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Optimal pollution control with distributed delays

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  • Augeraud-Véron, Emmanuelle
  • Leandri, Marc

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.

Suggested Citation

  • Augeraud-Véron, Emmanuelle & Leandri, Marc, 2014. "Optimal pollution control with distributed delays," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 24-32.
  • Handle: RePEc:eee:mateco:v:55:y:2014:i:c:p:24-32
    DOI: 10.1016/j.jmateco.2014.09.010
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    References listed on IDEAS

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    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.
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    4. Hippolyte d'Albis & Emmanuelle Augeraud-Véron & Hermen Jan Hupkes, 2012. "Discontinuous Initial Value Problems for Funtional Differential-Algebraic Equations of Mixed Type," Post-Print halshs-00717412, HAL.
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    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.
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    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

    Optimal pollution control; Distributed delays; Mixed type functional differential equations; Hopf bifurcation;
    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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