Characterizing Interdependent Renewable and Nonrenewable resources: A Stochastic Multi-sector Characterization of Bellman's Principle of Optimality

This paper focuses on the interaction of renewable and nonrenewable resources within the context of a stochastic model of optimal control. First, although existence of a multidimensional closed form solution to the general multi-sector Bellman model remains an open mathematical question, this analysis offers a characterization which can also be extended to other applications. Second, three stochastic golden rules with respect to resource exploitation are established. Finally, within the context of coastal development, this analysis explains why renewable resources become increasingly vulnerable to random external shocks as nonrenewable resources are depleted.