Gamma-distribution and wealth inequality

TL;DR

This paper reveals that wealth exchange models and particle collision models share a universal gamma-distribution equilibrium, linking wealth inequality to fundamental physical and statistical principles.

Contribution

It demonstrates the equivalence between kinetic wealth-exchange models and mechanical particle models, establishing a universal gamma-distribution for equilibrium wealth.

Findings

Equilibrium wealth distribution is a gamma-distribution in various models.

The distribution's parameters relate to exchange fraction and system dimensions.

Inequality correlates with the fraction of wealth exchanged during interactions.

Abstract

We discuss the equivalence between kinetic wealth-exchange models, in which agents exchange wealth during trades, and mechanical models of particles, exchanging energy during collisions. The universality of the underlying dynamics is shown both through a variational approach based on the minimization of the Boltzmann entropy and a complementary microscopic analysis of the collision dynamics of molecules in a gas. In various relevant cases the equilibrium distribution is the same for all these models, namely a gamma-distribution with suitably defined temperature and number of dimensions. This in turn allows one to quantify the inequalities observed in the wealth distributions and suggests that their origin should be traced back to very general underlying mechanisms: for instance, it follows that the smaller the fraction of the relevant quantity (e.g. wealth or energy) that agents can exchange during an interaction, the closer the corresponding equilibrium distribution is to a fair distribution.