Optimal Pricing Under Stochastic Inflation: State:Dependent (s,S) Policies

A model of firm-level optimal pricing under stochastic inflation and fixed costs of adjusting prices is solved and characterized. In this model, inflation alternates stochastically between some positive rate g and zero inflation. We find that a single (s,S) band is not optimal for the firm, as was claimed in the earlier literature. Rather, the firm will set a different (s,S) band for each state of the world, with the zero-inflation band wholly contained in the positive-inflation band. A numerical example is then presented, showing that a higher variance of aggregate price changes increases price dispersion in the positive-inflation state and decreases price dispersion in the zero-inflation state.