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