The Cournot model of oligopoly

Abstract

Of all oligopoly models, Cournot's is both the first and the most famous. Virtually any price theory textbook includes a discussion of it, even if nothing else is presented on the subject. Apart from historical interest, the model provides an excellent, simple vehicle for the understanding of important basic principles of oligopolistic behavior. The remainder of this chapter, which opens with a historical note, is written to draw as many insights as possible from Cournot's model of oligopoly and to lay foundations for all later chapters. Section 2.2, which follows the historical note, contains a simple duopoly (i.e., two-firm oligopoly) example that is used to introduce the Cournot equilibrium and show some of its properties. In Section 2.3 a large class of n -firm oligopoly models is described for which it is known that the Cournot equilibrium exists. Examples are presented to illuminate the roles of various assumptions in assuring that there is an equilibrium. Conditions guaranteeing the uniqueness of the equilibrium are also stated, and an example illustrates the way uniqueness is attained. The fourth section takes up the relationship between Cournot equilibrium and the competitive (price equals marginal cost) equilibrium. Examples are used to show the convergence of Cournot equilibrium to the competitive equilibrium and to show why this convergence might, sometimes, be impossible. Section 2.5 contains a brief look at the stability analysis made by Cournot and the beginnings of reaction functions.