On the Efficiency of Bertrand and Cournot Equilibria with Product Differentation

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 l/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.