Money in gas-like markets: Gibbs and Pareto laws

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 a saving propensity lambda of agents, such that each agent saves a fraction lambda of its money and trades with the rest. We show that 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 not equal 0 and Pareto-like when lambda is widely distributed among the agents. We compare these results with observations on wealth distributions of various countries.