Inflationary Equilibrium in a Stochastic Economy with Independent Agents

We argue that even when macroeconomic variables are constant, underlying microeconomic uncertainty and borrowing constraints generate inflation. We study stochastic economies with fiat money, a central bank, one nondurable commodity, countably many time periods, and a continuum of agents. The aggregate amount of the commodity remains constant, but the endowments of individual agents fluctuate "independently" 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 deterministically 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 and the real rate of interest is equal to the common discount rate of the agents. However, with genuine uncertainty in the endowments and with convex marginal utilities, no interior equilibrium can exist. The equilibrium inflation must then be higher than that predicted by the Fisher equation, and the equilibrium real rate of interest underestimates the discount rate of the agents.