The paper relaxes the one unit storage capacity imposed in the basic search-theoretic model of fiat money with indivisible real commodities and indivisible money. Agents can accumulate as much money as they want. It characterizes the stationary distributions of money and shows that for reasonable parameter values (e.g. production cost, discounting, degree of specialization) a monetary equilibrium exists. There are multiple stationary distributions of a given amount of money, which differ in their welfare levels. Thus, a redistribution of money affects real economic variables in this model. The monetary equilibrium reveals two essential features of money. First, the marginal expected utility of money decreases. Second, there exists an endogenous upper bound on the money holdings: agents willingly produce and sell for money up to this bound and refuse to do so if their money holdings exceed this bound.
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