This pollution accumulation model shows that the environmental absorption capacity is impacted by economic activity. The resulting optimal control problem has two inter-related state variables: the stock of pollution and the absorption capacity of the environment. The stock of pollution decreases with environmental absorption capacity and increases with the rate of current emissions, which is controlled by a production level as well as an emissions reduction effort. However, the environmental absorption capacity is positively affected by an absorption development effort, and negatively impacted by the stock of pollution. Under specific conditions, it is shown that an optimal path, which can be either monotonic or following transient oscillations, leads to a (nontrivial) saddle-point characterized by a positive environmental absorption capacity. Link to the article
EL OUARDIGHI, F., BENCHEKROUN, H. and GRASS, D. (2014). Controlling Pollution and Environmental Absorption Capacity. Annals of Operations Research, 220(1), pp. 111-133.