Inelastically scattering particles and wealth distribution in an open economy

TL;DR

This paper introduces a kinetic model for wealth distribution in society inspired by inelastic granular gases, revealing a power-law tail in the wealth distribution with an analytically derived closed-form solution in the continuous trading limit.

Contribution

It presents a novel kinetic model for wealth exchange based on granular gas analogy, deriving self-similar solutions with power-law tails and analytical expressions for wealth distribution.

Findings

Wealth distribution exhibits a power-law tail with an exponent from a transcendental equation.

Analytical closed-form solution obtained in the continuous trading limit.

Model captures key features of wealth inequality dynamics.

Abstract

Using the analogy with inelastic granular gasses we introduce a model for wealth exchange in society. The dynamics is governed by a kinetic equation, which allows for self-similar solutions. The scaling function has a power-law tail, the exponent being given by a transcendental equation. In the limit of continuous trading, closed form of the wealth distribution is calculated analytically.