THE NUMBER‐AVERAGE SIZE RULE: A NEW EMPIRICAL RELATIONSHIP BETWEEN INDUSTRIAL LOCATION AND CITY SIZE*

Abstract

ABSTRACT The spatial intensities of both industries and population are highly uneven across space. Moreover, these intensities differ not only across industries, but also change through time. Nevertheless, we show using Japanese data for metropolitan areas in two time periods that the location intensities of both industries and population are linked by surprisingly simple and persistent patterns. In particular, we identify a strong negative log‐linear relation between the number and the average (population) size of metro areas in which a given industry is found. This relation, which we designate as the Number‐Average Size (NAS) Rule, is also shown to be intimately connected to both the Rank‐Size Rule and Christaller's (1966) Hierarchy Principle applied to metropolitan areas. In particular, we show mathematically that in the presence of the Hierarchy Principle (which holds quite well in Japan) this NAS Rule is essentially equivalent to the Rank Size Rule.