This paper examines the existence of n-firm Cournot equilibrium in a market for a single homogeneous commodity. It proves that if each firm's marginal revenue declines as the aggregate output of other firms increases (which is implied by concave inverse demand) then a Cournot equilibrium exists, without assuming that firms have nondecreasing marginal cost or identical technologies. Also, if the marginal revenue condition fails at a “potential optimal output”, there is a set of firms such that no Cournot equilibrium exists. The paper also contains an example of nonexistence with two nonidentical firms, each with constant returns to scale production.

Introduction

Cournot equilibrium is commonly used as a solution concept in oligopoly models, but the conditions under which a Cournot equilibrium can be expected to exist are not well understood. The nature of each firm's technology, whether all firms have identical technologies, and restrictions on the market inverse demand vary from model to model, and are all important for the existence of Cournot equilibrium. This paper examines the question of existence of (pure strategy) Cournot equilibrium in a single market for a homogeneous good. In this context there are two known types of existence theorems. The first type allows general (downward sloping) inverse demand and shows the existence of Cournot equilibrium when there are n identical firms with convex technologies (nondecreasing marginal cost and no avoidable fixed costs). See McManus [1962, 1964] and Roberts and Sonnenschein [1976].