Efficiency Loss in a Cournot Oligopoly with Convex Market Demand

TL;DR

This paper analyzes how convex market demand affects the efficiency loss in Cournot oligopoly models, providing bounds on social welfare loss for various demand functions.

Contribution

It introduces a scalar parameter-based lower bound on Cournot equilibrium efficiency under convex demand functions, including collusive and monopolistic scenarios.

Findings

Lower bounds on efficiency depend on demand function slopes.

Tighter bounds are derived for monopoly and collusion cases.

Quantitative bounds are provided for common convex demand functions.

Abstract

We consider a Cournot oligopoly model where multiple suppliers (oligopolists) compete by choosing quantities. We compare the social welfare achieved at a Cournot equilibrium to the maximum possible, for the case where the inverse market demand function is convex. We establish a lower bound on the efficiency of Cournot equilibria in terms of a scalar parameter derived from the inverse demand function, namely, the ratio of the slope of the inverse demand function at the Cournot equilibrium to the average slope of the inverse demand function between the Cournot equilibrium and a social optimum. Also, for the case of a single, monopolistic, profit maximizing supplier, or of multiple suppliers who collude to maximize their total profit, we establish a similar but tighter lower bound on the efficiency of the resulting output. Our results provide nontrivial quantitative bounds on the loss of social welfare for several convex inverse demand functions that appear in the economics literature.