J. Phys. I France
Volume 7, Numéro 4, April 1997
Page(s) 635 - 650
DOI: 10.1051/jp1:1997181
J. Phys. I France 7 (1997) 635-650

Scaling Behavior in Economics: II. Modeling of Company Growth

Sergey V. Buldyrev1, Luís A. Nunes Amaral1, 2, Shlomo Havlin1, 3, Heiko Leschhorn1, Philipp Maass1, Michael A. Salinger4, H. Eugene Stanley1 and Michael H.R. Stanley1

1  Center of Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA
2  Institute für Festkörperforschung, Forschungszentrum Jülich, 52425 Jülich, Germany
3  Department of Physics, Bar-Ilan University, Ramat Gan 52900, Israel
4  School of Management, Boston University, Boston, MA 02215, USA

(Received 15 November 1996, accepted 30 December 1996)

In the preceding paper [1] we presented empirical results describing the growth of publicly-traded United States manufacturing firms within the years 1974-1993. Our results suggest that the data can be described by a scaling approach. Here, we propose models that may lead to some insight into these phenomena. First, we study a model in which the growth rate of a company is affected by a tendency to retain an "optimal" size. That model leads to an exponential distribution of the logarithm of the growth rate in agreement with the empirical results. Then, we study a hierarchical tree-like model of a company that enables us to relate the two parameters of the model to the exponent $\beta$, which describes the dependence of the standard deviation of the distribution of growth rates on size. We find that $\beta =-{\rm ln}\, \Pi/\,{\rm ln}\, z$ , where z defines the mean branching ratio of the hierarchical tree and $\Pi$ is the probability that the lower levels follow the policy of higher levels in the hierarchy. We also study the distribution of growth rates of this hierarchical model. We find that the distribution is consistent with the exponential form found empirically.

© Les Editions de Physique 1997