Dynamic Demand and Sequential Monop oly: A Model of Endogenous Screening (with V. Bhaskar)
Abstract:
We analyze a model in which the con
sumer’s flow utility depends on past as well as current consumption, i.e. i
s written u(ct; ct-1); where the function u is either strictly submodular o
r strictly super-modular. Suppliers are small, so that each interacts with
the consumer only at one date, but search frictions give rise to monopoly p
ower, and firms offer non-linear prices. Consumers have identical preferenc
es so that differences in taste only arise due to differences in past consu
mption. When firms observe past consumption, they induce excessive (resp. i
nsufficient) consumption when u is submodular (resp. super-modular). Our ma
in focus is on the case where past consumption is unobservable. We show tha
t pure strategy equilibrium fails to exist. In the two-period version of th
e model, we prove the existence and uniqueness of a mixed strategy equilibr
ium 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, w
e construct a stationary distribution of equilibrium consumption in the sup
ermodular case.