Horizontal Product Differentiation in Bertrand and Cournot Duopoly: the Bertrand Paradox Revisited and Comparative Competitiveness

This paper provides a simple model of endogenous horizontal product differentiation that has two important implications. First, the model can explain the “empirical Bertrand paradox” – the failure to observe homogeneous product Bertrand oligopoly. If product differentiation is possible at reasonable cost, then Bertrand firms would always invest in product differentiation. Using a quadratic utility (linear demand) structure we show that Cournot firms are much less likely to engage in product differentiation than Bertrand firms. And, assuming product differentiation takes place at all, Bertrand firms would always differentiate more than Cournot firms. The second major insight of our analysis is that Bertrand competition is not necessarily more competitive than Cournot competition (in the sense of having lower prices and profits) once we allow for endogenous product differentiation. For a significant range of parameter values a Bertrand duopoly charges higher prices and earns higher profits than a corresponding Cournot duopoly. keywords: Bertrand paradox, Cournot, horizontal product differentiation