Master equation for a kinetic model of trading market and its analytic solution

Arnab Chatterjee, Bikas K. Chakrabarti and Robin B. Stinchcombe

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Abstract: We analyze an ideal gas like model of a trading market with quenched random saving factors for its agents and show that the steady state income ($m$) distribution $P(m)$ in the model has a power law tail with Pareto index $\nu$ exactly equal to unity, confirming the earlier numerical studies on this model. The analysis starts with the development of a master equation for the time development of $P(m)$. Precise solutions are then obtained in some special cases.

Date: 2005-01, Revised 2005-08
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Published in Phys. Rev. E 72 (2005) 026126

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