An analytic treatment of the Gibbs-Pareto behavior in wealth distribution

TL;DR

This paper introduces a Boltzmann transport theory-based framework to analyze wealth distribution, deriving a combined model that explains both Boltzmann-Gibbs and Pareto behaviors observed in societies.

Contribution

It presents a novel analytical framework that integrates two different interaction models to explain wealth distribution patterns, including Pareto tails.

Findings

Wealth distribution exhibits a Boltzmann-Gibbs form for the poor.

A Pareto-like power-law tail emerges for the wealthy.

The model successfully captures the coexistence of different distribution regimes.

Abstract

We develop a general framework, based on Boltzmann transport theory, to analyze the distribution of wealth in societies. Within this framework we derive the distribution function of wealth by using a two-party trading model for the poor people while for the rich people a new model is proposed where interaction with wealthy entities (huge reservoir) is relevant. At equilibrium, the interaction with wealthy entities gives a power-law (Pareto-like) behavior in the wealth distribution while the two-party interaction gives a Boltzmann-Gibbs distribution.