Optimal Price Adjustment With Time Dependent Costs

The purpose of this paper is to analyze an optimal pricing rule for the case in which the costs of price adjustment are time dependent, and where those costs depend positively on the magnitude of the percentage price change. By means of discrete time model, it is shown that the optimal response to the problem under consideration is to pre-set prices for each period at the end of the previous period. Within the period prices will adjust if the unexpected shock exceeds a threshold level. In such a case the new price is established at a level that is a weighted average of the pre-set level and of the equilibrium level that would have obtained in the absence of costs of contemporaneous price adjustment. Under certain conditions, which are derived in the paper, higher volatility of unexpected inflation might reduce relative price volatility.