Inflationary Equilibrium in a Stochastic Economy with Independent Agents

We argue that even when macroeconomic variables are constant, underlying microeconomic uncertainty and borrowing constraints gen- erate inflation. We study stochastic economies with fiat money, a central bank, one nondurable commodity, countably many time periods, and a con- tinuum of agents. The aggregate amount of the commodity remains constant, but the endowments of individual agents fluctuate "indepen- dently" in a random fashion from period to period. Agents hold money and, prior to bidding in the commodity market each period, can either borrow from or deposit in a central bank at a fixed rate of interest. If the interest rate is strictly positive, then typically there will not exist an equilibrium with a stationary wealth distribution and a fixed price for the commodity. Consequently, we investigate stationary equilibria with inflation, in which aggregate wealth and prices rise determinis- tically and at the same rate. Such an equilibrium does exist under appropriate bounds on the interest rate set by the central bank and on the amount of borrowing by the agents. If there is no uncertainty, or if the stationary strategies of the agents select actions in the interior of their action sets in equilibrium, then the classical Fisher equation for the rate of inflation continues to hold