Inelastically scattering particles and wealth distribution in an open economy

Abstract

Using the analogy with inelastic granular gases 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, a closed form of the wealth distribution is calculated analytically.