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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.

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  • 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, Marseille, 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. Fabien Prieur, 2009. "The environmental Kuznets curve in a world of irreversibility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(1), pages 57-90, July.
    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.
    4. Raouf BOUCEKKINE & Giorgio FABBRI & Salvatore FEDERICO & Fausto GOZZI, 2017. "Growth and Agglomeration in the Heterogeneous Space: A Generalized AK Approach," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2017006, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    5. 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.
    6. Kallis, Giorgos, 2011. "In defence of degrowth," Ecological Economics, Elsevier, vol. 70(5), pages 873-880, March.
    7. Stern, David I., 2004. "The Rise and Fall of the Environmental Kuznets Curve," World Development, Elsevier, vol. 32(8), pages 1419-1439, August.
    8. Schumacher, Ingmar & Zou, Benteng, 2008. "Pollution perception: A challenge for intergenerational equity," Journal of Environmental Economics and Management, Elsevier, vol. 55(3), pages 296-309, May.
    9. Kenneth Arrow & Partha Dasgupta & Lawrence Goulder & Gretchen Daily & Paul Ehrlich & Geoffrey Heal & Simon Levin & Karl-Göran Mäler & Stephen Schneider & David Starrett & Brian Walker, 2004. "Are We Consuming Too Much?," Journal of Economic Perspectives, American Economic Association, vol. 18(3), pages 147-172, Summer.
    10. Dinda, Soumyananda, 2004. "Environmental Kuznets Curve Hypothesis: A Survey," Ecological Economics, Elsevier, vol. 49(4), pages 431-455, August.
    11. 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.
    12. BOUCEKKINE, Raouf & KRAWCZYK, Jacek B. & VALLEE, Thomas, 2011. "Environmental quality versus economic performance: a dynamic game approach," CORE Discussion Papers RP 2335, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Keywords

    growth; geography; transboundary pollution; infinite dimensional optimal control problems;

    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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