Central Place Theory and City Size Distribution

This paper proposes a theory of city size distribution via a hierarchy approach rather than the popular random growth process. It does so by formalizing central place theory using an equilibrium entry model and specifying the conditions under which city size distribution follows a power law. Central place theory describes the way in which a hierarchical city system with different layers of cities serving differently sized market areas is formed from a uniformly populated space. The force driving the city size differences in this model is the heterogeneity in economies of scale across goods. The city size distribution under a central place hierarchy exhibits a power law if the distribution of scale economies is regularly varying, which is a general class that encompasses many well-known, commonly used distributions. This model is also consistent with a power law for firms and a number-average-size rule, which is the log-linear relationship between the number and average size of the cities in which an industry is located. JEL: R12; L11; R13