A linear oligopoly model with adaptive expectations: Stability reconsidered

Abstract

It has been proven by Okuguchi (1976) that if the Cournot equilibrium for oligopoly without product differentiation and with linear demand and quadratic cost functions is stable for a continuous time system of firms' output adjustments under the Cournot behavioristic assumption for firms, it is also stable for a continuous time system of output adjustments under adaptive expectations. As is well known, the Cournot equilibrium may be unstable for a discrete time system of output adjustments even if it is stable for a continuous one. Fisher (1961) has derived necessary and/or sufficient conditions for the stability of the equilibrium for the Cournot oligopoly which depend on the magnitudes of the adjustment coefficients. The purpose of this paper is to derive a necessary and sufficient condition for the stability of the equilibrium for oligopoly without product differentiation and with linear demand and cost functions as a relation between the adjustment coefficients which are assumed to be the same for all firms, and the number of firms. The