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

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

2005-01-18

arxiv.org/abs/cond-mat/0501413v2

Phys. Rev. E 72 (2005) 026126

Physics

Condensed Matter

Other Condensed Matter

6 pages, 2 eps figures, RevTeX4, corrected final version

Scientific paper

10.1103/PhysRevE.72.026126

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.

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