City System Based on the Rank-Size Rule

Abstract

This paper proves to have a specific law about the size of the exponent for the rank-size model in the population system of the city. It has been said that an exponent of approximately 1 in the empirical evidence takes between 3 from 0.1 with the development of the computer software. Simon (Biometrica, 425–440, 1955) explained the exponent using the probabilistic theory and Krugman (The self-organizing economy, Blackwell, 1996) pointed out that it was difficult for us to understand Simon’s story. Therefore, without using the probabilistic theory, we clarify the implication of the range of the exponent for the rank-size model by supposing the case that migrants concentrate on the city having maximum population in a metropolis in one country, the case that migrants form a new city, and the case that migrants are distributed in proportion to the population of each city.