A strategic market game with active bankruptcy

We construct stationary Markov equilibria for an economy with fiat money, o ne nondurable commodity, countably many time periods, and a continuum of ag ents. The total production of commodity remains constant, but individual ag ents' endowments fluctuate in a random fashion from period to period. In or der to hedge against these random fluctuations, agents find it useful to ho ld fiat money, which they can borrow or deposit at appropriate rates of int erest; such activity may take place either at a central bank (which fixes i nterest rates judiciously) or through a money-market tin which interest rat es are determined endogenously). We carry out an equilibrium analysis, based on a careful study of Dynamic P rogramming equations and on properties of the invariant measures for associ ated optimally controlled Markov chains. This analysis yields the stationar y distribution of wealth across agents, as well as the stationary price (fo r the commodity) and interest rates (for the borrowing and lending of fiat money). A distinctive feature of our analysis is the incorporation of bankruptcy, b oth as a real possibility in an individual agent's optimization problem, an d as a determinant of interest rates through appropriate balance equations. These allow a central bank (a money-market) to announce (to determine endo genously) interest rates in a way that conserves the total money-supply and controls inflation. General results are provided for the existence of such stationary equilibri a, and several explicitly solvable examples are treated in detail. (C) 2000 Elsevier Science S.A. All rights reserved.