Evolutionary Model of the Personal Income Distribution

TL;DR

This paper presents an evolutionary model of personal income distribution in a free market, deriving income components and distributions from market dynamics and comparing them with empirical data.

Contribution

It introduces a novel evolutionary model that explains income distribution components and reproduces empirical income distribution patterns.

Findings

Income distribution includes lognormal, Pareto, exponential, and Gaussian components.

Model reproduces stylized facts of empirical income data.

Competition in free markets underpins income inequality.

Abstract

The aim of this work is to establish the personal income distribution from the elementary constituents of a free market; products of a representative good and agents forming the economic network. The economy is treated as a self-organized system. Based on the idea that the dynamics of an economy is governed by slow modes, the model suggests that for short time intervals a fixed ratio of total labour income (capital income) to net income exists (Cobb-Douglas relation). Explicitly derived is Gibrat's law from an evolutionary market dynamics of short term fluctuations. The total private income distribution is shown to consist of four main parts. From capital income of private firms the income distribution contains a lognormal distribution for small and a Pareto tail for large incomes. Labour income contributes an exponential distribution. Also included is the income from a social insurance system, approximated by a Gaussian peak. The evolutionary model is able to reproduce the stylized facts of the income distribution, shown by a comparison with empirical data of a high resolution income distribution. The theory suggests that in a free market competition between products is ultimately the origin of the uneven income distribution.