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Optimal control of pollutants with delayed stock accumulation

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Abstract

We study the optimal control of a pollutant that accumulates with a delay.We find that optimal paths are, in general, non-monotonic and oscillatory, but monotonic if the objective function is additively separable. Hence, using additively separable objective functions as an approximation to a general objective function may be a misspecification. With a numerical example we illustrate that an additively separable approximation performs considerably worse in delayed compared to instantaneous stock accumulation.

Suggested Citation

  • Ralph Winkler, 2008. "Optimal control of pollutants with delayed stock accumulation," CER-ETH Economics working paper series 08/91, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
  • Handle: RePEc:eth:wpswif:08-91
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    1. Smith, Vernon L., 1977. "Control theory applied to natural and environmental resources an exposition," Journal of Environmental Economics and Management, Elsevier, vol. 4(1), pages 1-24, March.
    2. Asea, Patrick K. & Zak, Paul J., 1999. "Time-to-build and cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1155-1175, August.
    3. Boucekkine, Raouf & Germain, Marc & Licandro, Omar, 1997. "Replacement Echoes in the Vintage Capital Growth Model," Journal of Economic Theory, Elsevier, vol. 74(2), pages 333-348, June.
    4. Goeschl, Timo & Perino, Grischa, 2007. "Innovation without magic bullets: Stock pollution and R&D sequences," Journal of Environmental Economics and Management, Elsevier, vol. 54(2), pages 146-161, September.
    5. Ulrich Brandt-Pollmann & Ralph Winkler & Sebastian Sager & Ulf Moslener & Johannes Schlöder, 2008. "Numerical Solution of Optimal Control Problems with Constant Control Delays," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 181-206, March.
    6. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 2005. "Vintage capital and the dynamics of the AK model," Journal of Economic Theory, Elsevier, vol. 120(1), pages 39-72, January.
    7. Frederick Ploeg & Cees Withagen, 1991. "Pollution control and the Ramsey problem," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 1(2), pages 215-236, June.
    8. Benhabib, Jess & Rustichini, Aldo, 1991. "Vintage capital, investment, and growth," Journal of Economic Theory, Elsevier, vol. 55(2), pages 323-339, December.
    9. Baumgärtner, Stefan & Jöst, Frank & Winkler, Ralph, 2009. "Optimal dynamic scale and structure of a multi-pollution economy," Ecological Economics, Elsevier, vol. 68(4), pages 1226-1238, February.
    10. Mauro Bambi, 2006. "Endogenous Growth and Time-to-Build: the AK Case," Economics Working Papers ECO2006/17, European University Institute.
    11. Falk Ita & Mendelsohn Robert, 1993. "The Economics of Controlling Stock Pollutants: An Efficient Strategy for Greenhouse Gases," Journal of Environmental Economics and Management, Elsevier, vol. 25(1), pages 76-88, July.
    12. Keeler, Emmett & Spence, Michael & Zeckhauser, Richard, 1972. "The optimal control of pollution," Journal of Economic Theory, Elsevier, vol. 4(1), pages 19-34, February.
    13. Christoph Heinzel & Ralph Winkler, 2007. "The role of environmental and technology policies in the transition to a low-carbon energy industry," CER-ETH Economics working paper series 07/71, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    14. Moslener, Ulf & Requate, Till, 2007. "Optimal abatement in dynamic multi-pollutant problems when pollutants can be complements or substitutes," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2293-2316, July.
    15. Goulder, Lawrence H. & Mathai, Koshy, 2000. "Optimal CO2 Abatement in the Presence of Induced Technological Change," Journal of Environmental Economics and Management, Elsevier, vol. 39(1), pages 1-38, January.
    16. El-Hodiri, Mohamed A & Loehman, Edna & Whinston, Andrew B, 1972. "An Optimal Growth Model with Time Lags," Econometrica, Econometric Society, vol. 40(6), pages 1137-1146, November.
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    Cited by:

    1. Augeraud-Véron, Emmanuelle & Leandri, Marc, 2014. "Optimal pollution control with distributed delays," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 24-32.
    2. Emmanuelle Augeraud-Véron & Catherine Choquet & Éloïse Comte, 2017. "Optimal Control for a Groundwater Pollution Ruled by a Convection–Diffusion–Reaction Problem," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 941-966, June.

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    More about this item

    Keywords

    additively separable objective; approximated objective; delayed optimal control; optimal pollution control;
    All these keywords.

    JEL classification:

    • Q50 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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