Monetary Equilibrium from an Initial State: The Case Without Discounting

This paper studies the existence of single-price price equilibrium from a given initial distribution of money holdings in a search-theoretic model of money where agents have no time preference. The model is similar to the authors' recent models of search economies with no constraints on money inventories, except that here money is modeled as indivisible and traders are assumed to have overtaking-criterion preferences rather than discounting. The equilibrium concept is dynamic equilibrium from an initial distribution of money holdings rather than steady-state equilibrium (which possibly might not be reachable from an initial state) which was studied earlier. In this environment, under some mild conditions on the initial distribution, single-price equilibrium always exists. More precisely, there is an equilibrium path, along which agents trade at the same price, and the money-holdings distribution converges asymptotically to a unique geometric distribution.