Derivation of the Negative Exponential Model by an Entropy Maximising Method

Abstract

All the inhabitants of a city who participate in the choice of a place of residence are assumed to have a propensity to visit the urban centre. The distribution of residential locations is represented by a probability density surface whose horizontal plane projection is coextensive with that of the city. A spatially continuous system is thus defined in which it is shown that, under conditions of maximum entropy and subject to specific normalisation and cost constraints, the population is distributed in accordance with the negative exponential model of urban population densities.