The comparative dynamics of closed-loop controls for discounted infinite horizon optimal control problems

摘要

A dual view of the Hamilton-Jacobi-Bellman equation corresponding to the class of discounted infinite horizon optimal control problems yields a concise proof of the envelope theorem and an exhaustive comparative dynamics characterization of the closed-loop optimal control vector in the form of a symmetric and positive semidefinite matrix. The theorems are applied to the Hotelling model of the nonrenewable resource extracting firm. Not only do they uncover numerous heretofore unknown qualitative properties of the model, they also yield a new and tractable method for empirically implementing the model in a manner fully consistent with the underlying theory.