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.

Geographic environmental Kuznets curves: The optimal growth linear-quadratic case / Boucekkine, R.; Fabbri, G.; Federico, S.; Gozzi, Fausto. - In: MATHEMATICAL MODELLING OF NATURAL PHENOMENA. - ISSN 0973-5348. - 14:1(2019), pp. ---. [10.1051/mmnp/2018076]

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

Gozzi F.
2019

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.
2019
Geography; Growth; Infinite dimensional optimal control problems; Transboundary pollution
Geographic environmental Kuznets curves: The optimal growth linear-quadratic case / Boucekkine, R.; Fabbri, G.; Federico, S.; Gozzi, Fausto. - In: MATHEMATICAL MODELLING OF NATURAL PHENOMENA. - ISSN 0973-5348. - 14:1(2019), pp. ---. [10.1051/mmnp/2018076]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11385/191119
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