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Statistical mechanics of money: How saving propensity affects its distribution

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  • Anirban Chakraborti
  • Bikas K. Chakrabarti
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    Abstract

    We consider a simple model of a closed economic system where the total money is conserved and the number of economic agents is fixed. In analogy to statistical systems in equilibrium, money and the average money per economic agent are equivalent to energy and temperature, respectively. We investigate the effect of the saving propensity of the agents on the stationary or equilibrium money distribution.The equilibrium probablity distribution of money becomes the usual Gibb's distribution, characteristic of non-interacting agents, when the agents do not save. However with saving, even for local or individual self-interest, the dynamics become cooperative and the resulting asymmetric Gaussian-like stationary distribution acquires global ordering properties. Intriguing singularities are observed in the stationary money distribution in the market, as function of the ``marginal saving propensity'' of the agents.

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    File URL: http://arxiv.org/pdf/cond-mat/0004256
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number cond-mat/0004256.

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    Date of creation: Apr 2000
    Date of revision: Jun 2000
    Publication status: Published in Eur. Phys. J. B 17, 167 (2000)
    Handle: RePEc:arx:papers:cond-mat/0004256

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    Web page: http://arxiv.org/

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    Cited by:
    1. 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.
    2. Angle, John, 2013. "How To Win Acceptance Of The Inequality Process As Economics?," MPRA Paper 52887, University Library of Munich, Germany.
    3. 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.
    4. 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.
    5. 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.
    6. Chakrabarti, Anindya S., 2012. "Effects of the turnover rate on the size distribution of firms: An application of the kinetic exchange models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6039-6050.
    7. Shu-Heng Chen & Sai-Ping Li, 2011. "Econophysics: Bridges over a Turbulent Current," Papers 1107.5373, arXiv.org.
    8. Yougui Wang & Ning Ding, 2005. "Dynamic Process of Money Transfer Models," Papers physics/0507162, arXiv.org.
    9. Michal Brzezinski, 2013. "Do wealth distributions follow power laws? Evidence from "rich lists"," Papers 1304.0212, arXiv.org.
    10. Chakrabarti, Anindya S. & Chakrabarti, Bikas K., 2010. "Inequality reversal: Effects of the savings propensity and correlated returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3572-3579.
    11. Huang, Jing & Wang, Yougui, 2014. "The time-dependent characteristics of relative mobility," Economic Modelling, Elsevier, vol. 37(C), pages 291-295.
    12. Baaquie, Belal E., 2013. "Statistical microeconomics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4400-4416.
    13. 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.
    14. Jan Lorenz & Fabian Paetzel & Frank Schweitzer, . "Redistribution spurs growth by using a portfolio effect on risky human capital," Working Papers ETH-RC-12-018, ETH Zurich, Chair of Systems Design.
    15. Sitabhra Sinha, 2005. "The Rich Are Different!: Pareto Law from asymmetric interactions in asset exchange models," Papers physics/0504197, arXiv.org.
    16. Andrey Sokolov & Andrew Melatos & Tien Kieu, 2010. "Laplace transform analysis of a multiplicative asset transfer model," Papers 1004.5169, 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. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
    19. 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.
    20. 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.
    21. Yougui Wang & Ning Ding & Ning Xi, 2005. "Prospects for Money Transfer Models," Papers physics/0507161, arXiv.org.
    22. Cui, Jian & Pan, Qiuhui & Qian, Qian & He, Mingfeng & Sun, Qilin, 2013. "A multi-agent dynamic model based on different kinds of bequests," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1393-1397.
    23. 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.

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