Dynamic Demand and Sequential Monopoly: A Model of Endogenous Screening (with V. Bhaskar)

Abstract:
We analyze a model in which the consumer’s flow utility depends on past as well as current consumption, i.e. is written u(ct; ct-1); where the function u is either strictly submodular or strictly super-modular. Suppliers are small, so that each interacts with the consumer only at one date, but search frictions give rise to monopoly power, and firms offer non-linear prices. Consumers have identical preferences so that differences in taste only arise due to differences in past consumption. When firms observe past consumption, they induce excessive (resp. insufficient) consumption when u is submodular (resp. super-modular). Our main focus is on the case where past consumption is unobservable. We show that pure strategy equilibrium fails to exist. In the two-period version of the model, we prove the existence and uniqueness of a mixed strategy equilibrium that gives rise to a distribution of period-one consumptions, and thus an endogenous screening problem in the second period. Consumers are better off when past consumption is unobservable. In the infinite horizon model, we construct a stationary distribution of equilibrium consumption in the supermodular case.