On the Stability of Price Adjusting Oligopoly

Abstract

Considerable attention has been given recently to the dynamic properties of the Cournot model under alternative assumptions.' The Cournot model is understood to be a market situation in which n firms sell a homogeneous product and in which each firm maximizes its profit on the assumption that its rivals' output levels remain unchanged. Under some simplifying assumptions concerning the form of the demand and cost functions the following conclusions have emerged from the analysis of the Cournot model: (1) The results of dynamic analysis depend heavily on whether the dynamic adjustment process is formulated as a discrete or as a continuous process; (2) in a discrete process increasing marginal cost tends to be stabilizing2; (3) for given demand and cost functions an increase in the number of firms tends to be destabilizing in a discrete process; and (4) some simple continuous dynamic adjustment processes are stable for all a priori admissible values of the parameters. The objective of the present paper is to investigate the dynamic properties of oligopoly models in which each firm sells a differentiated product and in which firms maximize their profits with respect to price on the assumption that their rivals' prices remain unchanged.3 The stability of such oligopoly models will be investigated with respect to (1) alternative assumptions about cost functions and (2) alternative assumptions about the manner in which price expectations are formed.