Local Social Interaction and Urban Equilibria

In this paper we investigate the effect of local interaction in a simple urban economics model. Agents interact with others if and only if their interaction benefit outweights their travel cost and therefore meet others only within finite geographic windows. We show that two or more cites may co-exist at the equilibrium provided that they are sufficiently distant. For any interaction surplus function, there exists a unique spatial equilibrium on not too large city supports. The population density within a city is determined by a second order advance-delay differential equation, whose solutions are fully characterized for linear interaction surplus functions. Numerical analyses show that more localized interactions yield flatter population density and land rents over larger extents of the city support. They do not give support to the idea that multiple subcenters can be caused by small and finite geographic windows of interaction.