Working Paper No. 12-25 a Tractable Circular City Model with an Application to the Effects of Development Constraints on Land Rents

A tractable production-externality-based circular city model in which both firms and workers choose location as well as intensity of land use is presented. The equilibrium structure of the city has either (i) no commuting (“mixed-use” form) or (ii) a central business district (CBD) of positive radius and a surrounding residential ring. Regardless of which form prevails, the intra-city variation in all endogenous variables displays the negative exponential form: x(r) = x(0)e−φxr (where r is the distance from the city center and φx depends only on preference and technology parameters). An application is presented wherein it is shown that population growth may lead to a smaller increase in land rents in cities that cannot expand physically because these cities are less able to exploit the external effect of greater employment density.