Urban Welfare Maximization and Housing Market Equilibrium in a Random Utility Setting

A welfare-maximization framework for the allocation of a given housing supply to urban submarkets is formulated. The approach is founded on a stochastic equilibrium model for the housing submarkets, the demands of which are based on generalized extreme value choice models. This allows the random utilities associated with different submarkets to be statistically dependent. The deterministic part of the utilities includes the submarket rent levels together with disutility measures related to the local population densities. This latter aspect can be regarded as a kind of spatial externality usually neglected in urban modelling. The optimization is performed with respect to a welfare criterion derived as the aggregated expected utility accruing to utility-maximizing households at normalized equilibrium rents. Since these rents are implicit functions of the policy variables, that is, the submarket housing supplies, the welfare maximization is not straightforward. However, as a main result it is shown that if the population density disutilities satisfy a convexity condition, the unique welfare-maximizing housing allocation can be found by solving a dual unconstrained convex minimization problem. Finally, the relationship with entropy maximization is clarified and the applicability of the framework to the joint choice of residential location and travel mode is demonstrated. Two examples of nested multinomial logit models illustrate the potential use of the approach.