385

CO-ORDINATION STRATEGIES AND NON-MEMBERS’ TRADE IN PROCESSING CO-OPERATIVES Rigoberto A. Lopez and Thomas H. Spreen* Rutgers University and University of Floridat

This paper addresses three major issues set forth by LeVay (1983). These may be summarised as (1) the conflict of interests of the individual vis-a-vis the co-operative, (2) the arrangements or contract provisions which may be used to increase the efficiency of the co-operative, and (3) modelling of the co- operative trade with non-members ond how members can derive maximum benefit from it.

A co-operative association is an organisation owned and operated by its members and operates solely for their benefit. Even though the basic behavioural motivation of increased well-being is what induces a group of farmers to ‘co-operate’ by forming a co-operative coalition, individually they are likely to engage in independent, non-co-operative behaviour. Olson (1971) points out that unless there is coercion or some type of device to make individuals act in their common group interests, self-centred individuals will not act in their common group interests.

The unattainability of an optimal co-operative operation due to the individualistic behaviour of the members has been shown by Trifon (1961) and Eschenburg (1971). Knutson (1966) and Zusman (1982) suggest inherent inefficiency in co-operative operations. This paper presents a perspective in the same vein as those works. In addition, co-ordination arrangements which may induce members to behave in their common interests are outlined.

The other issue-non-members’ trade-has been ignored in co-operative modelling (LeVay, p. 13), even though most agricultural co-operatives have active trade with non-member farmers. Models assume ‘closed’ marketing co- operatives in which implicitly or explicitly the only source of commodity supply is that from members and the only destiny of members’ supply is the co-operative (e.g., Helmberger and Hoos, 1962). This paper develops a theoretical analysis to determine optimal interactions with markets outside the co-operative and also probes into commodity quality and payment issues. The model developed draws from the works of Helmberger and Hoos, LeVay, and Trifon.

A Mathematical Model of Processing Co-operatives Consider a processing co-operative which transforms a homogenous raw product Y into a finished product Z. The co-operative sells Z at price Pz. Pz may or may not be a function of Z depending on market share of the co-

The authors are grateful to Robert D. Emerson, Lee F. Schrader. A. Robert Koch and an

t Address for correspondence: Deparrment of Agricultural Economics and Marketing, Cook anonymous reviewer for their helpful comments.

College, Rurgers University, New Brunswick, New Jersey, 08903.

386 RIGOBERTOA. LOPEZ ANDTHOMAS H . SPREEN

operative. The net revenue of the co-operative, called co-operative surplus (0, is

CS = PiZ - C(Z,U) - FCC, ( 1 )

where C(2, v) is the variable cost of transforming Y into Z. I/ is a vector whose elements are the prices of other inputs, and FCC is the fixed cost of the co- operative. Assume there are rn growers (i = 1, . . . ,m), membership is closed, and the co-operative and its members do business exclusively with each other. This assumption is relaxed later. Since the co-operative is organised solely for the benefit of its members, it must distribute all co-operative surplus back to the members. Thus,

where PAY; is the payment to grower i for the delivery of raw product y;. Assume that the members are identical so that yi = y, = y , where y is the supply of an individual member. Total raw product to be processed by the co- operative is Y = z y ; = my for all i. Following Helmberger and Hoos, let Py denote the member compensation per unit of Y delivered to the plant defined as the average net revenue product (ANRP). Thus, PA Y; = Pyy,, and using (2),

p , = = CS = ANRP. - my Y (3)

Co-operative Behaviour and Optimal Volume Although a co-operative member may have multiple objectives, including non- pecuniary benefits, i t is assumed that a typical co-operative member strives solely to maximise net returns,

where c(y, W) is the variable cost of producing y with variable inputs whose prices are denoted by the vector W, FC is the fixed cost of the grower, and Py is defined above. Under the assumption of identical membership, there is equivalence between maximizing each member’s profits and maximizing total members’ profits. The first order condition for profit maximization is

Equation ( 5 ) says that the individual should equate the marginal value of the delivery and marginal costs in order to attain maximum net returns. Two sub- cases arrive with respect to members’ behaviour. These are individualistic or myopic behaviour when members behave as price takers and the co-ordinated co-operative case in which members’ deliveries are co-ordinated so as to jointly maximise profits. The rationale behind myopic behaviour is discussed later.

CO-OKI>INATION & NON-MEMBERS’ .TRADE IN PKOCESSIN(; CO-OPERATIVES 387

I n the myopic case, members are driven by strategic individualistic rationality and thus behave solely as quantity adjusters, regarding P as a fixed, exogenous variable. I f members behave in a myopic manner, set gPy/ay equal to zero and solve (5) for y to obtain a member’s supply function. The aggregation of these functions is the members’ supply function. Assuming that such a function is monotonic. its inverse form is

Myopic co-operation equilibrium is established where (6) intersects (3 ) . This point corresponds to the co-operative equilibrium identified by Helmberger and Hoos.

Next, consider the case o f a co-ordinated co-operative in which members behave in a collectively rational manner. I f members recognise their inter- dependence, then they fu l ly internalise the impact of their output level on the price they receive. Differentiating (3) with respect t oy gives

so that pY Y y = - - . ap acs

dY a y

Substituting (8) into (5) gives

Equation (9) implies that for maximum profits the marginal cost of producing y incurred by a member must equal the co-operative marginal revenue product (MRP). The corresponding collective solution is the point at which the members’ supply intersects the marginal product curve. This represents a co-ordinated equilibrium which corresponds to the co-operative equilibrium identified by Phillips (1953) and Eschenburg. This point has also been identified graphically by LeVay and is consistent with the solution found by Zusman when the co-operative uses a marginal cost pricing rule, a necessary condition for Pareto optimality under competitive conditions.

In Figure 1, myopic and co-ordinated equilibria are depicted. Myopic equilibrium occurs at point e where the members’ supply function (S) inter- sects the average net revenue product function (ANRP) of the co-operative. Co-ordinated equilibrium occurs at point c, where the members’ supply curve intersects the marginal revenue product curve (MRP) of the co-operative.

388 RIGOBERTO A. LOPEZ AND THOMAS H . SPREEN

The myopic co-operative processes mye and pays P$, while the co-ordinated co-operative processes my* and pays P;.

Figure 1. Myopic and Co-ordinaled k:quilihria

L I 1

my- mye

TOTAL RAW PROOUCT

Consider the members’ benefits at co-ordinated equilibrium as compared to myopic equilibrium. Total profits are co-operative surplus (total payments to members) less members’ total costs. Following Just et al. (1982) in measuring producers’ welfare changes, the change in total profits or in producers’ quasi- rents from moving to a co-ordinated equilibrium from a myopic equilibrium in Figure 1, is given by the cross-hatched area less the solid shaded area.* If the raw product is available in the open market, the co-operative may further enhance its performance by interacting with the raw product market. This case will be discussed later.

Arrangements to Ensure Co-ordina fed Behaviour Myopic equilibrium is a consequence of individualistic behaviour. Such behaviour results from a member’s dilemma of whether to ‘free ride’ (and thus individually increase gains when other members are behaving for the co- operative welfare), or to protect himself when other members are attempting to free ride. To illustrate this point, define

* Quasi-rents are given by profits plus the members’ fixed costs. At myopic equilibrium, CO- operative surplus is given by Pcmy . The area below the supply curve represents the total variable costs of the members. Thus, the area below P a n d above S, measures the total quasi- rents that accrue to the members at a myopic equilihum. A similar welfare measurement technique applies for a co-ordinated equilibrium.

CO-ORDINATION & NON-MEMBERS’ TKADE I N PROCESSING COOPERATIVES 389

I f d is positive (e.g., co-ordinated equilibrium at point c in Figure l ) , a myopic member has an incentive to increase deliveries; if a is negative, that member would cut back on deliveries (e.g., point c i n Figure 3). As all members behave individualistically, an equilibrium such as point e in Figures 1 and 3 is ensured where members’ supply intersects A N R P curve and 0 is zero. The rationale for myopic behaviour has been noted by Eisenstat and Masson (1978) when they refer to the tendency of marketing co-operatives to oversupply when there are highly profitable entry opportunities in a market and the ‘internal supply expansion’ when co-operatives earn excess profits. The pursuit of self-interest produces an outcome that can be improved through co-operation. This behaviour, from a conceptual standpoint, is the CO- operative analogy of the Prisoner’s Dilemma game.

Axelrod (1984) outlines three approaches to promote mutual co-operation without central authority under a Prisoner’s Dilemma situation: making the future more important than the short run; changing the payoffs to the participants; and teaching players values and facts that will promote CO- operation. In the context of ou r short-run static analysis, three approaches are envisioned as potential instruments to ensure a co-ordinated co-operative operation:

Given m members, impose a delivery quota of y = y * on each member. In this case, the members’ supply curve becomes vertical at an aggregate supply level of my*. An analogous instrument is the institution of processing rights to be sold by the co-operative. In the context of this model, the co-ordinated equilibrium would be achieved i f the co-operative sells each member the right t o process y*. An interesting modification of this approach, in the case of heterogeneous members, is to vest a member with the right to market y;, where the total rights correspond to the co-ordinated raw product volume, and then let them trade the rights.

Educate the members as to the effect of co-ordination. However, if the optimal volume is not enforced, a ‘conscience-raising’ program seems rather utopic since an individual would have an incentive to free ride if a co-ordinated operation is initially established. Subsequent retaliation among the members would establish a myopic equilibrium.

Impose an internal tax on deliveries exceeding y*. a penalty at least equal to the difference of q*received at optimal capacity use and the grower’s marginal cost of producing y* (a unitary tax equal or greater than ? in equation (10)). In this way no individual gains occur beyond y*, and the incentives to cheat would be eliminated. Note that this tax is not intended to generate revenues. By applying a two-tier pricing scheme, a kink in the ANRP curve is made at co-ordinated equilibrium.

Zusman proposes marginal cost pricing along with side payments (arbitrary or allocated under some criteria) for an efficient co-operative cost allocation. The corresponding approach here is to set P equal to MRP at my* and allocate the remaining co-operative surplus b l s i d e payments. However, no voting equilibrium among the members exists to establish the allocation of the side payments (Zusman).

In the case where the co-operative plant is underutilized (operating in the rising region of ANRP), the arrangements to ensure co-ordinated behaviour are symmetrical: ( I ) supply control by imposing a minimum delivery volume of y = y* on each member; (2) educate members on the benefits of expanding volume; and (3) impose a unitary tax at least equal t o the absolute value of ? in equation (10). Note that for this case, a is negative.

1 . Supp/y conrrol srraregies.

2 . Education.

3 . Pricing Sfrafegies.

390 RIGOBERTO A. LOPEZ AND THOMAS H. SPREEN

The Shape of the ANRP Curve The impact of members’ supply on co-operative surplus and the price they receive is intimately related to the shape of the ANRP curve. The shape depends on technology of production (economies of scale) or on market power of the co-operative in the product market (Youde and Helmberger, 1966). I t is instructive to analyse the relationship among fu and CS and the level of members’ deliveries. Transform both sides of (3) to natural logarithmic units and take the derivative on both sides with respect to the log of Y to obtain

where q p = Y i s the elasticity of raw material price with respect Y , Y a y p y

to members’ deliveries and qcs, y = ~ - is the elasticity of co- operative surplus with respect to membg$ deliveries. Equation ( I 1) depicts the relationship between the sensitivity of co-operative surplus and member’s price to relative changes in deliveries. Of,,, is zero when rlcs, Y equals one at maximum ANRP. V,., y is positive (negative) when ANRP rises (declines) with members’ deliveries resulting from llcs, Y being greater (smaller) than one. This implies the existence of substantial economies (diseconomies) of scale and/or high (low) product price elasticity of demand faced by the co- operative. Accordingly, the greater hcs y - 11, the greater the impact of co- ordination and the greater the amount of raw material adjustment required to achieve a co-ordinated equilibrium.

a y

Interaction with the Raw Product Market A processing co-operative can enhance its performance by trading with non- members through buying or selling raw product so as to use the processing plant efficiently. LeVay points out that ‘the organisation earns profits from such trade, which after tax constitutes a welcome source of reserve funds,’ (p.23). If there is an open market for the raw product, a crucial question arises: how much should the members produce, and how much raw product should the co-operative buy or sell in the open market in order to maxirnise members’ profits? The literature has not considered this case, but rather has considered raw product supply change solely through membership adjustment (Youde and Helmberger) or price discrimination (Eisenstat and Masson).

Let the total raw product processed by the co-operative, Y , be equal to

Y = Y,, + Yo, (12)

where Y,,, is the total raw product supplied by the members. Thus Ym = my. Yo is the amount of raw product transacted by the co-operative in the open market. The quality of Yo is assumed to be identical to Y,,,. I f Yo is positive, the co-operative buys raw product in the open market. If Yo is negative, the co- operative sells part of the members’ raw product in the open market. If Y, equals zero, the co-operative does not interact with the raw product open market, or simply, such a market does not exist. Assume the price of the raw product in the open market is Po. Co-operative surplus under this strategy is

CO-ORDINATION & NON-MLMHEKS’ TRADE I N PROCESSIN(; (‘0-OPERATIVES 39 1

where the last term stands for expenditures (revenues) on raw material transacted outside the co-operative. Since Y,,, and Y,, are identical in quality, one can rewrite

cs, = cs - POYO, (14)

and assert

Note that

Allowing for open market activities, members’ total profits are given by

and the first order conditions for the maximisation of (1 7) are

and

The same conditions are obtained if one maximises individual members’ profits who behave in a co-ordinated manner. Using (16), (18) and (19), the optimal condition for individual production of y is

ac - = Po’ aY

392 RICOBERTO A. LOPEZ AND THOMAS H . SPREEN

An individual member will supply where his marginal cost of production equals the raw product price in the open market. At the aggregate level, the corresponding solution is the point at which Po intersects the members’

Condition (19) says that the co-operative should buy or sell Yo up to where its marginal co-operative surplus is exhausted. Using (15) and then (16), one can rewrite (19) as

supply.

acs ay- = Po. To use the plant efficiently, the amount of raw product to be processed in

the co-operative should be where its marginal co-operative surplus equals Po. By default, the amount the co-operative should buy (sell) in the open market is the difference between this amount and that supplied by the members from condition (1 8).

In summary, define Pc to be price where the members’ supply curve intersects the marginal net revenue product curve (co-ordinated equilibrium). If Po is less than P,, the co-operative should buy raw product in the open market. If Po exceeds P,, the co-operative should sell part of the member’s deliveries in the open market. If Po equals P,, the co-operative should not interact with the open market. These cases correspond to those of Po, Po’ and Po’ I , respectively, in Figure 2.

Figure 2 Optimal Marketing Strategies at Alternative Prices of the Raw Product in the Open Market

g p;

j Po 0 Q I ’ Buv \ ANRP

Underutilised Co-operative Plant A co-operative plant is underutilised when it operates in the rising region of

the ANRP curve. Thus, there exist economies of size or market power yet to be exploited by the members. LeVay points out three sources of supply to use more fully the co-operative plant: greater patronage by existing members, trade with nonmembers, and addition of new members. Greater patronage would be required under co-ordinated equilibrium (point ‘c’ Figure 3) than in a myopic co-operative (point ‘e’). The other two options for volume expansion are also compared in Figure 3.

CO-ORDINATION & NON-MEMBERS’ TRADE IN PROCESSING CO-OPERATIVES 393

Figure 3 Membership Expansion and Purchase of Raw Product in the Open Market as Strategies for an Underutiliwd Co-operalive Plant

9 1 2

TOTAL RAW PROOUCT

Let rnl denote the original number of members. An influx of mz-rnl new members shifts the raw product supply from S to S’ and increases the price received by existing members (to P2), and therefore the amount supplied by each member increases to Qz). With membership adjustment only, this corresponds to the optimal membership (maximum per capita profits) where profits of the ml existing members are increased by efPIP2. This point of maximum raw product price is where, according to Youde and Helmberger, a restricted membership co-operative should operate.

The other option available to the co-operative is to purchase raw product in the open market. The advantage of raw material purchases over expanding membership depends upon the price of the raw product in the open market. If the co-operative buys in the open market, it would not only capitalise on economies of scale of the co-operative plant, but also it will profit from the marginal value of raw material bought outside which exceeds its marginal acquisition cost (Po) - a surplus that would have to be paid to the would-be members if membership expansion occurs. The co-operative , however, may incur taxes on that part of the margin. In Figure 3 , the co-operative should buy Yo in the open market (at price Po) and members should produce Y,,, in order to maximise profits.

Variable Raw Product Quality This section addresses some of the complications that arise if raw product quality or level of characteristics is allowed to vary. The final commodity produced by the co-operative (Z) is assumed to be homogeneous, so that we abstract from the effect of quality variation in the final product.*

Let the raw product possess a single, continuous, and unambiguously measurable characteristic denoted by 4, whose level can be influenced by the growers. Further, q is measured as a ‘good’ so that the higher the level of q the

Implied in the analysis that follows is that the raw product identity, in terms of relevant characteristics, is kept throughout its processing. This excludes the case where the raw product undergoes a blending process in which the product identity is lost since in this case the nature of the finished product depends also on the choice of characteristics of other malerial that are mixed with the members’ raw product.

394 RICOBERTO A. LOPEZ AND THOMAS H. SPREEN

higher the co-operative surplus generated. For example, q could refer to ease of processing or the content of a desirable characteristic. Let the growers be identical with a variable cost function given by c = *,q) and the marginal costs of the arguments of c are positive and non-decreasing.

Allow for an arbitrary payment function to distribute the co-operative surplus back to the members. The payment per unit of y is defined to be P= P(Aq), where A is a pooling parameter. The term 'pooling' is intended to denote the averaging of co-operative costs and revenues associated with the characteristic. Thus, A = O if q is pooled and A = I i f i t is not. Allow the function P to be homogeneous of degree one in A so that aP/dq=AaP/aq. I t must be kept in mind that under member homogeneity, raw product supply (y) and the level of characteristic q will be the same across members. However, total raw product and characteristic level may be different across payment systems.

Let q" be the lower limit of the characteristic whose imputed value is given by p. Then, a typical member attempts to maximise

Using the Kuhn-Tucker conditions, E for (22) if they satisfy*

and Frepresent an optimal solution

a n - a4

' 4 = 0,

ax = aa 9" - -

-- Y . 4. p" 0.

* In what follows it is assumed that the production technology is characterised by non-jointness in the two outputs: characteristic level and quantity of the raw product. This implies that the marginal cost of each output is independent of the level of the other output (Hail, 1973).

395 CO-ORDINATION & NON-MEMBERS' TRADE IN PROCESSINti CO-OPERATIVES

Assume an interior solution for y . I f the payment function ignores 4 (A = 0), the first term on condition (25) vanishes and the member produces a t 4 = 4", at minimum cost level since he does not perceive a direct pay-off of producing higher levels of 4. The above system of equations is the heterogeneous-raw product analogy of ( 5 ) . If minimum levels of 4 are set such that 4' = q*, a co-ordinated-quality solution can be attained solely with the imposition of appropriate minimum levels of acceptable characteristics.

For the fully accurate case, A = 1, let equality hold in (23) and (25) and ignore the rest of the system (assume an interior solution for y and 4). Maximum profits are reached when y and 4 are set where their marginal cost o f production incurred by the members equals their marginal revenue product. Even though fully accurate pricing co-ordinates the members with respect t o quality level of q, it does not guarantee a co-ordinated operation with respect t o the volume of deliveries, that is, a state of maximum total and individual profits.

The effect of producing higher quality raw product from a more accurate payment system on quantity is indeterminate since an increase in quality implies an increase in both members' production costs (which decreases supply) and co-operative surplus (which increases ANRP) . In Figure 4, the effect of increasing quality from 41 to 42 is illustrated. For a supply that is relatively insensitive (sensitive), the increase in quality may lead to a new equilibrium at point 2 (point 3) with a net increase (decrease) in raw product amount.

Figure 4 Equilibria Localions fur Two Quality Levels

P

TOTAL RAW PRODOCT

Conclusion

The purpose of this paper is to develop a n analytical framework for individual and collective behaviour in processing co-operatives. The analysis focuses on co-ordination of members' deliveries and trade with markets outside the co- operative. Several conclusions generated by the model are sumrnarised below.

Self-centred behaviour of co-operative members leads to a stable suboptimal equilibrium. A preferred co-ordinated equilibrium (greater members' net

396 RIGOBERTO A. LOPEZ AND T H O M A S H. SPREEN

returns) can be attained by inducing compliance through supply control strategies, two-tier pricing schemes, or education of members.

A co-operative can attain greater net returns for its members by trading with non-members than by any other strategy involving members only. To use the plant efficiently, the co-operative should engage in buying or selling raw product to operate where marginal revenue product equals the open market raw product price. When variable raw product quality is considered, the analysis shows that more accurate payment systems lead to increased quality but not necessarily to more raw material supply by the members. Furthermore, a fully accurate payment system does not guarantee maximum members' profits.

Perhaps, the most significant drawback of the analysis is the assumption that members are identical. Although the assumption facilitates mathematical derivations, it clearly side-steps equity, redistribution, and other conflicts of interest among members. Another important limitation is that the analysis does not entail the cost of establishing the proposed co-ordination strategies. I f such costs are greater than potential benefits, a second-best solution or suboptimal operation of the co-operative may be preferred.

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