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The distribution by size of the cities of a region reflects the locational decisions made by the inhabitants concerned. Some of the factors underlying these decisions have a bearing on city size, and, it is assumed, make up a utility function that varies with city size according to the Weber-Fechner law of marginal effects. Under these conditions, the maximum entropy distribution of the population among the cities of the region gives rise to the hierarchical model described in the paper. Examples are given of calibrations of the model. It is shown that in the applicable statistical range this distribution and the Pareto distribution, although formally different, are quantitatively interchangeable. The derivation presented here may therefore be regarded as providing a new rationale for the Pareto city-size distribution model.

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.