The Long-Term Trend toward Increased Dispersion in the Distributions of City Sizes

City-size distributions follow a Pareto distribution, a property which is also known as the rank-size rule. Yet very different Pareto powers, α, are to be observed, ranging from 0.5 to 2. In this paper two complementary models are proposed to relate observed values of α to basic economic phenomena. In the first, the interdependence between cities and their economic environment is analysed. It is therefore a spatial model in which production, transportation, and land productivities are the pertinent variables. In the second model the economic evolution taking place inside cities is analysed. This involves the population of major occupation groups as significant variables. Historical data are presented showing that improved communication networks and economic progress result in decreasing values of α. Both models account for this long-term evolution. It is known, however, that in some areas the distribution of city sizes does not follow the rank-size rule. It is shown that a better understanding of such distributions can be obtained from a spatial decomposition of city-size distributions.