Master equation for a kinetic model of trading market and its analytic solution
Arnab Chatterjee, Bikas K. Chakrabarti, Robin B. Stinchcombe
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 ν 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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