Urban Structure and Rank-Size Rule of Cities : An examination of cases in Japan from 1975 to 1995 <論説>

The aim of this paper is to examine the rank-size rule of cities or the constant elasticity of city's rank to city's size in the case of Japan from 1975 to 1995. The main results obtained are as follows.

① The Pareto distribution indicates the good fitness for the relation between the city's rank and city's size.

② However, the value of elasticity of city's rank to city's size, i.e. Pareto exponent, considerably depends on the definition of city and the sample size (the number of cities adopted as samples in order of city's rank).

③ When we increase the sample size, the value of elasticity increases at first and soon reaches the peak and decreases gradually, without regard to the definition of city adopted in this paper.

④ When we adopt two criteria, i.e. the weak criterion (with the range of 0.5 in the elasticity of city's rank to city's size) and the strong criterion (with the range of 0.2 in the elasticity), neither the rank-size rule nor the constant elasticity is valid even on the basis of the weak criterion for the first category of city, i.e. "cities, towns and villages". For the second category, i.e. "cities", the rank-size rule is not valid but the constant elasticity is valid on the basis of the weak criterion, whereas neither the rank-size rule nor the constant elasticity is valid on the basis of the strong criterion. For the third category of city, i.e. "areas", both of the rank-size rule and the constant elasticity are almost valid on the basis of the weak criterion, although neither the rank-size rule nor the constant elasticity is valid on the basis of the strong criterion. For the forth category, i.e. "prefectures", neither the rank-size rule nor the constant elasticity is valid even on the basis of the weak criterion, so this is similar to the first category.

⑤ Generally speaking, we can say that the rank-size rule and the constant elasticity are apt to be valid for the middle category of city which is formed from point of economic activities, whereas neither the rank-size rule nor the constant elasticity is valid for the small or large category of city which is the district formed from point of administration.

⑥ The facts from ① to ⑤ mentioned above are all valid for the period of 1975-95 in Japan.

⑦ For the first, second and forth categories of city which are administrative districts, the values of elasticity of city's rank to city's size increase among the "upper ranking" members ("large" cities) of each category, whereas the values decrease among "all" members, as time passes. For the third category (areas), the values decrease both among the "upper ranking" members and among "all" members, as time passes. In other words, the small cities have turned out to be smaller relatively, and the cities of upper-middle size have grown larger, therefore differences of city's size as a whole increased from 1975 to 95.