Application of optimal control to the determination of an environmental levy

Abstract

This paper is concerned with establishing levies to regulate dam operations to environmentally accepted standards. We aim to establish a simple mathematical tool that could be used to set "appropriate" levels for the environmental levies which would allow the station operator to remain profitable, yet also to ensure that the operator's policy is environmentally acceptable. We shall use Pontriagin 's maximum principle to solve an optimal control problem which will simulate the station operator's behaviour, assuming that their objective is to maximise profits. The optimal solution will be parametric in the target lake level, target extraction rate, and the levels of the environmental levies. Comparing the simulated time paths of outflow and the lake level over a fixed time horizon with the environmental targets, the regulatory authority can then adjust the levies. In other words, we will investigate the sensitivity of the targets and the degree to which they are satisfied when the levies are altered.