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Laplace transform analysis of a multiplicative asset transfer model

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  • Andrey Sokolov
  • Andrew Melatos
  • Tien Kieu
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    Abstract

    We analyze a simple asset transfer model in which the transfer amount is a fixed fraction $f$ of the giver's wealth. The model is analyzed in a new way by Laplace transforming the master equation, solving it analytically and numerically for the steady-state distribution, and exploring the solutions for various values of $f\in(0,1)$. The Laplace transform analysis is superior to agent-based simulations as it does not depend on the number of agents, enabling us to study entropy and inequality in regimes that are costly to address with simulations. We demonstrate that Boltzmann entropy is not a suitable (e.g. non-monotonic) measure of disorder in a multiplicative asset transfer system and suggest an asymmetric stochastic process that is equivalent to the asset transfer model.

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    File URL: http://arxiv.org/pdf/1004.5169
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    Paper provided by arXiv.org in its series Papers with number 1004.5169.

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    Date of creation: Apr 2010
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    Publication status: Published in Physica A 389 (2010) 2782-2792
    Handle: RePEc:arx:papers:1004.5169

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    Web page: http://arxiv.org/

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    6. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
    7. M. Patriarca & A. Chakraborti & E. Heinsalu & G. Germano, 2007. "Relaxation in statistical many-agent economy models," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 57(2), pages 219-224, 05.
    8. Angle, John, 2006. "The Inequality Process as a wealth maximizing process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 388-414.
    9. Arnab Chatterjee & Bikas K. Chakrabarti & Robin B. Stinchcombe, 2005. "Master equation for a kinetic model of trading market and its analytic solution," Papers cond-mat/0501413, arXiv.org, revised Aug 2005.
    10. A. Chakraborti & B.K. Chakrabarti, 2000. "Statistical mechanics of money: how saving propensity affects its distribution," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 17(1), pages 167-170, September.
    11. Marco Patriarca & Anirban Chakraborti & Els Heinsalu & Guido Germano, 2006. "Relaxation in statistical many-agent economy models," Papers physics/0608174, arXiv.org, revised Aug 2008.
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