Gamma-distribution and wealth inequality

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.

Presented to the International Workshop and Conference on: Statistical Physics Approaches to Multi-disciplinary Problems, January 07-13, 2008, IIT Guwahati, India

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• Statistical mechanics of money
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• A statistical model with a standard Gamma distribution
• Distributions of money in model markets of economy
• Gibbs versus non-Gibbs distributions in money dynamics
• Generic features of the wealth distribution in ideal-gas-like markets
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• A new $\kappa$-deformed parametric model for the size distribution of wealth
• Laplace transform analysis of a multiplicative asset transfer model