Distributed optimal control models in environmental economics: a review

Optimal timing problems in environmental economics

Because of the uncertainties and irreversibilities that are often inherent in environmental degradation, its prevention, and its economic consequences, environmental policy design can involve important problems of timing. I use a simple two-period model to illustrate these optimal timing problems and their implications for environmental policy. I then lay out and solve a continuous-time model o...

Solving optimal timing problems in environmental economics

Two papers of Pindyck (2000, 2002) that modeled the control of stock pollutants as optimal stopping problems contained closed form solutions that are incorrect. This paper discusses a subtle error in the derivation and demonstrates how solutions to these and related problems can be obtained numerically. The numerical solutions are contrasted with the ones contained in Pindyck’s original papers....

Mathematical Models of Environmental Economics

The reproductive value in distributed optimal control models.

We show that in a large class of distributed optimal control models (DOCM), where population is described by a McKendrick type equation with an endogenous number of newborns, the reproductive value of Fisher shows up as part of the shadow price of the population. Depending on the objective function, the reproductive value may be negative. Moreover, we show results of the reproductive value for ...

Age-structured optimal control in population economics.

This paper brings both intertemporal and age-dependent features to a theory of population policy at the macro-level. A Lotka-type renewal model of population dynamics is combined with a Solow/Ramsey economy. We consider a social planner who maximizes an aggregate intertemporal utility function which depends on per capita consumption. As control policies we consider migration and saving rate (bo...