Determination of Singular Control in the Optimal Management of Natural Resources

A method is presented to simplify the determination of solutions of certain optimal control problems which commonly arise in natural resource management and bioeconomic contexts. The method, termed the resource-value balance method, essentially leverages an equivalent formulation of the original optimal control problem and, as described, in certain cases the method obviates the need for classical tools from optimal control theory, such as the Pontryagin Principle. Indeed, in these cases the method reduces the original problem to one solvable with elementary calculus techniques. Further, the solution provided by the resource-value balance method is shown to equal the singular solution of an associated (and more commonly considered) input-constrained optimal control problem, providing insight into the nature of singular control in this context. The theory is illustrated with examples from bioeconomics.