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Optimal pollution control with distributed delays

Author

Listed:
  • Marc Leandri

    (GREThA - Groupe de Recherche en Economie Théorique et Appliquée - UB - Université de Bordeaux - CNRS - Centre National de la Recherche Scientifique)

  • Emmanuelle Augeraud-Véron

    () (MIA - Mathématiques, Image et Applications - EA 3165 - ULR - Université de La Rochelle)

Abstract

We present a model of optimal stock pollution control with general distributed delays in the stock accumulation dynamics. Using generic functional forms and a distribution structure covering a wide range of distributions, we solve analytically the complex dynamic system that arises from the introduction of these distributed delays. From a theoretical standpoint, our contribution extends the dynamic optimization literature that focused on single discrete delays and develops an original method to address control problems written as mixed type functional differential equations with general kernels. Our results show the qualitative impact of acknowledging these distributed delays on the optimal pollution paths dynamics. We study analytically the properties of the dynamics and we identify the conditions for the occurrence of limit cycles. This theoretical work contributes to the design of efficient environmental policies in the presence of complex delays.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Marc Leandri & Emmanuelle Augeraud-Véron, 2014. "Optimal pollution control with distributed delays," Post-Print hal-01181235, HAL.
  • Handle: RePEc:hal:journl:hal-01181235
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01181235
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    References listed on IDEAS

    as
    1. Boucekkine, R. & Fabbri, G. & Gozzi, F., 2010. "Maintenance and investment: Complements or substitutes? A reappraisal," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2420-2439, December.
    2. Wirl, Franz, 1999. "Complex, dynamic environmental policies," Resource and Energy Economics, Elsevier, vol. 21(1), pages 19-41, January.
    3. 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.
    4. Hippolyte d'Albis & Emmanuelle Augeraud-Véron & Hermen Jan Hupkes, 2012. "Discontinuous Initial Value Problems for Funtional Differential-Algebraic Equations of Mixed Type," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00717412, HAL.
    5. Winkler, Ralph, 2011. "A Note On The Optimal Control Of Stocks Accumulating With A Delay," Macroeconomic Dynamics, Cambridge University Press, vol. 15(4), pages 565-578, September.
    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. Tahvonen, Olli & Salo, Seppo, 1996. "Nonconvexities in Optimal Pollution Accumulation," Journal of Environmental Economics and Management, Elsevier, vol. 31(2), pages 160-177, September.
    8. Cyril Bourgeois & Pierre-Alain Jayet, 2010. "Revisited water-oriented relationships between a set of farmers and an aquifer: accounting for lag effect," Working Papers 2010/06, INRA, Economie Publique.
    9. C. G. Plourde, 1972. "A Model of Waste Accumulation and Disposal," Canadian Journal of Economics, Canadian Economics Association, vol. 5(1), pages 119-125, February.
    10. Keeler, Emmett & Spence, Michael & Zeckhauser, Richard, 1972. "The optimal control of pollution," Journal of Economic Theory, Elsevier, vol. 4(1), pages 19-34, February.
    11. Cropper, M. L., 1976. "Regulating activities with catastrophic environmental effects," Journal of Environmental Economics and Management, Elsevier, vol. 3(1), pages 1-15, June.
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    Cited by:

    1. 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

    distribution; control; pollution; optimal;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • Q5 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics

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