The mean-field approximation model of company's income growth

We introduce a mean-field-type approximation for description of company's income statistics. Utilizing huge company data we show that a discrete version of Langevin equation with additive and multiplicative noises can appropriately describe the time evolution of a company's income fluctuation in statistical sense. The Zipf's law of income distribution is shown to be held in a steady-sate widely, and country dependence of income distribution can also be nicely implemented in our numerical simulation.