• Marlon Boarnet served as the editor for this paper.

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    We thank Asao Ando, Duncan Black, Pierre-Philippe Combes, Gilles Duranton, Masa Fujita, Robert Helseley, Vernon Henderson, Seiro Ito, Hideo Konishi, Maria P. Makabenta, Se-il Mun, Henry Overman, Komei Sasaki, Yasuhiro Sato, Akihisa Shibata, Takaaki Takahashi, Chiharu Tamamura, Jacques-François Thisse, Tatsufumi Yamagata, Atsushi Yoshida, two anonymous referees, and seminar and conference participants at Boston College, Institute of Developing Economies, Kyoto University, Nagoya City University, Tohoku University, University of Tokyo, Yokohama National University, the Annual Meeting of the Japanese Economic Association at Hiroshima University, October 13, 2002, the 49th North American Meeting of the Regional Science Association International in San Juan, November 8–11, 2002, the 16th Meeting of the Applied Regional Science Conference at Okayama University, December 1–2, 2002, for their constructive comments on earlier versions of this paper. We also thank Yoshi Kanemoto for helping us with metropolitan area data for Japan, and Noriko Tabata for helping us with county data. This research has been supported by The Murata Science Foundation, and The Grant in Aid for Research (Nos. 09CE2002, 09730009, 13851002, 19330049) of Ministry of Education, Science and Culture in Japan.


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.