Pareto Law in a Kinetic Model of Market with Random Saving Propensity

Details Pareto Law in a Kinetic Model of Market with Random Saving Propensity Pareto Law in a Kinetic Model of Market with Random Saving Propensity

2003-01-16

arxiv.org/abs/cond-mat/0301289v3

Physica A v.335 (2004) p.155-163

Physics

Condensed Matter

Statistical Mechanics

5 pages RevTeX4, 6 eps figures, to be published in Physica A (2004)

Scientific paper

10.1016/j.physa.2003.11.014

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 ($0 \le \lambda < 1$). The system remarkably self-organizes to a critical Pareto distribution of money $P(m) \sim m^{-(\nu + 1)}$ with $\nu \simeq 1$. We analyse 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.

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