# Ideal-Gas Like Markets: Effect of Savings

## Author Info

• Arnab Chatterjee
• Bikas K Chakrabarti
Registered author(s):

## Abstract

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

## Bibliographic Info

Paper provided by arXiv.org in its series Papers with number physics/0507136.

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 Length: 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/

## References

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1. 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.
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. 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.
4. F. Clementi & M. Gallegati, 2004. "Power Law Tails in the Italian Personal Income Distribution," Papers cond-mat/0408067, arXiv.org.
5. 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.
6. Sitabhra Sinha, 2005. "Evidence for Power-law tail of the Wealth Distribution in India," Papers cond-mat/0502166, arXiv.org.
7. 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.
8. Arnab Chatterjee & Bikas K. Chakrabarti & Robin B. Stinchcombe, 2005. "Analyzing money distributions in `ideal gas' models of markets," Papers physics/0505047, arXiv.org.
9. G. Willis & J. 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," Papers cond-mat/0406694, arXiv.org.
10. 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.
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