Spatial competition within urban areas: hotelling and Bertrand reconciled

In this paper, I assume the existence of distribution of urbanamenities having its maximum at the city center. These amenities are viewed as a surrogate for all kinds of outside opportunities taht consumers encounter within urban areas. Using the Hotelling model, I study the impact of these amenities on independent location and pricing decisions of duopolists. Consumers patronize the firm where the amount of aminities is larger, ceteris paribus. If this demand externality is strong at the midpoint then minimum differentiation occurs without moderation of price competition, in contrast to mainstream results in the literature. For intermediate values of the ration 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 induted to patronize the decentralized marketplace where they encounter less urban life opportunities.