Firm size distributions in an industry with constrained resources

We propose an equilibrium model for firm size distribution in an industry with a constrained essential input. The model applies when the population of firms is small and homogeneous and the supply of the necessary input factor is perfectly inelastic. We argue that although the Gibrat assumption obtains, this does not result in the lognormal distribution because of the entries, exits and mergers of firms competing for the inelastic essential resource. Using our own 32-year database of firms, we test the brokenstick, or random-ordered-interval, model that we call the Whitworth distribution, successfully applied by others to a number of data sets, including the abundances of bird species. We propose the Whitworth as the basic model of the equilibrium distribution of firm sizes for such supply-constrained industries, and find it fits our 31-year database best.