The regulation of groundwater quality with delayed responses

This research develops a dynamic model of input regulation in the presence of externalities that do not occur simultaneously with input use. The model is formulated to study the regulation of firms that apply fertilizer, where leachate from the application of fertilizer accumulates in groundwater over time. In the model we show the derivation of an optimal nitrogen user fee and the consequences of regulatory design when time lags between nitrogen application and nitrate contamination are present. This research also responds to the need of developing a general solution algorithm for an optimal control model when the control variable exhibits a delayed response. A multistage solution algorithm presented in this paper is different from other studies in that a typical relationship is not assumed for the state and adjoint variables.

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