Inflationary equilibrium in a stochastic economy with independent agents

We prove the existence of stationary monetary equilibrium with inflation in a “Bewley” model with constant aggregate real variables but with idiosyncratic shocks to the endowments of a continuum of individual agents, when a central bank stands ready to borrow or lend fiat money at a fixed nominal rate of interest and the agents face borrowing constraints. We also find that, in the presence of real micro uncertainty about individual endowments, the rate of inflation is higher (equivalently, the real rate of interest is lower) than it would be in a “certainty-equivalent economy”; to wit, one in which every agent's endowment is replaced by its expected value. Thus, underlying microeconomic uncertainty and borrowing constraints are shown to generate additional inflation.