Endogenous Market Structure and the Cooperative Fir Brent Hueth and GianCarlo Moschini Working Paper 14-WP 547 May 2014 Center for Agricultural and Rural Developent Iowa State University Aes, Iowa 50011-1070 www.card.iastate.edu Brent Hueth is Associate Professor, Agricultural and Applied Econoics Director, University of Wisconsin-Madiso. E-ail: hueth@wisc.edu. GianCarlo Moschini is Professor of Econoic, Iowa State University. E-ail:ischini@iastate.edu. This publication is available online on the CARD website: www.card.iastate.edu. Perission is granted to reproduce this inforation with appropriate attribution to the author and the Center for Agricultural and Rural Developent, Iowa State University, Aes, Iowa 50011-1070. Iowa State University does not discriinate on the basis of race, color, age, ethnicity, religion, national origin, pregnancy, sexual orientation, gender identity, genetic inforation, sex, arital status, disability, or status as a U.S. veteran. Inquiries can be directed to the Interi Assistant Director of Equal Opportunity and Copliance, 3280 Beardshear Hall, (515) 294-7612.
Endogenous Market Structure and the Cooperative Fir Brent Hueth a and GianCarlo Moschini b Abstract When the threat of entry by followers includes cooperative firs, the axiu fixed cost that a profit axiizing leader can endure is endogenous. The aggressive strategy required for entry deterrence curtails the leader s expected profit and can discourage its initial entry. In such circustances a cooperative fir ay yet be viable, despite having a cost handicap and no firstover advantage. Keywords: cooperatives, endogenous entry, entry deterrence, nonconvexity. JEL codes: L22, P13 a Departent of Agricultural & Applied Econoics, University of Wisconsin-Madison, Madison, WI 53706-1503 b Departent of Econoics and Center for Agriculture and Rural Developent, Iowa State University, Aes, IA 50011-1070 1
1. Introduction Industrial organization has long recognized that arket structure is the result of rational entry decisions by firs vis-à-vis the profit opportunities present in a arket. Mankiw and Whinston (1986) show that, with fixed set-up costs, the free entry equilibriu in a large class of oligopolistic odels typically exhibits an excessively large nuber of active firs. An eerging literature has introduced the Stackelberg notion of leadership in this endogenous arket structure (EMS) context, where one fir has the opportunity to ake its entry decisions before the other firs see Etro (2013) for a recent survey. A general insight fro this fraework is that a leader facing endogenous entry tends to behave ore aggressively (relative to the situation when the set of followers is predeterined). In this context the leader is ost interested in influencing the entry decision of the followers, rather than their production/price decision. Specific results depend on the nature of the odel. But in general the excessive entry result disappears, as it is coon to find that equilibriu entails entry deterrence, i.e., there is only one fir (the leader) in the arket (Etro, 2008). In this paper we extend the EMS fraework by posing that the leader, in addition to being concerned about entry by other profit axiizing (PM) firs, also faces the threat of entry by coalitions of consuers (i.e., cooperative firs ). In this context, the case of large fixed entry costs is of particular interest. For large enough fixed entry cost, even a fir unconstrained by the threat of subsequent entry cannot ake positive profits. This situation represents one instance in which the excessive entry result noted earlier ay not apply, i.e., equilibriu entry is of the too few by one kind (Mankiw and Whinston 1986): consuer surplus ay be sufficient to cover all (variable and fixed) costs, yet no fir finds it profitable to enter (under the standard assuption that a onopolist does not capture the full social surplus generated by entry). In such a case a cooperative fir ay feasibly produce, however, if its ebers bear a portion of fixed cost through a ebership fee or other lup su contribution. More interesting is the fact that the prospect of entry by a cooperative fir affects the strategy of the leader. Extending Etro s (2008) fraework, the leader ust consider entry deterrence strategies not only with respect to other firs, but also with respect to the possible entry of cooperative firs. Entry deterrence of consuer coalitions by an incubent onopolist was extensively analyzed by Sexton and Sexton (1987) and Innes and Sexton (1993). Deterrence of consuer coalitions calls for an even ore aggressive behavior than that required to deter other PM firs. The iplication of this observation for the EMS proble analyzed here is that, whereas the leader can succeed in securing the arket as a onopolist by exploiting its first over advantage, entry deterrence liits the profit that can be realized. This liits the range of fixed cost that can be borne by the leader, which in turn expands the region of paraeters where the cooperative fir enters in response to the absence of a PM fir. 2
2. EMS and entry deterrence We consider the siplest possible fraework to illustrate the result of interest. For all firs, the technology of production is represented by the cost function C( Q) = cq + K where c > 0 is the constant arginal production cost, and K > 0 is the fixed setup cost that is required to enter the arket. Following Etro (2008), the odel is a three-stage gae. In stage 1, the PM fir decides whether or not to enter after considering the prospect of copetition by followers (other PM firs or coalitions of consuers). In stage 2, if the leader PM fir has entered, it will play the entry-deterrence strategy as needed. For soe doain of K, it turns out that other firs do not enter, the consuer coalition does not for, and the leader operates as the only fir in equilibriu. In stage 3, if the leader PM fir has not entered, a consuer coalition ay for, without having to face deterrence. For the deand side of the odel, for concreteness we assue that there are N identical consuers with quasilinear preferences, such that the aggregate deand function is Dp ( ) = a p, with individual deand functions given by D( p) = Dp ( ) N, i= 1,2,..., N. i If the leader can behave as an unconstrained onopolist, given the assued aggregate deand function, then it solves ax ( a p)( p c) K p yielding the standard onopoly price p = ( a+ c)2 and production level Q = ( a c)2, provided K is not too large. The onopolist earns positive profit as long as K K where K is the axiu fixed cost that can be sustained by a onopolist unconstrained by the threat of entry: (1) ( ) 2 K a c 4 In Stackelberg copetition for hoogeneous goods where, upon entry, firs copete in quantities, the leader can deter entry of other PM firs by producing Q = a c 2 K, K ( a c)4 K (Etro, 2008). The liit price of this equilibriu is provided ( ) 2 L 3
(2) p = c + 2 K L Reark 1. The need to deter entry of other PM firs does not affect the axiu level of fixed cost that the leader can bear (because K < K ). 2.1. The cooperative fir Owing to their distinctive governance structure, cooperative firs behave differently than PM firs, but in ways that eschew a single odeling approach. The literature has ephasized various circustances in which cooperatives ight ake production decisions that are ore or less efficient than a PM fir (Hansann 1994, 2013; Hart and Moore, 1996; Mikai, 2011). They are ore responsive to the consuption needs of their ebers and thus pursue ore efficient production plans, but they also have coordination and governance costs that a PM fir does not face. We follow Innes and Sexton (1993) and capture such governance costs unique to cooperative firs by a function Gn ( ) that is increasing and concave in the size n N of the cooperative. Effectively, therefore, a cooperative fir faces the higher fixed cost of entry K+ Gn ( ). It is assued that the objective of the cooperative is to axiize the consuer surplus of its ebers, net of all production and governance costs. Hence, the cooperative fir would produce the efficient aount Dc (), which is then allocated to ebers by arginal cost c pricing p = c. Furtherore, if arket conditions are such that a coalition of consuers is fored, then it is reasonable to focus on the case n = N(i.e., the grand coalition) because [ K+ Gn ( )] nis decreasing in the cooperative size. In what follows, therefore, we siply write G rather than GN ( ) for the total governance cost of the cooperative. The foregoing structure is the siplest representation of the cooperative fir that perits us to illustrate the ain result of the paper. We note, however, that an analogous result can be obtained with ore general representations of the cooperative decision proble, for exaple one which allows for consuer heterogeneity and where decision are ade by ajority voting, as in Hart and Moore (1996). Given efficient production, the cobined payoff of the cooperative fir is (3) ( a c) 2 U = K G 2 Hence, the axiu fixed cost that the co-op fir can sustain and still be viable is 4
(4) c ( a c) 2 K G. 2 2.2. Deterrence of cooperative entry Deterrence of a consuer coalition by an incubent onopolist who relies on a policy of unifor price offers was considered by Sexton and Sexton (1987). Innes and Sexton (1993) extend this analysis by allowing the incubent fir to pursue a divide-and-conquer entry deterrence strategy, leading to a for of price discriination. They fully articulate two forulations of such a strategy. Our approach here is consistent with their odel II, which aintains the appealing condition that consuers can evaluate their individual offers vis-à-vis the gains fro various possible coalitions (which, inter alia, rationalizes the focus on the grand coalition invoked earlier). When all consuers have identical deands, as in our case, the entry-deterring onopolist does not price discriinate. Hence, to deter the cooperative foration the leader ust coit to a price (or production plan) that grants to the grand coalition as uch surplus as the latter could generate by itself if it integrated into production. The total net surplus enjoyed by the grand coalition is given by (3). When consuers instead 2 buy fro the leader at any given price p, they get a total surplus Sp ( ) = ( a p) 2. Hence, the price p D that just deters the foration of a cooperative solves Sp ( ) = Uyielding 2 (5) pd = a ( a c) 2( K + G). D Reark 2. For sufficiently low governance cost, pd < pl. To deter the foration of a cooperative fir the incubent ay need to behave ore aggressively than to deter other PM firs. 3. Equilibriu entry In the first stage the would-be onopolist has to decide whether or not to enter the arket. Let π D denote the ex post profit of the onopolist (that is, exclusive of its own fixed setup cost K ). First, note that deterrence can be achieved by the unconstrained onopoly price p if (6) ( a c) 2 ( a p ) 2 K G 3u K + G 2 2 5
2 where u ( a c) 8 is the consuer surplus at the onopoly price p. In this case entry is blockaded and the onopolist achieves its highest possible profit, which defines the axiu fixed cost that it can incur in stage 1 and still be viable, as identified in (1): π D = 2u K. p When K + G < 3u, on the other hand, blockaded entry is not possible and the onopolist ust use p D given in (5) to deter entry. The ex post profit of the onopolist π D = ( p c)( a p ) in D D this case depends on the fixed costs K and G that ust be incurred by the cooperative: ( [ ] ) π D ( K, G) = 2 4u 4 u ( K + G) 4 u + ( K + G). The relevant regions of the paraeters are illustrated in Figure 1. For a given K this ex post profit is non-decreasing in the cooperative s coordination cost G. For G 3u K, entry is blockaded by the unconstrained unifor price p and the leader reaches the axiu ex post D profit: π = 2u. But as the coordination cost decreases below u, price concessions are necessary to deter the foration of a consuer coalition, eaning that π D( KG, ) decreases in G for a given K. Hence, the axiu level of fixed cost that the would-be onopolist can endure in stage 1 also decreases. Specifically, the region of paraeters where the onopolist will ake nonnegative profit (fro a stage 1 perspective, eaning π D K ) is represented by the dotted-shaded area in Figure 1. To the East and South of the boundary of this region, the PM fir does not enter. The horizontal-line-shaded area in Figure 1 illustrates the paraeter space ( KG, ) where the PM fir does not enter and therefore cannot deter the cooperative fir foration and yet a coalition of consuers can be viable. There are two distinct regions of interest where the cooperative is viable while the PM fir is not. Areas y and z denote the region of the paraeter space where the cooperative reains viable, while the PM fir is not: here K > 2u K, and a PM fir cannot be profitable, regardless of whether or not it faces potential copetition by followers. This paraetric region is related to the too-few-by-one case of insufficient entry that arises in Mankiw and Whinston (1986). Area x pertains specifically to the EMS fraework analyzed in this paper and illustrates our ain result. Here, K < 2u K, and a PM leader who only needs to deter entry by other PM firs would find it profitable to be in the arket. The prospect of copetition by a cooperative fir, however, erodes the paraetric region where the PM fir can profitably enter. As the coordination cost G of the cooperative fir decrease, the level of fixed cost that the leader is able to sustain decreases. 6
Main result. In the EMS fraework, the need to deter the foration of cooperative firs, in addition to the entry of other PM firs, curtails the leader s ex post profit which affects the viability of entry. Thus no PM fir ay find it desirable to enter the arket, despite having a first-over advantage. A cooperative fir ay reain viable under the sae production conditions, despite having to bear coordination costs that the PM fir does not have. 4u G 3u u Leader enters and deters z x 2u y 3u 4u K 4. Conclusion An incubent PM onopolist has an incentive to practice entry deterrence strategies not just with respect to profit axiizing followers, but also to deter the foration of coalitions of consuers (Sexton and Sexton 1987, Innes and Sexton 1993). In this paper, rather than taking the position of the incubent as given, we have followed the EMS literature and assued that an entry cost applies to all active firs (although cooperative firs also have additional coordination costs). The analysis uncovers an appealing raison d etre for cooperative firs. It defers to the view that a PM fir ay be faster at exploiting a arket opportunity, copared with a cooperative, and thereby gain a first-over advantage. Such a leader ay then be able to use entry deterrence strategies to preclude entry by other firs and/or cooperatives. But if the fixed setup cost is large enough, the leader ay not find it profitable to enter the arket. Perhaps ore subtly, the foregoing analysis shows that the axiu fixed entry cost that the 7
leader can endure is endogenous and depends on whether or not it faces the threat of entry by a cooperative. In such a setting, a cooperative fir ay nonetheless be viable, despite being handicapped (relative to a PM fir) by the need to bear an additional coordination cost. This effect is particularly iportant in the case of nonconvexities because, as shown by Mankiw and Whinston (1996), the free-entry equilibriu nuber of PM firs ay well be one or zero. The role by which increasing returns to scale ay explain the existence of cooperative firs has typically been cast soewhat differently: increasing returns lead to onopolies, and patrons ay be induced to for cooperatives to avoid price exploitation (e.g., Hansann, 2013). Our analysis points to an additional echanis: fixed costs ay be such that no PM fir finds it profitable to operate, especially when it faces the threat of entry by consuer coalitions. The cooperative organization ight be the only viable solution in such an environent. 8
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