Quasi-Competitiveness and Cournot Oligopoly

Homogeneous Cournot oligopoly without product differentiation is said to be quasicompetitive if the equilibrium industry output increases and the equilibrium market price decreases with an increase in the number of firms in the industry. Assuming a strong case in which all firms have identical cost functions, Ruffin [13] analysed the quasi-competitiveness of Cournot oligopoly 3 and clarified the relevance of stability conditions to quasi-competitiveness. Earlier McManus [10] noted the close connection between the uniqueness of the Cournot oligopoly equilibrium and quasi-competitiveness. Okuguchi and Suzumura [12], on the other hand, dealt systematically with the uniqueness problem. Their principal finding was that the stability condition as proposed by Hahn [7] and used later by Okuguchi [11] ensures uniqueness. In this paper we intend to analyse the quasi-competitiveness of Cournot oligopoly more thoroughly for a weak case in which differences in cost functions among firms are admitted. Frank [4], in his proof of convergence of the Cournot oligopoly equilibrium to the competitive one, has considered differences in cost functions. We depart from Frank, however, in assuming that there exist initially an identical number of firms in each category of conceivable cost functions and then we let the number increase equally in each category. This approach was suggested by the proof in Debreu and Scarf [3]. They demonstrated the equivalence of the core and competitive equilibrium in a pure exchange model in which they assumed the existence of an identical number of exchange participants for each category of initial endowments and the participants are then increased equally in each category successively. We shall find that the uniqueness condition due to Okuguchi and Suzumura also ensures quasi-competitiveness. Ruffin has shown that when Hahn's stability condition is violated, Cournot oligopoly may not be quasi-competitive. For our model, however, it is conjectured that when the stability condition is not met, Cournot oligopoly may or may not be quasi-competitive.