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A spatiotemporal framework for the analytical study of optimal growth under transboundary pollution

Author

Listed:
  • Raouf Boucekkine

    (Aix-Marseille University (IMéRA and AMSE), CNRS, EHESS and Ecole Centrale de Marseille.)

  • Giorgio Fabbri

    (Univ. Grenoble Alpes, CNRS, INRA, Grenoble INP, GAEL)

  • Salvatore Federico

    (Universita degli Studi di Siena, Dipartimento di Economia Politica e Statistica, Siena, Italy)

  • Fausto Gozzi

    (Dipartimento di Economia e Finanza, LUISS Guido Carli, Rome, Italy)

Abstract

We construct a spatiotemporal frame for the study of optimal growth under transboundary pollution. Space is continuous and polluting emissions originate in the intensity of use of the production input. Pollution flows across locations following a diffusion process. The objective functional of the economy is to set the optimal production policy over time and space to maximize welfare from consumption, taking into account a negative local pollution externality and the diffusive nature of pollution. Our framework allows for space and time dependent preferences and productivity, and does not restrict diffusion speed to be spaceindependent. This provides a comprehensive setting to analyze pollution diffusion with a close account of geographic heterogeneity. The involved optimization problem is infinite-dimensional. We propose an alternative method for an analytical characterization of the optimal paths and the asymptotic spatial distributions. The method builds on a deep economic concept of pollution spatiotemporal welfare effect, which makes it definitely useful for economic analysis.

Suggested Citation

  • Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2019. "A spatiotemporal framework for the analytical study of optimal growth under transboundary pollution," LIDAM Discussion Papers IRES 2019016, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    • Handle: RePEc:ctl:louvir:2019016
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    References listed on IDEAS

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    1. Emmanuelle Augeraud-Véron & Raouf Boucekkine & Vladimir Veliov, 2019. "Distributed optimal control models in environmental economics: a review," Post-Print hal-02194184, HAL.
    2. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2018. "Geographic Environmental Kuznets Curves: The Optimal Growth Linear-Quadratic Case," AMSE Working Papers 1813, Aix-Marseille School of Economics, France.
    3. Camacho, Carmen & Pérez-Barahona, Agustín, 2015. "Land use dynamics and the environment," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 96-118.
    4. Emmanuelle Augeraud-Véron & Raouf Boucekkine & Vladimir Veliov, 2019. "Distributed optimal control models in environment economics," Post-Print hal-02145182, HAL.
    5. Emilio Barucci & Fausto Gozzi, 2001. "Technology adoption and accumulation in a vintage-capital model," Journal of Economics, Springer, vol. 74(1), pages 1-38, February.
    6. Ballestra, Luca Vincenzo, 2016. "The spatial AK model and the Pontryagin maximum principle," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 87-94.
    7. Dockner Engelbert J. & Van Long Ngo, 1993. "International Pollution Control: Cooperative versus Noncooperative Strategies," Journal of Environmental Economics and Management, Elsevier, vol. 25(1), pages 13-29, July.
    8. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2019. "Growth and agglomeration in the heterogeneous space: a generalized AK approach," Journal of Economic Geography, Oxford University Press, vol. 19(6), pages 1287-1318.
    9. de Frutos, Javier & Martín-Herrán, Guiomar, 2019. "Spatial vs. non-spatial transboundary pollution control in a class of cooperative and non-cooperative dynamic games," European Journal of Operational Research, Elsevier, vol. 276(1), pages 379-394.
    10. Raouf Boucekkine & Jacek Krawczyk & Thomas Vallée, 2011. "Environmental quality versus economic performance: A dynamic game approach," Post-Print hal-03193660, HAL.
    11. W.A. Brock & A. Xepapadeas & A.N. Yannacopoulos, 2014. "Optimal Control in Space and Time and the Management of Environmental Resources," Annual Review of Resource Economics, Annual Reviews, vol. 6(1), pages 33-68, October.
    12. Fabbri, Giorgio, 2016. "Geographical structure and convergence: A note on geometry in spatial growth models," Journal of Economic Theory, Elsevier, vol. 162(C), pages 114-136.
    13. Emmanuelle Augeraud-Véron & Raouf Boucekkine & Vladimir Veliov, 2019. "Distributed Optimal Control Models in Environmental Economics: A Review," AMSE Working Papers 1902, Aix-Marseille School of Economics, France.
    14. Paulo B. Brito, 2022. "The dynamics of growth and distribution in a spatially heterogeneous world," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 21(3), pages 311-350, September.
    15. Barucci, Emilio & Gozzi, Fausto, 1998. "Investment in a vintage capital model," Research in Economics, Elsevier, vol. 52(2), pages 159-188, June.
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    Cited by:

    1. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2021. "From firm to global-level pollution control: The case of transboundary pollution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 331-345.
    2. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2021. "From firm to global-level pollution control: The case of transboundary pollution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 331-345.

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    More about this item

    Keywords

    Optimal growth; spatiotemporal modelling; transboundary pollution; infinite dimensional optimal control;
    All these keywords.

    JEL classification:

    • Q53 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Air Pollution; Water Pollution; Noise; Hazardous Waste; Solid Waste; Recycling
    • R11 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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