IDEAS home Printed from
   My bibliography  Save this paper

Ideal-Gas Like Markets: Effect of Savings


  • Arnab Chatterjee
  • Bikas K Chakrabarti


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.

Suggested Citation

  • Arnab Chatterjee & Bikas K Chakrabarti, 2005. "Ideal-Gas Like Markets: Effect of Savings," Papers physics/0507136,, revised Jul 2005.
  • Handle: RePEc:arx:papers:physics/0507136

    Download full text from publisher

    File URL:
    File Function: Latest version
    Download Restriction: no

    References listed on IDEAS

    1. 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;EDP Sciences, vol. 36(1), pages 149-153, November.
    2. Karen E. Dynan & Jonathan Skinner & Stephen P. Zeldes, 2004. "Do the Rich Save More?," Journal of Political Economy, University of Chicago Press, vol. 112(2), pages 397-444, April.
    3. Arnab Chatterjee & Bikas K. Chakrabarti & Robin B. Stinchcombe, 2005. "Analyzing money distributions in `ideal gas' models of markets," Papers physics/0505047,
    4. Sinha, Sitabhra, 2006. "Evidence for power-law tail of the wealth distribution in India," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 555-562.
    5. 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.
    6. 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.
    7. 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.
    8. Clementi, F. & Gallegati, M., 2005. "Power law tails in the Italian personal income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 427-438.
    9. 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,, revised Jan 2004.
    10. Sitabhra Sinha, 2003. "Stochastic Maps, Wealth Distribution in Random Asset Exchange Models and the Marginal Utility of Relative Wealth," Papers cond-mat/0304324,
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Diniz, M. & Mendes, F.M., 2012. "Effects of taxation on money distribution," International Review of Financial Analysis, Elsevier, vol. 23(C), pages 81-85.

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:physics/0507136. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.