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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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    2. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi & Ted Loch-Temzelides & Cristiano Ricci, 2025. "Differential climate games with heterogenous players," AMSE Working Papers 2534, Aix-Marseille School of Economics, France.
    3. 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).
    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 & Ted Loch-Temzelides & Cristiano Ricci, 2025. "An integral transformation approach to differential games: a climate model application," LIDAM Discussion Papers IRES 2025001, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    6. 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).
    7. 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).
    8. 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.

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    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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