Modelling of income distribution in the European Union with the Fokker–Planck equation

Abstract

Herein, we applied statistical physics to study incomes of three (low-, medium- and high-income) society classes instead of the two (low- and medium-income) classes studied so far. In the frame of the threshold nonlinear Langevin dynamics and its threshold Fokker–Planck counterpart, we derived a unified formula for description of income of all society classes, by way of example, of those of the European Union in years 2006 and 2008. Hence, the formula is more general than the well known formula of Yakovenko et al.. That is, our formula well describes not only two regions but simultaneously the third region in the plot of the complementary cumulative distribution function vs. an annual household income. Furthermore, the known stylised facts concerning this income are well described by our formula. Namely, the formula provides the Boltzmann–Gibbs income distribution function for the low-income society class and the weak Pareto law for the medium-income society class, as expected. Importantly, it predicts (to satisfactory approximation) the Zipf law for the high-income society class. Moreover, the region of medium-income society class is now distinctly reduced because the bottom of high-income society class is distinctly lowered. This reduction made, in fact, the medium-income society class an intermediate-income society class.