Geographic environmental Kuznets curves: the optimal growth linear-quadratic case

Raouf Boucekkine (), Giorgio Fabbri, Salvatore Federico () and Fausto Gozzi

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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.

Keywords: Growth; geography; transboundary pollution; infinite dimensional optimal control problems (search for similar items in EconPapers)
Date: 2019
New Economics Papers: this item is included in nep-agr, nep-ene, nep-env and nep-res
Note: View the original document on HAL open archive server: https://amu.hal.science/hal-02194227v1
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Citations: View citations in EconPapers (10)

Published in Mathematical Modelling of Natural Phenomena, 2019, 14 (1), pp.105. ⟨10.1051/mmnp/2018076⟩

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Related works:
Working Paper: Geographic Environmental Kuznets Curves: The Optimal Growth Linear-Quadratic Case (2018)
Working Paper: Geographic environmental Kuznets curves: The optimal growth linear-quadratic case (2018)
Working Paper: Geographic environmental Kuznets curves: The optimal growth linear-quadratic case (2018)
Working Paper: Geographic Environmental Kuznets Curves: The Optimal Growth Linear-Quadratic Case (2018)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02194227

DOI: 10.1051/mmnp/2018076

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