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

¹ Aix-Marseille University (Aix-Marseille School of Economics and IMéRA), CNRS, EHESS and Ecole Centrale de Marseille, Senior Member of the Institut Universitaire de France, Marseille, France.
² Univ. Grenoble Alpes, CNRS, INRA, Grenoble INP, GAEL, 38000 Grenoble, France.
³ Università degli Studi di Siena, Dipartimento di Economia Politica e Statistica, Siena, Italy.
⁴ Dipartimento di Economia e Finanza, LUISS Guido Carli, Rome, Italy.

^* Corresponding author: giorgio.fabbri@univ-grenoble-alpes.fr

Received: 3 May 2018
Accepted: 13 December 2018

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.