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

✍ Scribed by Michael R. Caputo

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
248 KB
Volume
27
Category
Article
ISSN
0165-1889

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✦ Synopsis

A dual view of the Hamilton-Jacobi-Bellman equation corresponding to the class of discounted inΓΏnite 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 semideΓΏnite matrix. The theorems are applied to the Hotelling model of the nonrenewable resource extracting ΓΏrm. 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.

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