A Simple Model of Functional Specialization of Cities

Resorting to the method proposed by Matsuyama (2013), this paper develops a static equi- librium model of a system of cities in which ex ante identical locations specialize in stages of production different in the degree of dependence on routine and nonroutine local services sec- tors, the latter of which is tied to an agglomeration force due to monopolistic competition a ́ la Dixit and Stiglitz (1977). The model is simple in that the system is summarized by a second-order differential equation, which has a unique non-degenerate city size distribution with the comove- ment of income, population, factor prices, and urban diversity as observed for the U.S. cities. Two examples of use of the model are then illustrated: analyses of welfare gain from functional specialization and optimal income redistribution, the latter of which provides an important impli- cation of an increasing importance of interactive activities in a modern developed economy for income redistribution. Although extending the model makes the model analytically intractable, it is still characterized by a differential equation easily solved with a numerical method and thus useful for further analyses.