Pareto law in a kinetic model of market with random saving propensity

We have numerically simulated 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 (quenched) saving propensity of the agents, distributed widely between the agents (0less than or equal tolambda<1). The system remarkably self-organizes to a critical Pareto distribution of money P(m) similar to m(-(nu+1)) with nu-1. We analyze the robustness (universality) of the distribution in the model. We also argue that although the fractional saving ingredient is a bit unnatural one in the context of gas models, our model is the simplest so far, showing self-organized criticality, and combines two century-old distributions: Gibbs (1901) and Pareto (1897) distributions. (C) 2003 Elsevier B.V. All rights reserved.