A Note on Product Differentiation under Concave Transportation Costs

Concavity of transportation costs has been rarely considered in the linear model of product differentiation, although it seems a reasonable assumption in many contexts. In this paper, we extend the results by Gabszewicz and Thisse (1986) about the existence of the sequential first-location-then-price equilibrium to the case where transportation costs are concave in distance. Thus, there exists a unique sequential equilibrium in the model of vertical differentiation which involves maximal differentiation, while the sequential equilibrium under horizontal differentiation fails to exist. In this latter case, under given locations, firms need not be sufficiently far from each other for a price equilibrium to exist. In fact, a possible equilibrium involves both firms being located near one extreme of the city. In that case, the demand of the furthest firm is non-connected.