An investigation of firm size distributions involving the growth functions

Following the ideas of prospect theory, a class of growth functions is used to characterize deterministic variations of firm size, which portrays the asymmetric efforts of the firm to achieve the desired size. Considering the differences in the ability of different firm size to cope with uncertainties, the Boltzmann equation for the evolution of firm size is constructed. Utilizing a suitable scaling limit, the Fokker–Planck equation is acquired and its explicit steady-state solution is derived. Our results illustrate that different choices of parameters in the growth function lead to various statistical laws for firm size, such as the Amoroso distribution, the lognormal distribution and Zipf’s law. Under certain conditions, inequality for the distribution of firm size decreases as firm size increases. The numerical analyses are presented to illustrate our results.