Optimal emission-extraction policy in a world of scarcity and irreversibility[Politique optimale d'émission/extraction dans dans un monde de rareté et d’irréversibilité]

This paper extends the classical exhaustible-resource/stock-pollution model with the irreversibility of pollution decay. Within this framework, we are wondering first how the potential irreversibility of pollution affects the extraction path. Our aim is also to emphasize the conditions under which the economy will optimally adopt a reversible policy. Once the situation has turned irreversible, we show that the pollution problem does affect the total amount of resource extracted. In particular, it may be optimal to leave a positive amount of resource in the ground forever. As far the optimal extraction/emission policy is concerned, three types of solutions may arise. We derive a simple condition that guarantees that it is optimal to stay in what is called the reversible region. When this condition does not hold, it is difficult to conclude whether the optimal policy is reversible or irreversible. Using a numerical example, one can find a situation where the optimal path is unique and identify the set of initial conditions associated with each possible policy. Due to the non-convexity introduced by the decay function, the occurrence of multiple optimal solutions cannot be ruled out. Indeed, we present another numerical example in which two optimality candidates – one being reversible, the other irreversible – simultaneously exist. The computation of the present values of both paths reveals that the reversible policy yields the highest value.