Inflationary Bias in a Simple Stochastic Economy

We construct explicit equilibria for strategic market games used to model an economy with fiat money, one nondurable commodity, countably many time- periods, and a continuum of agents. The total production of the commodity is a random variable that fluctuates from period to period. In each period, the agents receive equal endowments of the commodity, and sell them for cash in a market; their spending determines, endogenously, the price of the commodity. All agents have a common utility function, and seek to maximize their expected total discounted utility from consumption. Suppose an outside bank sets an interest rate rho for loans and deposits. If 1+rho is the reciprocal of the discount factor, and if agents must bid for consumption in each period before knowing their income, then there is no inflation. However, there is an inflationary trend if agents know their income before bidding. We also consider a model with an active central bank, which is both accurately informed and flexible in its ability to change interest rates. This, however, may not be sufficient to control inflation