The Dependence of Population Distribution on Location Costs

Abstract

Part of a household's constrained budget is assumed to be comprised of a general cost of location. By using a simple generalisation of Muth's economic theory of the spatial pattern of urban housing, the population density distribution in a plane city is shown to be dependent on the distribution of this generalised cost of location. If housing demand is elastic, then this dependence is shown to be exponential, a conclusion which agrees with a familiar result obtained by maximising the entropy of a population system subject to a cost constraint. If the housing demand is less or more elastic, then the dependence is binomial. Implications of the theory are discussed and illustrations given.