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Advances in Mathematical Physics
Volume 2016, Article ID 9303480, 6 pages
Research Article

Firm Growth Function and Extended-Gibrat’s Property

1Kanazawa Gakuin University, 10 Sue, Kanazawa, Ishikawa 920-1392, Japan
2National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
3Department of Informatics, The Graduate University for Advanced Studies, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
4PRESTO, Japan Science and Technology Agency, 7 Gobancho, Chiyodaku, Tokyo 102-0076, Japan
5Graduate School of Economics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
6The Canon Institute for Global Studies, 5-1 Marunouchi 1-chome, Chiyoda-ku, Tokyo 100-6511, Japan

Received 21 September 2015; Accepted 6 March 2016

Academic Editor: Doojin Ryu

Copyright © 2016 Atushi Ishikawa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We analytically show that the logarithmic average sales of firms first follow power-law growth and subsequently follow exponential growth, if the growth-rate distributions of the sales obey the extended-Gibrat’s property and Gibrat’s law. Here, the extended-Gibrat’s property and Gibrat’s law are statistically observed in short-term data, which denote the dependence of the growth-rate distributions on the initial values. In the derivation, we analytically show that the parameter of the extended-Gibrat’s property is identical to the power-law growth exponent and that it also decides the parameter of the exponential growth. By employing around one million bits of exhaustive sales data of Japanese firms in the ORBIS database, we confirmed our analytic results.