Nonconvexities in Optimal Pollution Accumulation

With a few exceptions, the analysis of optimal pollution accumulation or detrimental stock externalities rests on the assumptions that the level of damage is unbounded and that pollution decay increases monotonically with the level of pollution stock. We show that these assumptions are restrictive and that their generalization alters the basic economic properties of optimal pollution control. We specify a decay function which is concave with low stock levels and convex when pollution is higher. We show that, although multiple steady states may exist, the globally optimal solution may be independent of the initial pollution level. It is also possible that there are cutoff levels which determine the optimal long-run equilibrium, implying that the feedback control law is discontinuous and nonmonotonic. Bounded damage may have similar implications, but in contrast to concave–convex decay, they may occur even with zero discounting.