This paper studies optimal experimentation by a monopolist who faces an unknown demand curve subject to random changes, and who maximizes profits over an infinite horizon in continuous time. We show that there are two qualitatively very different regimes, determined by the discount rate and the intensities of demand curve switching, and the dependence of the optimal policy on these parameters is discontinuous. One regime is characterized by extreme experimentation and good tracking of the prevailing demand curve, the other by moderate experimentation and poor tracking. Moreover, in the latter regime the agent eventually becomes “trapped” into taking actions in a strict subset of the feasible set.

This paper presents a dynamic theory of housing market fluctuations. It develops a life-cycle model where households are heterogeneous with respect to income and preferences, and mortgage lending is restricted by a down-payment requirement. the market interaction of young credit-constrained households with order or richer unconstrained households generates the following results. (1) Current income of young credit-constrained households affects housing prices independently of aggregate income. (2) Housing prices and the number of housing transactions are positively correlated. (3) Housing prices over-react to income shocks. (4) A relaxation of the down-payment constraint triggers a boom-but cycle. These results are consistent with patterns observed in the US and the UK.