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

TL;DR

This paper presents a mean-field approximation model using a Langevin equation to describe company income growth, successfully reproducing income distribution patterns like Zipf's law across countries.

Contribution

It introduces a novel mean-field approximation framework with Langevin dynamics for modeling company income fluctuations and distributions.

Findings

Income fluctuations are well-described by a Langevin equation with additive and multiplicative noise.

Zipf's law of income distribution holds in the steady state across various countries.

The model captures country-specific income distribution differences through numerical simulations.

Abstract

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 hold in a steady-sate widely, and country-dependence of income distribution can also be nicely implemented in our numerical simulation.