases inslope, and crosses the TC0 curve at the competitive market solution. At the competitive solution themarket price is also on the supply curve. However, at this point the slope of the TC1 curve is steeper thanthe TC0 curve, and therefore also steeper than the TR curve. The maximum profit point must lie to theleft of the competitive solution.3.5) The Cooperative Processor.The cooperative processor is a little different. We assume the cooperative distributes all of the profitsgenerated to the members, and that there is no member capital within the cooperative to worry about.This cooperative is also unable to carry losses or profits between periods, allowing us to avoid the issue ofdistinguishing between farmer cash receipts and cooperative performance. A cooperative must decide onother fixed and variable input levels. We assume these inputs are chosen consistent with our chosenobjective, and are therefore ignored. All production costs consist of the cost of the milk input supplied bythe farmers, making it easy to model. We first take the independent processor’s objective function and setthe profit equal to zero. The total amount that can be distributed to members, mv, is equal to the totalrevenues generated.3.7 mv =pf(v)There are a variety of objectives the cooperative could pursue. It might maximize aggregate farmerwelfare by trying to force the competitive outcome. It could maximize member return as a verticallyintegrated firm, including the costs at the farm level. Or it might maximize the patronage dividend,ignoring the costs at the farm level. We model only dividend maximization because it is the simplestcase.49$ $Q10Figure 3.5.1: Cooperative total revenue Figure 3.5.2: Cooperative marginal valueproduct and average value product.3.8ôm 1—=—pof (vj/ov ----pf(v)avc vcmilk Qi Qo milkSome conclusiom are dependent on this specification. However, provided that the cooperative is pursuingan objective which offers the members an effective price above the competitive market price, our generalresult continues to hold; the competitive yardstick is not guaranteed under supply management.In its simplest form, maximizing the patronage dividend is equivalent to maximizing the price thecooperative pays for the member supplied input.m= pf(v )/vTo find the amount of input associated with the maximum price that can be paid to the fanner, we cantake the derivative of this relation with respect to the quantity of milk processed. This derivative is:3.9Setting 3.9 equal to zero and eliminating terms we simplify it to the following:3.10 paf(v )/av = (1/va )pf(v)50The left hand side of this equation is the marginal value product. The right hand side is the average valueproduct, the total revenue, divided by the total amount of input used.Graphically the total revenue curve is the same as that for the IOF, as shown in figure 3.5.1. However, itdoes not make sense to include a cost curve, since the profits are totally distributed against the milk usedin production. The marginal curves show where the cooperative would operate, if it was able to maximizeits objective function. The maximum price that the cooperative can pay for the milk received is themaximum of the average value product. This point occurs where the MVP curve intersects the AVP curvein figure 3.5.2, at an output of Q. For the given curves, this point is below the free market equilibriumwhich would occur at the intersection of the price line and the MVP, at Qo.3.6) The Cooperative Member Farmer.The cooperative member farmer is assumed to have the same objective function as the non-member. Theonly differences are that the ‘price’ the farmer receives is the patronage dividend, the total revenues of thecooperative divided by all member production.3.11 =[pf(vj/v]v—c(v:)The amount of milk that the cooperative processes, v, is equal to the sum of all the milk the memberschoose to produce, 2 v:. This implies that öv /öv is equal to one. For the moment we are ignoringthe effect this farmer may have on the production of other farmers. Evaluating the derivative of 3.11, itcan be written as:3.12 ör /Ov =-—pf(v)÷ .i{[p13f(Vc)]— -_pf(v )} — oc(v:)/av:Setting this relation equal to zero, and rearranging, we get the following:51pf(vjv pf(v) v ôf(v) öc(v)3.13 vc vc vc vc t3vPatronage Dilution Output Marginal+ =Dividend Effect Effect CostIn equation 3.13 we have split the left hand side of the equation, the cooperative member’s marginalrevenue, into three terms. The patronage dividend is the per unit revenue the member receives. Thedilution effect is the impact that a change in this member’s production level will have on the share of thepatronage dividend this farmer receives. If this member chooses to increase production, then the existingcooperative revenues will be diluted over a larger patronage, reducing the share captured by this member.The output effect is the amount by which revenues increase in response to an increase in output. If theextra production of the cooperative increases efficiency, then revenues available for distribution will belarger, and the patronage dividend will increase accordingly. The member’s optimal production point setsthe sum of these effects equal to the marginal cost of attaining the farm’s output level.If we were strictly correct, we would need to acknowledge that the dilution effect also affects the othermembers, so they would be expected to reduce their own production. Therefore, the absolute magnitude ofthe dilution effect will be less than shown here.3.13 is easiest to interpret at the extremes of one infinite membership and a single member. If there arean infinite number of member farmers in the cooperative, then the ratio V’ /v is equal to zero. The onlyfactor the farmer considers is the size of the patronage dividend. This is typically assumed [Cotterill,1987...], with the result that the farmer acts as if the patronage dividend is a predetermined price.If we have only one only supplier to the cooperative, v’ /v equals one. The only factor that the farmerconsiders is the marginal value product of the milk. The farmer’s own marginal revenue is equal to themarginal value product to the cooperative of the milk shipped, and the farmers decision will completelyinternalize the final market. This corresponds to vertical integration by a single farmer. A typicalmember faces is a linear combination of these two extremes.52$Figure 3.6.1: Cooperative member total Figure 3.6.2: Cooperative member marginalrevenue and total cost, revenue and marginal cost.The farmer’s individual marginal revenue is changed when he/she belongs to a cooperative. Since we areassuming that the industry is earning some rents, the cooperative is able to distribute a return to thefanner above the market price for milk. This generates a steeper total revenue curve as shown in figure3.6.1. However, the total revenue curve is no longer linear. As the farmer increases production, theaverage value product of the cooperative falls. Since the price that the farmer receives for the milk isdrawn directly from the average value product, the slope of the total revenue curve falls as the farmersindividual production increases. The degree to which the AVP falls depends on the scale of the farmerschange in production relative to the overall product the cooperative receives.37) The Unregulated Market with a CooperativeAs was done for the unconnected agents, we now interact the objectives of the cooperative and itsmembers. The objective functions we specified are:v1 milk v milk533.8 max {pf (v )/v } Cooperative processor objective function.V V = choice of input level.3.11max{[pf(v )/v }‘“ — c(v1”)} Member farmer’s objective function.vc= member’s production level.3.14 v, Equilibrium conditionThe objective of the cooperative is to maximize the size of the patronage payment. The objective of themember is to maximize profit. To make things balance, the cooperative is required to process all of themilk that is delivered to it by its members, as expressed in the equilibrium condition shown in equation3.14. We assume throughout that membership and member production is unrestricted. As for the simpleIOF case, we are assuming that the output price is fixed. The first order conditions we developed for thisproblem are:3.10 The cooperative processor.paf(v)/av = pf(vj/v3.13 The member farmer.ac(v:)v v v öv v ôvThe objective of the cooperative is satisfied when the average value product of the cooperative is set equalto the marginal value product. The member solves its optimization problem by choosing a marginal valueproduct that is equal to a farm adjusted patronage dividend.The farmer’s have the ultimate power over the level of input the cooperative will process. If we have alabour managed firm, then membership could be adjusted or restricted until the highest possible wage isbeing paid [Bonin, 1993]. However, this violates the principle of open membership, and could clearly notbe maintained if new labourers can freely enter. We are studying a marketing cooperative, wheremembers are free to choose their own production level, making it very difficult to be stable at themaximum of the AVP. Farmers are assumed to the MR and MC they see on the farm. If there are manyfarmers, this occurs where the marginal cost of the average farmer is equal to the average value product of54$ $Figure 3.7.2: Aggregate marginal revenueand supply curves.the cooperative. This is beyond the patronage dividend maximizing point the cooperative would like to beoperating at, assuming it is trying to maximize the patronage dividend it can pay. As we build the model,we introduce a milk pooling system that breaks the direct link between member production and theamount the cooperative processes. This policy instrument breaks the competitive yardstick result we findat this level.Graphically, figure 3.7.1 combines the marginal value product and the average value product with themember’s supply curve. The market solution is shown as Qo in this figure. If we assume that the farmerdoes not internalize the cooperative incentives, and that there are profits available in the industry, then theaverage value product represents the farmer’s marginal revenue. Fanners will continue to join thecooperative, expanding the member supply curve. This will continue until the supply curve has expandedfrom S0 to S1. When S1 has been reached, the average value product has been lowered to the point whereit is equal to the market price at the input level that is finally established. At this point, the farmers areindifferent between belonging to the cooperative and no belonging.Qo Qi milk Qo Q1 milkFigure 3.7.1: Marginal and average value__________product against member supply.55However, if the number of farmers is small enough that the individual fanner somewhat internalizes thecooperatives problem, the average value product no longer represents the price that the farmer optimizesagainst. The fanner’s marginal revenue will instead lie along a line that is a linear combination of theMVP and AVP curves. This line is labeled MR in figure 3.7.2. The amount by which the farmer’s jointhe cooperative will be somewhat lessened by this effect.3.8) The unregulated market with one cooperative and one forprofit firm.The interactions when there is a cooperative in a market can range from one cooperative and one for profitfirm, to one cooperative among a very large number of for profit firms. In the later case, we would expectthe free market outcome to occur. Processors will compete for the output of the farmers, to the point thatall rents are exhausted. It is questionable if a cooperative would ever appear in a competitive market, butif there was one, it would not create any economic benefit for its members relative to the free market price.This is not be particularly interesting to explore.The case that we explore has two processors, an IOF and a cooperative. In parallel we develop thetraditional duopsony case to illustrate the differences. As above, we assume a simple revenue function forthe processors, depending only on the amount of input used. The farmer’s individual actions areaggregated into a supply curve.3.15max{f (vt) — m(v + VP )v } First oligopsonist’s objective function.3.16rnax{f (v‘) — m(v + i } Second oligopsonist’s objective function.3.17 m = m(V) V = v,, + Input price relationship.We first consider the two agent oligopsony, two processors with identical technology in the same market,facing an upward sloping input supply.56of Omp———v =mOV,, Ov “The oligopsonist chooses an input level where the marginal value product, adjusted by the effect of thefirm’s input decision on the input price, equals the marginal input cost, the price itself.With functional forms, this relation is used to generate a reaction function. The equilibrium solution forthe competition between these two firms would be the intersection of these reaction functions. Thederivative of the revenue function is assumed to be negative, while the derivative of the supply function isassumed positive. Relative to the free market, the oligopsonist purchases less of the input, so that farmersreceive a lower price.Next we introduce a cooperative in the place of one of the oligopsonists. We assume Cournot conjecturesfor the processors, and atomistic and opportunistic actions for the individual farmers agents and membersof the cooperative. Cooperative members assume that the patronage payment from the cooperative is fixedand independent of their actions. The objective functions for the agents in this market are:3.20 max{f(v) — m(v +, ).i } Oligopsonist’s objective function.3.21 max’mv” — c(v” )} Independent farmer’s objective function.vip I.With Cournot assumptions each firm believes that its rival will hold output fixed. The firm optimizesagainst the slope of the supply curve. To find the firm’s profit maximizing point, we take the firstderivative of the objective function.Mathematically, the oligopsonist believes that Ov, ‘/Ov = 0. We impose this condition, and set thederivative to zero. After rearranging we get:3.19573.22 max{f(v )/v } Cooperative’s objective function.3.23 max{[pf(v )/v ]v’ — c(v: )} Member farmer’s objective function.3.24 m = m(v); v = + v Input price relationship.We have four agents, the IOF, the independent farmer, the cooperative processor, and the member farmer.The IOF believes its actions have some effect on the milk price, while the independent fanner feels thatthe farm’s production is too small to have any effect. The objective of the cooperative is to maximize thepatronage dividend. However, it has no control over how much it processes. The actual productiondecision of the cooperative is made by its members, who choose this level by choosing how much to shipto the cooperative. Strictly speaking, the cooperative does not have an objective function. The marketmust clear, and we apply the law of one price.The first order conditions that derive from this problem are:3.25 The oligopsonist’s objective./ ‘+v)—-—— vaV3.26 The independent farmer.at’/avf =m_ac(vr)/avr3.27 The member farmer.or/av; = m÷!L{[t’iIWe have ignored the first order conditions of the cooperative. The important condition that determineswhat happens in this market is the one price condition. The cooperative distributes all of its surplus to itsmembers, so that if one price is to prevail, the following must hold:3.28 f(v )/v = m(v + v)Effectively this states that the cooperative patronage dividend must equal the market price.58This solution is usually used to argue that the presence of a cooperative in the market will lead to therestoration of a competitive result. The cooperative pays out all its returns to its members, as a result ofthe zero profit assumption. The members will earn a profit as long as there are rents available in theindustry. The IOF must pay a price equal to the return the member receives if it is to acquire any input.New farmers will enter the industry until all these rents are exhausted. At this point, the free marketsolution has been restored.This need not be the case. The cooperative’s production point occurs where the AVP is equal to theaggregate supply price. However the IOF can choose an input level where it is earning rents against thisprice. As long as it has an average revenue that is above the market determined price for the milk input,the IOF processor will earn a profit.If we maintain the same Cournot conjectures that we investigated by comparing the two oligopsonists, weget the following first order conditions:3.29 The oligopsonist’s objective.of / 3mp—=mv +v)+—v,,(3V Ov3.30 The independent farmer.a c(v” )/av[ =3.31 The member farmer.pf(vjifpf(v) Of(v)v’ Oc(v)vc vc vc Ovc vc OvThis is almost identical to the first order conditions for the situation where two IOFs are competing, sinceunder the Cournot conjectures the IOF takes the production of the cooperative as fixed with respect to itsown actions. The independent farmer and the cooperative member have not changed their actions. Thecooperative does not deal with the milk price, so this is not internalized into the member’s actions.59$ $Figure 3.8.2: Cooperative in imperfectlycompetitive market.Supplyv-t-vp milkFigure 3.8.3: Aggregate market supply curve.Figure 3.8 shows the relations presented above. Figure 3.8.3 is the total supply of milk produced by allthe producers, the sum of the member and independent farmer supply curves. In 3.8.2 the intersection ofthe member supply curve and the average value product determines how much the cooperative willprocess. Figure 3.8.1 shows the situation for the IOF. If the IOF produces at the point where themarginal revenue intersects the price line, its average revenue is greater than its marginal revenue, and itearns positive profits. This outcome relies on the identical revenue curves for the cooperative and themMYPVp milk VC milkFigure 3.8.1: IOF Oligopsonist.$mVp60IOF. The IOF can do even better. It can act strategically to manipulate how the cooperative and itsmembers interact to determine the input market price. As it reduces its purchases of inputs, the price ofmilk falls. It shorts the market until it reaches its maxhnum profits. Since the IOF is shorting the market,and since we have assumed one price, this shorting translates into a situation where the farmerscollectively are receiving a price that is below the competitive result.The sustainability of this solution is a function of the entry barriers. As in most simple introductions toimperfect competition, we just assume that these barriers to entry exist. In the dairy industry returns toscale and market structure may generate entry barriers. The efficiency of larger dairy processingoperations, and the fact that most processors have moved to small numbers of plants for their processing,indicates that there are returns to scale over some range of production sizes. This fact is compounded bythe ease of market saturation. In BC there are in effect two markets for milk. The large volume market isoccupied by large buyers, such as grocery chains and convenience stores, which translates into a smallnumber of customers purchasing large amounts of product. The smaller market of home delivery andsmall retailers is easily saturated. These facts make it difficult for new firms to start up.We can take this analysis one step further, to the realm of the Stackleberg leader-follower model. In thismodel one of the firms, the leader, internalizes the reaction of the other finn, the follower. The leaderanticipates how the follower will react to its own production decision, and chooses its optimum taking thisinto account. The objective function for both firms are still the same. However, the first order conditionsare different. The leader is the only firm that changes its conjectures. The first order conditions that resultfrom these effects are:61The Stackleberg leader knows that its own actions affect how the follower acts. The derivativeöv ‘/ôv is no longer equal to zero. Using the technique of implicit differentiation on equation 3.33 wecan sign this derivative. The partial derivative of 3.33 with respect to V is:334ö2f öv1,’ öm ôV,ôV ôm ôVöV’ãv’2 c3i’,, öv aV 9v ôV2 ôv öVIf we rearrange this, isolating aV ‘/aV ,we generate the following:335 f ömôm-1öV ôv av2) av’2 ÔV cJv2From our assumptions about the supply curve, we know that the first and second derivative of the supplyfunction are positive. This makes the numerator a positive quantity. The second derivative of the revenuefunction is negative by assumption, which is demanded by the downward slope of the marginal valueproduct. The resulting negative denominator makes the right hand side of 3.35 negative.The optimization condition for the leader is:/ am ôv3.36 —=mlv +v 1+— 1÷— vC1 ôv, “With the condition outlined above, we see that ôv,, ‘/ôv will be less than zero. This means that theterm on the far right will obeyt3m3.37 — v —vav aV,,The optimization condition for the leader will require a smaller marginal value product than with Cournotconjectures. Along with the decreasing marginal value product assumption, the Stackleberg leader will62purchase more input than a Cournot oligopsonist with the same technology. The leader is capturing alarger share of the profits by anticipating its rivals reaction.In markets with a cooperative, we often see the cooperative accounting for the largest single share of theproduction received. This is the case in the BC dairy industry, and is similar elsewhere. Superficially thecooperative appears to be the logical choice as the leader firm. This conclusion is a little premature. Thecooperative is bound by the actions of its members. It cannot autonomously determine its level of output.It is more logical to conclude that the IOF will be the leader, in spite of the fact that we see the IOFcapturing a smaller market share.We can develop the Stackleberg model with the cooperative as one of the firms. The objective function forthe IOF is again3.38 max{f(vp)_m(vp +v)v}while the equilibrium condition between the cooperative and its members is3.39 f(vj/v =m(v +v).The first order condition for the IOF can be defined as above, and is/ am 0v3.40 —=miv +v 1+— V\p C) pp p pNow we must again determine the sign of the conjectural variation, in this case what will be theproduction response of the cooperative to the decision of the oligopsonist. We again proceed by implicitdifferentiation to get the sign of . Completely differentiating 3.37 with respect to V we get:3.41iafaVif(jf3vamv öv öv, V VC ÔVp öV63We can rearrange this and isolate öv/öv to get:3.42avam of f(v)o,n_1vOv öv, v OvCAs above, we assume that the supply curve is upward sloping, which translates into a positive numeratoron the right. The denominator is equal to the difference between the marginal value product of thecooperative and the average value product, less a scaled slope term. Since we are assuming that at theproduction point for the cooperative is in the range where the AVP is above the MVP, the denominator isgoing to be negative.This result indicates that the IOF, when in competition with a cooperative, can respond strategically inanticipation of the behavior of the cooperative. The profit maximizing point for the IOF is at an inputlevel above that of the equivalent oligopsonist with Cournot conjectures. However, it is still less than thepoint where the intersection of the IOF’s marginal value product and the price line occurs. The IOFanticipates that if it increases the price it offers, relative to the Cournot situation, it will attract farmersaway from the cooperative. The higher price will attract new farmers to the industry, so that the overallprice increase in the input market is not as large as the firm with Cóurnot conjectures believes. The inputsupply effect felt by the IOF is modified by the interaction between the cooperative and its members.3.9) SummaryIn this chapter we defined the objective functions and technology for our model. We have a singlecommodity, milk, being traded between the farmers who produce it an the processors who purchase it andsell it into a further market.With no market regulatory constraints, and ignoring the potential strategic interactions, wereproduce the standard ‘competitive yardstick’ outcome. If we have entry barriers or downward slopingmarginal and average product curves, then an IOF can act strategically against a cooperative. It uses thefact that the cooperative dividend must equal the aggregate supply price to choose its output level, such64that its input cost is reduced. Oligopoly profits are not earned, but the competitive yardstick is notcomplete.65Chapter 4: A Quantity RestrictionIn the last chapter we introduced the problem and solved it for the unregulated case. We found that theintersection of the members’ incentives with the cooperative structure generate the competitive yardstickeffect. We also found that with the right technological constraints we can soften the competitive yardsticka little.In this chapter we continue our analysis by introducing our first restriction, an upper bound on theaggregate production of milk. This restriction simulates the effect of the supply management quota on thedairy sector. We first investigate the effect of the restriction on the processor-producer and cooperative-member relationship in isolation. We then locate an equilibrium between two IOFs and an IOF andcooperative in competition.4.1) The for profit processorWe now add the first restriction, constraining the amount of raw milk available. Under supplymanagement, the total amount of the raw product available to all processors is established by an externalauthority, the milk board. From the perspective of an individual processor, the production that otherprocessors are carrying out is beyond their control. The processor’s production must be less than or equalto the difference between the total amount of production allowed and the production of all otherprocessors. The problem is defined as:4.1rnax{pf(v) — mv } IOF objective function.4.2maximv” — c(yr )} Independent farmer’s objective function.4.3= , + Market clearing condition.In this definition, the IOF is maximizing the profits over the choice of input volume Vi,. Theindependent farmer is maximizing the difference between the market revenues and the production costsover the choice of vf. The market clearing condition requires that the sum of the production of all the66producers is equal to the amount of milk used by all the processors. As written, v_ is the amount ofinput used by all the other processors. However, we now have a restriction attached to the market clearingcondition which must be obeyed. The sum of the production of all farmers must equal the milk used by allthe processors, and this amount must be less than the upper limit given by V.Since we have a restriction to contend with, we solve this problem using lagrangians. The lagrangianfunctions for this problem are:4.4 The IOF processor.+[(v_v)_v]4.5 The independent farmerL(vr,)= mvr — c(v”)÷ M[(v — vf]We will first look at the processor’s problem. We are maximizing the amount of input chosen and theshadow value of the constraint. To be completely general, we would allow the possibility that therestrictions would not be binding. To allow this, we search for a solution by way of the Kuhn-Tuckerconditions. The Kuhn-Tucker conditions we derive from this optimization are:4.6.1 aL(v, )/ov = p[af (v)/ov]_ m— .,0,0, [aL(v , )/av]i= 04.6.2 oL(V,.)/oA. = (v — v,, 0,o, =0These Kuhn-Tucker conditions allow for corner solutions and binding constraints. Normally one tests allthe possible combinations of binding and free constraints until the best solution is found. In thisparticular case there would be four possible combinations,{(v = 0, = o),(v 0,,= o),(v = 0, o),(v 0, o)}.67We can make a couple of simplifying assumptions to eliminate all but one of these choices. Our firstassumption is that the constraint on the amount of input used is binding. All the firms in the industrycollectively use all the raw product available. With this constraint, the shadow value of another unit ofraw product, were it available, might be positive. This reduces our set of conditions to{(v = o,, o),(v o,.., o)}. The next condition we impose is that the finn we areinvestigating is using input. This constraint eliminates the situation where the input level is restricted tobe zero. With these restrictions we can generate two equalities that reveal the details of the solution.These are:4.7.1 4af(v)/av]= m+4.7.2 v=V—vEquations 4.7.1 and 4.7.2 characterize the solution. In 4.7.1 we see that the marginal value product isequal to the sum of the marginal cost of the input, the price of the raw product and a shadow value. 4.7.2shows that the sum of all the raw product used is equal to the total available, reproducing the constraint.Figure 4.1 shows the solution graphically. Without restrictions, the firm would purchase Q0 units of input.$Shadow/ Value::::::::::::Q10 milkFigure 4.1: Marginal value product, free market price and shadow value.68At this point, profits are maximized since the value to the firm of the next unit of input used is less thanthe free market price m. This firm is unable to reach Q0, for example, when the other firms have securedenough of the input so that this firm can only get Q1. Under this constraint, the last unit of input is worthm’ to the firm. The difference between m and m’ is the shadow value for the last unit of input, extraprofit this firm would earn if it could get another unit of milk. The price m’ is the maximum that thefirm is willing to pay to get that extra unit.4.2) The independent farmer.The farmer’s objective function is unchanged, except that all farmers together face an upward bound onthe amount of milk that they can produce. The farmer can produce no more than the difference betweenthe maximum allowable production, V, and the amount that is being produced by other producers in theindustry. We assume that the farmer is producing a positive amount of output, and that at the margin it isnot unprofitable to produce the last unit of output, eliminating the Kuhn-Tucker problem. In effect wehave made the output restriction binding. No farmer would choose to produce less than the amount theyare entitled to produce.SuppJy management changes the nature of the production decision. Changes in the level of productioninvolve a cost, in whichever direction one may deviate. To escape these costs, one buys or sells quota.However, this is an investment decision, not a production decision, and is not an explicit part of thismodel. For simplicity, we assume that the farmer has chosen the profit maximizing quota amount, and allfarmers are identical to the point that if the constraint is binding on one farmer, it is binding on all. Inthis way we have changed what is accurately an inequality constraint to an equality constraint for thismodel.Why are we evaluating a single variable optimization problem with an equality constraint? The solutionidentifies the cost, at the margin, of this production constraint. This cost is the source of the farmer’swillingness to pay for quota. In chapter nine we test our model using the price of quota. The theoreticalfoundation for this test lies with the assumption that farmers will capitalize economic rents into the quota69$mv’ v1 milkFigure 4.2: Fanner’s marginal cost with and without supply management.price. Economic rents are identified by a positive shadow value, which this analysis allows us todemonstrate.The first order condition comes out as:4.8 t3L(vr, . )/öv” = m — oc(vf )/av[ +Equating this to zero we have:4.9 m— oc(vr)/ovr — = oAnd rearranging we get:4.10 m= ac(vr)/avr +pWe see the fanner again equates marginal revenue, the price they receive, with marginal cost. However,the restriction adds a shadow value to the marginal cost, reflecting the extra profits the farmer could earnif another unit could be produced.Shadow70In figure 4.2. v1’ represents the share of the total output that this farmer produces. The institutionalshorting of the market pushes the price up to m’. The shadow value is the distance between the MC andm’ at the limit of production. The supply restriction is equivalent to an upward shift of the supply curve.The forgone revenues on the next unit of production are represented by the shadow value, the amount bywhich the supply shifts up. For a fixed milk price, the individual farmer, is now supplying only v’ unitsof milk to the market, instead of the desired production of vg.4.3) The supply controlled market with independent agents.We now explore the interaction of the IOF processor and the independent farmers. The first orderconditions that we generated above are:4.7 The IOF processor.p[af(v)/ov]= m÷4.10 The independent farmerm=ac(vf)/ovf ÷‘These conditions indicate that at the equilibrium outcome, at least one of the players will face a shadowcost at the margin. Who gets the rents is unclear, but the market equilibrium condition that there be onlyone price must be satisfied. The lack of any formal mechanism for distributing these rents in the modelmeans that the main way these rents are distributed is through bargaining.Graphically, figure 4.3 shows what is going on. The supply restriction holds the production of theindustry at the level V, which is below the free market solution. At this production level, there are rentsavailable to the total industry, represented by ?. + 4. How these rents are distributed between theprocessors and producers depends on the negotiation power of the agents. As drawn, the restriction hasallowed farmers to receive enough of the rents to push their effective price above the free market solution.However, this need not be the case, and since processors are usually more concentrated than producers,one would expect that under a system like this, they probably have the majority of the bargaining power.71$SupplyV milkFigure 4.3: Aggregate processor MPV and aggregate producer MC.4.4) The Cooperative Processor.The cooperative processor must also operate under the restrictions that govern the industry. We add thevolume restriction to the cooperative’s problem. The objectives will now be:4.11rnax{pf(v )/v } Cooperative objective function.4.12max {[pf(v )/v }c — C(yc )} Member’s objective function.4.13= + v Market clearing condition.v_ represents the amount of input used by all the other processors. As before, the flexibility for thecooperative is limited, but knowing where the objective is maximized allows us to see how the incentivesof the members change this. We again evaluate this problem using lagrangians:4.14 The cooperative processor.L(v,) = pf(v )/v + [(v — v) — v]4.15 The cooperative memberL(v(,) = pf(v )v/v — c(v:) +—..v;) — v:]72If we assume that the restrictions are binding, then the first derivatives are:4.16 The cooperative processor.i3L(v, ) )/ôv = p[of(v )/av J/v — pf(v )/v2—4.17 The cooperative memberaL(vr,r)/avr + [am(vr)/av1]vr — ac(vr)/avr—We have evaluated this derivative without replacing the member’s price with the patronage dividend. Theaggregate supply restriction generates a shadow value at both the processor level and the producer level.We can see that the cooperative structure transfers the effect of the restriction to the members. We locatethe cooperative’s solution by setting equation 4.16 equal to zero. After rearranging we find:4.18 p{af(v)/vJ/v=pf(v)/v2+Multiplying through by the volume of milk received as above, we get the following:4.19 4of(vj/av]= pf(v)/v +Like the for profit processor, there is a shadow value resulting from the industry wide constraint on theproduction level. This shadow value takes on a somewhat different form than it does for the IOF solution.It appears that the size of this shadow value varies with the amount of milk that the cooperative receivesfrom its members. The structure of this shadow value is an artifact of the first order condition. We arelooking for the maximum of an average value product. The optimization is per unit of input used ratherthan for total profit. At the margin, the shadow value is equal to the sum of the shadow value over everyunit, multiplied by the totul number of units being taken.73$mQ1 milkFigure 4.4: Cooperative MVP, AVP and adjusted AVP.In figure 4.4, the scaled shadow value is given by the increasing linear function This function isan artifact of the optimization, which is evaluated on a per unit basis. When we adjust this to get theMVP and AVP for the entire cooperative, we get a linear shadow value. We add the shadow value to theAVP to generate an adjusted AVP curve. To find an optimum, we locate the intersection of the MVPcurve with the adjusted AVP curve. To maximize the patronage dividend that the cooperative can pay itsmembers, it should operate at Q1, left of the unregulated market solution.4.5) The Cooperative Member FarmerThe cooperative member faces the same optimization as the independent farmer, except that the price thefarmer receives is tied to the return generated by the cooperative. Since the return generated by thecooperative is a function of the amount of milk that is processed, subject to the restriction imposed by theregulations, there is again an endogenizing of the price received that is not the case for the independentfanner. Rearranging equation 4-17 into the standard form, we get:4.23 m + [om(vr )/avr ]vI = oc(vr )/ovf + T =+74Into this we need to substitute the marginal impact that the fanner would have on the cooperative, if thefanner could ship another unit of milk. We take this from the lagrangian that defines the cooperative’sbehavior, equation 4.14 above. At the point where the average value product of the cooperative ismaximized, this number is zero. However, where this occurs the fanner’s own marginal cost might bebelow the average value product, which generates an incentive for the farmer to ship more milk to thecooperative. With the assumption that the cooperative must take and process all of the production of itsmembers, this moves the cooperative away from its maximum average value product. The behavioralequation will look like:4.24 m+ {p[of(v)/ovJ/v —pf(v)/v2—= oc(vr)/avr +iq’ = oMultiplying out, rearranging, and replacing m with the average value product, we get:4.25 (i—vf /v, )pf (v )/v + (v[ /v, )p{af (v )/av] ac(vf )/ivf + r + = 0Here we see that the marginal revenue the fanner faces is again a combination of the marginal valueproduct and the average value product. The marginal cost is now adjusted by two different shadow values.The shadow value represented by is the farmers individual shadow value. The shadow valuerepresented by the term ?.vf is the farmers individual share of the cooperatives shadow cost ofThis shows that we can interpret the shadow value which is experienced by the cooperative as a rotation ofthe member’s marginal revenue curve, or a rotation of the member supply curve faced by the cooperative.4.6) The Supply Controlled Market with a Cooperative and a ForProfit Firm.Having looked at the individual agents, we now turn to the effect of these controls on the interactionbetween the cooperative and the for profit finn. As in chapter three, we assume that there are two milkprocessors with identical revenue functions. The revenue function is continuously differentiable andassumes the standard three stage shape. We also assume that the restriction on the total quantity of raw75milk on the market is binding. This assumption decouples the IOF’s input cost from the supply curve.The two oligopsonists are competing against each other to secure a share of the fixed size input market.The general form of the supply relationship on the farmer’s side is taken to be unaffected. They take theprice offered as given. However, due to the restriction, there may be a shadow value related to the nextunit of production. The structure of this problem is:4.26rnax{pf(V) — m(v)v } First oligopsonist’s objective function.4.27rnax{pf(v’) — m(v)v } Second oligopsonist’s objective function.4.28 m = m(v); v = v, + Input price condition.4.29 v,, + v,,’ V Market clearing condition.As we have been doing all along, we will construct the lagrangians to represent the problem of theoligposonists. The problem is symmetric, so we only need to construct one lagrangian.4.30 L(v,?)= f(v)_mv +[(v—v’)—v]Alter setting the first derivative to zero, the first order condition is:4.31 af(v)/av =m+This result is very similar to the competitive result, which it resembles. The firm is no longer able to usethe supply curve to optimize its profit.We must investigate the stability of the solution 4.31 represents. The most obvious potential equilibriumpoint is at the equality of the marginal value products of both firms. Identical firms are expected to sharethe market equally. The equilibrium condition can be written as:4.32 af )/öv,, = ôf(v ‘)/av’76$Figure 4.6: Oligopsonist’s marginal value products.We can use the fact that the market size is fixed to write everything in terms of v:4.33 of(v)/ov = of(v — v)/o(v — v)Relying on this makes it easy to continue with a graphical analysis. We reflect the marginal value productof the rival finn, moving its origin to the total market size at V. This is shown in figure 4.6.The symmetry inherent in the definition being used means that each firm will use exactly half of theavailable input, under this equilibrium assumption. If the finn holds Cournot conjectures, it believes thatits rival will keep production fixed. The firm cannot increase its production, since the total input supply isfixed. However, it does not need to keep its own price fixed. Given that the rival finn holds itsproduction fixed, this firm should reduce the price it offers, down to the point where the aggregatefarmer’s supply curve intersects the limit on the aggregate volume.If both firms hold strictly to the Cournot conjectures, we would expect the market price to fall to theminimum price where all of the supply would be brought to market. However, if we propose that theatomistic suppliers to this market are indifferent with respect to who they supply their product to, then thesituation becomes a little different. If both firms are offering the minimum price, mm, then one firm couldof(v )/o v1,S.S.S.af(V- v)/o(v-Supplyv, V milk77$Figure 4.7: Cooperative’s marginal value products.achieve a larger share of the market by raising its price a little. The firm will then be able to process at itsoptimal point, the intersection of its new price offer with its marginal value product. The rival firm hasexactly the same options available to it, and it will therefore raise its own price, and the price will ratchetup to a maximum at m. With these modified Cournot conjectures, the milk price will be unstable and liesomewhere between m, the intersection of the two firms marginal value product curves, and mm, theminimum price to have V brought to market.If we introduce a cooperative, we modify the equilibrium condition slightly. The cooperative must obeythe condition that its average value product is equal to the market price, which follows from theassumption that the members behave opportunistically. This can be written as:4.34 f(v)/v =mAt the equilibrium point between the cooperative and the oligopsonist, both firms face the same marketprice. Relying on the fact that the IOF’s production is equal to V-va, the equilibrium condition is:4.35 f(v)/v af(v — vj/a(v — v)V milk78We can explore this relation graphically as we did for the two oligopsonists. The equilibrium condition issatisfied where the cooperative’s average value product intersects the marginal value product of theoligopsonist. This intersection occurs at a higher price, and a lower production level for the oligopsonist,than for the two oligopsonist equilibrium. If the oligopsonist holds Cournot conjectures, it will again bethe profit maximizing decision for the oligopsonist to reduce the price it offers. However, assumingindifference on the part of the fanner suppliers, this will result in more members joining the cooperative.To respond to this, the oligopsonist will offer a higher price, with the highest price it will pay being thatprice where its marginal value product intersects the average value product for the cooperative. Thisbecomes the only stable outcome, since the cooperative does not price discriminate against its members.We have restored a result that is much like the competitive yardstick.We can also build a Stackleberg model. The input purchase identity is still V - = V. Assuming thatthe follower chooses to operate where its marginal value product is equal to the price, we get the followingprofit function for the leader:4.36 = f(v)—[öf(V—v)/ö(V--v)JvThe leader firm knows that the follower will choose to operate at the point where the marginal valueproduct is equal to the marginal input cost. It can maximize its own profit against this fact. The firstderivative of this relation is:4.37 ô/öv =Of(v)/övIf we set this condition equal to zero and rearrange it, we get:4.38 af(v)/ov =af(V_v)/a(V_vp)_[o2f(V_vp)/a(V_v)2]vpThe optimal point of operation for the leader incorporates the second order effect on the leader’s profits ofa change in the followers point of production. To interpret this we compare it to the equally split market79explored above. At the equal split point the equality does not hold. The slope of the MVP is negativehere, so the far right term is greater than zero. The entire right hand term is therefore less than the lefthand side. The optimal point for the Stackleberg leader is to choose a production level that is less thanhalf of the market. It maximizes its profits by allowing the follower to take a larger share of the market,generating a lower price for the input.We can conduct the same analysis for the combination of the cooperative and the oligopsonist. Here thefactor that the oligopsonist internalizes is the price identity of 4.34. The cooperative’s input choice, andthe resulting market price, are determined by the atomistic actions of the members. The profit functionfor the oligopsonist is now:4.39 = f(v)—[f(V—v)/(V—v)]vThe rival IOF controls the market price, through the control of its own production level. This control iseffected by offering a price that gets it the amount of input it needs. It can use its offer price to controlv, and thereby move the market price around to maximize its own profit. When we take the firstderivative of this function with respect to the oligopsonists production level, we get:4.40aof(v)f(V_v) öf(V—v)f(V—v) v,av V—vs o(v_v) v—vs v—vsIf we set the above equal to zero and rearrange terms, we get:4.41af(v)f(V-v) of(V_v)f(V_v) Vovp V—v, a(V—V) V—Vs V—v1,We can inspect this equation the same way that the for profit oligopsony was looked at. We need toinvestigate the sign of the far right term. This term is equal to the cooperative’s marginal value productless the average value product, scaled by the share of the total production conducted by the IOF. Thisterm is going to be negative. The IOF’s profit maximizing point is below that when the IOF holds80Cournot conjectures. The IOF maximizes its profit by allowing the cooperative to take a larger share ofthe market, and allowing the price to fall as a result. If we think in terms of the residual supply availableto the IOF, we see that it is downward sloping. The IOF is essentially pricing its input against the AVP ofthe cooperative, rather than the MC of the farmers.4.7) The Quantity and Price Restricted Single Input OptimizationProblemAdding a minimum price to the problem does not change the situation presented above. If the minimumprice is set above the maximum price which the oligopsony models generate, then we will restore acompetitive situation between the competing firms. On the farm side, the high minimum price will meanthat there are farmers who are willing to produce milk, milk which fits in the upper limit imposed by thegovernment, which cannot be sold. Effectively the high milk price has shifted the rents resulting from theoutput restriction entirely to the farmers, and in fact ‘cheated’ some farmers out of some of these rents.If the minimum price is below the price required to get farmers to produce the legislated volume, it willhave no effect at all. The competing oligopsonists do not offer a price below the price which will result inthe total volume being produced. As such, the minimum price will be ignored altogether.If the minimum price falls between these ranges, it will act as a floor for the oligopsonist’s price offering.As such, it will reduce some of the variability in the distribution of rents. Altogether, imposition of aminimum price condition adds little to the analysis. The principle impact of a minimum price is fixinghow part of the rents will be distributed. If the minimum price is set above the supply price the farmer’swill accept, then the minimum price guarantees that the IOF cannot generate as much profit from themarket as it might.814.8) SummaryIf we add a volume restriction to the problem presented in chapter three, we force a gap between theprocessors’ MVP and the farmers’ MC. This gap translates into rents. If the input market is occupied bytwo IOF firms, we find that the input price becomes unstable. We have reproduced the Bertrand resultfrom Cournot conjectures.The volume restriction means that the IOF can act strategically when facing a cooperative. Thelower bound for the input price is given by the cooperative’s AVP. It is against this downward slopingcurve, rather than the upward sloping supply curve, that the IOF optimizes. The farmer price will behigher, but the IOF can still secure some rents.82Chapter 5: The Pooled Milk SupplyWe have now solved our model without regulations, and with an aggregate volume restriction. In thischapter we explore the implications of a price pooi for all the input produced in the market.A price pool is a policy instrument that guarantees all producers of the input receive the same price fortheir production. It is as if all the milk produced by the farmers is thrown into a giant vat, and all theprocessors purchase their input form this vat. The proceeds of these sale to the processors is collected,and distributed to the farmers according to how much they delivered to the pool.If a cooperative is operating in isolation, or if there are no cooperatives present, the introduction of apooling scheme adds little to our analysis. Since we already assume all the producers are identical, it is ofno advantage to the processors to be able to differentiate between them. Further we are supposing that allthe processors are the same and that one price must prevail in the market, so in effect we are acting as ifwe have a pool in place. However, the introduction of a milk pool when there is a cooperative incompetition with an IOF is a little more complicated. In this chapter we explore the interaction between acooperative and an IOF if both are securing their input from a common pool.5.1) A Cooperative and an IOF In Competition with NaiveConjectures.As in the previous chapters, this situation will be modeled with a large number of farmers producing milkfor the raw milk input market. There are two processors with identical technologies. One is investorowned, while the other is a cooperative. All milk produced is made available to both processors at themarket price, irrespective of whether or not the farmer is a member of the cooperative. There will be novolume restriction and no price floor. The milk pool guarantees all farmer’s who ship milk the same pricefor their production, and allows all processors to purchase milk at the same price.The basic problem is set up below. We take the first derivatives of these functions, set them equal to zero,and use the equilibrium conditions to solve.835.1 p p(y); y = f(v)+ f(v) Output market demand.5.2 m = m(v) v = + Supply function for raw milk.5.3 w = W(V) V V + V Pool price functionAmax Iw(v)v”— c(vr )} Independent farmer’s objectivevf 1. fUnction.5.5 1i F p(y)f( ) — 1 Cooperative member’s objectivemax .J [ v C j V [ function.V [ ÷ w(V)v: — c(V:) j5.6max {p(y)f(vi,) — w(v)v } IOF objective function.5.7max[p(y)f(v)— w(v)vV } Cooperative’s objective function.5.8 + “ = + V, Market clearing conditionWe have introduced a new function, w(v), to the problem definition. This function represents the pricethat the IOF and cooperative must pay to get milk from the pool, and the price that independent farmersand cooperative members get from the pool for the milk they deliver. This fact has changed the objectivefunction of the cooperative and of the cooperative member in particular. In 5.7 we see that the cooperativenow has an objective function that is almost identical to 5.6, the objective of the IOF. The principledifference between the two lies in the denominator in 5.7, the shipments to the cooperative from itsmembers. In 5.5 we see that the objective of the cooperative member is equal to the objective of theindependent farmer, shown in 5.4, with the addition of the patronage dividend term. Belonging to thecooperative entitles the farmer to a share of any dividend that it is able to earn. Both farmers receive thesame basic price for the milk that they deliver to the pool.The first case we explore involves what we will call naive conjectures. The naive conjectures we postulatefollow the competitive assumptions. We assume that the individual agents believe that their own effect onthe market is zero. Mathematically, these conjectures can be written as:84aw(v)_0 a(’)=0,öv O, i j, k = c, p, 1 = c, pand —=öv” [1, i=j, k=c,p, l=c,pAll the actors believe that their own actions will not have any effect on the input or output prices. Thecooperative processor feels that its own input use decision will not affect the input use decision of the IOFprocessor. Similarly the IOF processor believes that its actions will not affect the input choice of thecooperative. Finally, the individual farmer believes that any changes in this farm’s production level willnot affect the production decision of other farmers in the milk industry.These simplifying assumptions are typically made for a basic analysis, and we have used them in previouschapters without identifying them. Alone they add little to the analysis, but we have not yet explored allthe conjectures that exist. With a milk pool in place, the cooperative is free to choose its input levelindependently of the decisions of its members. The only interaction that exists between the cooperativeand the membership is by way of conjectures about the responses. The conjectures that we are going touse for this stage of the analysis are:—-=0 and L=0avThe cooperative believes that its own input use decision will not affect the production decisions of itsmembers, and the individual members believe that their decision will not affect the input use of thecooperative. These conjectural assumptions are critical, and identify the principle effect of the milk pool.The cooperative is decoupled from the incentives of the members who ship milk to it. With somerearranging, the first order conditions for the model under naive assumptions are:855.9 The independent producerw(v)= ac(vr)ovr5.10 The cooperative member farmerp(y)f(v ) — w(v)v p(y)f(v ) — w(v)v v: ÷ — ae(v:)v: — v.c‘%‘5.11 The for profit processor, ..of(v,,) ,PI%Y) =WIVôv,5.12 The cooperative processorof(v) 1 1p’y) c= cYi3vThe first result is that for the independent producer. The producer chooses to operate at a point where theprice that is received for the milk that is delivered to the pooi is set equal to the marginal cost ofproducing the milk. From the perspective of the independent producer, the fact that the milk is deliveredto an anonymous pool is no different from if the milk was sold to a specific processor.Now we turn to the problem of the cooperative member. The cooperative member delivers the farm’s milkproduction to an anonymous milk pool, but receives a patronage dividend from the cooperative accordingto how much milk is delivered. Unlike the previous case, the cooperative is not bound to process the milkwhich its member’s produce.p(y)f(v)— w(v)v — p(y)f(v)— W(V)V+ w(v) =_____5.13av:MarginalPatronage Dividend - Dilution Effect + Pnce =CostThe marginal revenue which the cooperative member faces includes three factors which represent theeffect of the farmer’s production on the revenue generated. The patronage dividend is the amount whichthe farmer receives, per unit of milk produced, of the surplus on operations generated by the cooperative.The dilution effect is the amount by which the member’s production changes the size of the patronage86dividend. These two terms are added to the price which is prevalent for the milk that is delivered to thepooi to determine the marginal effect on the member’s revenue of a change in production.The investor owned firm’s optimal input use level is identified by the standard simple relationship. Thisrelationship is the equating of the marginal value product with the marginal input cost, here representedby the price that must be paid for the milk purchased from the pool. This result follows logically since theprocessor must pay the going milk price when making the input decision, and profits are maximized whenthe processor chooses an input level where the marginal value product of the last unit of production isequal to the marginal cost of the last unit of input.The optimal point for the cooperative processor is similarly straight forward. If we eliminate unnecessaryterms, the optimal input level is determined by the relation:5.140af(v)= w(v)c3vThis is identical to the relation that identifies the IOF’s optimal input choice. When the cooperative andthe IOF are purchasing their input from a common anonymous pool, and paying the same price, the factthat the cooperative is distributing its earnings to its members on the basis of how much milk they producewhile the IOF is generating a return on investment is irrelevant. Given these naive assumptions about theconjectures of the agents, and accepting that the objective of the cooperative is to maximize the patronagedividend, the behavior of the cooperative and the IOF should be indistinguishable.Figure 5.1 shows the interaction between the cooperative and the IOF in the input market. For themoment we ignore the effect of the cooperative’s patronage dividend on the pool price. The two firmsmust share the market, so the cost curves of both finns have been drawn side by side. The curves for theIOF begin at the point where the cooperative chooses to procure its inputs, and fills the gap to theintersection of the supply curve and the price line. Both firms pay the same price, w, to the pool for themilk that they use. The two processors are splitting the market evenly between them, which follows fromtheir use of identical technology.87$Co-op’s MVP IOF’s MVPwFigure 5.1: The rents of the cooperative when it has been decoupled from its membership.The behavioral difference that occurs in this market is a result of the actions of the farmers. The IOF andthe cooperative behave in an analogous way. However, the patronage dividend generated by thecooperative is like a price bonus, which affects the profitability of the cooperative member and theindependent fanner differently. Under these conjectures, and given the assumption that the fanner is anopportunistic profit maximize, it is optimal for all fanners to belong to the cooperative, so long as thecooperative is generating a positive profit. The cooperative and the independent fanner face the sameprice for the milk that they contribute to the pool. However, the cooperative member receives an extrapayment on top of this. Given that profit maximization is the only objective of the farmer, this extrapayment will mean that all farmers will want to be members of the cooperative.The distribution of the patronage dividend to the member farmers, while the cooperative does not itselfhave to handle all of the product that its members produce, has a supply effect. At the equilibrium thefarmers must be operating at a zero profit point. Assuming all farmers are members of the cooperative,and farmer produces where marginal cost equals marginal revenue—the sum of the patronage dividendand the pool price—the pool price will be less than the supply price. The rents generated by thecooperative are distributed to its members. The cooperative distributes these rents to the farmers in theform of a patronage dividend. The farmer sees an effective price that is above the pool price. As a result,ientsIOF’s AVPmilk*8$Co-op’s MVP IOF’s MVP/ \ S...;;;;;;N%%__ / 7 ‘\..%.S.—’...—._—m ++:y +x+x+x+x.r.ww”.—1- ‘w/ / PatronageFigure 5.2: The supply effect of the patronage dividend.the fanner is willing to accept a pool price which is below the supply price. The IOF buys milk at thispooi price, not at the higher supply price. In competition with a cooperative, the IOF faces a lower inputcost than if it was in competition with another IOF.Investigating this result in detail, we find that all the rents captured by the cooperative are transferred tothe cooperative. We assume that farmers are atomistic and opportunistic. No farmer is large enough toaffect the actions of any other agent in the model, and all act to maximize their individual welfare. With alarge number of farmers, their own interactions dictate that the effective price they receive lies on theiraggregate supply curve. Entry, exit, and adjustment of production level must by assumption force thefarmers’ economic profits to zero. This fact allows us to write a pool price identity:5.15{P(Y)f(t’c)_ w(v)v } + w(v) = m(v)This identity follows directly from the assumptions stated above. The sum of the pool price and thepatronage dividend, the effective price the farmer sees, must be equal to the supply price. Farmers cannotearn economic rents through their membership in the cooperative.Iv milk89We can rearrange this relationship to isolate the pool price function. The identity which defines the poolprice is:5.16 w(v) vm(v) — p(y)f(v)V—The price farmers are willing to receive from the pool is equal to the product of the supply price and thetotal milk produced—total farm revenues—less the cooperative’s earnings, divided by the share of theindustry output not handled by the cooperative.We can use the identity in 5.16 to evaluate the profits of the cooperative. If we insert 5.16 into 5.6, and doa little rearranging, we find:5.17,= p(y)f(v,,) — p(y)f(v )}If we recognize that V—V,, = V and f(v ) + f(v) = y then we can immediately rearrange 5.17 tobe:5.18=yp(y)— vm(v)All the profits in the industry accrue to the IOF which is competing with the cooperative. This result isnot unexpected. The cooperative redistributes any rents it captures to its members. The members competeto be part of the industry and receive these rents. They succeed by offering to accept a lower price for themilk they ship to the pooi. This process continues until the farmers are again earning zero profits, whilethe IOF captures all the benefit of the reduced pool price.905.2) A Cooperative and an IOF In Competition with CournotConjectures.The second set of conjectures we imagine have the Cournot form. Under Cournot assumptions, the agentsassume that their rivals, or comrades, hold their production fixed. We can summarize these conjecturesas:öm(v)0 a&)0,öv #3y t3vôv 0, i f, k = c,p, 1 c,p—=0 and —=öv [1, i=j, k=c,p, l=c,pWe assume that the supply curve for the input market is upward sloping from the perspective of theprocessor. We also assume that the demand curve for the final processed product is downward sloping.All the agents still believe view that their actions will not affect the actions of their rivals.If we apply these conjectures to the derivatives derived above, we get the following first order conditions.5.19 The independent producerac(vr)w(v)= övf5.20 The cooperative member farmerp(y)f(vj— w(v)v(v’ “i p(y)f(vj— w(v)v ãc(v)+v)=v: — v)5.21 The for profit processoraP(Y)af(vP)f() ôf(v) öw(v)+p(y)3y öv5.22 The cooperative processor1 IöP(Y)öf(VC) )‘ 1 ôm(v)1c 1=Jm(v)2 v ay Ov av J [ + 2For the farmer, ptimization with Cournot conjectures does not change the result we found above.Independent farmer, and the cooperative member, are both small producers with respect to the total91market size. They maintain their belief that they have no impact individually on the market price. Asabove, the optimal decision for all producers is to belong to the cooperative.The processors results are also similar to the finding above. When we simplify the first order conditionsfor the cooperative, we reproduce the same optimization condition. The IOF and the cooperative will stillbehave identically if the IOF is maximizing its profit, and the cooperative its patronage dividend. Theequation presented in 5.21 and 5.22 is the standard first order condition for a Cournot oligopsonistoperating between a supply curve and a demand curve. On the left we have the marginal revenue. Theoligopsonist believes that its rival will keep its production fixed. As a result, this firm faces the slope ofthe demand curve as its price effect on the revenue side. On the right we have the marginal cost. Againthe firm assumes its rival’s production level is fixed. It therefore faces a similar price effect from theinput supply slope as from the output demand slope. These price effects scale the marginal value produceand marginal input cost that we equated under the naive conjectures.The next case is the Stackleberg leader-follower model. With the conjectures that identify this model, wepropose that one of the agents internalizes the optimization problem of the other, who has Cournotconjectures. Normally one considers firms that are characterized by the same objective, so that it isirrelevant which agent is assumed to be the leader. Before this point the cooperative has been bound bythe actions and could not assume the leader’s role. However, we have broke this tie, so that there is nolonger any reason to assume that the IOF will be the leader.We will avoid the mathematics and explore this relationship intuitively. The basic result in the traditionalStackleberg model is that the leader produces more than the follower. The total production is greater thanin the Cournot case, so that the market price is lower. However, the leader gels a sufficiently large shareof this to generate greater profits than if the Cournot solution. The follower is left to ‘take up the slack.’It has a lower production level, and usually much lower profits, than in the Cournot case. However, sinceit makes its production choice second in this sequential game, it cannot do any better for itself.92In isolation from the actions of the members, the Stackleberg case is identically repeated here. However,we cannot really look at it in isolation of the fanner. If the cooperative takes the larger share of the inputmarket, it generates a greater patronage dividend. However, as we pointed out earlier, the farmers willadjust so that the profit is still zero even with this patronage dividend. This allows a lower price to prevailfor the pooled milk, actually lowering the cost for the IOF. If we reverse the situation, giving the IOF thelargest share of the market, the cooperative will generate a smaller patronage dividend, and the zero profitoutcome at the farm level will require a higher price. With a larger market share, the IOF actuallyincreases its input costs relative to the Cournot case and when it has a smaller market share. The totaleffect on profitability is of course dependent on the revenue effects, but it is clear that the IOF is not aswell off capturing a large share of the market as when it has a smaller share.5.3) A Cooperative and an IOF In Competition with UnrestrictedConjectures.With this model, the remaining step is to explore the relations when everything is allowed to vary. If thisis the case, and after setting the first derivatives equal to zero, the first order conditions are:5.23 The independent producerw(v)= ac(vr)avr5.24 The cooperative member farmerFoP(y)Fof(viaf(vP)avPlf() af(vjOw(v) 3v 1+p(y) (__L+1’L11 [ avc öv öv I., öv ) j v: av:p(y)f(vj—w(v)v v: övc+ +p(y)f(v)— w(v)v öw(v) c3vtv:’ Ov av: av93We look first to the independent farmer. The optimization condition here is identical to the previous case.We maintain the assumption that this farmers impact on the market is too small to be considered.The picture for the IOF, equation 5.25, is a little more complicated. The IOF now takes into account theeffect it has on the output market. Labeling this relation we get:ap(y) öf(v) + öf(v)övf(v )+ ()af(vP) = w(v) + äw(v) öv +5.27y t3v #3v ovp övInput Input MarketOutput Market Effect + MVP = . ÷Pnce EffectThe output and input effects have grown a little more complicated than for the Cournot case. Now theIOF must take into consideration the response its rival, the cooperative, will make to its actions. On theoutput side, the cooperative might change its production. This will affect the size of the price response theIOF’s change in production. On the input side, the cooperative’s input purchase response will affect howthe input price moves. Overall, one would expect the cooperative to act in the opposite direction to thattaken by the IOF. This will result in a mitigation of the effects that the IOF’s own actions are having,tending to increase the amount of input it will utilize.The cooperative will now also take into consideration the responses of its rival, the IOF.94ap(y) af(v) ãf(v)öv f(v) p(y)f(v) w(v)v ôv’öy ôv, av,, ôv, C —Market Price Member Response528 Effect — Effectaf(v) ãw(v) ôv,+p(y) —+1i3v t3v ôv,Pool Price+ MVP =MIC+EffectThe market price effect is analogous to the output market effect in the IOF case. As for the IOF, itincludes a component for the response of the cooperative’s rival, the JOF. This effect is also present in thepool price effect. As for the IOF, the cooperative will probably expect the IOF to respond to its productiondecision in an opposite direction, thus mitigating some of the own effect on the result. The memberresponse effect is a new component here. It is equal to the negative of the patronage dividend, multipliedby the total member production effect of a change in the cooperative’s input level. When the conjecturesare wide open, the cooperative will expect a response from its members when it changes the size of thepatronage dividend. The effect on the overall objective function of a change in the amount of milkproduced by the membership will be equal to the current size of the patronage dividend, multiplied by thesize of the change. All these factors need to be considered when trying to identify the optimal point forthe cooperative to operate. When the conjectures are wide open, we finally find a breakdown of the earlierresult that the IOF and cooperative will behave in the same way. The member response effect reduces theimpact of the Market price effect and the MVP, thus reducing the size of response required to marketchanges.The last step is to look at the response of the members. The cooperative member must now consider theeffect of the cooperative, its rival, and the other member farmers on this one member’s revenues.95ap(y) öf(v) + ö’- f(v ) + öf(V) — öw(v) (avg + 1 v: öv,[ 9y ôv öv,, öv öv t3v 2 v. övPatronage Dividend Effect5.29— p(y)f (vj.... w(v)v v ôv. p(y)f(v)_ w(v)v+ v) öc(v)2 2 L’i tv: 2 av:MarginalDilution Effect + Patronage Dividend + Pnce =CostThe patronage dividend effect is the term that internalizes the impact of the member on the cooperativesobjective function. It is equal to the cooperative’s marginal condition, scaled according to how much ofthe total milk received by the cooperative is the result of this member, and then multiplied by the amountwhich this member thinks the cooperative will respond to the member’s change in production. If themember believes the cooperative will not change its input decision, then this term becomes zero. Thedilution effect has been modified a little. The term 2• 0v /ôvc incorporates the effect of a change inthis member’s production on all the other members of the cooperative. The value of this term will usuallybe less than one, reducing the impact of the dilution effect to a certain extent. The patronage dividend isthe same as presented above. If the member is small relative to the total production of the cooperativemembership, then the combination of the decoupling and the member’s size will reduce this relation to theearlier result. In most cases that is what one would expect. However, these have been included to showthat with the right conditions, the member will internalize some of the cooperative’s problem, and theresulting optimization will not be the same as for the naive case. However, it is still optimal for allfarmers to join the cooperative.Why do we find that there are farmers who do not ship their milk to a cooperative? There are severalfurther factors which can explain this. In the first place, milk in BC is not truely delivered to ananonymous pool. Rather it is shipped to a particular processor, and if that processor is unable to use it foras high a class value, it will be shipped to a processor who can. This transaction has a cost, and theprocessor who transfers the milk away is compensated for the hauling cost. One would expect that the96JOF will want to keep a few shippers whose milk is first shipped to them so that they will not have to relyon the highest class of milk being available from another processor. On top of this, if the compensationrate for interplant transfers of milk is higher than the hauling cost to collect milk from the individualfarmers, then it may be optimal for the processor to receive some of its milk directly.The farmers may also have an interest in not belonging to the cooperative. All the farmers in this modelare making a profit at the margin. The government determined floor price is such that all the productioncosts of the fanner are fixed. At the margin, the farmer would still make a profit on a further unit ofproduction, should they be able to produce more. The critical factor for the farmer is then the opportunitycost of not belonging to the cooperative. Various non-market factors may for some fanners balance thisopportunity cost. Some farmers place a very high value on their independence, and see the ‘collective’nature of a cooperative as conflicting with their individual values. The opportunity cost of not joining thecooperative would need to be very high before they would join. Other farmers may be unable to join thecooperative for reasons pertaining to the bylaws of the organization. One important way that cooperativesmaintain member cooperation is by having strict bylaws with eviction as a punishment for violation.There may be farmers who are banned from being members.At the market equilibrium point, assuming there are a fairly large number of farmers with diverse beliefsand attitudes, one would expect most farmers to belong to the cooperative, but some to choose to remainoutside it. If this distribution is going to be stable over time, the profitability of the member fanner mustbe the same as for the non-member. This can only be assured if the IOF pays a rate that is equivalent tothe return that the members are receiving to those farmers shipping to it. Over the long term, one wouldexpect the profitability of the producer’s farms to follow quite closely the profitability of the cooperative,regardless of whether or not the producer was a member.In a market where there are rents being generated for one party, these rents are usually capitalized into thescarcest input required for production. In the BC dairy industry the scarcest input is the right to produce.The farmer must hold a quota if they are legally entitled to produce milk. This quota is tradable betweenfarmers, and fetches a price according to how much farmers are willing to pay. Since the rents that the97farmer receives are expected to follow the profitability of the cooperative, one would also expect the pricethat farmers are willing to pay to follow the profitability of the cooperative. An empirical test of thismodel could involve looking for a relationship between the price of fluid milk quota and the patronagedividend or pmfitability of the cooperative being considered.5.4) SummaryIn this chapter we have explored how an input price pooling scheme affects the relationship between acooperative and its membership. Under price pooling we see that the cooperative is able to make anoptimization decision independent of its membership. The pool serves to partially decouple thecooperative and its membership.When we solve the problem using either naive conjectures or Cournot conjectures the cooperative and theJOF have identical first order conditions, and it is optimal for all farmers belong to the cooperative. Boththe cooperative and the IOF purchase milk from the pool for the same price, but cooperative membersreceive a patronage dividend as a bonus on top of the price. Assuming that there are rents available to theprocessors, it will pay these to the membership. As a result, the members of the cooperative will alwaysreceive a higher effective price than non members.We also find that the competitive yardstick result breaks down. The members are assumed to beatomistic, and act opportunistically. With these assumptions, economic rents cannot be secured inequilibrium by the farmers. They will compete with each other to ship milk, reducing the pool price theyare willing to accept, until they are again earning zero economic profits. The lower pool price means thatthe IOF is able to secure its input requirements for less, and effectively recapture much of the rents thatwere initially taken by the cooperative.98Chapter 6: The Milk Market with a Supply Restriction, a PooledMilk Supply, and a Minimum Price.The main restrictions that define dairy supply management in British Columbia are a milk pool, anexternally determined milk price and an aggregate market size restriction. In chapter three weconstructed the general problem and solved it without restrictions, recovering the competitive yardstickresult. Chapter four was used to explore how the agents would behave under an aggregate marketrestriction. In general, the competitive yardstick is restored, qualified by the fact that the volumerestriction prevents the true competitive outcome. Chapter four looked at an input price pool, in isolationof any other policies. The price pool allows the cooperative to purse an objective independently of itsmembership. At the same time, any rents the cooperative manages to capture will be transferred to thecompeting IOF through the opportunistic actions of the its members.In this chapter we put all the regulations together, the volume restriction, the pool price, and the pricefloor. As in chapter four, the price pool is only interesting when we look at how it affects the interactionbetween a cooperative and its membership, and between a cooperative and a competing IOF, which are theonly interactions we consider.6.1) Problem DefinitionIncluding the price pool, volume restriction, and price floor, the problem becomes:6.1p = p(y) y = f(v)-,- f(v) Output market demand.6.2 m = v=v + VP Supply Price.6.3= Iw(v) v such that w(v) Pool Price1 vsuchthatw(V)<ñi6.4 max {w(v)v’— c(vr )} Independent farmer’s objective.yr6.5max.Fp(y)f(V)— w(v)v 1[ 2 c j v + w(v)v — c(v’ } Cooperative member’s objective.6.6 max‘1p(y)f(v) — w(v) } IOF objective function.99This construction incorporates the input price pooi, the aggregate volume restriction, and the price floor.The pooi price appears in equation 6.3. The price farmers receive for their milk is distinct from thesupply price of equation 6.2. It is the amount processors pay, and farmers receive. The Aggregate volumerestriction shows itself in equation 6.8. The total milk delivered to the market must be no greater than V.The price floor also shows itself in equation 6.3. The pool price is not allowed to fall below the price floorgiven by ñï. The combination of these restrictions means that the pool price identity we constructed inthe last chapter no longer applies. Equation 6.9 shows us that the sum of the pool price and the patronagedividend must be no less than the supply price, m(v).The aggregate volume restriction again demands a lagrangian solution:6.8 The independent producerL(vj’,))= w(v)vf — c(vf)÷ [(v — vç)_ vr]6.9 The cooperative member farmerL(v,?) Ip(y)f(v)— w(v)v.= [v’ + w(v)v — c(v: ) + — v) — v]6.10 The for profit processorL(v,) = p(y)f(v,)_ w(v)v + — vj_ VP]6.11 The cooperative processorL(v,?)-p(y)f(vJ- w(v)V+ - v)_ v]-We have four objective functions. The milk pool allows the cooperative to make an optimization decisionindependently of its members. The constraints are identical to those in chapter four. Agents are restricted100to produce or use no more than the gap between the production of all the other agents and the aggregaterestriction.6.2) Solution with Naive ConjecturesAs in chapter five, we fonnulate conjectural assumptions that are consistent with the competitive model.aw(v)_0°“()=0, .E-=o,öv fO, i j, k = c, p, 1 = c, pand —=öv’ [1, i= j, k = c,p, 1 = c,pAll actors believe their own actions do not affect input or output prices. The cooperative processorbelieves its own input decision does not affect the input use decision of the IOF. Similarly the IOFprocessor believes that its actions do not affect the input choice of the cooperative. Finaily, individualfarmers believe that their actions do not affect the production of other farmers in the milk industry.The unique feature of this model is the pool price. With a milk pool, the cooperative is free to choose itsinput level independently of the decisions of its members. The conjectural relationship between thecooperative and its members is:E=0 and —-=03v avThe cooperative believes its own input decision does not affect the production of its members, and theindividual members believe that their decisions do not affect the input used by the cooperative. The firstorder conditions with our naive assumptions are:1016.12 The independent producera)w(v)= (9vr6.13 The cooperative member farmer- j + w(v) = +p(y)f(v)_ w(v)v [P(Y)f(Vc)_ w(v)v 1 v i3v,6.14 The for profit processor0af(v)= w(v)+öv6.15 The cooperative processoraf(v) 1 1‘a’) = w(v) +The first order conditions for the farmer and the IOF processor are little changed. The farmer setsmarginal revenue—the price in the input supply market—equal to marginal cost, adjusted by a shadowvalue reflecting the production constraint. The IOF processor’s optimal input level occurs where marginalvalue product is equal to the price of the input, scaled by a shadow value.The optimal production point for the cooperative is very similar to that for the IOF. If we rearrange therelation in the table, we get the following:af(v)6.16 p(y)=m(v)-i-).2v7Under the naive assumptions we are working with, the sum of the production of the cooperative membersis constant. This constant is then multiplied by some shadow value to allow the equilibrium to be located.The cooperative maximizes its objective, the size of the patronage dividend, by following the sameoptimization steps as an IOF with identical technology would choose. The magnitude of the shadow valueis unclear a priori; we camiot determine if the IOF and cooperative operate at the same point.The solution for the cooperative member is little changed from that presented in chapter five, becoming:102p(y)f(v)— m(v)v — p(y)f(v)— m(v)v “+ m(v)= ÷6.17av:Marginal ShadowPatronage Dividend + Dilution Effect + Pnce = +Cost ValueThe patronage dividend is the member’s share of the cooperative’s surplus. The dilution effect reflectshow a change in member i’s production dilutes the overall patronage dividend. The price is the amountthe producer receives from the pool. The farmer chooses a production level such that these terms equalthe sum of the farm’s marginal cost and the shadow value. With a large number of farmers, the dilutioneffect approaches zero; members treat the patronage dividend as constant. The shadow value incorporatesthe effect of the constraint.In this chapter we have overlaid the model of chapter four on the model of chapter five, and added a floorprice. We are solving the problem of a pooled market with an aggregate volume restriction guaranteeingthat there are economic rents available to the agents. Joining the first order conditions to locate a marketsolution, we first see that the cooperative behaves just like an investor owned firm. The marketequilibrium is as for two oligopsonist competing in a market with a restricted overall supply of input.In figure 6.1 we are again using the technique introduced in chapter four; the IOF’s cost curves begin at Vand its input use is increasing to the left. The legislated market price is given by ñï. All of the surplusbelow this price goes to the farmer. The difference between ñï and the supply price, ), is the rentsavailable to all farmers. This amount is shown as in the figure. The shaded area marked by the label‘Co-op’s rents’ is the difference between the average value product at this input level and the legislatedprice, multiplied by the total amount of milk used. This is redistributed to the members. The rents that amember captures are equal to the difference between the supply price, and the sum of the price floor andthe patronage dividend, ñï + ), shown asThe rents generated by the IOF are not redistributed to the shippers. The absolute size of these rents isbounded from below by the legislated price, which the IOF must pay. However, since the IOF buys milk103Figure 6.1: Interaction between the decoupled cooperative and an IOF.from the pooi, and not directly from its shippers, it need not compete with cooperative members for themilk input.The independent fanner has a fairly simple problem to solve, equate price with marginal cost. Not beinga cooperative member, and believing that this individual is an atomistic agent, there is no own effect onthe price. However, the cooperative member’s marginal revenue is not equal to the price alone. Weassume that the cooperative is capturing positive rents. We need not worry about the marginal revenueand marginal cost and need consider only the differential profits.Figure 6.2 shows the opportunity cost to the farmer of not being a member of the cooperative. The shadedrectangle is the rents that are generated by the cooperative. These are distributed among all themember’s, as shown by the rectangle. If a fanner is not a member, and produces an amount of milk equalto v•, then the area labeled RF is the opportunity cost of not being a member. If all farmers are strict profitmaximizers, then one would expect every fanner to be a member of the cooperative.The size of the opportunity cost is governed primarily by the position of the legislated price. Thisdetermines the size of the rents available to the cooperative and the IOF. If the milk price is high, thereare little rents available to the processor. There is not much for the cooperative to distribute, and a smallv, V milk104$Figure 6.2: Interaction between the decoupled cooperative and an IOF.opportunity cost to not being a member. If the price is low, there is a large opportunity cost to not being amember. The decoupling of the farmer from the cooperative means that there is no competitive reason forthe investor owned firm to pay a price equal to the effective price the members are receiving. The farmerwho chooses not to join the cooperative will be distinctly worse off than the member.6.3) Solution with Open ConjecturesRelaxing all the conjectural assumptions, the solution is similar to the Cournot case in the last chapter.However, the Cournot conjectures are unreasonable. If the cooperative purchases more input, or thefarmer produces more, other processors or farmers must adjust to keep overall production fixed. Thisimposes adding up restrictions on some of the conjectures, which can be summarized as:äw(v).0 t3p(y)0,—1,and----=O k=p,c.övThe milk price is bounded from below by a price floor, and since we are assuming that the price floor issufficient to guarantee the required output level, the variability of the pool price is zero. The outputdemand function has a downward slope. If one processor increases its input use, the other must reduce itsCo-op’s MVP -/ S/ 51111111111 liii I iii II II lillIllIll 1111 I IIIIIII2[ll:fv, V milk105input use by an equal amount. Finally, the sum of all production changes for all farmers must be zero.The complete derivatives for this problem are:6.18 The independent produceröw(v) 1thc÷p1vP+w(v) ac(vl’)av by! 3vf1 vf6.19 The cooperative member farmer[ap(y) [af(vjov af(v) öv 1 of(v )av öw(v) [ — (V)a1C 1()j ay [ ôv ov: ôv öv av: ôv [ov: avjVc p(y)f(vj— m(v)v — p(y)f(vj_ m(v)v ( i’c ‘ ãvcx +v vövöw(v) öv 3vV’+W(V)ôc(vc)+ c+ =a [6.20 The for profit processor+p(y) =ap(y) [&f(v) + af(v) övJf(vp)öf(v) ôw(v) Fôv +11 +m(v)+?ô [ ãv ôv öv av ]6.21 The cooperative processor“ f(v)÷p(y) c —Iop(y) Fa.f(v) + 9f(v ) [p(Y)f(l’c)_ m(v)v 1avd1j öy [ av ôv j ôv J1 1ôm(v)[övx =[__+1] + m(v)} 2v +The first equation describes the optimal point for the independent farmer. From our assumption that theaggregate market restriction is binding, we first that ôv/övf + is equal to zero. The totalsupply of milk on the market cannot be increased. Equation 6.18 reduces to:ôc(v’)6.22 w(v)= ‘övfOnce again we recover the same first order condition we saw with only an aggregate supply restriction.The supply restriction generates economic rents, which translate into a shadow value. The price pool is106responsible for the pool price relationship replacing the supply price. However, the floor price is assumedto dominate, so that the pool price does not actually have any direct impact on the independent farmer.Equation 6.19 describes the cooperative member’s solution. If we assume that the aggregate marketrestriction is binding, and that all farmers belong to the cooperative, then the sum.öv /öv mustequal zero. With these observation, equation 6.19 reduces to:op(y) ôf(v)öv öf(v)öv f(v )+p(y) ‘c_w(v)PY... v’I av av: öv av: C avC öv6.23 1p(y)f(v )- m(v)v + w(v) = öc(v) +This equation is easier to interpret than 6.19. We can use the fact that Ov, /Ovr + 9v /av[ = 0 torearrange the top term in the equation.v op(y) af(v) af(v) f(v ) + ôf(V) — w(v) !!-3y av öv1, CMarket Revenue Effect6.24p(y)f(vj- m(v)v+ w(v) = öc(v) +Pool ShadowPatronage Dividend + . = MC +Pnce ValueThe market revenue effect represents the effect that the cooperative member has on the size of thepatronage dividend through a change in farm production. It is equal to the first order condition of thecooperative, scaled by the share of the membership’s production this member produces, and the amount bywhich this member believes that his or her production will cause the cooperative’s input decision to bechanged. However, since all the farmers are assumed to be part of the cooperative, it is somewhatunrealistic to suppose that any member believes their production will change the actions of the107cooperative. The cooperative is receiving the same amount of milk before and after the rearrangement ofproduction. If a particular output level was optimal before, it should still be optimal. Thereforeav/av: = 0, and equation 6.19 reduces to:6.25p(y)f(v)—m(v)v÷w(v)=ôc(v)The members’ optimal decision is in fact to treat the patronage dividend as fixed. The aggregate marketrestriction, combined with the fact that all production in the industry comes from cooperative members,means that the dilution effect is no longer a factor.The behavior of the for-profit producer has changed a little relative to the naive case. The input useresponse of the cooperative must exactly balance the change made by the IOF, so that 6.20 becomes:6.26a() öf(v)— af(v)f(v)÷()of(vP)=ôy 8v .3vChanges in the processor’s input use decision may affect the output price. The price change is equal tothe net change in output of both processors, multiplied by the slope of the demand curve. The processor’srevenue changes by the multiple of the price change and total production at this point. Due to theregulation, there is no net change in aggregate input purchased, and therefore no change in the inputprice. If the IOF and cooperative have the same marginal productivity, then we reproduce the first orderconditions for the naive case.In the previous chapter we found that when the conjectures are wide open, the first order conditions forthe IOF and the cooperative are no longer the same. In this chapter we have requiredöv /avf + ôv,, /avf = 0 and.i3v = 0. 6.21 now takes the following form:6.27 { ‘(“) [f() — j f(v ) + 3f(v )} 1 = m(v) +108Except for the unusual shadow value, equation 6.26 and equation 6.27 are the same. The combination ofthe price pool and the aggregate volume restriction completely separates the cooperative from itsmembership. This result relies on our assumptions about the behavior of the members, and the fact thatthey will all choose to be members of the cooperative. However, considering that most farmers in the B.C.dairy industry do ship first to a cooperative, this is quite reasonable.A cooperative is governed by a board of directors selected from among the members. This board hires themanagement group, and also sets down guidelines about organizational activities. The heterogeneousnature of the membership virtually ensures that management will not internalize the farmers’ problem.However, so far as it is possible, the guidelines imposed by the board of directors may do so. In theextreme, when almost all farmers are members of the cooperative, the board may make some decisionsthat are geared towards maximizing overall farmer welfare.This analysis has been built on the assumption that given the freedom to do so, a cooperative will pursuepatronage dividend maximization. This approach affords us the luxury of treating the cooperative’sobjective as independent of the members. Separation of the objective functions is critical to the explicitsolution we have generated. This may be unreasonable. However, supply management affords themanagers more autonomy than a cooperative in an unregulated market could give. In so far asmanagement’s performance is evaluated by the payments it generates, we expect management to seek tomaximize the payment to the members. Guidelines and directives from the board of directors simply limitthe extent to which management is autonomous.Our principle qualitative result, that the competitive yardstick breaks down, depends on the cooperativepursuing an objective different from maximizing aggregate welfare. Maximizing aggregate welfare isaccomplished by minimizing the patronage dividend, driving the market to the competitive solution. Ifthe cooperative chooses a production level such that the competitive solution is not attained, our result stillholds. Members like cash payments from their cooperative, and management likes to protect its positionby satisfying the membership. These reasons alone make it unlikely that the cooperative will act toreproduce the competitive market solution.1096.4) SummaryWe have now completed our theoretical construction of a model of the B.C. dairy industry. The mainfeatures of this industry are an aggregate volume restriction, a price pool and a price floor. On their own,the components of the supply management system partially decouple the cooperative from its membership.The aggregate volume restriction accomplishes this by forcing rents to exist in the industry, and therebypreventing the complete competitive yardstick result we would expect from the traditional theory.The input price pool breaks the competitive yardstick by allowing the cooperative to pursue an objectiveindependently of its membership. The result of this is that it may be able to pay a patronage dividend thatcontains economic rents. However, we have assumed that the farmers are opportunistic profit maximizes.They will compete the rents they are capturing away in this model by offering to accept a lower milk pricefrom the pool. The final result is that any rents which the cooperative is able to capture will be transferredto the IOF competitor.When we add a price floor to the model we fix a distribution of the rents between the producers and theprocessors. When combined with the aggregate volume restriction it acts as a lower bound to the share ofthe rents which an oligopsonist might capture. With a cooperative in the market, the price floor has littleeffect beyond possibly restricting the small remaining rents that the competing IOF can extract.When we put all the restrictions together in one model, we find that the cooperative and the member aretotally decoupled. It is still optimal for all the farmers to belong to the cooperative. However, there are nolonger any interaction effects between the cooperative and its membership, even when beliefs are notrestricted. The cooperative and IOF behave like an oligopsony, and members receive half of the industryrents as their patronage dividend. The patronage dividend, which is surplus to the rents which accrue tofarmers from the price floor and output control, encourages all farmers to join the cooperative.110Chapter 7: A Linear Example.In this chapter we explicitly extract the theoretical results shown above. We build the market solution forthree different market structures, the unregulated competitive market, a market with two oligopsonisticfirms, and a market with a cooperative and an IOF in competition. Each of these is developed under fivedifferent policy environments, an unregulated market in isolation, a market in an importing country, aninput supply restricted market, a market with an input floor price, and a market with a price pool for thesuppliers. The underlying demand and supply curves are specified as linear and marginal processing costare fixed, independent of production.7.1) The Unregulated Market in Isolation.The problem of the unregulated market in isolation is specified as:7.1 p(X) = 10 — X Output Demand Curve7.2 c(x) = i Marginal Processing Cost7.3 m(X) = X / 2 Input Supply CurveXis the total supply of the input brought to the market. We are assuming that the processing technologyis perfectly efficient, but involves a cost of one dollar per unit of input processed. The competitiveoutcome is located by the intersection between the output demand curve and the output supply curve—thesum of the marginal processing cost and the input supply curve. The equation we solve is:7.4. (10— X) = X / 2+1generating a solution where X = 6.Figure 7-1 shows the outcome when we assume that the competitive result will occur. The price in theoutput market, p, is equal to 4. This price is found as the intersection between the output demand curve,DD, and the derived output supply curveS’S’. The price paid to the suppliers of the input is located at the111s,SFigure 7.1: Unregulated competitive market.intersection between the quantity of input demanded by the processors,Q*,and the input supply curve SS,3 dollars.With two oligopolists, the problem constmction becomes:7.5 = p(X)x1— c(x1)x — ,n(X)x1 First Oligopsonist7.6 = p(X)x2— c(x2)x — m(X)x2 Second OligopsonistWith two firms processing the total input supplied, the input level X is equal to the sum of the inputchoices of the two oligopsonists, x1 +x2. Replacing the functional representations with their explicitform, and substituting for the total supply, the profit function for the first oligopsonist can be written as:The symmetry of the problem forces the solution for the second oligopsonist to parallel the solution for thefirst oligopsonist. This allows us to avoid evaluating the problem twice. The first order condition thatfollows from this profit function is:105-D112s,SFigure 7.2: Unregulated competitive market.7.8 Tht1/öx = 9— 3x1 — (3/2)x2This equation defines the rate of change of the oligopsonist’s profit with respect to the level of input itchooses to purchase and the amount that its competitor chooses. For simplicity, we will avoid dealingwith the two stage leader-follower game. Setting this equal to zero and rearranging to isolate theoligopsonist’s own input amount generates the set of best responses to the rivals production decision. Thisreaction function is:7.9 x1=3—x2/2The synunetry of the profit functions of the two oligopsonists means that these reaction functions areidentical. We use this fact to solve for the joint equilibrium point. For this case, each oligopsonist willchoose to use 2 units of input, so that the total input purchased in the market is equal to 4.The market outcome when there are two oligopsonists is shown in figure 7.2. The oligopsonists willjointly short the market, raising the consumer price top° and causing the price paid to producers to fall tom°. The shaded area represents the profits generated by the oligopsonists in this market. TheDQo 5 10113oligopsonists have captured a portion of the consumer and pmducer surplus, and a deadweight lossresults.To complete this analysis, we replace one of the oligopsonists with a cooperative. The cooperativedistributes any profits it generates as a dividend to its members. The patronage dividend and profitfunctions for the cooperative and the IOF are:7.10 = p(X)x1,— c(x)x — m(X)x Investor Owned Firm7.11 div = [p(x)x — c(x)xJ,/x CooperativeThe traditional cooperative acts as an agent for its members, marketing the member’s production. Thereturn the members see for their production is equal to the net return per unit generated by thecooperative. Once again, the total input that is used is equal to the sum of the production of thecooperative and the IOF, x,, ÷ xe.. We can immediately simplify the cooperative’s dividend function byeliminating terms common to the numerator and denominator. Doing this we reduce the dividend to:7.12. div = p(X)— c(x)The cooperative dividend is equal to the profit per unit of input used, which is the difference between theprice received for the output and the net cost of the production process. A solution can be generated byassuming that all producers of the input are strict profit maximizers. If this is true, then the cooperativedividend must equal the supply price. Adding this condition to the definition of the cooperative dividendwe get:7.13. p(X) — c(x) = m(X)When we substitute the functional definitions and the adding up condition into 7.13, we get:7.14 [io_(x ÷x)J—i=(x ÷x)/2114Ds,SFigure 7.3: Unregulated competitive market in an open economy.If we simplify this relationship, the outcome we get is:7.15 x÷x=6This shows us the ‘competitive yardstick’ result that is often presented in the literature [Cotterill, 1987].The cooperative will choose an input level such that the total production in the industry is equal to thecompetitive outcome. If we evaluate the objective of the IOF we get a reaction function that is identical toequation 7.9 above. Solving 7.9 and 7.15 simultaneously we find that the cooperative will capture theentire market. This extreme result is due to the linear nature of the curves used, but highlights theoutcome predicted by Cotterill [1987] and others.7.2) Open Economy in an Importing CountryWe introduce an open economy model by adding a world price for the final product that is below thecompetitive outcome in this economy in isolation. Output will only be produced where the total cost ofprocessing it and procuring the required input is less than this world price.Figure 7.3 shows the market result when the final product is available for a world price ofp. Theconsumers demand QC of the output. However, at the world price, domestic processors demand only QC10115for their use. This input demand results in an input price of m’. Total imports equal the differencebetween Q’ and QdWith an oligopsony, the world price prevents the oligopsonists from capturing rents at the expense of theconsumer. However, we are assuming that only the output is traded, so that rents can still be extractedfrom the producers. Raw milk is a highly perishable product, which contains more weight and volumethan many of the products it is processed into, making it unlikely that raw milk will be imported. Theobjective function for the oligopsonists, after the identifying substitutions have been made are:=pxi — x1 — [(x1 + 2 )/2}, First Oligopsonist2 = — — [(xi ÷ 2 )/2}2 Second OligopsonistTaking the first order conditions for 7.16, and rearranging to get the reaction function, we find:7.18 x1=—1)—x2/2In our example the world price has been set at 3 dollars. Using this price, and the symmetry of theproblem, we can solve for the oligopsonist’s optimal production level. In this case, it is equal to 4/3.In figure 7.4 we see the outcome when there are two oligopsonists purchasing the production of thedomestic producers. The oligopsonists are still able to secure some of the surplus that goes to thedomestic producers in the competitive case. However, they are unable to get any of the consumer’ssurplus. The rent seeking behavior of the oligopsonists reduces the price that is paid to the producers, m’from 2 to 4/3. At the same time, imports, the difference between QC and Q”, are expanded from 3 to4 1/3 units. Consumer surplus is unchanged, producer surplus is decreased, and processor profits areincreased.Replacing one of the oligopsonists with a cooperative generates the following patronage dividend andprofit functions:116Ds,S5Figure 7.4: Oligopsonist in an open economy for the final output.7.19r = — x — [(xe + ,, )/2} Investor Owned Firm7.20 div = [px—x, CooperativeAgain we solve the problem for the cooperative by requiring the cooperative dividend to equal thefanner’s supply price. After substituting the supply function for the dividend, and rearranging, we findthat the cooperative solution is identified by the relation7.21 x, +x = 4The output point chosen by the cooperative, as a result of its interaction with its members, is such that theindustry output is in aggregate equal to the competitive solution. The competitive yardstick has surfacedagain. If we solve the IOF’s reaction function simultaneously with the cooperative’s solution identity, weagain get the solution that the cooperative would capture the entire market.7.3) Closed Economy with an Aggregate Volume RestrictionNext we investigate the effect of an aggregate volume restriction, in isolation of any other policies. Theproduction quota shorts the market, and restricts consumer purchases to those that are willing to pay theQC 10117s,SFigure 7.5: Quantity restricted competitive market.higher price. At the same time, it reduces the supply price that producers must see to produce the requiredlevel of input. The increasing difference between the consumer price and the supply price generates rentswhich will be captured by some or all of the agents in the market.Figure 7.5 shows the effects of an aggregate quantity restriction. The price that consumers are required topay has been increased top, while the producer’s supply price has fallen to m. The shaded rectanglerepresents the excess rents or profits that will be available to some group of agents in this economy. It isunclear who will get them, given the specification so far. The presence of arbitrage opportunities on theconsumer side will quickly be eliminated, so that either the processors or the producers are capturing theserents.The oligopsonist’s problem is specified as:7.22= [io— (x1 + x2 )} — x1 — [(x1 + 2 )/2} First Oligopsonistsubjecttox1Q—x27.232 = [io — (x1 + x2 )}2 — — [(x1 + 2 )/2}2 Second Oligopsonistsubjecttox2Q—x1mD118The oligopsonist maximizes its return subject to a restricted aggregate market size. To optimize this weconstruct a lagrangian function:7.24 L(x1, 1) = [io — (x1 + x2 )} — x1 — [(x1 + x2 )/2} ÷ + x2 ) — x1]The first order condition that follows from 7.22, assuming that the constraint is binding, is:7.25 öL/öx1 = 9— 3x1 — (3/2)x2—We set this equal to zero, and rearrange to get the reaction function for the oligopsonist.7.26 x1 =3—x2/2—A,The symmetric technologies of the two firms allows us to solve for the intersection of the reactionfunctions. The production point for firm one is identified by the relation7.27 x1We also know that the sum of the production of the two oligopsonists is equal to Q, which in this exampleis three. This would allow us to place limits on the value of ? and ? 2• The principle outcome of theoligopsonistic model is that the oligopsonists may capture all of the rents available. However, we cannotsay how the rents are distributed between the oligopsonists. The actual distribution of market share willdetermine what the shadow value for each firm. The shadow value indicates that this situation may beunstable. There are profits available at the margin. In the real world these may be absorbed by severecompetition between the firms, with the result that the producers and the consumers may end up capturingsome of the rents.Replacing one of the oligopsonists with a cooperative, the patronage dividend and profit functionsbecome1197.28 div = {[io— (x + )} — ,}/ Cooperativesubject tox Q—x7.29= [io— (x + x, )jx, — x,, — [(xe + )/2Jx For Profit Processorsubject to x,, Q — xThe cooperative pays its dividend to its members. However, the dividend will be greater than the supplyprice. We need to introduce a shadow value to absorb the difference between the cooperative dividend andthe supply price. If we assume that the producers are strict profit maximizers, then the IOF will have tomatch the cooperative’s dividend price to receive milk. Introducing such a producer’s shadow value intothe equation, we get:7.30 9—(x +x)= (x +x)/2+.,We know that the total input use must equal Q if the constraint is binding. The cooperative will pay adividend equal to the output price, less the processing cost. For the input market, the presence of acooperative once again restores the competitive outcome. Further, the resulting output price will exhaustall the profits attainable by the IOF, so that the cooperative may take the entire market.7.4) Closed Economy with a Floor PriceA floor price is introduced as a way of guaranteeing a certain level of producer welfare. However, a floorprice is not sustainable without some means of supporting it. There are at least three ways of supporting afloor price: a consumer subsidy, a government offer to purchase, and an aggregate supply restriction. Aconsumer subsidy is modeled as a subsidy provided by the government to allow the market to clear. Anoffer to purchase can be modeled in two ways, as a government payment to purchase the surplus from themarket, at either the price transacted in the market or a predetermined government price. The aggregate120Figure 7.6: Competitive market with a floor price.restriction will be set at the intersection between the output supply price derived from the price floor andthe output demand function, and may be supported by a consumer subsidy to clear the market.Figure 7.6 shows the impact of a floor price on the competitive market. The floor price has beenestablished atpf, where producers want to supply Q. However, consumers only want to purchase Q” atthe after processing price ofpS• Some supporting program must be introduced to maintain the supportprice. A consumer subsidy in the amount of QS multiplied by the difference between the after processingpricep5 and the demand price at Q5 d will allow the market to clear. Alternatively, the governmentcould purchase the surplus amount, the difference between Q and Qd, at a price ofp5. One furtheralternative the government could use is to impose an aggregate supply restriction, setting the aggregateproduction quota at Q. Under this option, producers would loose some of the surplus possible ifproduction was unrestricted. This is the triangle bounded above by the floor price, on the left by thedomestic consumption Qd, and below by the input supply curve.Evaluating the problem when there are two oligopsonistic processors or a for profit firm and a cooperativewhen the price floor is supported through government expenditures is very complex. Each agent has twodecisions to make, how much to supply to the market, and how much to supply to the supporting agency.QS 10121Since the oligopsonist has the most market power, we suspect that they will be the greatest beneficiaries ofthe government expenditure. When a cooperative is introduced, the IOF will still have to match its price,exhausting its rents. However, the government is an extra player in the game, against which thecooperative may be able to act strategically.7.5) Closed Economy with an Input Price PoolAn input price pool is easy to evaluate without a cooperative presence. We get the same outcome as ifthere was no pool. When there is no connection between the processor and the producer, the situation isidentical to a price pool. A price pool forces one price to prevail. Generally one price is assumed toprevail anyhow, so nothing about the result will change.When there is a small number of firms, one of which is a cooperative, a price pool generates a uniqueresult. The new objective functions are:7.31= p(x)x — c(xjx — M(x)x Investor Owned Firm7.32 div = [p(x)x— c(xjx — M(x)x],/x CooperativeWe assume all farmers are members, as predicted by the theoretical development above. M(X) is theprice that must be paid for milk that is bought from the pool.We assume farmers are strict profit maximizers. Each farmer chooses an output level such that theeffective price received is equal to the marginal cost. The producers take the effective price as given.In chapter five we showed that if farmers are strictly profit maximizers, then a price pool transfers anyrents the cooperative is able to earn to the competing IOF. When all farmers are members of thecooperative, the effective price is the sum of the pool price and the patronage dividend. The patronagedividend is paid to all the farmers, so that the net cost of producing the required output is equal to the122supply price less the patronage dividend. The relationship between the pooi price, the cooperativepatronage dividend, and the supply price can be written as:7.33 M(X) = m(x) — divThis pool price identity defines the condition that must hold for a cooperative operating in a marketwhere there is a price pooi for the members’ production, and all the members are atomistic and strictprofit maximizers.After substituting the cooperative dividend into this identity and rearranging, the pool price M(X) is:7.34 M(X) = {Xm(X) — p(x)x + C’(x ),ç J/(x— x)The pool price is equal to a weighted sum of the supply price, the output demand price, and thecooperative’s processing cost. This function defines the price that the IOF and the cooperative must payfor the input that is purchased from the pooi.Substituting 3.34 into the IOF’s profit function, and simplifying, we find:7.35 3t = p(X)X — m(X)X — c(x )x1,— C(x )xThe profit of the IOF is equal to the total revenues from the market, less the total cost of all the inputproduced, and less the processing costs of both the cooperative and the IOF. The pooling of all the milkallows the cooperative to pursue an objective independently of the membership. If the objective chosenresults in a greater than zero dividend, the member will accept a lower price from the pool. The drop inthe pool price allows the IOF to capture all of the rents that are available.We can use the explicit functions that we have been using above to solve for the solution in this problem.The pool price function becomes:(3x +x Xx +x )_18x7.36 M(x , )_c v cC 2x123In all the other cases looked at, the input choice of the IOF did not have any effect on the price that theproducers received for their production. The cooperative chose an input level such that the competitiveoutcome was maintained. The cooperative’s response to the IOF’s decision always restored the zero profitresult for the IOF. However, the pooling of the input generates a pool price response to the IOF’s inputdecision.Figure 7.7 shows the pool price as a function of the total output level. The cooperative input use has beenfixed at 2, 3, and 4 units. Therefore the curves represent the price that the IOF faces for the milkdelivered to the pool. The farmer is prepared to produce milk for this price. The linear demand andsupply curves, combined with the fixed unitary cost and perfect efficiency of the production processgenerates the peculiar price lines that become asymptotic to the cooperative’s output level, going tonegative zero. As expected, the curves all intersect the supply price at a production level of 6, where in acompetitive market all the rents would be exhausted. These curves show that for this problem, the optimalinput level the IOF will choose will be infinitesimally close to zero. A more realistic cost structure wouldproduce a more believable result.If we substitute this into the cooperative patronage dividend function we find that the relationshipsimplifies to:3xr /7.37 div = — + x2xIf the cooperative is assumed to maximize the patronage dividend, then we can derive a reaction functionfor the cooperative.7.38 x = 3_x/2When we substitute the pool price function into the JOF profit function we find7.39 9(x +x)_ 3(x i-x)2/2124Figure 7.7: Pool price as a function of total milk brought to poolThe reaction function that follows from this relation is:7.40 x+x=3The intersection of these two reaction functions occurs where the cooperative is producing three unils ofoutput for the consumer market, and the IOF is producing nothing. The linear functions force theintersection point to the boundary. The IOF allows the cooperative to have most of the production,, andthe cooperative’s patronage dividend acts like a subsidy, allowing the IOF to purchase its input from thepool at a much reduced price.7.6) SummaryOn their own, each of the policy instruments of supply management has a distorting effect on the market.Closing the border increases the domestic price, reducing consumer welfare and increasing producerwelfare. Processors with market power extract rents from both the consumer and producer in a closed125market, but can only act strategically against the producer if the market is open. The presence of acooperative restores the competitive outcome in both of these cases. If we add a volume restriction to aclosed market we fix available rents. The distribution of the rents is unclear, but likely accrue to theagents with the greatest amount of bargaining power. When there is a cooperative, the farmers becomeone of the agents with bargaining power, and all the rents are captured by the farmers.Establishing a floor price adds a new level of complexity. It is not possible to maintain a floor pricewithout some form of government intervention to ensure that it is not optimal for the market agents tocircumvent the established price. Assuming such regulations are in place, producer welfare will beincreased. Consumer surplus may be increased or decreased depending on the form of the governmentintervention. If agents have market power, then these agents will interact strategically with the newplayer, the government, to capture a share of the intervention benefits. If it can strategically manipulatethe government controls, a cooperative may not perfectly restore the competitive outcome.A price pool decouples the membership from the cooperative. Member production need not be processedby the cooperative, so the member’s own production decision does not need to change the amountprocessed by the cooperative. The cooperative can pursue an objective independent of the producermembers. If the cooperative processes such that it is paying a positive dividend, it becomes optimal forfarmers to belong to the cooperative. Members will accept a lower price from the milk pool. They treatthe patronage dividend as a production subsidy. The lower pool price transfers the rents that thecooperative captures to the IOF competing with it. In the extreme case presented above, the IOF willchoose to produce a very small amount, allowing the cooperative to act monopolistically in the outputmarket. The subsidy on the pool price transfers all of the industry’s rents to the IOF.Supply management combines all of these policies into one program. The most critical impact on theindustry is a function of the most binding constraint. Import controls may increase farmer welfare byallowing them to receive a price above the open economy price. The supply restriction may furtherincrease farmer welfare by increasing the input price above the competitive equilibrium. The floor priceguarantees that some portion of the rents created by the supply restriction accrue to the farmers. A126cooperative in an environment like this ensures that all rents go to the farmer. If we pool the price formilk, we may reduce farmer welfare. The pooling of the milk price allows the IOF to get away withoutpaying a price that matches the dividend the cooperative pays, so that it can capture some share of theindustry rents which would go to the farmer without this pool. However, the pool also allows thecooperative to pursue its own objective, with the result that total industry rents may be increased. Inaggregate, the combination of all these policies enhance producer welfare, and reduce consumer welfare.The competitive yardstick outcome that standard cooperative theory predicts is unlikely to occur.127Chapter 8: The Financial Statements of the FVMPCAWe have explored the definition of a cooperative, and the details of the dairy industry in British Columbia.Using these facts we have constructed and evaluated a stylized model of a cooperative in this industry, andinvestigated how the various elements of this environment impact on the cooperative. The cooperativebehaves more like an JOF than we might expect at first glance. We now turn to the empirical structure ofthe dairy industry in B.C.. We begin by exploring the financial statements of the FVMPCA. After thiswe turn to a simple model of the quota price to see if it lends support to our model.The financial statements of a cooperative are somewhat different than that of an investor owned finn. Theprimary purpose of the traditional financial statement is to give information to the owners of the firm, whoare the residual claimants. The residual claim is conducted through the return generated by the sharesthat the equity holder has. This return comes as dividends paid out or an increase in the value of theshare.For a cooperative the equity has a return that is either zero or fixed at a low level. The profit generated bythe cooperative is returned to the members via the patronage dividend. This dividend can appear in theform of an increased price for the conunodity the member ships to the cooperative, a reduced price for anygoods the member buys from the cooperative, a final payment to the member of any surplus thecooperative generates, distributed according to the members patronage, etc. Note that a final payment isdistinct from the patronage dividend. The final payment is the amount the farmers would see as cash in aparticular period, while the patronage dividend is the member’s share of the cooperative’s earnings,irrespective of whether it is paid out or not. What a cooperative does not do is pay a dividend on theshares held, and the member cannot sell these shares to realize any capital gains in the asset base theyrepresent.These differences make most of the traditional ratios used to analyze a financial statement unusable, andmakes comparison between cooperatives and investor owned firms very difficult. The extensive set ofratios that reflect the position of the common shareholder are meaningless when a cooperative is128considered. This also means that any effort to compare cooperatives to IOFs on the basis of theshareholder’s position is of little value. The ratios that analyze the positions of the creditors are of a littlemore value, as are some of the general performance indicators. Several of these will be presented below,along with an explanation of how they are calculated and their meaning. Following the more commonratios, several ratios that are unique to the cooperative will be shown.8.1) Return on TotalAssetsThe return on total assets measures how well the assets have been utilized. For the traditional firm this iscalculated as:Income before extraordinary items+ [Interest expense x (i — Tax rate)]= Return on total assetsAverage total assetsOne takes the net income and then adds back the interest expense, adjusted by the tax rate. Theadjustment is made to correct for the fact that taxes are not paid on the interest expense. The averageassets can be calculated as the average of the beginning and end of year asset values. This is not strictlycorrect, but is adequate for the analysis. What this ratio measures is the return the shareholders wouldrealize if the entire firm was equity financed, and was still in the same tax bracket.In the case of the cooperative the calculation we make is similar.Income before extraordinary items + Interest expense= Return on total assetsAverage total assetsA cooperative is essentially an agent for its members, and so in Canada it does not pay any taxes on itsearnings. This somewhat changes the interpretation of the ratio. The return on total assets for acooperative measures how much would be available, on an asset basis, for distribution to the owners of thefirm. However, in a cooperative the returns are paid to the owners according to how much they patronize129the cooperative. As a result, this number is, strictly speaking, of little value to the cooperative members.However, it can serve as a basis for comparison to the IOF firms that operate in the same industry.The return to assets was calculated for the investor owned firm using the data available from the StatisticsCanada database CANSIM. This data series extends from 1972 to 1987. The total interest expense wascalculated as the sum of the bond interest, mortgage interest, and other interest expenses. The appropriatetax rate was calculated by using the assumption that the difference between the net income before taxesand the net income after taxes is equal to the taxes paid. These numbers were used to calculate theequivalent to equity financed amount that had to be added to the net income after taxes to calculate thereturn on total assets.For the cooperative the amount available for distribution, less the market value of the milk that themembers have shipped to the cooperative, was taken to be equivalent to the net income after taxes. Thisamount is the remainder after all production, interest, and tax expenses are deducted. However, the taxexpenses for the cooperative are minimal, so they are ignored. The interest on long term debt and theinterest due on loan certificates was then added back to the amount available for distribution, and this wasthen divided by the total assets. This would be the return on assets if the cooperative did not have to pay0.400.35_______0.300.250.20> 0.1504- 0.100.050.00-0.05-0.10Return to Assets Comparison•• FVMPCA + TaxesA CANSIMFigure 8.1: Return on assets comparison1% 0 ,- N cq to C I- C 0 0 —U U U U U 0 U (.) ()U U• it it it0000000<0000000000130Average Variance of Correlat’n Slope of Goodness ofreturn return with time regression fitFVMPCA 14.01% 0.00861 0.19 0.0028 0.04FVMPCA + taxes 8.94% 0.00478 0.09 0.0013 0.01CANSIM 8.97% 0.00021 0.63 0.0019 0.40Table 8.1: Return on assets comparison between the FVMPCA and the average Canadian dairy processorout any interest. This would be the effective return to a totally equity financed processor if that processorcould escape taxes.A more appropriate comparison might be with the taxes deducted from the cooperative’s income. The taxrate that was calculated above for the average Canadian firm was used as the appropriate tax rate thatwould apply to the FVMPCA, should it be more traditionally funded. These results are presented as thesecond line in the figure.Table 8.1 presents a sunury of the results. The average return for the cooperative assets, given the taxbenefit the cooperative, is slightly over 14% for the twenty years considered. However, if we deduct anamount equivalent to the taxes that would be paid for an average Canadian dairy processor, we get anaverage return that differs from that calculated for the IOFs in Canada by only 0.03%. The correlationwith time and the slope of the time trend regression are included to see what is happening over the twentyyear interval. The regression is between the data series mentioned and time. Time was a series of daynumbers, and the reported number was multiplied by 365 to get a proxy for an annual figure. The mainpurpose of the regression is to get a sign on the slope parameter and a rough estimate of the amount of thevariation explained by time. All the results show a positive trend, but it is weak for the individual firm.In terms of assets, the FVMPCA has been using them about as effectively as any other firm in theindustry, both in terms of the average return generated and the general trend over time. Based on theReturn on Total Assets, we cannot say that the FVMPCA behaved any differently than any other firm inthe industry.1318.2) Current RatioThe current ratio is a commonly used measure of the liquidity of the firm.Current assets= Current ratioCurrent liabilitiesShort term creditors are concerned with this ratio. It measures the number of times that the firm would beable to pay the short term liabilities that are outstanding, if they all had to be paid now. Current assets arethose assets which can be liquidated rapidly. Current liabilities are liabilities that are coming due withinthe year. Interpretation of the current ratio must be done cautiously. The current assets of the firminclude inventory. Increases and decreases of the current ratio can be indicative of poor financial health,or indications of shifts in the inventory management. Holding large inventories can drive the current ratioup, even if the items in the inventory cannot be sold for the value recorded on the books. Disposing ofthese assets can cause a drop in the current ratio while at the same time actuaily improving the short termliquidity of the firm.For the average Canadian diary processing firm, the current ratio was calculated using CANSIM data.Current Ratio Comparison3.00.ao • FVMPCA2.60 • CANSIMo o o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0Q 0 0 0 0 0 0 0 0 0 0 0 0 0 0000000Figure 8.2: Current ratios for the FVMPCA and the average Canadian diary processor.132Average Variance of Correlat’n Slope of Goodness ofCurrentreturn with time regression fitRatioFVMPCA 1.817 0.0503 -0.42 -0.0148 0.17CANSIM 1.517 0.0178 0.80 0.0224 0.64Table 8.2: Summary statistics for the current ratio analysis.Since CANSIM reports the current liability and the current asset totals of the Canadian industry as awhole, it is very straightforward to calculate these numbers.For the FVMPCA, the calculation of the current ratio took a little more work. The biggest issue wasaggregation of the data over the twenty year interval. During this period a number of categories on thebalance sheet were changed. Some of these categories shifted out of or into the current assets category. Aconsistent method of calculation was approximated by tracing where the values in a particular categorywere distributed to or aggregated from when a change occurred. This change was then moved forward tomaintain a consistent method of analysis. This works provided that the elements in a particular categoryhave been consistent over time.Figure 8.2 shows a peak in the current ratio of the FVMPCA occurring in 1978, followed by a large dropin 1979. The spike occurred a year after a rearrangement of the items that appear in the current assetsportion of the balance sheet, indicating that it is likely not a result of a change in the factors included.Similarly, rearrangements of the balance sheet categories during 1976 and 1977 did not translate intosignificant movements in the current ratio. However, in 1978 a new comptroller was hired. This couldindicate that there might have been some changes in the accounting practices and the management ofhighly liquid assets during this time.The summary in table 8.2 of the current ratios for the FVMPCA and the national average shows a slightdifference. The national value is within two standard deviations of the current ratio for the FVMPCA.The downward trend indicated by the correlation coefficient and the slope of the regression is a result ofthe higher current ratio for the FVMPCA prior to 1979. The current ratio indicates that for a period in itshistory the FVMPCA was maintaining a degree of liquidity that was significantly above that of the133average finn in the diary industry in Canada. Following 1978 the current ratio for the FVMPCA closelyparallels that of the national average. The step-like change in the current ratio probably indicates eitheran accounting policy change on the part of the FVMPCA, or an error in how the data was made consistentover the long time period. Overall, the FVMPCA still appears to be behaving like an IOF.8.3) Debt to Equity RatioThe debt to equity ratio, as traditionally calculated, is a rather dubious quantity when one is dealing with acooperative. A cooperative is financed principally through member capital. This capital is acquired byretaining from the members a portion of their share of the cooperatives earnings for some period. In thecase of the FVMPCA this calculation is even more dubious since the FVMPCA allocated the retainedsurplus as a ‘loan certificate.’ This loan certificate was essentially a bond, and as such these funds wererecorded as a liability, and the earnings they generated were considered an interest expense.For the traditional firm, the debt to equity ratio is calculated as:Total liabilities= Debt - to - equity ratioShareholde& equityThis ratio measures the degree to which the financing of the firm is provided by equity holders, and towhich degree by financiers. The cooperative raises capital by holding back for a period of time a portionof the profit that it has to distribute to the members. However, the members do have a portion of theirfunds tied up in the cooperative. This member capital can be grouped into four general categories.In the first category are the net short term liabilities to the members by the cooperative. Unlike mostinvestor owned firms, a cooperative transacts most of its business with its owners. This means that a largepart of the current liabilities, in the case of a marketing cooperative, are owed to the members. This is apool of funds with a high turnover, but gives the cooperative a source of funds to use against other shortterm liabilities.134Distribution of Member Capital in the FVMPCAAnother category is the allocated long term equity. These funds are the retained earnings that have beenheld in the cooperative. They have been allocated to the individual members, and are usually scheduled tobe paid out at a particular date in the future.The third category is the share capital. Most cooperatives require some up-front contribution of funds thatentitles the individual to the benefits of membership. These shares are usually held for the duration of theindividual’s membership, and are redeemed at their purchase price when the individual stops transactingwith the cooperative.The final category is unallocated equity. This category consists of retained earnings and reserve fundswhich are not allocated to members for payment. In an investor owned firm these funds affect the price ofthe shares, and thereby are effectively still part of the owner’s equity. However, in a cooperative thisbecomes a pool of funds which is not allocated to anyone. For the purpose of the management of theorganization however, this pool of funds does provide a source of capital.OD/. I . . . . .o — N ( 0 0 N N 0 0 —00 0 00o o o 000066 o o o o o• • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0o o o o o o o o o o 0000000000Figure 83: Composition of member funds in the FVMPCA.135The figure shows how the members’ funds in the cooperative have been distributed between the fourdifferent categories. The disappearance of the share equity is an outcome of the merger with theShuswap-Okanagan Dairy Industries Cooperative Association (SODICA) in 1982. At this time the sharepolicy was changed so that members would only be required to hold a small number of shares. Before1982, the retained portion of the cooperative’s surplus was allocated as shares and bonds. Following themerger, all of the retained amount was allocated as the ‘loan certificate’ bond.These different pools of member capital give us several different ways which we could form a proxy forthe debt-to-equity ratio. The most obvious of these is to look at the total member capital contribution.This would be:Total liabilities= Debt - to - equity ratioTotal member captial in the cooperativeThis ratio would measure the total portion of the asset base which is allocated to members compared tothat which is allocated to other creditors. In the case of a marketing cooperative, a large part of thecurrent liabilities will be occupied by amounts owed to members. These amounts are member equity, butare entitled to be paid out in a short period of time.As a measure of the extent to which the asset base is financed by external creditors, including the shortterm liabilities to the members may not be appropriate. The short term liabilities are of no use as securityfor borrowings. If we remove these short term liabilities, we get the following relationship:Total liabilities .= Debt - to - equity ratioTotal member captial in the cooperative- short term liabilities to members136This more closely approximates the traditional measure of the financial structure of the cooperative. Forthe cooperative, this ratio measures what share of the total assets is financed by member capitalcontributed for this purpose, as distinct from short term liabilities. Over the long term, this measureshows how ownership of the asset base has been changing.The figure shows the time path of the Debt-to-Equity ratio for the average dairy processing firm inCanada, as determined using the CANSIM database, and the path of the debt to long term member capitalfor the FVMPCA. Inspection of these figures indicates that the share of debt financing for the cooperativehas grown over the period shown, while the ratio has been slightly downward trending for the industry asa whole.The table shows a statistical summary of the data presented in the figure. We can see that the debt toequity ratio for the cooperative is trending upwards. The correlation with time shows a strong positivetrend for the FVMPCA, while there is a weak negative trend with the data drawn from CANSIM. If weDebt-to-Equity Ratios3.002.50_______2.001.501.000.500.0000000000000 0000000000Figure 8.4: Comparison of the debt-to-equity ratio for the FVMPCA and the average Canadian diaryprocessor.• Long Term Member CapitalA CANSIM— — —— — —137Average Variance of Correlat’n Slope of Goodness of‘ ratio ratio with time regression fitMember Capital lesscurrentliab. 1.632 0.345 0.73 0.0675 0.53CANSIM 1.320 0.028 -0.17 -0.0059 0.03Table 8.3: Summary statistics for the debt to equity ratio analysis.look at the slope of the regression of the data, then we see this repeated. The regression shows that overtime, the trend line has an upward slope for the FVMPCA debt to equity ratios. At the same time, theslope of the trend line for the data gathered from CANSIM is downward sloping. The statistical analysisconfirms the observation that the debt to equity ratio was rising for the FVMPCA.This observation can be seen as an example of the equity crisis that many cooperatives eventually face. Asthe cooperative ages and becomes more stable, its members are less willing to finance its operations. Theyno longer share the same motivations and beliefs that existed when the original members formed thecooperative. As a result, the cooperative must rely to a growing extent on other sources of financing. Thecontrol of an organization lies with the people who contribute the capital. The equity holders do have thefinal decision making control, but other financial contributors place their own restrictions on what anorganization can do. Excessive reliance on debt financing can place extensive restrictions on acooperative, reducing its ability to respond to changes in the market environment. Under such conditions,a cooperutive needs some way to increase the level of equity. Refinancing methods may range fromappeals to membership for extra contributions to share offerings, all of which have been seen when othercooperatives have encountered this problem.In terms of financing, the FVMPCA is not showing the same trend as the average finn in the Canadiandairy industry. However, this result is explained best by the structural problems we identified in chaptertwo, and not the competitive yardstick. We cannot hereby establish a production difference between theFVMPCA and a typical IOF.138Surplus Above Market ReturnIcnU0.Figure 8.5: Percent surplus above market return.8.4) Surplus above market returnThis is the first of a couple of ratios that are unique to a cooperative. If the cooperative is operating in amarket where there is a price for the product it is dealing in, then we can compare the return it generatesagainst that generated by the market price. We will define this ratio as:Total return generated by cooperative- market value of cooperative product= Surplus above market returnMarket value of cooperative productThis ratio measures the benefit to the members generated relative to the market. In the case of amarketing cooperative like the FVMPCA, which deals in only one major product from its members, thatbeing milk, this is a fairly straightforward number to calculate. The supply management system furthersimplifies this calculation. The market price that the farmer can receive is simply that administered bythe milk board.25%20%15%10%0%iiiilIiiI139Average Variance of Correlat’n Slope of Goodness ofratio ratio with time regression fitSurplus above market 6.24% 0.0028 0.21 0.0018 0.04returnSurplus as ItUrfl t4 34.95% 0.0798 0.34 0.0153 0.11capitalTable 8.4: Summary statistics for the surplus above market return.Figure 8.5 shows the percent surplus above the market return. There is no clearly discernible trend, andover the interval considered, the surplus has generally been positive. If we look at the statistical summaryin the table, we see the same result. The correlation coefficient and the regression slope show that there isa positive trend, but the low value for the correlation coefficient and the goodness of fit indicates that thisrelationship is quite weak.The main conclusion we can draw from this is that the FVMPCA has for the most part been able togenerate a return for the members on the equity they have invested in the cooperative. If we look at thereturn as a return to the members’ long term equity in the cooperative, we have another measure of theactivities of the cooperative. This ratio can be expressed as:Total return generated by cooperative- market value of cooperative product — Surplus above market returnTotal member captial in the cooperative— as return to capital- short term liabilities to membersThe table shows the results of this calculation as well. The average value for the return to the capital, asmeasured in the way above, is over thirty percent. This is the return to all the member capital in thecooperative that is not due to be paid in the next year. The total return to the farmer is higher, since thefarmer is being paid a return on the loan certificates.It is not possible to compare these returns to the industry average. This ratio is unique to the cooperative.However, both of the performance measures are positive, and the return to capital appears to be quite high140considering the relative stability of the dairy industry. Overall this suggests that we do not see acompetitive yardstick outcome in the B.C. dairy industry.8.5) Percent of Surplus Retained.This is another ratio that is unique to cooperatives. Since a cooperative generates its operating capital byretaining a portion of the surplus it generates on operations, an illuminating piece of information is whatportion of the surplus is retained. The retained amount is distinct from the conventional retainedearnings. For a cooperative, the retained amount is a fraction of the patronage dividend, allocated to aparticular member. It is retained for a number of periods as ‘operating capital’ for the cooperative. Theconventional retained earnings is a blind pool of profits that have not been paid out as dividends. We canmeasure this in two ways. In the first place, we can measure this as a portion of the total surplus that thecooperative generates. This would be calculated as:Retained portion of net income= Share of total surplus retainedNet incomeAs an alternative, we could look at the amount retained as a portion of the difference between the potentialmarket revenues and the surplus generated by the cooperative. For a marketing cooperative, this would beakin to the fraction of the final payment retained., Since the potential market revenue is sometimes greaterthan the surplus, this value may be negative. However, the cooperative will still most likely retain apositive amount of the surplus. In such a situation this ratio will become very difficult to interpret. Forthis reason, we will focus on the simpler form shown above.The figure shows the amount of the surplus retained for the FVMPCA. It is clear from the figure that thesize of the retention has been declining over time. This is consistent with the observation that the debt toequity ratio has been increasing. The deferred payment is the means by which the cooperative secures itsequity. If the inflow into the equity pool declines, then over time the size of the equity pool will decline,leading to a greater share of the assets financed by debt and a larger debt-to-equity ratio.141Portion of Surplus Retained2.5%2.0%1 1.5%I1.0%0.5%0.0%;U U U U U U U U U U U U U U U U U U U U U Ua . 0 0 0 0 0 0 0 0 0Figure 8.7: Percent of the surplus retained as a share of the total surplus earned.The size of the equity pool in a cooperative is always a matter of concern. The traditional cooperativedoes not have any fixed equity. The financial stability of the organization is always subject to thedemands of its members. Since most people are assumed to be risk averse, they will always be reluctant toconunit capital to the cooperative. From a portfolio perspective, the individual can minimize risk bydiversifying out of the dairy industry, rather than investing in vertical integration within the industry.However, to be successful in the market, the cooperative needs access to capital. As the organizationgrows, the members become more atomistic, and act more like independent agents. At the same time, theneed for large pools of funds to finance investments increases. These two forces pull in oppositedirections, with the result that the cooperative may stagnate, or be forced to look to non-traditional sourcesfor its financing.111111111428.6) SummaryAnalyzing the financial statements of a cooperative is a challenging task. Most of the traditionalmeasures of a firm’s performance relate to the position of the shareholders. Since a cooperative does nothave shareholders, but rather returns its earnings to its members on the basis of their patronage, manyfinancial ratios do not provide any meaningful information. We introduce a couple of ratios which areunique to the cooperative, and make some inferences from these. The surplus above market returnshows how the cooperative is performing relative to the alternatives available to the member. If weevaluate this measure in relation to the amount of member capital, we can see how ‘healthy’ a return thecooperative is generating. The percent of the surplus retained is a measure of the degree to which themembers are contributing capital to the cooperative. It tracks how member equity contribution haschanged over time.Combining these two new ratios with the traditional ratio analysis, we can construct a picture of theperformance of the cooperative. The surplus above market return, along with the return on total assetsand the current ratio indicate that the FVMPCA is performing very competitively in the milk market inB.C. In the case of the traditional ratios, the FVMPCA’s performance is closely in line with theperformance of other firms in the industry in Canada. The surplus above market return echoes this fact.This measure is on average positive, and has been trending upwards, indicating that the FVMPCA hasbeen successful at generating a return on the equity its members have invested.The ratios that measure the capital structure of the organization tell another interesting story. The debt toequity ratio, even though strictly speaking it cannot be applied to a cooperative, shows a trend to increasethe amount of debt financing in the cooperative. This occurs at a time when for the average finn in theindustry, there was somewhat of a decrease in the portion of debt. The percent of the surplus retainedechoes this. Over the period surveyed, the amount of the surplus that was retained has fallen significantly.These facts indicate that the FVMPCA is beginning to face the same equity constraint that has forcedother cooperatives to look for non-traditional sources of financing.143Our theoretical model predicts that under the regulatory scheme in British Columbia, a cooperative in thedairy industry would not lead to the competitive yardstick solution. We expect that a cooperative willbehave analogously to the IOF it is competing with. An inspection of the financial statements of theFVMPCA lends some support to this model. We see that the FVMPCA shows a return on total assetsand a current ratio that is remarkably similar to the industry average. Along with this, the surplusabove market return, when expressed as a return on member capital, is quite large. It appears that overthe last twenty years the behavior of the FVMPCA has been similar to that of the IOFs it competes with,and it may have been able to capture some rents on behalf of its membership. The one area where we seea difference is in the debt to equity ratio. This ratio has been climbing for the FVMPCA, while it hasbeen stable for the rest of the industry. This can be explained at least in part by a decline in the percentof surplus retained. As the literature predicts, members of the FVMPCA seem to have been reluctant tomaintain the same level of capital contribution over time.144Chapter 9: Econometric AnalysisThe financial records of the FVMPCA provide some firm specific support for our theoretical model. Wecan also look at the price of fluid milk quota for the presence of the implications of our model. Supplymanagement requires all farmers hold a quota equal to the amount of milk they ship. This quota is tradedbetween fanners. We expect its price to be related to the potential return it offers. In this chapter weexplore the relationship between the quota price and the expected success of dairy cooperatives in BC.9.1) Theoretical Background.The theoretical model of a cooperative in an imperfectly competitive supply managed sector points to arelationship between the performance of the cooperative and the price farmers are willing to pay for thequota asset. In British Columbia, for most of the last twenty years, provincially issued fluid milk quotawas the only milk quota traded in the province. Federal market sharing quota was traded on par with thefluid quota, depending on the ratio of holdings by the farmer.Milk quota in British Columbia is, for all intensive purposes, a license for a perpetual cash flow[Barichello, 1984]. If one holds quota, then so long as one is able to maintain the production that thequota requires, the cash flow is guaranteed. The size of the payments is determined by an administrativebody, in part using a ‘cost of production’ formula. The risk that this cash flow will change is mostly afunction of policy risk. Active political involvement by the dairy industry has kept this risk to aminimum.The standard capital asset valuation models used in finance propose that the value of a capital asset willbe equal to the present value of the cash flow that this asset can generate, discounted in a way thatincorporates the riskiness of this cash flow. Mathematically we can write this as:9.1. a=E(1+i)’The present value of the asset is equal to the sum of the expected value of the discounted cash flows.145Calculating the expected cash flow is difficult. A formula determines the size of the cash payments.However the rate at which the flow must be discounted is more difficult to determine, as is any riskinessassociated with the cash flow. The expected discount rate is a function of the expected inflation rate andthe rate of return required for an asset with similar riskiness. The expected value of the payments dependson the components of the formula and any factors that the farmers feel affect the riskiness or the absolutesize of the payments.Our theoretical model finds that the cash flow will be the sum of the pool price and the patronagedividend of the cooperative. Net of costs, this is the sum of the independent farmer’s shadow value, ),and the patronage dividend, which equals the member’s shadow value ?. Any factors that affect thefarmer’s expectations for the patronage dividend affect how the price of quota moves.Asset valuation models are plagued by the problem of evaluating expectations. The current value ofvariables like the interest rate and a particular cash flow are valid only in so far as they containinformation about the future. The interest rate is particularly problematic in this regard because historicaldata contains inconsistencies that can only be supported through unknown information. The theory ofcapital markets requires that arbitrage opportunities cannot be maintained. This requires that negativeinterest rates cannot exist. However, if we look at the historical evidence, we find negative real interestrates. This result occurs because agents incorrectly forecast the inflation rate, not because they expected anegative real interest rate. Therefore, the real interest rate is not a good predictor of expected interestrates. At best, it measures expected inflation, assuming that the underlying asset does not change itsriskiness, and that the relevant opportunity cost does not change.9.2) Data.It is impossible to accurately model the expectations of any economic actor. However, we can postulatethat certain variables are more important than others in predicting the cash flow of a particular asset. Inthis case, we are trying to find factors that will predict the cash flow generated by holding milk quota.14625015010o-50Fluid Quota Price— —— Blended Milk PriceFresh Fluid PriceC) ) ) ) e) ) C’) C’) C’) C’) C’) C’) C’) C’) C’) C’) C’) C’) C’) C’) C’)00000 e 000000000000000000,- r-r- r- r- r- r- r- r- r- 000000000)0)00)0)0)0)0000000000000000000001 - I- 1 I- 1 1 I 1 1 I- 1 V-QuarterFigure 9.1: Quota price with fresh fluid price and blend milk price.The model we have built indicates that the surplus generated by the cooperative should be an importantfactor in determining how much farmers will be willing to pay for the quota. We therefore need toidentify variables that might predict the return generated by being a cooperative member, and the returngenerated by producing milk.The data presented in figures 9.1, 9.2 and 9.3 shows a twenty year history for the quota price and anumber of other variables that might be important. Several of these series, such as the quota price and thecomposite leading indicators, show a large nominal increase over this period. All data shown has had alinear time trend removed. Each series is also adjusted to have an overall range of about two hundred,centered around a value of 100. These adjustments make the series more comparable.In figure 9.1, the time trend for the price of fluid quota follows a pattern that is similar to the patternshown by both the blend milk price, which farmers receive, and the fresh milk price as paid by consumers,lagged by two to three years. Looking closely, the extra volatility of the fresh milk price is somewhat50 I%.S147250200150100500-50)C C’) C’) C’) C’) C’) C’) C’) C’) C’) C’) C’) C’) C’) C’) C’) C’) C’) C’) C’) C’) C’) C’) C’)000000000000000000000000F- F- F- F- F- F- F- F- F- F- 0)0)0)0)0)0)0)0)0)0)0)000000000000000 00)1 I ,- I- I- I- I I ,- 1QuarterFigure 9.2: Quota price and economic indicators.more reflective of the quota price. This is particularly evident in the downward movement of both curvestowards the right of the figure. Here the fresh milk price and the quota price have almost identical slopes,while the blend price is not as steep.The consumer price is grossly determined by the administrative price represented by the blend price line.All processors pay this blended price to the farmers, making large deviations a practical impossibility.However, fine deviations will occur as a result of the competition between the various participants in themarketing channel. A cooperative processor’s patronage dividend is expected to deviate with variations inthe marketing margin. This should change the producers expectations about the return to cooperativemembership. The lag effect may result from information delays, and ‘wait and see’ behavior by industryparticipants. Qualitatively, the figure indicates that the consumer milk price appears to be having someimpact on the price farmers are willing to pay for quota. We would not expect this relationship if farmerreturn was independent of the consumer price level.Fluid Quota PriceComposite Indicators— —— Prime Loan Rate/.—-,__%,•I gI‘I148In figure 9.2 we see a Statisitics Canada composite leading indicator, composed of ten leading indicatorstracked by this agency. The indicator have more variability than the quota price, but we can see that it ison a roughly similar path. The peaks and troughs on both sides of the figure are generally consistent withthe quota price trend, although the amplitude of the variation is quite different. The peculiar feature ofthis pattern is that the quota price leads the indicator by between several quarters and several years.The largest discrepancy in the relationship occurs in the center of the figure. Here we can look at theinterest rate. The early eighties corresponded to a period of high inflation. The administrative formula islagged through a moving average, so inflation would eat up some of the profits generated on the farm.This high inflation period seems to correspond to a lower quota price. Overall, the quota price follows apattern similar to the economic indicators. However, the leading behavior of the quota price hints thatfarmers who buy quota are incorporating more information than just economic performance variables intotheir investment decision.Figure 9.3 shows the quota price along with the surplus earned by the FVMPCA per unit of milk received,and the TSE 300 composite index. The cooperative’s surplus follows a pattern that is similar to the quotaprice, with the quota price lagging behind anywhere from two to six years. We expect the presentperformance to be some indicator of its future performance, but as for any organization it is not a completeindicator.The predictive value of the present surplus of the cooperative is further complicated by the changes thatthis organization has undergone. During the period modeled, the FVMPCA acquired one large dairyprocessor and merged with another dairy cooperative. At the end of the series, the organization was in thefinal stages of a merger which would lead to a radical restructuring and a huge increase in size. Thesefactors would greatly complicate the process through which members make their expectations, making thesurplus earned an unreliable indicator.The TSE 300 composite shows a remarkably close fit with the quota price, if we ignore the significantlyhigher volatility. Like the other indicators shown in figure 9.2, the TSE 300 seems to lag behind the149250200150100500-50YearFigure 9.3: Quota price against surplus earned and TSE 300 composite.quota price by about a year. However, unlike the other indicators, the TSE 300 does not present aninconsistent relationship during the high inflation period of the early eighties. As shown above, quotaprices are often modeled like other asset valuation models. This model comes from capital market theory,which has as its most obvious application the stock market. The agents buying quota likely uses much ofthe same infonuation as the capital market participant, such as interest and inflation rates.If the nominal cash flow generated by quota were guaranteed, then it would be similar to a bond, whichwe expect to be quite counter cyclical. It appears to have a smaller variance, and be slightly out of phasewith the TSE 300. The security of the cash flow can explain the lower variance, while the stability of thereturn to producers may account for the leading behavior. The stability might lead farmers to believe theirmaximum earning potential occurs before the economy peaks, generating a somewhat leading behavior.Quota PriceTSE300— —— Surplus per UnitI’I’I’ I’I’I —‘S s SS S S• 51I —ISSS,bs‘_.5/••15I “i N C’)1 Cl C’) U) U) 1% U) U) 0—ClS— — _ — — —— _ — — — — _ — — — _ — — — — — —150The relatively close match between the TSE 300 and the quota price and between the composite leadingindicator and the quota price supports our model. Many of the factors that increase stock prices, such asincreases in consumer spending, also increase the return generated by a marketing cooperative. Withsupply management, such increases in earning potential are transfonned into a willingness to pay forquota.If the quota is considered as guaranteeing a fixed income stream over time, then one would best considerthe quota asset as a bond. The price of a bond is inversely related to the expected inflation rate. Byassuming that the riskiness of corporate bonds is fixed, we can assume that the prime corporate interestrate incorporates the same real rate of interest over time. This number then reflects the expected inflationrate that investors believe will occur in the future. The corresponding effect on the willingness to pay foraccess to this income stream on the part of producers should be negative regardless of the source of thefunds.Holding fluid milk quota gives one access to the income generated by the cooperative. We want toseparate variables that will indicate future success of the cooperative from those that identify changes inthe underlying fixed income stream generated by the quota. Two variables that could indicate this are themarket price for the good the cooperative sells, and the rate of return generated by the Toronto Composite300 (TSE 300) index.The price for the cooperative’s output acts as a relatively short term indicator of cooperative performance.If the cooperative is engaged in a price war, and the price for milk is low, then its profitability will alsosuffer. A rational member would therefore expect the final payment generated by the cooperative to bereduced, all other things remaining unchanged. If this is true, we would expect to see a positiverelationship between the price for milk in the consumer market and the price quota is being traded for.Conversely, if the quota’s income stream is believed to be fixed, then its price should be unrelated to theconsumer milk price. The variable we will use is the consumer price index for milk in British Columbia.151The TSE 300 is an index of the price of stocks on the Toronto stock exchange. Basic finance theoryproposes that the price investors in the capital market are prepared to pay for a share reflects accurately allthe presently available information about the future cash flows this stock will generate [Brealey et a!,1992]. Using a diversified composite index eliminates any finn specific effects from the return calculated,allowing one to see a risk correct expected present value for the income stream generated by the market.The period by period changes in the value of the TSE 300 will reflect changes in the expectations of theinvestors.The stock market can be seen as indicating two different key pieces of infonnation about the future valueof the income stream generated by the fluid milk quota. On the one hand, the TSE 300 return can be seenas reflecting the opportunity cost of keeping ones assets involved in the dairy industry. If this is true,when the TSE 300 falls, the price of fluid quota should rise. One would expect a negative relationshipbetween changes in the value of the stock market and the price of milk quota.On the other hand, the stock market is also an indicator of the strength of the economy in the future.Investors bid up the price of stocks when they discover that the expected future income stream of a stockhas increased. If an index of the market increases in value, then investors expect the income stream ofmost stocks in the market to increase. If this is true, then a cooperative member is also likely to expectthat the return generated by the cooperative to increase. A simple causal mechanism may be increasedconsumer spending which will include increased spending in the food sector. One would expect a positiverelationship between changes in the value of the TSE 300 index and the price of fluid quota.Another important factor to consider is technological change. Theoretically, technological innovationsare not adopted unless they reduce the cost of production relative to current technology. As technologyhas improved we expect the present value of the income stream to increase, all other things constant. Weexpect the relationship between an index of technology and the price for quota to be positive. For thisanalysis, a time trend was used to try and capture the effect of technical change.152Table 9.1.1. Summary statistics for quarterly series.QuotaThe quota values were gathered from three different sources. The data for the 1981 to 1991 period wastaken from BC Ministry of Agriculture, Fisheries, and Food publications. The 1972 to 1976 period wascovered by data taken from a study by the Fraser Institute [Grubel, 1977]. The interval from 1977 to 1980was filled in through prices taken from the records of Paten and Smith Auctioneers in the Fraser Valley.The TSE 300 data series, the CPI for milk in Vancouver., and the Prime Rate were taken from StatisticsCanada sources. The Quota Price, the TSE 300 close, and the CPI for milk were adjusted using theIndustrial Product Price Index to generate a ‘real’ value.Tables 9.1.1 and 9.1.2 show the summary statistics for the quarterly and annual data series being used.The Quota series is the price paid for quota trades. The Milk series is the CPI series for fresh fluid milkfrom Statistic Canada. The Rate series is the prime bank rate on corporate loans. The TSE rate series isMilk Rate TSE rateMean 197.34 122.80 11.67 0.20Standard Error 6.72 0.78 0.35 0.98Median 205.60 124.65 11 0.67Standard Deviation 55.44 6.45 2.89 8.10Standard Dev. Percent 28.1% 5.25% 24.8% 4050%Sample Variance 3074.00 41.59 8.36 65.57Range 226.02 26.64 14.59 43.87Minimum 75.89 108.28 7.08 -24.02Maximum 301.90 134.92 21.67 19.85Count 68 68 68 68Table 9.1.2: Summary statistics for annual series.Quota Milk Rate TSE rateMean 199.49 123.25 11.79 -1.57Standard Error 13.08 1.56 0.70 4.91Median 206.80 124.62 10.79 1.68Standard Deviation 52.31 6.24 2.79 19.65Sample Variance 2736.57 38.98 7.78 386.23Range 194.02 21.98 10.79 70.82Minimum 85.65 111.08 8.50 -42.53Maximum 279.67 133.06 19.29 28.29Count 16 16 16 16153Table 9.2.1. Quarterly Regression ResultsRegression StatisticsMultiple R 0.8576 Standard Error 29.40R Square 0.7356 Observations 68Adjusted R Square 0.7029 Durbin-Watson 0.3533Coefficients Standard Error t StatConstant -46.24 81.87 -0.5648Milk 1.508 0.6087 2.477Rate -1.771 1.379 -1.285TSE Rate 1.042 0.4701 2.219Time 2.287 0.1936 11.81Table 9.2.2. Annual Regression ResultsRegression StatisticsMultiple R 0.9274 Standard Error 22.85R Square 0.8601 Observations 16Adjusted R Square 0.7183 Durbin-Watson 1.249Coefficients Standard Error t StatConstant 18.34 148.0 0.1239Milk 1.063 1.074 0.9895Rate -1.792 2.378 -0.7536TSE rate 0.7721 0.3383 2.282Time 8.535 1.405 6.076the percentage change in the value of the ThE 300 composite between the last period and this period. Allthe summary statistics are for the data actually used in the regressions. Notice that the milk price variablehas a standard deviation equal to 5.25% of the mean, and that the range is only a little over 10% of themean. The other variables have much more dispersion.9.3) Results.The hypotheses were tested using both annual and quarterly data. The quarterly data had 9 missingobservations over the 68 observations used. These were patched by linear interpolation. The two serieswere analyzed to see if there would be any difference in results beyond sample size effects. A priori therewas no reason to expect a difference in the results. The coefficients generated by the regressions arepresented in tables 9.2.1 and 9.2.2.154The coefficients on the TSE and the Milk data series have a sign that is consistent with the hypothesis thatthe quota price is dependent on the profitability of the cooperative. For the annual data, the four variablesexplain more than 70% of the variation in both cases. For the quarterly data, the parameters on Milk, TSErate, and Time are significant. If we believe that the quota price is independent of the expectedperformance of the cooperative, then we would expect the sign of the TSE rate parameter to be negative,reflecting the opportunity cost of remaining in farming. However, the sign is positive, which is consistentwith the dependence on expected cooperative return. The fact that the Milk parameter is significantprovides a further challenge to the traditional model. If the fanner’s expected cash flow from producingmilk is exogenous, then there is no reason to expect it to be related to what the consumer pays for milk.The significance of this variable supports our model that cooperative performance affects quota value.When we move from quarterly data to annual data we go from 68 observations to 16. With annual datawe find that the parameter on the milk variable is no longer significant. The return the fanner expects toreceive from the cooperative will depend on the cooperative’s market share, the consumer price, and otherfactors such as the weather which will affect consumer demand. During a hot summer we expect the milkprice to be higher, as consumers are demanding more products like ice cream and fluid milk. This wouldlikely indicate a larger final payment in this period, which would be reflected by a higher willingness topay for the quota. The annual averages would eliminate or flatten many of these seasonal variations, withthe result that we may not be able to see the effect.The relatively high R-squared values, along with small t-stats indicates that there is probably a problemwith multicollinearity. To explore the interactions between the different variables, we have constructedauxiliary regressions between the different variables. Table 9.3.1 and table 9.3.2 present the results forthe annual and quarterly data respectively. There is a high degree of collinearity between the milk priceand the constant term. This result agrees with the small variation that this data shows. Themulticollinearity between the constant and the milk price is probably largely responsible for the low t-statfor these variables. The signs are all consistent with the expectations, but the confidence interval around155the parameter estimates is quite large. This fact would aggravate the difficulty in finding a relationshipbetween the quota price and the milk price.Table 9.3.1. Quarterly Data Auxiliary Regressions.R Squared Milk Rate TSE Time InterceptMilk 0.16271 -0.7270 0.1330 -0.0251 132.1271(0.1078)2 (-2.71 06) (1.3987) (-0.6345) (42.0874)Rate 0.1886 -0.1417 -0.0464 0.0329 27.9368(0.1349) (-2.7106) (-1.1000) (1 .9262) (4.2664)TSE 0.1096 0.2230 -0.3996 0.1065 -26.1986(0.0523) (1.3987) (-1.1000) (2.1409) (-1.2174)Time 0.1199 -0.2485 1.6670 0.6276 45.4482(0.0631) (-0.6345) (1.9262) (2.1409) (0.8650)Corist 1.0000 0.0073 0.0079 -0.0009 0.0003(0.9844) (42.0874) (4.2664) (-1.2174) (0.8650)Table 9.3.2. Annual Data Auxiliary Regressions.R Square Milk Rate TSE Time InterceptMilk 0.2257 -0.8669 0.0516 -0.2440 135.6243(0.0322) (-1.4732) (0.5755) (-0.6578) (19.0317)Rate 0.2091 -0.1767 -0.0184 0.0745 32.9054(0.0114) (-1.4732) (-0.4508) (0.4402) (2.1579)TSE 0.2129 0.5201 -0.9071 1.81 48 -70.4018(0.0162) (0.5755) (-0.4508) (1.6836) (-0.5648)Time 0.2220 -0.1426 0.2134 0.1053 23.7237(0.0275) (-0.6578) (0.4402) (1.6836) (0.8004)Const 1.0000 0.0071 0.0085 -0.0004 0.0021(0.91 67) (1 9.0317) (2.1579) (-0.5648) (0.8004)1 Unadjusted R-Squared2Adjus R-Squared3T-Statistic156Table 9.4.1. Autocorrelation corrected quarterly Regression ResultsRegression StatisticsObservationsDurbin-WatsonRhoR Square 0.9341 -Adjusted R Square 0.9299Standard Error 14.68Our regressions generated Durbin-Watson values of 1.247 and 0.3533 for the annual and quarterly datarespectively. The critical values for the Durbin-Watson statistics are 0.73 and 1.94 for the annual dataindicates that we cannot say if there is a problem with autocorrelation. However, the residual plot appearsto be quite cyclical, with a normal statistic of -1.941 for the runs test. The small value for the DurbinWatson value with the quarterly data clearly indicates the presence of autocorrelation.When we correct for autocorrelation with the Cochrane-Orcutt procedure, we generate the results in table9.4. The only parameter estimate which remains significant is the parameter on the time trend. However,all signs except that on the constant term are unchanged. In the case of the annual data, the parameter onthe TSE variable retains the largest t-stat after the time trend. It appears that there is a relationship681.46270.9017Coefficients Standard Error t StatConstant 37.17 104.3 0.3562Milk 0.9034 0.7648 1.182Rate -2.4740 1.712 -1.445TSE Rate 0.1557 0.2046 0.7610Time 2.023 0.6590 3.069Table 9.4.2. Autocorrelation corrected annual Regression ResultsRegression StatisticsR Square 0.8852 Observations 68Adjusted R Square 0.8435 Durbin-Watson 1.2791Standard Error 20.70 Rho 0.5547Coefficients Standard Error t StatConstant 16.41 138.7 0.1183Milk 1.116 1.015 1.100Rate -2.649 2.708 -0.9784TSE rate 0.4396 0.2647 1.660Time 8.698 2.170 4.008157between the TSE 300 index and the quota value, although the TSE 300 is probably not the best proxy forthe factors that affect the price of quota.Our empirical hypothesis is that factors which are used by agents who purchase quota includesinformation investors use when purchasing equity shares. If the farmers willingness to pay for quotadepends on the expected return of a cooperative, then the quota price should follow a path similar to theTSE. A proper analysis requires the identification of all the factors that determine economic activity, andpossibly regression by simultaneous equation to eliminate any endogeneity problems. This analysis isbeyond the scope of the current work.These results indicate that the price farmers are willing to pay for quota rights is a function of more thanjust the formula price and the interest rate. The results are also consistent with our proposal that thereturn generated by cooperatives in the BC dairy industry impacts on the price farmers are willing to pay.The principle source of the change in the quota price is the time trend, which reflects technologicalchange. The net cash flow the farmer is receiving is increasing because costs are falling faster than theprice received. However, the next best explanatory variables are those that would affect the expectationsmembers have about the return their cooperative generates.94) SummaryIn the preceding chapters we developed a theoretical model of the interaction of a cooperative, itsmembers, and an IOF competitor. One principle conclusion of this model was that the opportunity cost tothe farmer of the supply management quota will be related to the expected success of the cooperative. Inthis chapter we investigated how some variables that might be expected to predict the success of thecooperative relate to the quota price. We find that the price of quota is positively related to the consumermilk price and the TSE 300 price, a powerful economic indicator. These results provide empirical supportfor our model of the relationship between farmers and their marketing cooperative.158ConclusionCooperatives are a pervasive feature in production agriculture throughout the world. This is true inalmost all jurisdictions, seemingly irrespective of the different regulations which may exist. This fact mayexplain why the interplay between the structure of a cooperative and government regulations has not beeninvestigated to any great extent. With this work we have tried to look at this problem for a highly specificcase, the dairy industry in British Columbia. We have developed a theoretical model of this marketstructure, and have looked to the FVMPCA and the quota market for supporting evidence.In the first chapter we identified the key characteristics of a cooperative and looked at some of theimplications that follow from these. A cooperative is a form of industrial organization where those whobenefit most from the services of the organization also contribute the capital and control its activities.Cooperatives almost by definition do not pay a return on the member’s equity. They return their earningsto their members on the basis of their patronage. Control of the organization is conducted democratically,and membership is usually, though not always, open.There is an inherent attractiveness to the cooperative structure, arising primarily from the egalitarianflavour that naturally follows from the democratic style of the organization. This attractiveness howevercomes at a price. At least in theory, if not also in reality, cooperatives are plagued by problems arisingfrom conflicting incentives and objectives on the part of its membership. One of the most glaring of theseis the unwillingness of the membership to contribute equity to the organization. It is ironic that thisproblem becomes more significant as the cooperative grows in size, and would otherwise be consideredsuccessful.Chapter two developed the specifics of the supply management system. Supply management arose as aresponse to a prolonged and painful adjustment in the dairy industry. It is the latest and perhaps mostpervasive response to the perception, true or not, that dairy farmers suffer from irreconcilable asymmetriesin their bargaining power vis-a-vis the processors who buy their production. The main features of thissystem are an aggregate volume restriction, a restriction or prohibition on imports, a controlled price, and159a price pool for all the milk produced. The first three features have been studied at length, and the resultthat the institutional shorting of the market generates rents which may accrue to the producers is wellknown. The further result that the atomistic producers will capitalize these rents away has also beenwidely commented on. The price pooi however is little studied. It is this price pool which we foundgenerates a change in the traditional behavior expected for a cooperative.In chapters three through six we developed a theoretical model of a cooperative and explored how itbehaves under the regulations of supply management. When the regulations are not present, we restorethe standard competitive yardstick result. We find however, that if there are entry barriers in theprocessing sector, a cooperative will not be able to completely restore the competitive outcome. Thecompeting IOFs are able to optimize against the producer price, which is now determined by thecooperative’s average value product rather than the producer’s marginal cost.Adding an aggregate volume restriction changes this result little. The principle effect of a supplyrestriction is to guarantee that there are profits available. For two competing oligopolists, an aggregaterestriction on the amount of input available seems to generate a Bertrand outcome from a model withCournot conjectures. However, the presence of a cooperative essentially restores the competitiveyardstick. The competing IOF is still able to use the cooperative’s AVP as the pricing curve, but it canonly do so provided that total production remains within the aggregate volume restriction. Adding a pricefloor to the volume restriction has one principle effect, it restricts how far the down the farmer’s price canfall.A price pool does have a significant impact. Under a price pool, the cooperative is no longer forced toprocess all of the milk its members produce. The cooperative and the IOF both purchase their inputrequirement from the common milk pool. There is now little reason for the cooperative to behavedifferently from the IOF. The patronage dividend now consists of the profits the cooperative is able togenerate above the input price, allocated according to the production of the members. Those who chooseto belong receive a ‘bonus’ which non-members do not receive, with the result that it is optimal for allfarmers to belong to the cooperative. However, if the pool price is determined as an ‘average offer price’160from the processors, the net result of the pooling structure will be that all rents captured by the cooperativewill be transferred to the IOF.When we put all the pieces together, we find an even stronger result. We now see that regardless of theconjectures, the cooperative will behave exactly like an IOF with identical technology, and the cooperativemember will not internalize any of the cooperative’s objective. They will take the patronage dividend as afixed price, and make their production decision accordingly. The price pool has decoupled thecooperative from its membership, and the volume restriction has removed the impact of the farmer’sproduction decision on overall industry prices.In chapter seven we built a simple model of the cooperative, based on linear supply, demand, and costcurves. As we expect, the linear functions translate into extreme outcomes. In most of the situationsmodeled, we find that the competitive yardstick is completely restored. However, the price pool does notreproduce this outcome. Here we find that the IOF will choose to produce nothing, while the cooperativeproduces at the monopoly point. This result is a consequence of the complete rent transfer to the IOF,because the maximum rents available occur at the monopoly outcome.The financial statements of the FVMPCA are explored in chapter eight. The FVMPCA is the largestreceiver of milk in British Columbia, so that it might well represent the cooperative we are modeling. Wesee in the financial statements that the FVMPCA is generating a return for its members that is almostperfectly in line with the performance of other dairy processors in the Canadian dairy industry. This iswhat we expect if the cooperative is performing in the same way as an IOF would. However, we also seethat the FVMPCA is being plagued by the equity crunch that often befalls cooperatives.In the last chapter we explore how the price of quota might vary with the expected success of thecooperative. The valuation of the quota ‘asset’ is traditionally modeled like any other capital asset. Theasset should capture in its value the present value of the expected cash flows it entitles the holder to.Since most of the dairy producers in B.C. are members of the FVMPCA, their expected cash flow frommilk production will be tied to the expected success of the FVMPCA. It is difficult to measure ‘expected161success.’ However, we propose that the ThE 300 serves as a measure of expected economic strength, andtherefore likely indicates something about the expected success of the cooperative. We find that the TSE300 has significant predictive power for the price of quota, and the sign of the parameter agrees with ourproposed model.Our model results and empirical investigations indicate that the supply management system caneffectively separate a dairy marketing cooperative from the adverse incentives of its membership. Thecooperative is free to follow an objective in the same way as a competing IOF would. At the same timethe market for quota between farmers in effect becomes a capital market, where farmers capitalize theexpected patronage dividend into the quota price. This result relies on the interaction between all theelements of the supply management system. Each of the components on its own does not produce thisresult. In the present time of uncertainty, and of pressure to restructure supply management, we need toconsider what form we want the industry to take in the future, and how the different policy instrumentsinteract with each other and with the main agents that are active in the dairy industry.162ReferencesAgricultural Products MarketingAct. R.S., c. A-7, s.1. Queen’s Printer for Canada, Ottawa, 1985.B.C. Legislature. Reg.101/90: Natural Products Marketing Act (BC): British Columbia Milk MarketingBoard Regulation. Victoria. 1990.Bailey, Jack. The British Co-operative Movement. Hutchinson & Co. Ltd. 1955.Barichello, Richard R. Analyzing an Agricultural Marketing Quota. University of British Columbia, 1984.Barichello, Richard. The Economics of Canadian Dairy Industry Regulation. University of BritishColumbia Technical Report No. E/I 2. March 1981.Barichello, Richard. Quota Allocation and Transfer Schemes in Canada. 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