State-dependent pricing under infrequent information: a unified framework

We characterize optimal state-dependent pricing rules under various forms of infrequent information. In all models, infrequent price changes arise from the existence of a lump-sum \\"menu cost.\\" We entertain various alternatives for the source and nature of infrequent information. In two benchmark cases with continuously available information, optimal pricing rules are purely state-dependent. In contrast, in all environments with infrequent information, optimal pricing rules are both time- and state-dependent, characterized by \\"trigger strategies\\" that depend on the time elapsed since the last date when information was fully factored into the pricing decision. After considering the case in which information arrives infrequently for exogenous reasons, we address pricing problems in which gathering and processing information also entails a lump-sum cost. When the information and adjustment costs must be incurred simultaneously, the optimal pricing policy is a fixed-price time-dependent rule. When the costs are dissociated, the optimal rule features price stickiness and inattentiveness. Finally, we consider versions of the price-setting problems in which firms continuously entertain partial information. We characterize the optimal pricing rules and provide numerical solution algorithms and examples in a unified framework.