A Unified Theory of Cities

How do people arrange themselves when they are free to choose work and residence locations, when commuting is costly, and when increasing returns may affect production? We consider this problem when the location set is discrete and households have heterogenous preferences over workplace-residence pairs. We provide a general characterization of equilibrium throughout the parameter space. The introduction of preference heterogeneity into an otherwise conventional urban model fundamentally changes equilibrium behavior. Multiple equilibria are pervasive although stable equilibria need not exist. Stronger increasing returns to scale need not concentrate economic activity and lower commuting costs need not disperse it. The qualitative behavior of the model as returns to scale increase accords with changes in the patterns of urbanization observed in the Western world between the pre-industrial period and the present.