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Ideal-Gas Like Markets: Effect of Savings

  • Arnab Chatterjee
  • Bikas K Chakrabarti
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    We discuss the ideal gas like models of a trading market. The effect of savings on the distribution have been thoroughly reviewed. The market with fixed saving factors leads to a Gamma-like distribution. In a market with quenched random saving factors for its agents we show that the steady state income ($m$) distribution $P(m)$ in the model has a power law tail with Pareto index $\nu$ equal to unity. We also discuss the detailed numerical results on this model. We analyze the distribution of mutual money difference and also develop 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/physics/0507136
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    Paper provided by arXiv.org in its series Papers with number physics/0507136.

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    Date of creation: Jul 2005
    Date of revision: Jul 2005
    Handle: RePEc:arx:papers:physics/0507136
    Contact details of provider: Web page: http://arxiv.org/

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    1. F. Clementi & M. Gallegati, 2004. "Power Law Tails in the Italian Personal Income Distribution," Papers cond-mat/0408067, arXiv.org.
    2. Chatterjee, Arnab & K. Chakrabarti, Bikas & Manna, S.S, 2004. "Pareto law in a kinetic model of market with random saving propensity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 155-163.
    3. Sitabhra Sinha, 2005. "Evidence for Power-law tail of the Wealth Distribution in India," Papers cond-mat/0502166, arXiv.org.
    4. N. Ding & N. Xi & Y. Wang, 2003. "Effects of saving and spending patterns on holding time distribution," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 36(1), pages 149-153, November.
    5. Geoff Willis & Juergen Mimkes, 2004. "Evidence for the Independence of Waged and Unwaged Income, Evidence for Boltzmann Distributions in Waged Income, and the Outlines of a Coherent Theory of Income Distribution," Microeconomics 0408001, EconWPA.
    6. Karen E. Dynan & Jonathan Skinner & Stephen P. Zeldes, 2000. "Do the rich save more?," Finance and Economics Discussion Series 2000-52, Board of Governors of the Federal Reserve System (U.S.).
    7. Sitabhra Sinha, 2003. "Stochastic Maps, Wealth Distribution in Random Asset Exchange Models and the Marginal Utility of Relative Wealth," Papers cond-mat/0304324, arXiv.org.
    8. Levy, Moshe & Solomon, Sorin, 1997. "New evidence for the power-law distribution of wealth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 242(1), pages 90-94.
    9. Arnab Chatterjee & Bikas K. Chakrabarti & Robin B. Stinchcombe, 2005. "Analyzing money distributions in `ideal gas' models of markets," Papers physics/0505047, arXiv.org.
    10. Arnab Chatterjee & Bikas K. Chakrabarti & S. S. Manna, 2003. "Pareto Law in a Kinetic Model of Market with Random Saving Propensity," Papers cond-mat/0301289, arXiv.org, revised Jan 2004.
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