Fokker-Planck Description of Wealth Dynamics and the Origin of Pareto's Law

TL;DR

This paper presents a simplified derivation of a Fokker-Planck equation modeling wealth distribution dynamics, explaining the emergence of Pareto's law through a kinetic wealth exchange model with redistribution.

Contribution

It provides a more straightforward derivation of the Fokker-Planck equation for wealth distribution, linking kinetic models to Pareto's law.

Findings

Wealth distribution follows a Pareto-like power law.

The model reproduces stationary wealth distributions similar to empirical data.

Simplified derivation enhances understanding of wealth dynamics.

Abstract

The so-called "Yard-Sale Model" of wealth distribution posits that wealth is transferred between economic agents as a result of transactions whose size is proportional to the wealth of the less wealthy agent. In recent work [B.M. Boghosian, "Kinetics of Wealth and the Pareto Law," {\it Phys. Rev. E} {\bf 89} (2014) 042804], it was shown that this results in a Fokker-Planck equation governing the distribution of wealth. With the addition of a mechanism for wealth redistribution, it was further shown that this model results in stationary wealth distributions that are very similar in form to Pareto's well known law. In this paper, a much simpler derivation of that Fokker-Planck equation is presented.