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 recent models (Green and Zhou [2] and Zhou [5]) 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. J.E.L. Classification: D51, E40 The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.