The Amazing Geometry of Price Competition with Quality Dependent Production Costs

Abstract

This paper explores in detail a price game with two potential competitors who sell products with different qualities and where unit production costs are increasing with quality. Depending on the quality combinations, many types of price equilibria configurations may exist, besides the classical cases of high-quality monopoly or duopoly with partial or full coverage. In accordance with previous results, there exists a duopoly corner solution. But we also show that there are quality combinations where the monopolist is the low-quality firm, and this firm may or not be constrained by the presence of the other competitor. We determine, in a general setup concerning firms’ marginal cost and quality valuation dispersion, the parameter combinations under which each price Nash equilibrium holds and show graphically the different market regions for different values of the valuation parameter, which reveals an amazing geometry. Besides providing a full characterization of the different market configurations, our findings are the backbone of future analysis of quality choices and may be relevant both for firms and policy makers.

Keywords: Vertical differentiation, market coverage configurations, price competition

JEL Classification: L13, L15, D43