Statistical mechanics of money: how saving propensity affects its distribution

We consider a simple model of a closed economic system where the total mone y is conserved and the number of economic agents is fixed. Analogous to sta tistical systems in equilibrium, money and the average money per economic a gent are equivalent to energy and temperature, respectively We investigate the effect of the saving propensity of the agents on the stationary or equi librium probability distribution of money. When the agents do not save, the equilibrium money distribution becomes the usual Gibb's distribution, char acteristic of non-interacting agents. However with saving, even for individ ual self-interest, the dynamics becomes cooperative and the resulting asymm etric Gaussian-like stationary distribution acquires global ordering proper ties. Intriguing singularities are observed in the stationary money distrib ution in the market, as functions of the marginal saving propensity of the agents.