Kinetic theory models for the distribution of wealth: power law from overlap of exponentials

Details Kinetic theory models for the distribution of wealth: power law from overlap of exponentials Kinetic theory models for the distribution of wealth: power law from overlap of exponentials

2005-04-21

arxiv.org/abs/physics/0504153v2

"Econophysics of Wealth Distributions" (New Economic Windows series), pp. 93-110 (Springer, Milan, 2005), ISBN 978-88-470-0329

Physics

Physics and Society

18 pages, 9 figures, Springer style. Submitted to the Proc. Vol. for the International Workshop on the "Econophysics of Wealth

Scientific paper

Various multi-agent models of wealth distributions defined by microscopic laws regulating the trades, with or without a saving criterion, are reviewed. We discuss and clarify the equilibrium properties of the model with constant global saving propensity, resulting in Gamma distributions, and their equivalence to the Maxwell-Boltzmann kinetic energy distribution for a system of molecules in an effective number of dimensions $D_\lambda$, related to the saving propensity $\lambda$ [M. Patriarca, A. Chakraborti, and K. Kaski, Phys. Rev. E 70 (2004) 016104]. We use these results to analyze the model in which the individual saving propensities of the agents are quenched random variables, and the tail of the equilibrium wealth distribution exhibits a Pareto law $f(x) \propto x^{-\alpha -1}$ with an exponent $\alpha=1$ [A. Chatterjee, B. K. Chakrabarti, and S. S. Manna, Physica Scripta T106 (2003) 367]. Here, we show that the observed Pareto power law can be explained as arising from the overlap of the Maxwell-Boltzmann distributions associated to the various agents, which reach an equilibrium state characterized by their individual Gamma distributions. We also consider the influence of different types of saving propensity distributions on the equilibrium state.

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