Endogenous Amenities and the Spatial Structure of Cities

This paper examines the endogenous dynamics of the social structure of a city where the spatial repartition of amenities is endogenously modified by the spatial repartition of social groups. We start from the fact that, in most European cities, central locations are occupied by rich households; while in American cities, they are occupied by poor households. In a standard urban model without amenities, for rich households to locate downtown, their unit transport cost must be very high compared to the poor. Bruckner et al. (1999) show that, when there are historical amenities mainly located in the city center, we no longer need a high differential between transport costs: if demand for amenities by the rich is strong enough, this advantage could attract the rich households in the city centre. This explanation fits well with the fact that the most European cities have a long history, with the consequence that they accumulated many amenities in their city centre. However, the paper by Brueckner et al. is purely static and does not explicitly consider the historical dimension of the process generating amenities. Our model explicitly takes account of time: at every period, the equilibrium spatial structure of the city is determined by the transport costs and by the spatial repartition of amenities; but, between periods, the spatial repartition of amenities changes, rich households generating local amenities in the locations they occupy, and then the spatial structure of the city changes. We show that this endogenous generation of local amenities has two consequences. The first one is that the city may have several long term equilibria. We explicitly analyse two of them: an “American equilibrium†with the poor living in the centre, and a “European equibrium†with the rich living in the centre. We show that the conditions for the existence of an European equilibrium are more restrictive. The second consequence is that, when the city develops, it may move from an American equilibrium to an European one. If the city starts without amenities, poor households locate in the city centre, rich households in the periphery. However, the production of new local amenities by the rich generates a lock in effect: rich go on occupying locations where they were living previously and, as the city develops, these locations become central ones.