Abstract
It is possible to think of numerous economic problems involving dynamic constrained optimization where dual representations exist and possibly can be characterized. One example arises in the theory of dynamic factor demand and, more generally, investment decisions. Its duality structure has been studied by Eptein in several papers. The extraction of non-renewable resources is an investment problem and, furthermore, specific boundary conditions must be satisfied at the date of exhaustion if it occurs in a finite time. This paper shows how the theory of dynamic duality can be worked out in such problems. A family of functions which satisfy the properties of the corresponding value function is also provided. While natural resource extraction is a prime candidate for empirical applications, other applications could be carried out in such areas as R and D, the management of information, and advertising.
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