Money in Gas-Like Markets: Gibbs and Pareto Laws

Abstract

We consider the ideal-gas models of trading markets, where each agent is identified with a gas molecule and each trading as an elastic or money-conserving (two-body) collision. Unlike in the ideal gas, we introduce saving propensity $\lambda$ of agents, such that each agent saves a fraction $\lambda$ of its money and trades with the rest. We show the steady-state money or wealth distribution in a market is Gibbs-like for $\lambda =0$, has got a non-vanishing most-probable value for $\lambda \ne 0$ and Pareto-like when $\lambda$ is widely distributed among the agents. We compare these results with observations on wealth distributions of various countries.

4 pages, 2 eps figures, in Conference Procedings of International Conference on "Unconventional Applications of Statistical Physics", Kolkata, India, March 2003; paper published in Physica Scripta T106 (2003) 36

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