Spatial Competition within Urban Areas: Hotelling and Bertrand Reconciled

In this paper, we assume the existence of a distribution of urban amenities having its maximum at the city center. These amenities are viewed as a surrogate for all kinds of opportunities, economic, social, cultural, that consumers encounter within urban areas. Using the Hotelling model, we study the impact of these amenities on independent location and pricing decisions of duopolists. Consumers patronize the firm where the amount of outside opportunities is larger, ceteris paribus. If this demand externality is strong at the city center then minimum differentiation occurs without moderation of price competition, in contrast to mainstream results in the literature. For intermediate values of the ratio of transportation cost to spatial concentration of amenities, firms tacitly play an asymmetric equilibrium with one firm near (or at) the midpoint and its rival at a more suburban location. This causes intra-urban inequalities since some consumers are induced to patronize the decentralized firm in the vicinity of which they encounter fewer urban life opportunities. Yet, if amenities are congestible (public goods) then the city planner optimally sets an intermediate value of the relative transportation cost, inducing firms to play an asymmetric equilibria with only one firm at the midpoint and its rival at a suburban site.