A spatiotemporal framework for the analytical study of optimal growth under transboundary pollution

Raouf Boucekkine (1, 2) , Giorgio Fabbri (3) , Salvatore Federico (4) , Fausto Gozzi (5)

1 AMSE - Aix-Marseille Sciences Economiques
2 IMéRA - Institute for Advanced Studies - Aix-Marseille University
3 GAEL - Laboratoire d'Economie Appliquée de Grenoble
4 DEPS - Dipartimento di Economia Politica e Statistica
5 LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma]

We construct a spatiotemporal frame for the study of optimal growth under transboundary pollution. Space is continuous and polluting emissions originate in the intensity of use of the production input. Pollution flows across locations following a diffusion process. The objective functional of the economy is to set the optimal production policy over time and space to maximize welfare from consumption, taking into account a negative local pollution externality and the diffusive nature of pollution. Our framework allows for space and time dependent preferences and productivity, and does not restrict diffusion speed to be space-independent. This provides a comprehensive setting to analyze pollution diffusion with a close account of geographic heterogeneity. The involved optimization problem is infinite-dimensional. We propose an alternative method for an analytical characterization of the optimal paths and the asymptotic spatial distributions. The method builds on a deep economic concept of pollution spatiotemporal welfare effect, which makes it definitely useful for economic analysis.

Mots clés: infinite dimensional optimal control; optimal growth; spatiotemporal modelling; transboundary pollution

Domaines: Economies et finances

Raouf Boucekkine, Giorgio Fabbri, Salvatore Federico, Fausto Gozzi. A spatiotemporal framework for the analytical study of optimal growth under transboundary pollution. 2019. ⟨hal-02314035⟩