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A Boltzmann-type Approach to the Formation of Wealth Distribution Curves

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  • Bertram Düring

    ()
    (TU Vienna)

  • Daniel Matthes
  • Giuseppe Toscani

Abstract

Kinetic market models have been proposed recently to account for the redistribution of wealth in simple market economies. These models allow to develop a qualitative theory, which is based on methods borrowed from the kinetic theory of rarefied gases. The aim of these notes is to present a unifying approach to the study of the evolution of wealth in the large- time regime. The considered models are divided into two classes: the first class is such that the society’s mean wealth is conserved, while for models of the second class, the mean wealth grows or decreases exponentially in time. In both cases, it is possible to classify the most important feature of the steady (or self-similar, respectively) wealth distributions, namely the fatness of the Pareto tail. We shall also discuss the tails’ dynamical stability in terms of the model parameters. Our results are derived by means of a qualitative analysis of the associated homogeneous Boltzmann equations. The key tools are suitable metrics for probability measures, and a concise description of the evolution of moments. A recent extension to economies, in which different groups of agents interact, is presented in detail. We conclude with numerical experiments that confirm the theo- retical predictions.

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Bibliographic Info

Paper provided by Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number 08-05.

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Length: 57 pages
Date of creation: 07 Oct 2008
Date of revision:
Handle: RePEc:knz:cofedp:0805

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  1. Yougui Wang & Ning Ding & Li Zhang, 2005. "The Circulation of Money and Holding Time Distribution," Papers physics/0507147, arXiv.org.
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  3. Chatterjee, Arnab & Chakrabarti, Bikas K., 2007. "Ideal-gas-like market models with savings: Quenched and annealed cases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 36-41.
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  8. Marco Patriarca & Anirban Chakraborti & Guido Germano, 2005. "Influence of saving propensity on the power law tail of wealth distribution," Papers physics/0506028, arXiv.org.
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  10. Anirban Chakraborti & Bikas K. Chakrabarti, 2000. "Statistical mechanics of money: How saving propensity affects its distribution," Papers cond-mat/0004256, arXiv.org, revised Jun 2000.
  11. Jean-Philippe Bouchaud & Marc Mezard, 2000. "Wealth condensation in a simple model of economy," Science & Finance (CFM) working paper archive 500026, Science & Finance, Capital Fund Management.
  12. Marco Patriarca & Anirban Chakraborti & Els Heinsalu & Guido Germano, 2006. "Relaxation in statistical many-agent economy models," Papers physics/0608174, arXiv.org, revised Aug 2008.
  13. S. Ispolatov & P.L. Krapivsky & S. Redner, 1998. "Wealth distributions in asset exchange models," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 2(2), pages 267-276, March.
  14. Patriarca, Marco & Chakraborti, Anirban & Germano, Guido, 2006. "Influence of saving propensity on the power-law tail of the wealth distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 723-736.
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