Economic characterization of reciprocal isoperimetric control problems

Fundamental identities between the optimal solution functions and optimal value functions for reciprocal pairs of isoperimetric control problems are established in a simple, direct, and economically intuitive fashion. The relationships between the derivatives of the aforementioned functions, the objects of interest in qualitative economic analysis, are shown to follow as a corollary to the identities. The theorem and corollary are applied to the nonrenewable resource extracting model of the firm, where an economic interpretation of them is given, and where new and original comparative dynamics results are derived in a general fashion, without the aid of a phase diagram or specific functional forms.