The Stability of Price Adjusting Oligopoly: The Effects of Adaptive Expectations

The problem of stability of equilibrium in Cournot type oligopoly models in which oligoplistic firms producing a homogenous product expecting that outputs of all other firms will remain unchanged has been extensively studied.' The similar problem under product differentiation has been discussed quite recently by Hadar [2] and Quandt [5]. While Hadar considers quantity adjusting oligopoly, Quandt considers price adjusting oligopoly. After treating a model with Cournot type assumption in which oligopolistic firms behave as if the prices of other firms will remain as before, Quandt considers a model with expected prices extrapolatively formed. He gets the conclusion that if equilibrium is stable in the former model, it is stable also in the latter one under fairly plausible assumption on the magnitudes of the parameters appearing in equations of price expectations. The purpose of this paper is to investigate the problem of stability of equilibrium of price adjusting oligopoly with an alternative assumption on price expectations, i.e., adaptive expectations. It will be made clear that if the equilibrium is stable under Cournot type assumption, it is stable also in a model with adaptive expectations under fairly general conditions.