Finding endogenous market coverage equilibria in vertically differentiated markets under quality dependent costs

This paper endogeneizes the level of market coverage in a vertically differentiated market where firms decide first their qualities and next their prices. We extend the few endogeneization results to a more realistic setup, with quality dependent unit production costs. We show that, depending on the level of the lowest quality valuation with respect to the quality valuation dispersion, there are four possible types of subgame perfect Nash equilibria. When the lowest quality valuation is low, the equilibrium involves quality choices that lead to a partial coverage duopoly. For slightly higher lowest valuation levels, firms choose qualities in the interior of the region where a full coverage duopoly with a corner solution holds. For even higher lowest quality valuation, there are multiple equilibria quality combinations which are located at the frontier between the interior and the corner full coverage duopoly regions. Finally, for high lowest quality valuations the qualities chosen are in the interior of the region where a full coverage duopoly holds. We also show that quality differentiation may decrease with quality valuation dispersion, although quality differentiation is increasing with quality valuation dispersion within each of the market regions. Our results have important implications in terms of firms’ quality market positioning and pricing decisions