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
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