Just One of Us: Consumers Playing Oligopoly in Mixed Markets

Abstract

Abstract. Consumer cooperatives represent a highly successful example of democratic form of enterprises operating in developed countries. They are usually medium to largescale companies competing with the pro…t-maximizing …rms in the retail sector. This paper describes this situation as a mixed oligopoly in which consumer cooperatives maximize the utility of consumer-members and, in return, refund them with a share of the pro…ts corresponding to the ratio of their individual spending to the cooperative's total sales. We show that when consumers possess quasi-linear preferences over a bundle of symmetrically di¤er-entiated goods, and companies operate using a linear technology, the presence of consumer cooperatives positively a¤ects total industry output, as well as welfare. The e¤ect of cooperatives on welfare proves to be even more signi…cant when goods are either complements or highly di¤erentiated, and when competition is à la Cournot rather than à la Bertrand.Keywords: Consumer Cooperatives, Pro…t-maximizing Firms, Mixed Oligopoly. JEL codes: L13, L21, L22, L31, L33, L81, P13Date: May 2011. Corresponding author: Marco A. Marini, Università degli Studi di Urbino "Carlo Bo" and CREI, Università Roma III. Address: via Sa¢ , 42, 60129, Urbino (Italy). Tel. +39-0722-305557; Fax: +39-0722-305550. E-mail: marco.marini@uniurb.it.Alberto Zevi, Università degli Studi di Roma, La Sapienza, Roma (Italy).E-mail: alberto.zevi@uniroma1.it and zeviecon@libero.it.We wish to thank Gani Aldashev, Panu Kalmi, Michael Kopel, Clemens Lö-er, Domenico Mario Nuti, Jean-Philippe Plateau, two anonymous referees and the participants of the AISSEC Conference in Siena, the IAFEP Conference in Trento, the MDEF Workshop in Urbino, the CREI Seminar in Rome and the FUNDP seminar in Namur for their useful comments and discussions.

Strategic delegation in consumer cooperatives under mixed oligopoly

“…Since in our model the Coop is assumed to act on behalf of all potential consumers of its products, it maximizes the joint utility of all its consumer-members subject to their budget constraints. As is shown below, by aggregating for all consumers, the objective function of the Coop corresponds to the maximization of total consumer welfare subject to the collective budget constraint (see also Marini and Zevi, 2011…”

Welfare Enhancing Coordination in Consumer Cooperatives Under Mixed Oligopoly

“…Goering () studies a homogeneous good duopoly with one profit‐maximizing firm and one nonprofit firm assumed to maximize a combination of profit and consumers’ surplus. Marini and Zevi () show that in a mixed oligopoly with symmetrically differentiated goods and constant returns to scale the presence of consumer cooperatives increases the welfare if compared to a pure profit‐maximizing oligopoly. In terms of separation of ownership and control, Kopel and Marini () show that, differently from profit‐maximizing firms, consumer cooperatives may refrain from using profit‐and‐sale incentive schemes to pay their managers, due to their peculiar objective function.…”

“…As a result, for this type of cooperative, the average cost pricing rule , widely known in the literature on consumer cooperatives (Helmberger and Hoos , Anderson et al , Ireland and Law ), also holds under mixed oligopoly. This depends on the fact that, whereas a price reduction has a second‐order effect on the shares of profit of individual consumers, it has a first‐order effect on their surplus (see also Kelsey and Milne , , Marini and Zevi ). However, we show now that this result does not necessarily hold if each cooperative acts coordinately to maximize the joint utilities of all consumers (see also Enke () and Farrell () for the monopoly case).…”

“…Let us first assume a constant‐return‐to‐scale technology such that every firm possesses a linear cost function, , with . Using the results obtained in Marini and Zevi () for the decentralized case (here denoted ), we can just consider here the mixed oligopoly equilibrium (denoted ) with m centralized cooperatives competing in quantity against profit‐maximizing firms. Relegating all calculations to the Appendix, it is easy to see that at the unconstrained equilibrium , for every centralized cooperative , and, therefore, its resulting profit is negative.…”

Optimal Compensation Structure in Consumer Cooperatives Under Mixed Oligopoly

“…Since in our model the Coop is assumed to act on behalf of all potential consumers of its products, it maximizes the joint utility of all its consumer-members subject to their budget constraints. As is shown below, by aggregating for all consumers, the objective function corresponds to the maximization of total consumer welfare subject to the collective budget constraint (see also Marini and Zevi, 2011). More formally, at an interior solution where all consumers are served by the two firms, we have…”