Perfectly competitive markets as the limits of Cournot markets

Abstract

A perfectly competitive, partial equilibrium market for a single homogeneous good with a (bounded) continuum of infinitesimal firms is considered. Cost functions are essentially unrestricted and are allowed to vary smoothly across firms. A sequence (net) of Cournot markets (each with a finite number of firms) which converge smoothly to the perfectly competitive limit in terms of both the inverse demand functions and the distributioon of firm technologies is introduced and it is shown that all markets sufficiently far along the sequence have a Cournot equilibrium and all the Cournot equilibria converge to the perfectly competitive equilibrium of the limit market.