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Multiproduct Duopolists

Paul Champsaur
Jean-Charles Rochet

Abstract

We study a differentiated industry in which two firms compete by offering intervals of qualities to heterogenous consumers, in the spirit of the monopolist of Mussa and Rosen (1978). We establish conditions which, for perfect competition and monopoly, preclude the possibility that a given quality level is bought by more than one type of consumer (there is no "bunching"). Under these assumptions we show the existence of a unique price equilibrium in the duopoly case where firms must offer intervals of qualities. At all price equilibria in which both firms make a positive profit, discrimination of consumers is incomplete. When the firms choose their product lines they are influenced by two opposite effects. Discrimination among heterogeneous buyers requires a broad quality range. On the contrary, price competition lowers profit margins on neighboring qualities sold by different firms, creating the Chamberlinian incentive for a firm to differentiate its products from those of its competitors. We show that the second effect dominates the first for intermediate qualities: at a Nash equilibrium of the quality game where each firm makes a positive profit, there is always a gap between the two product lines.