Optimal Control of Pollutants with Delayed Stock Accumulation

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract: We study the optimal control of a pollutant that accumulates with a delay. We find that optimal paths are, in general, non-monotonic and oscillatory, but monotonic if the objective function is additively separable. Hence, using additively separable objective functions as an approximation to a general objective function may be a misspecification. Terms of use: Documents in EconStor mayWith a numerical example we illustrate that an additively separable approximation performs considerably worse in delayed compared to instantaneous stock accumulation.

Optimal pollution control with distributed delays

“…Delays have only quantitative but not qualitative effects on the optimal trajectory. An intuitive result, shown by Winkler (2008) and Bourgeois and Jayet (2011), and for which we present a full proof in A.2 (Lemma 5), is that an increase of the delay increases the optimal steady state pollution stock. The optimality conditions, derived and discussed in A.1 (equation 13), allow us to show that a higher delay leads to a higher emission level at the steady state.…”

“…This problem has been studied by Winkler (2008) and Bourgeois and Jayet (2011). As we recall in A with a full resolution, on the optimal path, c (t) depends only on p (t − τ ), for every t ≥ 0.…”

Optimal Control for a Groundwater Pollution Ruled by a Convection–Diffusion–Reaction Problem

“…This time delay is mainly included through black-box models. Using delay equations, Winkler [5] proves that optimal pollution emission paths are monotonous if the objective is separable into an emission component and a stock component, but that they may display damping oscillations if not. Bourgeois and Jayet [6] consider the impact of the time delay taken by the pollution to reach the aquifer on the optimal path, and they prove that this effect is amplified by asymmetric information.…”