Bertrand and Price-Taking Equilibria in Markets with Product Differentiation

Abstract

In this paper we show that a homogeneous-product market with multiple Bertrand equilibria becomes a market with a single Bertrand equilibrium when we introduce a small degree of product differentiation. When differentiation tends to zero, that Bertrand equilibrium converges to the unique price-taking equilibrium of the homogeneous-product market, which is in turn one of the multiple Bertrand equilibria for that market.Bertrand equilibrium, price-taking equilibrium, product differentiation