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Pareto law in a kinetic model of market with random saving propensity

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

    We have numerically simulated 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 (quenched) saving propensity of the agents, distributed widely between the agents (0⩽λ<1). The system remarkably self-organizes to a critical Pareto distribution of money P(m)∼m−(ν+1) with ν≃1. We analyze the robustness (universality) of the distribution in the model. We also argue that although the fractional saving ingredient is a bit unnatural one in the context of gas models, our model is the simplest so far, showing self-organized criticality, and combines two century-old distributions: Gibbs (1901) and Pareto (1897) distributions.

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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 335 (2004)
    Issue (Month): 1 ()
    Pages: 155-163

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    Handle: RePEc:eee:phsmap:v:335:y:2004:i:1:p:155-163

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Econophysics; Income distribution; Gibbs and Pareto laws;

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    Cited by:
    1. 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, vol. 4(4), pages 1-31.
    2. Angle, John, 2011. "The particle system model of income and wealth more likely to imply an analogue of thermodynamics in social science," MPRA Paper 28864, University Library of Munich, Germany.
    3. Schinckus, C., 2013. "Between complexity of modelling and modelling of complexity: An essay on econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3654-3665.
    4. Yougui Wang & Ning Ding & Ning Xi, 2005. "Prospects for Money Transfer Models," Papers physics/0507161, arXiv.org.
    5. Chami Figueira, F. & Moura, N.J. & Ribeiro, M.B., 2011. "The Gompertz–Pareto income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 689-698.
    6. 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.
    7. Huang, Jing & Wang, Yougui, 2014. "The time-dependent characteristics of relative mobility," Economic Modelling, Elsevier, vol. 37(C), pages 291-295.
    8. Arnab Chatterjee & Bikas K Chakrabarti, 2005. "Ideal-Gas Like Markets: Effect of Savings," Papers physics/0507136, arXiv.org, revised Jul 2005.
    9. G. Toscani & C. Brugna & S. Demichelis, 2012. "Kinetic models for the trading of goods," Papers 1208.6305, arXiv.org.
    10. Lorenzo Pareschi & Giuseppe Toscani, 2014. "Wealth distribution and collective knowledge. A Boltzmann approach," Papers 1401.4550, arXiv.org.
    11. Sitabhra Sinha, 2005. "The Rich Are Different!: Pareto Law from asymmetric interactions in asset exchange models," Papers physics/0504197, arXiv.org.
    12. 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.
    13. Maldarella, Dario & Pareschi, Lorenzo, 2012. "Kinetic models for socio-economic dynamics of speculative markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 715-730.
    14. Chakrabarti, Anindya S., 2011. "An almost linear stochastic map related to the particle system models of social sciences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4370-4378.
    15. Coelho, Ricardo & Richmond, Peter & Barry, Joseph & Hutzler, Stefan, 2008. "Double power laws in income and wealth distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3847-3851.
    16. Shu-Heng Chen & Sai-Ping Li, 2011. "Econophysics: Bridges over a Turbulent Current," Papers 1107.5373, arXiv.org.
    17. John Angle, 2007. "The Macro Model of the Inequality Process and The Surging Relative Frequency of Large Wage Incomes," Papers 0705.3430, arXiv.org.
    18. J. R. Iglesias & R. M. C. de Almeida, 2011. "Entropy and equilibrium state of free market models," Papers 1108.5725, arXiv.org.
    19. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
    20. Yougui Wang & Ning Ding, 2005. "Dynamic Process of Money Transfer Models," Papers physics/0507162, arXiv.org.
    21. Bertram Düring & Daniel Matthes & Giuseppe Toscani, 2008. "A Boltzmann-type Approach to the Formation of Wealth Distribution Curves," CoFE Discussion Paper 08-05, Center of Finance and Econometrics, University of Konstanz.

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