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
