Optimum Pricing Policy under Stochastic Inflation

We describe aggregate inflation as a stochastic process in which the rate of change of the price level can be positive or zero, where the times spent in each state are of random duration. This class of processes includes Two-State Markov Chains and Renewal Processes as special cases. It is shown that the optimal pricing policy of a monopolistic firm with non-convex costs of price adjustment is (S, s) in its real-price, i.e. its nominal price relative to the price level. A basic certainty-equivalence result is proved: i.e. the firm behaves as if it faces a certain and fixed rate of inflation, higher than the actual expected rate, the difference between the two rates being a risk premium which depends on the real interest rate and the parameters of the stochastic process. One can thus apply previous results from the case of certainty (Sheshinski and Weiss, The Review of Economic Studies, 1977) to obtain comparative static results. In particular, one finds that an increase in the variance of expected inflation leads firms to choose a pricing policy with larger amplitude in real price. The paper also addresses the question of consistency in firms' expectations when the price level is determined by the firms' actions.