Eutrophication is a biological process that has an unfavorable economic impact on the
economic value of the water basins it affects. Eutrophication depends on thresholds effects,
and optimal policies for the regulation of eutrophication must take this into account. Such
optimal policies are derived in the present article by utilizing a novel technique in optimal
control theory. This technique facilitates a proper analysis of deterministic stock pollutants
with thresholds effects, a topic it is argued has been poorly understood in the literature.

In a large number of practical environmental regulation problems, the damage done by
pollutants depends on stocks and/or flows of pollutants exceeding certain thresholds. A
typical example is eutrophication which occur when stocks of nutrients in a lake exceeds a
certain threshold. The present paper presents a model of eutrophication that accounts for
such thresholds. The paper does so by applying a novel technique in optimal control theory
that allows for the analysis of systems where state-variables bounce back and forth over …