Optimal price setting with observation and menu costs

We study the price setting problem of a firm in the presence of both observation and menu costs. In this problem the firm optimally decides when to collect costly information on the adequacy of its price, an activity which we refer to as a price ``review''. Upon each review, the firm chooses whether to adjust its price, subject to a menu cost, and when to conduct the next price review. This behavior is consistent with recent survey evidence documenting that firms revise prices infrequently and that only a few price revisions yield a price adjustment.The goal of the paper is to study how the firm's choices map into several observable statistics, depending on the level and relative magnitude of the observation vs the menu cost. The observable statistics are: the frequency of price reviews, the frequency of price adjustments, the size-distribution of price adjustments, and the shape of the hazard rate of price adjustments. We provide an analytical characterization of the firm's decisions and a mapping from the structural parameters to the observable statistics. We compare these statistics with the ones obtained for the models with only one type of cost. The predictions of the model can, with suitable data, be used to quantify the importance of the menu cost vs. the information cost. We also consider a version of the model where several price adjustment are allowed between observations, a form of price plans or indexation. We find that no indexation is optimal for small inflation rates.