Equivalence between welfare and entropy approaches to residential location

An optimization model for residential location in an urban area is presented. As the objective, a welfare measure is considered which is derived as aggregated expected utility based on utility-maximizing individual behaviour. The utilities include travel costs for work trips as well as a measure of the disutility with high-density living. The problem of finding a welfare maximizing housing allocation is shown to be equivalent to an entropy maximizing problem provided that a certain condition is met. By considering a dual formulation, a computationally more expedient problem is obtained. The model approach is illustrated by a few applications to the Stockholm region.