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Master equation for a kinetic model of trading market and its analytic solution

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  • Arnab Chatterjee
  • Bikas K. Chakrabarti
  • Robin B. Stinchcombe
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    Abstract

    We analyze an ideal gas like model of a trading market with quenched random saving factors for its agents and show that the steady state income ($m$) distribution $P(m)$ in the model has a power law tail with Pareto index $\nu$ exactly equal to unity, confirming the earlier numerical studies on this model. The analysis starts with the development of a master equation for the time development of $P(m)$. Precise solutions are then obtained in some special cases.

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    File URL: http://arxiv.org/pdf/cond-mat/0501413
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number cond-mat/0501413.

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    Date of creation: Jan 2005
    Date of revision: Aug 2005
    Publication status: Published in Phys. Rev. E 72 (2005) 026126
    Handle: RePEc:arx:papers:cond-mat/0501413

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    Web page: http://arxiv.org/

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    Cited by:
    1. Bertram Düring & Giuseppe Toscani, 2008. "International and Domestic Trading and Wealth Distribution," CoFE Discussion Paper 08-02, Center of Finance and Econometrics, University of Konstanz.
    2. Andrey Sokolov & Andrew Melatos & Tien Kieu, 2010. "Laplace transform analysis of a multiplicative asset transfer model," Papers 1004.5169, arXiv.org.
    3. 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.
    4. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
    5. Shu-Heng Chen & Sai-Ping Li, 2011. "Econophysics: Bridges over a Turbulent Current," Papers 1107.5373, arXiv.org.
    6. G. Toscani & C. Brugna & S. Demichelis, 2012. "Kinetic models for the trading of goods," Papers 1208.6305, arXiv.org.
    7. John Angle, 2007. "The Macro Model of the Inequality Process and The Surging Relative Frequency of Large Wage Incomes," Papers 0705.3430, arXiv.org.
    8. Sokolov, Andrey & Melatos, Andrew & Kieu, Tien, 2010. "Laplace transform analysis of a multiplicative asset transfer model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2782-2792.
    9. Düring, B. & Toscani, G., 2007. "Hydrodynamics from kinetic models of conservative economies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 493-506.
    10. Lorenzo Pareschi & Giuseppe Toscani, 2014. "Wealth distribution and collective knowledge. A Boltzmann approach," Papers 1401.4550, arXiv.org.
    11. Ren, F. & Zhang, Y.C., 2008. "Trading model with pair pattern strategies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5523-5534.

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