On the uniqueness of Bertrand equilibrium

We introduce product differentiation in the model of price competition with strictly convex costs in which firms have to supply all the forthcoming demand. We find that although a continuum of equilibria exists in a homogeneous product market, the competitive price equilibrium is the only robust one. Specifically, as long as the equilibrium correspondence is nonempty, the equilibrium price converges to the competitive price when the degree of product differentiation shrinks to zero. JEL classification numbers: C72, L13