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

Arnab Chatterjee·Bikas K. Chakrabarti·S. S. Manna
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Abstract

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 ($0 \le λ< 1$). The system remarkably self-organizes to a critical Pareto distribution of money $P(m) \sim m^{-(ν+ 1)}$ with $ν\simeq 1$. 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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Arnab Chatterjee, Bikas K. Chakrabarti, S. S. Manna. 2004-01-27. Pareto Law in a Kinetic Model of Market with Random Saving Propensity. https://doi.org/10.1016/j.physa.2003.11.014

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