On the foundations of land use theory: Discrete versus continuous populations

Abstract

Urban economists and location theorists have long employed land use models with a continuum of agents distributed over a continuum of locations. However, these continous models have been criticized on behavioral grounds in that individual households can consume only zero amounts of land in equilibrium. Hence the central purpose of this paper is to propose an alternative interpretation of these continous models as limiting approximations of discrete population models. In particular, it is shown that for large population sizes, the population distributions of the classical continuous model uniformly approximate the equilibrium population distributions generated by an appropriately defined class of discrete population models.