Optimal Exploitation of Nonrenewable Resources
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 presup...
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| Published in | Journal of optimization theory and applications Vol. 167; no. 3; pp. 928 - 948 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.12.2015
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0022-3239 1573-2878 |
| DOI | 10.1007/s10957-013-0429-y |
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| Abstract | 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. |
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| AbstractList | 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. Issue Title: Deterministic and Stochastic Variational Principles and Applications 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. |
| Author | Weiser, Christoph Kunow, Angela Tammer, Christiane Rosche, Sandy |
| Author_xml | – sequence: 1 givenname: Angela surname: Kunow fullname: Kunow, Angela email: angela.kunow@wiwi.uni-halle.de organization: Department of Economics and Business, Martin-Luther-University Halle-Wittenberg – sequence: 2 givenname: Sandy surname: Rosche fullname: Rosche, Sandy organization: Department of Mathematics, Martin-Luther-University Halle-Wittenberg – sequence: 3 givenname: Christiane surname: Tammer fullname: Tammer, Christiane organization: Department of Mathematics, Martin-Luther-University Halle-Wittenberg – sequence: 4 givenname: Christoph surname: Weiser fullname: Weiser, Christoph organization: Department of Economics and Business, Martin-Luther-University Halle-Wittenberg |
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| Cites_doi | 10.4171/ZAA/17 10.1023/A:1022697700986 10.1515/9783110856149 |
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| DOI | 10.1007/s10957-013-0429-y |
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| References | FeichtingerG.HartlR.F.Optimale Kontrolle ökonomischer Prozesse1986Berlinde Gruyter0612.9000110.1515/9783110856149 BrecknerW.W.Derived sets for weak multiobjective optimization problems with state and control variablesJ. Optim. Theory Appl.199793731020903.90139144309710.1023/A:1022697700986 SethiS.P.ThomsonG.L.Optimal Control Theory: Applications to Management Science and Economics20002BostonKluwer BenkerH.KossertS.Remarks on quadratic optimal control problems in Hilbert spacesZ. Anal. Anwend.1998131321720181 Caldentey, R., Epstein, R., Saure, D.: Optimal Exploitation of a Nonrenewable Resource. Mimeo (2006) KlötzlerR.On a general conception of duality in optimal controlLecture Notes Math.1979BerlinSpringer183196 Pontrjagin, L.S.: Mathematische Theorie optimaler Prozesse Wien (1964) DixitA.K.Optimization in Economic Theory1997OxfordOxford University Press BP: Statistical Review of the World 2007 BP Distribution Services, London (2007) TammerC.Multiobjective optimal control problemsInt. Ser. Numer. Math.1998124971061728776 GorochowikB.B.KirillowaF.M.About scalarization of vector optimization problemsDokl. Akad. Nauk Sov. Union197519588591 Salukvadze, M.E.: Vector optimization problems in control theory. Tbilisi (1975) Rosche, S.: Ausbeutung erschöpfbarer Ressourcen—ein kontrolltheoretischer Ansatz (2005) SeierstadA.SydsæterK.Optimal Control Theory with Economic Applications19932AmsterdamNorth-Holland ChiangA.C.Fundamental Methods of Mathematical Economics19843New YorkMcGraw-Hill 429_CR8 A.K. Dixit (429_CR9) 1997 429_CR7 W.W. Breckner (429_CR10) 1997; 93 R. Klötzler (429_CR15) 1979 429_CR6 429_CR5 429_CR12 A.C. Chiang (429_CR1) 1984 G. Feichtinger (429_CR2) 1986 H. Benker (429_CR14) 1998; 1 C. Tammer (429_CR13) 1998; 124 B.B. Gorochowik (429_CR11) 1975; 19 S.P. Sethi (429_CR4) 2000 A. Seierstad (429_CR3) 1993 |
| References_xml | – reference: Pontrjagin, L.S.: Mathematische Theorie optimaler Prozesse Wien (1964) – reference: BrecknerW.W.Derived sets for weak multiobjective optimization problems with state and control variablesJ. Optim. Theory Appl.199793731020903.90139144309710.1023/A:1022697700986 – reference: FeichtingerG.HartlR.F.Optimale Kontrolle ökonomischer Prozesse1986Berlinde Gruyter0612.9000110.1515/9783110856149 – reference: GorochowikB.B.KirillowaF.M.About scalarization of vector optimization problemsDokl. Akad. Nauk Sov. Union197519588591 – reference: Salukvadze, M.E.: Vector optimization problems in control theory. Tbilisi (1975) – reference: ChiangA.C.Fundamental Methods of Mathematical Economics19843New YorkMcGraw-Hill – reference: SethiS.P.ThomsonG.L.Optimal Control Theory: Applications to Management Science and Economics20002BostonKluwer – reference: TammerC.Multiobjective optimal control problemsInt. Ser. Numer. Math.1998124971061728776 – reference: BP: Statistical Review of the World 2007 BP Distribution Services, London (2007) – reference: SeierstadA.SydsæterK.Optimal Control Theory with Economic Applications19932AmsterdamNorth-Holland – reference: KlötzlerR.On a general conception of duality in optimal controlLecture Notes Math.1979BerlinSpringer183196 – reference: Rosche, S.: Ausbeutung erschöpfbarer Ressourcen—ein kontrolltheoretischer Ansatz (2005) – reference: Caldentey, R., Epstein, R., Saure, D.: Optimal Exploitation of a Nonrenewable Resource. Mimeo (2006) – reference: BenkerH.KossertS.Remarks on quadratic optimal control problems in Hilbert spacesZ. Anal. Anwend.1998131321720181 – reference: DixitA.K.Optimization in Economic Theory1997OxfordOxford University Press – volume-title: Optimal Control Theory: Applications to Management Science and Economics year: 2000 ident: 429_CR4 – ident: 429_CR6 – ident: 429_CR5 – ident: 429_CR12 – ident: 429_CR7 – ident: 429_CR8 – volume: 19 start-page: 588 year: 1975 ident: 429_CR11 publication-title: Dokl. Akad. Nauk Sov. Union – start-page: 183 volume-title: Lecture Notes Math. year: 1979 ident: 429_CR15 – volume-title: Optimization in Economic Theory year: 1997 ident: 429_CR9 – volume: 1 start-page: 13 issue: 3 year: 1998 ident: 429_CR14 publication-title: Z. Anal. Anwend. doi: 10.4171/ZAA/17 – volume-title: Optimal Control Theory with Economic Applications year: 1993 ident: 429_CR3 – volume: 93 start-page: 73 year: 1997 ident: 429_CR10 publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1022697700986 – volume: 124 start-page: 97 year: 1998 ident: 429_CR13 publication-title: Int. Ser. Numer. Math. – volume-title: Fundamental Methods of Mathematical Economics year: 1984 ident: 429_CR1 – volume-title: Optimale Kontrolle ökonomischer Prozesse year: 1986 ident: 429_CR2 doi: 10.1515/9783110856149 |
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| SubjectTerms | 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 |
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| Title | Optimal Exploitation of Nonrenewable Resources |
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