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Money in Gas-Like Markets: Gibbs and Pareto Laws

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  • Arnab Chatterjee
  • Bikas K. Chakrabarti
  • S. S. Manna

Abstract

We consider the ideal-gas models of trading markets, where each agent is identified with a gas molecule and each trading as an elastic or money-conserving (two-body) collision. Unlike in the ideal gas, we introduce saving propensity $\lambda$ of agents, such that each agent saves a fraction $\lambda$ of its money and trades with the rest. We show the steady-state money or wealth distribution in a market is Gibbs-like for $\lambda=0$, has got a non-vanishing most-probable value for $\lambda \ne 0$ and Pareto-like when $\lambda$ is widely distributed among the agents. We compare these results with observations on wealth distributions of various countries.

Suggested Citation

  • Arnab Chatterjee & Bikas K. Chakrabarti & S. S. Manna, 2003. "Money in Gas-Like Markets: Gibbs and Pareto Laws," Papers cond-mat/0311227, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0311227
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    Citations

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    Cited by:

    1. Lai, Li-Hua, 2015. "Statistical premium in correlated losses of insurance," Economic Modelling, Elsevier, vol. 49(C), pages 248-253.
    2. John Angle, 2007. "The Macro Model of the Inequality Process and The Surging Relative Frequency of Large Wage Incomes," Papers 0705.3430, arXiv.org.
    3. Adams Vallejos & Ignacio Ormazabal & Felix A. Borotto & Hernan F. Astudillo, 2018. "A new $\kappa$-deformed parametric model for the size distribution of wealth," Papers 1805.06929, arXiv.org.
    4. 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.
    5. 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.
    6. Vallejos, Adams & Ormazábal, Ignacio & Borotto, Félix A. & Astudillo, Hernán F., 2019. "A new κ-deformed parametric model for the size distribution of wealth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 819-829.
    7. Geoff Willis, 2004. "Laser Welfare: First Steps in Econodynamic Engineering," Microeconomics 0408003, University Library of Munich, Germany.
    8. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    9. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: II. Agent-based models," Post-Print hal-00621059, HAL.
    10. Chakrabarti, Anindya S. & Chakrabarti, Bikas K., 2010. "Statistical theories of income and wealth distribution," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 4, pages 1-31.
    11. Sebastian Guala, 2009. "Taxes in a Wealth Distribution Model by Inelastically Scattering of Particles," Interdisciplinary Description of Complex Systems - scientific journal, Croatian Interdisciplinary Society Provider Homepage: http://indecs.eu, vol. 7(1), pages 1-7.
    12. Richmond, Peter & Repetowicz, Przemek & Hutzler, Stefan & Coelho, Ricardo, 2006. "Comments on recent studies of the dynamics and distribution of money," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 43-48.
    13. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    14. Thomas Lux, 2009. "Applications of Statistical Physics in Finance and Economics," Chapters, in: J. Barkley Rosser Jr. (ed.), Handbook of Research on Complexity, chapter 9, Edward Elgar Publishing.
    15. Lux, Thomas, 2008. "Applications of statistical physics in finance and economics," Kiel Working Papers 1425, Kiel Institute for the World Economy (IfW Kiel).
    16. Kočišová, J. & Horváth, D. & Brutovský, B., 2009. "The efficiency of individual optimization in the conditions of competitive growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3585-3592.
    17. Aydiner, Ekrem & Cherstvy, Andrey G. & Metzler, Ralf, 2018. "Wealth distribution, Pareto law, and stretched exponential decay of money: Computer simulations analysis of agent-based models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 278-288.

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