Firm Growth and Selection in a Finite Economy

A model of firm dynamics is presented in which the growth rate of knowledge capital is linked to productivity, and productivity fluctuates randomly. The distribution of productivity forms a stable traveling wave, representing a growing economy. Granularity is maintained by way of spinoffs, resulting in a firm size distribution that rapidly approaches the Zipf distribution. An unexpected consequence of the model is that the growth rate is proportional to the log of the number of firms. The model also implies that specialization is positive for growth