When can the environmental profile and emissions reduction be optimised independently of the pollutant level?

Abstract

Consider a model for optimal timing of a policy measure which changes the emission rate, e.g. trading off the cost of reduction against the time-additive aggregate of environmental damage, the disutility from the pollutant stock the infrastructure contributes to. Intuitively, the optimal timing for an infinitesimal pollution source should reasonably not depend on its historical contribution to the stock, as this is negligible. Dropping the size assumption, we show how to reduce the minimisation problem to one not depending on the history of , under linear evolution and suitable linearity or additivity conditions on the damage functional. We employ a functional analysis framework which allows for delay equations, non-Markovian driving noise, a choice between discrete and continuous time, and a menu of integral concepts covering stochastic calculi less frequently used in resource and environmental economics. Examples are given under the common (Markovian Itô) stochastic analysis framework.

Keywords:

• optimal control
• optimal stopping
• environmental policy
• emissions reduction
• linear model
• Banach space
• stochastic differential equations

Acknowledgements

While carrying out this research, the author has been associated with the Oslo Centre for Research on Environmentally friendly Energy (CREE) and the Centre for the Study of Equality, Social Organization (ESOP) at the University of Oslo. CREE and ESOP are supported by The Research Council of Norway. This work was initiated, and part of the results were obtained, under contract with the Development Research Group, Environment and Energy Team at the World Bank, Washington, DC. The content solely reflects the author’s view, and not those of any of his affiliations.

The author is indebted to an anonymous referee for suggesting improvements to readability, and to Bård Harstad for a fruitful discussion. Any errors are, of course, the author’s sole responsibility.