Evolutionary model of the personal income distribution

The aim of this work is to develop a qualitative picture of the personal income distribution. Treating an economy as a self-organized system the key idea of the model is that the income distribution contains competitive and non-competitive contributions. The presented model distinguishes between three main income classes. 1. Capital income from private firms is shown to be the result of an evolutionary competition between products. A direct consequence of this competition is Gibrat’s law suggesting a lognormal income distribution for small private firms. Taking into account an additional preferential attachment mechanism for large private firms the income distribution is supplemented by a power law (Pareto) tail. 2. Due to the division of labor a diversified labor market is seen as a non-competitive market. In this case wage income exhibits an exponential distribution. 3. Also included is income from a social insurance system. It can be approximated by a Gaussian peak. A consequence of this theory is that for short time intervals a fixed ratio of total labor (total capital) to net income exists (Cobb–Douglas relation). A comparison with empirical high resolution income data confirms this pattern of the total income distribution. The theory suggests that competition is the ultimate origin of the uneven income distribution.