Computation Techniques for Intertemporal Allocation of Natural Resources

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Abstract
Application of optimal control theory to applied problems is limited by the difficulty of numerical solutions. Typically, terminal values for the production period, price, or production level have been assumed rather than optimized. The use of an objective functional with explicit discounting gives direct solution values for n, y(t), p(t), and rent (or consumer surplus) for continuous or discrete problems. The method is usable for numerical solutions to problems with linear demand, cost trend, or expropriation risk. It is illustrated with Fisher's widely used discrete problem and with application to parameters representing remaining world oil resources for competitive and monopolistic assumptions.

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