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

  • Marco Patriarca
  • Anirban Chakraborti
  • Kimmo Kaski
  • Guido Germano

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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File URL: http://arxiv.org/pdf/physics/0504153
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Paper provided by arXiv.org in its series Papers with number physics/0504153.

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Date of creation: Apr 2005
Date of revision: May 2005
Publication status: Published in New Economic Windows 2, 93-110, 2005
Handle: RePEc:arx:papers:physics/0504153
Contact details of provider: Web page: http://arxiv.org/

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