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We analyze an ideal gas like models of a trading market. We propose a new fitfor the money distribution in the fixed or uniform saving market. For themarketwith quenched random saving factors for its agents we show that thesteady state income ($m$) distribution $P(m)$ in the model has a power law tailwith Pareto index $\nu$ exactly equal to unity, confirming the earliernumerical studies on this model. We analyze the distribution of mutual moneydifference and also develop a master equation for the time development of$P(m)$. Precise solutions are then obtained in some special cases.

Analyzing money distributions in ‘ideal gas’ models of markets