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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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    Cited by:

    1. Geoff Willis, 2004. "Laser Welfare: First Steps in Econodynamic Engineering," Microeconomics 0408003, EconWPA.
    2. Lai, Li-Hua, 2015. "Statistical premium in correlated losses of insurance," Economic Modelling, Elsevier, vol. 49(C), pages 248-253.
    3. 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.
    4. John Angle, 2007. "The Macro Model of the Inequality Process and The Surging Relative Frequency of Large Wage Incomes," Papers 0705.3430, arXiv.org.
    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. Lux, Thomas, 2008. "Applications of statistical physics in finance and economics," Kiel Working Papers 1425, Kiel Institute for the World Economy (IfW).
    7. 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.
    8. 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.
    9. 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.
    10. repec:eee:phsmap:v:490:y:2018:i:c:p:278-288 is not listed on IDEAS
    11. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: II. Agent-based models," Post-Print hal-00621059, HAL.
    12. Chakrabarti, Anindya S. & Chakrabarti, Bikas K., 2010. "Statistical theories of income and wealth distribution," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 4, pages 1-31.
    13. 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.
    14. Thomas Lux, 2009. "Applications of Statistical Physics in Finance and Economics," Chapters,in: Handbook of Research on Complexity, chapter 9 Edward Elgar Publishing.

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