SCALING BEHAVIOR IN ECONOMICS .2. MODELING OF COMPANY GROWTH

In the preceding paper [1] we presented empirical results describing t he growth of publicly-traded United States manufacturing firms within the years 1974-1993. Our results suggest that the data can be describe d 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 gr owth rate of a company is affected by a tendency to retain an ''optima l'' size. That model leads to an exponential distribution of the logar ithm 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 = - lnII/ln z, where z def ines the mean branching ratio of the hierarchical tree and IT is the p robability 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.