Central Place Theory and Zipf’s Law Wen-Tai Hsu∗

This paper provides a theory of the location of firms and, as cities are groups of firms, the emergence of cities. Using a model of equilibrium entry, this paper provides a microfoundation for central place theory and the conditions under which Zipf’s law for cities emerges. Central place theory describes how a hierarchical city system with different layers of cities serving different sized market areas forms from a uniformly populated space. Zipf’s law for cities, that is, the size distribution of cities following the Pareto distribution with a tail index close to 1, is a robust empirical regularity. In the model, the main force driving the size difference of cities is the tradeoff between transportation cost and scale economies, which differs across goods due to different fixed costs of production. Since a central place hierarchy also implies a hierarchy of firms, Zipf’s law for firms is also approximated. The theory is also consistent with a newly discovered empirical regularity, the number-average-size rule, which is a log-linear relationship between the number of cities and the average size of cities where an industry is located