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 their benefit outweighs travel cost therefore meet within finite geographic windows. We show that two or more cites may co-exist at equilibrium provided they are sufficiently distant. For any surplus function, there exists unique spatial on not too large city supports. The population density is determined by second order advance-delay differential equation, whose solutions fully characterized for linear functions. Numerical analyses localized interactions yield flatter land rents over larger extents support. They do give support to idea multiple subcenters can be caused small windows interaction.