  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.
