Labor Di¤erentiation and Agglomeration in General Equilibrium

The aim of this paper is to explore the structure of cities as a func-tion of labor di¤erentiation, gains to trade, a \u85xed cost for constructing the transportation network, a variable cost of commodity transport, and the commuting costs of consumers. Firms use di¤erent types of labor to produce di¤erent outputs. Locations of all agents are endogenous as are prices and quantities. This is among the \u85rst papers to apply smooth economy techniques to urban economics. Existence of equilibrium and its determinacy properties depend crucially on the relative numbers of outputs, types of labor and \u85rms. More di¤erentiated labor implies more equilibria. We provide tight lower bounds on labor di¤erentiation for existence of equilibrium. If these su ¢ cient conditions are satis\u85ed, then generically there is a continuum of equilibria for given parame-ter values. Finally, an equilibrium allocation is not necessarily Pareto optimal in this model