Competitive Approximation of a Cournot Market

Abstract

It is a longstanding intuitive notion that a market with small Cournot firms and free entry is well approximated as a perfectly competitive market. Not until Novshek's recent paper (1980), however, was this folk theorem turned into a real theorem. The basic ingredients of Novshek's model are a downward sloping demand curve for the market and a U-shaped average cost curve common to all firms. Let y * denote the smallest firm output which achieves minimum average cost; and let Y* denote the market output which would prevail under a perfectly competitive approximation (the market demand when price equals minimum average cost). A small value for the ratio y */ Y* indicates that the market can accommodate a sizeable number of firms. Roughly speaking, Novshek's main result is this. If y*/Y* is sufficiently close to zero, then there exists one or more Cournot equilibria (with free entry), each of which has market output Y in the interval Y* - ' Y_ Y*. Given a small y */ Y*, this interval is tight; hence Novshek's result supports the use of the competitive approximation Y = Y*. This paper presents an alternative model of the same issue, based on the same demand and cost curve ingredients. Novshek's model is static and (to me at least) technically demanding. The model below, in contrast, is dynamic and simple. The train of thought which led me to the alternative model may be of interest.