an agricultural cooperative using the Emelianoff-Robotka framework was by Phillips .... accepted definition of a "firm," so, essentially, each group was free to.
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A Perspective on HeImberger and Hoos' Theory of Cooperatives Richard J. Sexton
Helmberger and Hoos' (HH) 1962 paper is a landmark in the economic theory of agricultural cooperatives, Along with the related work by Helmberger (1964), it represented the definitive treatment of marketing cooperative behavior and standard reading for graduate students in agricultural marketing for more than two decades, To understand fully HH's paper, appreciate its many strengths, and also recognize its weaknesses: one must interpret it both in the context of the work on cooperatives that preceded it over the prior two decades and in the framework ofdevelopments in general economic theory at that time, In this comment I attempt to provide such a perspective,
Antecedents to HeImberger and Hoos Analytical inquiry into farmer cooperatives did not begin in earnest until around the time of World War II. Prior to that time, work was descriptive, institutional, and generally imbued with a cooperative fervor. As is well known, the economic theory ofcooperatives developed along two seemingly distinct philosophical frameworks. One group, pursuing ideas developed by Emelianoff (1942) and Robotka (1947), studied cooperatives within the framework of economic integration. To these scholars, the cooperative was not a firm and, as such, should not be analyzed using tools from the theory of the firm. Rather, the appropriate methodology involved use of theories for vertically integrated firms. The first attempt to derive an equilibrium price-output configuration for an agricultural cooperative using the Emelianoff-Robotka framework was by Phillips (1953). The theory was clarified and expanded in comments on Phillips' work by Aresvick (1955) and Ohm (1956). Further advances were provided in an excellent but under appreciated 1961 article by Trifon. Direct antecedents to HH were those who studied cooperatives as special types of firms. A key article in this tradition is Enke (1945). Enke proffered a specific equilibrium solution for a consumer cooperative. Although his work was relevant to agricultural cooperatives, it was not cited by either Phillips or HH. Some years later Clark (1952) produced a study that yielded rather opposite policy conclusions to Enke's work and touched off harsh criticism, including an important commentary by Gislason (1952). Richard J. Sexton is proJessor and chair, Department oj Agricultural Economics, University oj California, Davis.
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This body of work tends to leave the reader frustrated and confused for several reasons: (1) The writers are approaching the theory from different analytical perspectives, Le., vertical integration vs. theory-of-the firm; (2) much of the theory is provided in verbal or graphical form vs. a mathematical exposition that can be unambiguously interpreted and evaluated; (3) the work collectively contains a number of errors and misinterpretations by its authors; and (4) it often develops through a series of rather elliptical comments and replies. Surveys of this work have been provided by LeVay (1983b), Sexton (1984), and Staatz (1987), and it is not the intent to provide such a treatment here. However, to put HH's contribution into perspective, it is necessary to re-introduce some familiar concepts from the theory of marketing cooperatives. The net average revenue product (NARP) of the members' raw product, M, is the revenue from processed product sales less all processing costs. Mathematically NARP is represented by HH equation (9) and is what they term the net returns function. The net marginal revenue product (NMRP) of M is the incremental contribution to net revenue from each successive unit of M employed. Mathematically, it is the derivative of the HH surplus function (equation (2)) with respect to M. The inverse supply function of M to the cooperative, if such a function exists, is denoted by Pm = Pm(M), Pm'(M) > 0, where Pm is the price received by members (see HH equation (U)). The following conclusions about antecedent work to HH can be established (Sexton 1984): 1. Writers in the vertical integration framework were inconsistent and confused as to whether cooperative members should be perceived as price takers in their dealings with the cooperative. Only price-taking members' behavior may be represented with a supply curve. The alternative assumption invoked was Cournot-Nash behavior, wherein the members recognized the effect of their supply on the cooperative's NARP and NMRP functions but made their supply decisions taking other members' production as given. Writers invoking the CoumotNash assumption were Phillips (implicitly) and Trifon (explicitly). Aresvick and Ohm assumed price-taking behavior. Writers within the theory-of-the-firm framework consistently assumed price taking behavior. 2. The writers in the vertical integration framework who assumed price taking and those of the theory-of-the-firm persuasion collectively derived the same set ofshort-run equilibrium outcomes for a cooperative. These solutions are the following: a) The welfare maximizing solution. The marketing cooperative operates where NMRP(M) = Pm(M). This solution was first offered in the context of a consumer cooperative by Enke, using a theoryof-the-firm framework, and later adapted to marketing cooperatives by Ohm, working within the vertical integration context. b) The price maximizing/ minimizing solution. The marketing cooperative chooses M to attain the maximum value of NARP(M). This solution was first proposed for both purchasing and marketing
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cooperatives by Clark. Phillips also proffered this solution as a long-run equilibrium. c) The zero surplus solution. The marketing cooperative operates where NARP(M) = Pm(M). This solution was first proposed by Gislason within the theory-of-the firm framework and later stated by Aresvick within the vertical integration context.
The Heimberger and Hoos Contribution The Firm vs. Not-a-Firm Controversy. HH argued strongly that cooperatives were viewed appropriately as special types of firms and proceeded to develop a model of marketing cooperative behavior derived from the neoclassical theory of the firm. They were critical of Phillips and others who had pursued the economic integration framework, arguing (p. 290) that "[it] led several writers astray, [and] should be abandoned in favor of recognizing a cooperative enterprise as a decision-making entity." HH justified their position based on the work of organization theorists such as Herbert Simon, whose views were attracting considerable interest at the time within economic theory circles. Indeed, HH present compelling arguments for considering cooperatives as a variant of the neoclassical firm. However, their criticism of the economic integration school is too harsh. Whatever the respective merits ofthe three traditional equilibrium solutions for cooperative behavior outlined above, it is undeniable that the economic-integration theorists independently arrived at each of them. So it is unclear in what sense they were "led astray" by their analytical framework. I Because you can arrive at the same operational solutions from either perspective, my view is that the debate over whether or not a cooperative is a firm is primarily one of semantics. There is not a single, universally accepted definition of a "firm," so, essentially, each group was free to define the term in a sufficiently narrow or broad context so as to either exclude or include the cooperative organizational form. Students ofcooperatives no longer debate this issue, and I hope it is based on the recognition that the issue is not important to understanding cooperatives. 2 Indeed, among the branches of economic theory in existence today, club theory probably provides the best analytical framework for theoretical analysis of cooperatives. Club theory, however, was launched in a seminal article by Buchanan published in 1965, three years after HH. The HeImberger and Hoos Model. The HH paper was written during an era when economic theorists were actively considering alternatives to the traditional profit maximization model. Theories of satisficing behavior and pursuit of possible "managerial goals," such as sales maximization, were gaining popularity. Economic theory has now backed away from these views and once again emphasizes utility or profit maximization goals to underpin decision makers' behavior. Suboptimal behavior emerges as a consequence of attitudes toward risk or imperfect and asymmetric information, rather than from satisficing or managerial discretion. Nonetheless, to appreciate fully the theory constructed by HH, it is important to consider it within the economic climate in which it was written.
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To establish the operating objective for a cooperative, HH wrote that "Investors in the usual type of business enterprise seek a high return on their investments. When agricultural producers jointly undertake the creation of a cooperative association, they seek goods and services provided at cost" (p. 280). This viewpoint leads directly to a model in which the marketing cooperative's operational goal is the maximization of price for members' raw product. A key contribution of HH is the construction of both short- and longrun models for the cooperative and a clear statement of distinguishing characteristics between the short and long run, In addition to the fundamental goal of price maximization, other key assumptions girding both the short- and long-run models are that 1. the cooperative accepts members' entire production, 2. members are treated uniformly, 3. members are bound contractually to deliver their entire production to the cooperative, 4. members act as price takers in dealings with the cooperative, and 5. the cooperative operates at cost-Le., subject to a break-even constraint. The assumptions that apply to cooperatives are rather descriptive ofactual behavior-the cooperative is usually a "home" to member production, and the laws governing cooperatives generally favor break-even pricing and symmetrical treat of members. The assumptions pertaining to members may be somewhat less descriptive. Exclusive sales contracts exist, but in my view are not the norm, and whether members are appropriately modeled as price takers must be evaluated on a case-by-case basis. The additional key assumption in the short-run model is that membership is fixed. HH establish that, as necessary conditions to achieve its price maximization goal, the cooperative must achieve cost minimization for the marketing inputs it employs and profit maximization for the output it sells. Invoking these rules enables HH to derive the NARP or short-run net returns (SRNR) function. Given the assumptions they have set in place, it is very straightforward to then adduce that the cooperative's equilibrium occurs where the NARP function intersects members' aggregate inverse supply curve (HH figure 1). That is, the cooperative pays the maximum price possible, subject to members' supply function and the break-even requirement. This, of course, is the so-called "zero surplus" solution offered earlier by Gislason and Aresvick. This solution does indeed have some desirable properties as an equilibrium. Given the cooperative's price maximization goal, its break-even constraint, and willingness to accept members' entire production, the NARP or SRNR functions represent the cooperative's "demand curve" for members' raw product. The NARP(M) and Pm(M) intersection, thus, effectively represents a supply-demand equilibrium. In the long run, membership is variable, and HH developed alternative long-run models for a cooperative that either maintains open membership or retains the option to restrict membership. A long-run NARP or net returns function differs from its short-run counterpart due to the variabil-
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ity of all marketing inputs. A restricted membership cooperative effectively chooses M by regulating membership so that members' aggregate supply curve intersects the long-run NARP function at its maximum. The cooperative thus pays members the maximum price possible for M subject to covering costs. An open-membership cooperative, however, does not choose M and acts much like the cooperative in HH's short-run model by operating wherever NARP intersects with the aggregate supply curve of all who wish to join the cooperative. Importantly, HH note that when adding members reduces Pm to existing members, open membership is inimical to the extant members' interests. They speculate that open vs. restricted membership in these cases may depend on whether management or the membership are in effective control of the cooperative. They further note that when NARP is increasing, new members cause price to rise, thus benefiting extant members.
Evaluating the Heimberger and Hoos Contribution Several writers in the past fifteen years have been somewhat critical of the HH models. This group includes LeVay (1983a), Lopez and Spreen (1985), Sexton (1986), and Fulton (1986). At the outset it should be stated clearly that the short- and long-run solutions adduced by HH are correct within the model frameworks they posited. Assertions to the contrary are incorrect. Those who advocate alternatives to the HH solutions must argue that one or more of the HH assumptions are inappropriate. The key problem with the HH short-run solution is that it does not maximize the welfare of the given group of members. As is well known, the welfare maximum occurs where NMRP(M) = Pm(M), Le., the intersection of NMRP and members' supply curve. This, of course, is the Enke-Ohm solution. That HH don't attain the overall optimum is a simple consequence oftheir assumption that the cooperative offers a single price to its members and is subject to a break-even constraint. These assumptions effectively compel the cooperative to set price and output along the NARP curve, which is suboptimal except at the level of M where NMRP = NARP. The HH solution is, in fact, a very simple example of welfare maximization subject to constraint, a class of problems known generally as Ramsey optima. The HH critics and Enke-Ohm advocates offer alternative prescriptions, all involving relaxation of one or more of the HH assumptions, whereby the preferred solution may be attained. The HH and Enke-Ohm solutions are usually depicted as occurring to the right of maximum NARP. In this case, Enke-Ohm can be attained as part of an explicit rationing scheme by the cooperative (LeVay 1983, Lopez and Spreen 1985), Le., the cooperative no longer acts as a "home" for members' production. Alternatively, it can be attained by offering the members the price associated with the NMRP(M) and Pm(M) intersection. This price will not satisfY a break-even condition, so a deficit or surplus must be funded through side payments that are not tied directly to patronage (Zusman 1982 and Sexton 1986). There should be no confusion surrounding the alternative cooperative equilibria. Enke-Ohm is the first-best, short-run (fixed membership) solu-
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tion and HH is a Ramsey optimum. So from a normative perspective EnkeOhm is preferred. From a behavioral perspective the key issue is whether the HH assumptions are too restrictive. I tend to side with the critics. First, as a fixed-membership organization, a cooperative is ideally suited to employ the multi-part prices needed to attain the first-best optimum. Second, we do observe instances where cooperatives restrict their members' deliveries. The fact that we don't see it very often may indicate that cooperatives seldom operate to the right of maximum NARP.3 Finally, I find it very consistent with the HH view of the cooperative as a firm and a conscious decision making entity that a cooperative manager and/or board of directors could put forth the price and output policies needed to achieve the overall optimum. The HH analysis of the long run is set on a comparatively strong foundation. The closed-membership model leads the cooperative to operate at the maximum of NARP, the overall price maximizing solution offered first by Clark and Phillips. If supply is restricted to cut NARP at its maximum, this solution also represents the NMRP and Pm(M) intersection, and, as such, is the confluence of the three traditional solutions offered for cooperatives. Closed membership is an option for all cooperatives except those that provide an essential service such as electricity. so it is hard to see how self-interested members would allow an open-membership policy when it contributed to diminishing extant members' returns. Even if management perSisted with such a policy, a subgroup of the membership would have incentive to break away and form an alternative cooperative that operated nearer to the maximum of NARP (Sexton 1986). Additional alternatives to the HH model emerge as other assumptions are modified. Assuming Cournot-Nash, rather than price taking behavior by members, generates a different set of equilibrium conditions. For example, see Ireland and Law (1983). Studying potential members' decisions involving cooperative membership vs. assuming that members are bound contractually to the cooperative leads naturally to the game-theoretic approaches studied by Staatz (1983) and Sexton (1986). The development of these alternative models does not imply weakness of the HH or other traditional models. Rather, it reflects the application of advances in economic theory to cooperatives and, more importantly, the richness of the environments in which cooperatives operate and the need to have alternative models that apply in different settings. Just as a single model cannot hope to depict the range of behavior exhibited by for-profit firms, so too are multiple models needed to represent the behavior of cooperatives. Whereas the many models of oligopoly firms' behavior were once cited as a weakness of oligopoly theory, they are now recognized as a strength and a reflection of the richness and diversity of oligopoly environments. The same reasoning in my view should apply to models of the cooperative. Multiple models are an asset, and the researcher must consider which model is best on a situation-by-situation basis. I hope this discussion might contribute to that choice by indicating clearly the assumptions on which the HH model was based vs. those under which alternative solutions emerge.
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Summary My goal has been to provide a balanced treatment of HeImberger and Hoos' contribution. I believe this is the best route to recognizing a landmark contribution. Let me summarize by restating briefly what I believe to be the main contributions of the HH paper. First, it represents a breath of fresh air in the development of cooperative theory. This is because it very clearly sets forth a list ofassumptions on cooperative and member behavior and then derives correctly the equilibrium behavior given those assumptions.ln this sense, it can be considered to be the first completemathematical model of behavior of an agricultural cooperative. Second, it provides a very clear basis for distinguishing short- vs. long-run behavior in a cooperative. Alongwith the companion work by HeImberger (1964) it establishes a clear, policy-relevant distinction between the behaviors ofcooperatives that maintain open membership vs. those that restrict membership. Third, by establishing a clear mathematical framework with carefully stated assumptions, HH set the stage for further advances in the theory of cooperatives that took place in the 1970s and 1980s.
Notes I. CUriously, HH were aware that their proposed equilibrium solution was the same as that offered by economic-integration proponent Aresvick (see HH note 24). 2. The vertical integration framework, however, is very useful for understanding the economic role cooperatives play within a market economy. 3. When a cooperative lacks sufficient volume to attain maximum NARP, the Enke-Ohm solution involves greater output than the HH solution. Although this is not the situation typically depicted, it may be the norm, given the small size of many cooperatives relative to their for-profit counterparts.
References Aresvick, O. 1955. Comments on 'Economic nature of the cooperative association.' Joumal ojFarm Economics 37:140-4. Buchanan, J. 1965. An economic theory of clubs. Economica 32: 1-14. Clark, E. 1952. Farmer cooperatives and economic welfare. Joumal oj Farm Economics 34:35-51. Emelianoff, l.V. 1942. Economic theory ojcooperation. Washington: l.V. Emelianoff. Enke, S. 1945. Consumer cooperatives and economic efficiency. American Economic Review 35: 148-55. Fulton, M. 1986. The theory of marketing co-operatives revisited. University of Saskatchewan, Saskatoon, Saskatchewan: Mimeographed. Gislason, C. 1952. Cooperatives and resource allocation. Joumal ojFarmEconomics 34:558-64. HeImberger, P.G. 1964. Cooperative enterprise as a structural dimension of farm markets. Joumal oj Farm Economics 46:603-17. HeImberger, P.G., and S. Hoos. 1962. Cooperative enterprise and organization theory. Joumal oj Farm Economics 44:275-90. Ireland, N.J., and P.J. Law. 1983. A Coumot-Nash model of the consumer cooperative. Southem Economic Joumal49:206-16. LeVay, C. 1983a. Some problems of agricultural marketing co-operatives' price/ output determination in imperfect competition. Canadian Joumal ojAgricultural Economics 31: 105- 10.
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LeVay, C. 1983b. Agricultural co-operative theory: A review. Journal oJAgricultural Economics 34: 1-44. Lopez, RA., and T.H. Spreen. 1985. Co-ordination strategies and non-members' trade in processing cooperatives. Journal ojAgricultural Economics 36:385-96. Ohm, H. 1956. Member behavior and optimal pricing in marketing cooperatives. Journal oJFarm Economics 38:613-21. Phillips, R. 1953. Economic nature of the cooperative association. Journal ojFarm Economics 35:74-87. Robotka, F. 1947. A theory of cooperation. Journal oJFarm Economics 29:94-114. Sexton, RJ. 1984. Perspectives on the development of the economic theory of cooperatives. Canadian Journal ojAgricultural Economics 32:423-36. Sexton, R.J. 1986. The formation of cooperatives: A game-theoretic approach with implications for cooperative finance, decision making, and stability. American Journal ojAgricultural Economics 68:214-25. Staatz, J.M. 1983. The cooperative as a coalition: A game-theoretic approach. American Journal oj Agricultural Economics 65: 1084-89. Staatz, J.M. 1987. Recent developments in the theory of agricultural cooperation. Journal oj Agricultural Cooperation 2:74-95. Trifon, R 1961. The economics of cooperative ventures-Further comments. Journal oJFarm Economics 43:215-35. Zusman/ P. 1982. Group choice in an agricultural marketing cooperative. Canadian Journal oj Economics 15:220-34.
