10 - On the efficiency of Bertrand and Cournot equilibria with product differentiation

Summary

In a differentiated products setting with n varieties it is shown, under certain regularity conditions, that if the demand structure is symmetric and Bertrand and Cournot equilibria are unique then prices and profits are larger and quantities smaller in Cournot than in Bertrand competition and, as n grows, both equilibria converge to the efficient outcome at a rate of at least 1/n. If Bertrand reaction functions slope upwards and are continuous then, even with an asymmetric demand structure, given any Cournot equilibrium price vector one can find a Bertrand equilibrium with lower prices. In particular, if the Bertrand equilibrium is unique then it has lower prices than any Cournot equilibrium. Journal of Economic Literature Classification Numbers: 022, 611.

© 1985 Academic Press, Inc.

Introduction

It is a well-established idea that Bertrand (price) competition is more efficient than Cournot (quantity) competition. In fact with an homogenous product and constant marginal costs the Bertrand outcome involves pricing at marginal cost. This is not the case with differentiated products where margins over marginal cost are positive even in Bertrand competition. Shubik showed in a model with a linear and symmetric demand structure that the margin over marginal cost is larger in Cournot competition, and that, under certain conditions, as the number of varieties grows equilibrium prices go to marginal cost in either Bertrand or Cournot competition (see Shubik [16, Chaps. 7 and 9]).