Why Does Zipf's Law Break Down in Rank-Size Distribution of Cities?

Abstract

We study rank-size distribution of cities in Japan on the basis of data analysis. From the census data after World War II, we find that the rank-size distribution of cities is composed of two parts, each of which has independent power exponent. In addition, the power exponent of the head part of the distribution changes in time and Zipf's law holds only in a restricted period. We show that Zipf's law broke down due to both of Showa and Heisei great mergers and recovered due to population growth in middle-sized cities after the great Showa merger.