New Developments on the Oligopoly Front: Cournot and the Bain-Sylos Analysis

Abstract

THE recent review article by Franco Modigliani on books by Sylos Labini and Bain2 reports on new and interesting work on the empirical and theoretical consequences for the study of oligopoly of considerations of entry and potential competition. The theoretical model he presents, however, may at first glance cause a feeling of deId vu, since the behavior assumed in it seems at least reminiscent of Cournot. I discuss this question here primarily with reference to the way in which the results of the BainSylos model as presented by Modigliani compare with the results of a Cournot model enlarged to take account of entry. I do not discuss the question whether the behavior assumed in one model can be considered more realistic than assumed in the other or, indeed, the question whether either behavioral assumption can be considered plausible. For convenience, I restrict my attention to what may be termed the pure case of the Bain-Sylos model. Here the product is homogeneous and, for each firm (potential entrants included), long-run average cost is assumed to be perfectly constant for output greater than, or equal to, a certain minimum optimal size, x, and prohibitive for output below size. The level of long-run average (equals long-run marginal) cost for outputs greater than or equal to x is k. In perfect competition,3 equilibrium price would be k and total industry output Xc, output for which the demand and marginal-cost curves intersect. Modigliani defines the size of the market, S, as the ratio of competitive output to minimum optimal size: S = Xc/x. In the model presented by Modigliani, a Sylos' postulate is made: that potential entrants behave as though they expected existing firms to adopt the most unfavorable to them, namely, the of maintaining output while reducing the price (or accepting reductions) to the extent required to enforce such an output policy (p. 217). On this assumption, it follows immediately the smallest entry-blocking industry output, X0, is