Beyond the Uniform Distribution: Equilibrium Prices and Qualities in a Vertically Differentiated Duopoly

Abstract

The paper proves the existence of a subgame perfect Nash equilibrium in a vertically differentiated duopoly with uncovered market, for a large set of symmetric and asymmetric distributions of consumers, including, among others, all logconcave distributions. The proof relies on the ’income share elasticity’ representation of the consumers’ density function, which ensures the analytical tractability of the firms’ optimality conditions at a high level of generality. Some illustrative examples of the solution are offered, in order to assess the impact of distributive shocks on the equilibrium market configuration