Applications to Natural Resources

The increase in the world population is causing a corresponding increase in the demand for the consumption of natural resources. As a consequence, the optimal management and utilization of natural resources are becoming increasingly important. There are two main kinds of natural resource models: those involving renewable resources such as fish, food, timber, etc., and those involving nonrenewable or exhaustible resources such as petroleum, minerals, etc. In Sect. 10.1 we deal with a fishery resource model, the sole owner of which is considered to be a regulatory agency. The management problem of the agency is to control the rate of fishing over time so that an appropriate objective function is maximized over an infinite horizon. Section 10.2 deals with an optimal forest thinning model, where thinning is the process of removing some trees from a forest to improve its growth rate and quality. An extension to a chain of forests model is presented in Sect. 10.2.3. The final model presented in Sect. 10.3 deals with an exhaustible resource such as petroleum, which must be utilized optimally over a given horizon under the assumption that when its price reaches a given high threshold, a substitute will be used instead. Therefore, the analysis of this section can also be viewed as a problem of optimally phasing in an expensive substitute. There are many exercises at the end of the chapter.