Pollution effects on disease transmission and economic stability

Abstract

In this article, we embed a model of disease spread into a Ramsey model. A stock of pollution, viewed as a productive externality, affects both the disease transmission and the consumption demand. An eco-friendly government levies a proportional Pigouvian tax on production to depollute. We show the coexistence of two steady states in the long run: a disease-free and an endemic steady state. At the endemic steady state, a higher green-tax rate always reduces the pollution level. In the short run, we show the existence of limit cycles (through a Hopf bifurcation) as well as more complex dynamics of codimension two (a Gavrilov-Guckenheimer bifurcation). We complete the study with a numerical illustration of these bifurcations and a new facet of the Green Paradox: a higher tax rate can allow more scope for cycles by lowering the critical aversion to pollution and, thus, contribute to destabilization of the economy and promotion of the intergenerational inequalities.

COVID-19 and a Green Recovery?

“…The papers most close to this one are Bosi and Desmarchelier, 2018 , 2021 , and Goenka and Liu, 2020 . These papers use SIS dynamics in a growth model and model the disease externality.…”

“…directly. Bosi and Desmarchelier, 2021 , extend their earlier paper by making utility depend on pollution and by considering abatement of pollution which is modeled as a stock rather than flow. The current paper studies the effect of both pollution and health and includes health responses as well as abatement activity.…”