The logical foundations of urban economics are consistent

The logical foundations of models in urban economics with continua of agents distributed over continuous spaces have recently been questioned. It was argued, among other things, that these models cannot represent properly models with discrete numbers of households, each occupying a parcel of land. In this paper we propose a mapping, based on the continuous model utility and defined over discrete parcels of land, which determines the discrete model utility so that the equilibrium solutions of the two models coincide. Hence the continuous model of urban economics can be used as a tool for studying equilibria and comparative statics of a discrete model which appears to have sound logical foundations.