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Geographic Environmental Kuznets Curves: The Optimal Growth Linear-Quadratic Case

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Abstract

We solve a linear-quadratic model of a spatio-temporal economy using a polluting one-input technology. Space is continuous and heterogenous: locations differ in productivity, nature self-cleaning technology and environmental awareness. The unique link between locations is transboundary pollution which is modelled as a PDE diffusion equation. The spatio-temporal functional is quadratic in local consumption and linear in pollution. Using a dynamic programming method adapted to our infinite dimensional setting, we solve the associated optimal control problem in closed-form and identify the asymptotic (optimal) spatial distribution of pollution. We show that optimal emissions will decrease at given location if and only if local productivity is larger than a threshold which depends both on the local pollution absorption capacity and environmental awareness. Furthermore, we numerically explore the relationship between the spatial optimal distributions of production and (asymptotic) pollution in order to uncover possible (geographic) Environmental Kuznets Curve cases.

Suggested Citation

  • 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.
    • Handle: RePEc:aim:wpaimx:1813
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    References listed on IDEAS

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    1. Raouf Boucekkine & Aude Pommeret & Fabien Prieur, 2013. "Technological vs. Ecological Switch and the Environmental Kuznets Curve," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 95(2), pages 252-260.
    2. Raouf Boucekkine & Aude Pommeret & Fabien Prieur, 2013. "Technological vs. Ecological Switch and the Environmental Kuznets Curve," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 95(2), pages 252-260.
    3. Silvia Faggian* & Fausto Gozzi, 2004. "On The Dynamic Programming Approach For Optimal Control Problems Of Pde'S With Age Structure," Mathematical Population Studies, Taylor & Francis Journals, vol. 11(3-4), pages 233-270.
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    5. 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.
    6. Boucekkine, R. & Camacho, C. & Fabbri, G., 2013. "Spatial dynamics and convergence: The spatial AK model," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2719-2736.
    7. 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.
    8. Kallis, Giorgos, 2011. "In defence of degrowth," Ecological Economics, Elsevier, vol. 70(5), pages 873-880, March.
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    12. Dinda, Soumyananda, 2004. "Environmental Kuznets Curve Hypothesis: A Survey," Ecological Economics, Elsevier, vol. 49(4), pages 431-455, August.
    13. BOUCEKKINE, Raouf & KRAWCZYK, Jacek B. & VALLEE, Thomas, 2011. "Environmental quality versus economic performance: a dynamic game approach," LIDAM Reprints CORE 2335, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Barucci, Emilio & Gozzi, Fausto, 1998. "Investment in a vintage capital model," Research in Economics, Elsevier, vol. 52(2), pages 159-188, June.
    15. Torre, Davide La & Liuzzi, Danilo & Marsiglio, Simone, 2021. "Transboundary pollution externalities: Think globally, act locally?," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    16. Thomas Bassetti & Nikos Benos & Stelios Karagiannis, 2013. "CO 2 Emissions and Income Dynamics: What Does the Global Evidence Tell Us?," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 54(1), pages 101-125, January.
    17. E. Barucci & F. Gozzi, 1999. "Optimal advertising with a continuum of goods," Annals of Operations Research, Springer, vol. 88(0), pages 15-29, January.
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    Cited by:

    1. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2022. "A dynamic theory of spatial externalities," Games and Economic Behavior, Elsevier, vol. 132(C), pages 133-165.
    2. Upmann, Thorsten & Uecker, Hannes & Hammann, Liv & Blasius, Bernd, 2021. "Optimal stock–enhancement of a spatially distributed renewable resource," Journal of Economic Dynamics and Control, Elsevier, vol. 123(C).
    3. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2022. "Managing spatial linkages and geographic heterogeneity in dynamic models with transboundary pollution," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    4. William Brock & Anastasios Xepapadeas, 2020. "Spatial Environmental and Resource Economics," DEOS Working Papers 2002, Athens University of Economics and Business.
    5. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2019. "A spatiotemporal framework for the analytical study of optimal growth under transboundary pollution," Working Papers hal-02314035, HAL.

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    More about this item

    Keywords

    growth; geography; transboundary pollution; infinite dimensional optimal control problems;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • O44 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Environment and Growth
    • R11 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes

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