General Equilibrium Models with Discrete Choices in a Spatial Continuum

Abstract

The treatment of spatial characteristics through probability distributions makes it possible to use stochastic optimization methods and to obtain efficiency results and competitive equilibrium prices for general equilibrium models with discrete choices in spatial continuum. Along these lines, and combining results from stochastic optimization with principles established by Aumann and Hildenbrand for economies with continuum of traders the paper develops a practical modeling framework that can combine the spatially distributed aspects of land-use with processes such as market clearing or telecommunication investments concentrated at specific points. It also presents associated stochastic algorithms for numerical implementation. We discuss both a general equilibrium version in which all consumers meet their own budget, and a welfare maximizing version with transfers adjusting among consumer groups for which we formulate a dual approach that solely depends on a finite number of prices.