Optimal emission-extraction policy in a world of scarcity and irreversibility

Abstract

This paper extends the classical exhaustible-resource/stock-pollution model with irreversibility of pollution decay, meaning that after reaching some threshold there is no decay of the pollution stock. Within this framework, we answer the question how the potential irreversibility of pollution affects the extraction path. We investigate the conditions under which the economy will optimally adopt a reversible policy, and when it is optimal to enter the irreversible region. In the case of irreversibility it may be optimal to leave a positive amount of resource in the ground forever. As far as the optimal extraction/emission policy is concerned, several types of solutions may arise, including solutions where the economy stays at the threshold for a while. Given that different programs may satisfy the first order conditions for optimality, we further investigate when each of these is optimal. The analysis is illustrated by means of a calibrated example. To sum up, for any pollution level, we can identify a critical resource stock such that there exist multiple optima i.e. a reversible and an irreversible policy that yield exactly the same present value. For any resource stock below this critical value, the optimal policy is reversible whereas with large enough resources, irreversible policies outperform reversible programs. Finally, the comparison between irreversible policies reveals that it is never optimal for the economy to stay at the threshold for a while before entering the irreversible region. JEL-Code: Q300, Q530, C610.

Technological vs. Ecological Switch and the Environmental Kuznets Curve

“…There are however two major differences with respect to the latter contribution: the existence of capital accumulation and of pollution decay. We also introduce a key feature: irreversible pollution as in Prieur, Tidball and Withagen (2011).…”

Optimal transition to renewable energy with threshold of irreversible pollution

“…With the plausible parameters values used by Prieur et al (2011), we shall determine the factors favoring adoption or not. We shall notably find the importance of initial fossil resource and initial level of pollution in the maximal inter-temporal utility.…”

Self-regenerating environmental absorption efficiency and the $$\varvec{ soylent~green~scenario}$$ s o y l e n t g r e e n s c e n a r i o

“…Accordingly, once a certain level of the stock of pollution is reached, the pollution absorption efficiency vanishes (e.g., Tahvonen and Withagen 1996;Chevé 2000;and more recently Prieur 2009;Boucekkine et al 2013a, b;Prieur et al 2013;Ayong Le Kama et al 2014). This extension implies that when the initial stock of pollution is close to the saturation level of the absorption efficiency, there is a trade-off between "reversible" and "irreversible" steady states, that is, one possible optimal trajectory leads to a heavily polluted environment with exhausted absorption efficiency, while the other allows for positive absorption efficiency.…”