Consistent Conjectures in a Value-Maximizing Duopoly

Abstract

Recent literature on consistent conjectures has established that, under a variety of conditions, only competitive behavior is rational. Rationality or consistency is defined in this literature as the condition that the slope of a firm's profit-maximizing reaction function must equal the conjecture made about the firm's reactions by its rivals. This concept of consistency is due to Bresnahan [5], who uses it to select among the many possible conjectural equilibria in duopoly as defined by Bowley [3].' Perry [24] extends the duopoly analysis to the case of an arbitrary fixed number of identical firms, as well as to the case of free entry and exit. Both papers show that only the Bertrand conjecture, in which firms accommodate rivals' output changes by making equal and opposite changes, is consistent when marginal costs are constant. In addition, Perry shows that this result also holds when entry and exit are free. The Bertrand conjecture is identified with competitive behavior since it implies price taking and marginal cost pricing. The equivalence that both papers establish between consistent conjecture equilibrium (CCE) and competitive equilibrium under constant marginal cost may have important practical implications. Johnston summarizes his thorough survey of cost functions with the comment: Two major impressions, however, stand out clearly. The first is that the various short-run studies more often than not indicate constant marginal cost and declining average cost as the pattern that best seems to describe the data that have been analyzed [15, 168]. Therefore, the results of Bresnahan and Perry would seem to apply to a wide range of observed behavior, making a strong theoretical case that much economic activity is truly competitive regardless of the number of firms.2 Even when marginal costs are not constant and the number of firms is fixed, the implication of the consistent conjectures hypothesis for profit-maximizing firms is that behavior is more competitive than Coumot. This result in itself is important, since recent work has indicated that Cournot equilibrium approaches the competitive limit in the case of large economies; see for