The bang-bang production of depletable natural resources
This paper considers the problem of determining the optimal production path for a depletable natural resource. The classical result of Hotelling is that when the market is in equilibrium, the net price paid to the owner of the resource must increase with the interest rate. Three problems are considered: the basic problem, the general problem, and the social optimum problem. For the basic problem, the market is not in equilibrium and the classical solution does not determine the production rate. For the general problem and the social optimum problem, the classical solution does work and we have extended the classical solution to the case of increasing extraction costs. For the basic problem, we have used the Pontryagin Maximum Principle to find a bang-bang solution for the production rate. The classical solution determines the switch points; the times to stop or start production. For all three problems, we have found a differential equation that determines the rent that a resource owner should charge to maximize his profits. The magnitude of the rent depends on its initial value. The proper initial value depends on the total resource and the level of demand. For the general problem with a logit demand function, the classical solution results in a bang-bang production schedule. Thus, we have found two cases where the optimal production path for depletable natural resources is bang-bang.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- DOE Contract Number:
- AC05-84OR21400
- OSTI ID:
- 6555350
- Report Number(s):
- ORNL/TM-10375; ON: DE87009772
- Resource Relation:
- Other Information: Portions of this document are illegible in microfiche products. Original copy available until stock is exhausted
- Country of Publication:
- United States
- Language:
- English
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