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Dynamical methods in Environmental and Resource Economics

Author

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  • Halkos, George
  • Papageorgiou, George

Abstract

This paper presents, in brief, the fundamentals of optimal control theory together with some notes for differential games, which is the game theoretic analogue of the optimal control. As it is recommended by literature references the main tool of analysis in open loop information structure for environmental models is the Pontryagin’s Maximum Principle, while the Hamilton–Jacobi–Bellman equation is the tool of analysis for any closed loop informational structure. As applications of the above theoretic considerations we present some environmental economic models which are solved both as optimal control problems and as differential games as well.

Suggested Citation

  • Halkos, George & Papageorgiou, George, 2015. "Dynamical methods in Environmental and Resource Economics," MPRA Paper 67845, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:67845
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    File URL: https://mpra.ub.uni-muenchen.de/67845/1/MPRA_paper_67845.pdf
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    References listed on IDEAS

    as
    1. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, June.
    2. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    3. HALKIN, Hubert, 1974. "Necessary conditions for optimal control problems with infinite horizons," LIDAM Reprints CORE 193, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Harold Hotelling, 1931. "The Economics of Exhaustible Resources," Journal of Political Economy, University of Chicago Press, vol. 39(2), pages 137-137.
    5. Forster, Bruce A., 1980. "Optimal energy use in a polluted environment," Journal of Environmental Economics and Management, Elsevier, vol. 7(4), pages 321-333, December.
    6. Halkin, Hubert, 1974. "Necessary Conditions for Optimal Control Problems with Infinite Horizons," Econometrica, Econometric Society, vol. 42(2), pages 267-272, March.
    7. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, November.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Silvia Bertarelli & Chiara Lodi & Stefania Ragni, 2022. "An optimal strategy to control mining and recycling of non-renewable resources," Working Papers 2202, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2022.

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    More about this item

    Keywords

    Optimal control; Differential games; Renewable resources; Environmental and Resource Economics.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • H21 - Public Economics - - Taxation, Subsidies, and Revenue - - - Efficiency; Optimal Taxation
    • Q0 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General
    • Q2 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation
    • Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General
    • Q50 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - General
    • Q52 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Pollution Control Adoption and Costs; Distributional Effects; Employment Effects
    • Q53 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Air Pollution; Water Pollution; Noise; Hazardous Waste; Solid Waste; Recycling

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