Optimal abatement in dynamic multi-pollutant problems when pollutants can be complements or substitutes

We analyze a dynamic multi-pollutant problem where abatement costs of several pollutants are not separable. The pollutants can be either technological substitutes or complements. Environmental damage is induced by the stock of accumulated pollution. Optimal emission paths are found to be qualitatively different for substitutes and complements. We derive general properties governing optimal emission paths and present numerical examples to illustrate our main results. In particular we find that optimal emission paths need not be monotonic, even for highly symmetric pollutants. Finally, we describe a comparatively simple method to implement the optimal path without explicitly knowing its shape.