Optimal Exploitation of Nonrenewable Resources

• Published in: Journal of optimization theory and applications Vol. 167; no. 3; pp. 928 - 948
• Main Authors: Kunow, Angela, Rosche, Sandy, Tammer, Christiane, Weiser, Christoph
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2015; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Approximation; Calculus of Variations and Optimal Control; Optimization; Contracts; Control theory; Demand curves; Dynamics; Economic models; Economic theory; Energy resources; Engineering; Exploitation; Gasoline; Human; Industrial development; Mathematical analysis; Mathematics; Mathematics and Statistics; Maximum principle; Monopolies; Operations Research/Decision Theory; Optimization; Petroleum; Shadow prices; Studies; Theory of Computation; Petrol; Maximum principle; Demand curve
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-013-0429-y

Since the oil-crisis in the seventies of the last century humans have become aware of the finite availability of scarce resources and the influence of today’s exploitation on future wealth. Thus following the demand to integrate lasting (sustained) effects of human acting into economic models presupposes long-term thinking in form of a generation contract. Only dynamic modeling matches the prerequisites of solving these problems. Therefore, we develop a model of dynamic exploitation for oil-exploitation and use the maximum principle to generate algorithm to find an approximate solution. We use this algorithm to solve an example and give interpretation of the results.