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Advances in Operations Research
Volume 2011, Article ID 269239, 21 pages
Research Article

Fluctuation of Firm Size in the Long-Run and Bimodal Distribution

1Graduate School of Science, Kyoto University, Yoshida, Sakyo, Kyoto 606-8501, Japan
2Department of Mathematics, University of Frankfurt, Robert Mayer Street 8-10, 60054 Frankfurt, Germany
3Center for Empirical Macroeconomics, 33615 Bielefeld, Germany and New School University, New York, NY 10011, USA
4ATR Human Information Science Laboratories, Kyoto 619-0288, Japan

Received 3 April 2011; Accepted 27 June 2011

Academic Editor: Walter J. Gutjahr

Copyright © 2011 Hideaki Aoyama 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 study empirically and analytically growth and fluctuation of firm size distribution. An empirical analysis is carried out on a US data set on firm size, with emphasis on one-time distribution as well as growth-rate probability distribution. Both Pareto's law and Gibrat's law are often used to study firm size distribution. Their theoretical relationship is discussed, and it is shown how they are complementable with a bimodal distribution of firm size. We introduce economic mechanisms that suggest a bimodal distribution of firm size in the long run. The mechanisms we study have been known in the economic literature since long. Yet, they have not been studied in the context of a dynamic decision problem of the firm. Allowing for these mechanism thus will give rise to heterogeneity of firms with respect to certain characteristics. We then present different types of tests on US data on firm size which indicate a bimodal distribution of firm size.