A Dynamic Model of the Optimal Rotation of Forests

The introduction of the “maximum principle” by Pontryagin et al. (1964) elevated optimal control as a research tool in economics to prominence. Optimal control model describe the evolvement of a system over a time horizon and determine optimal levels of decision variables over time. Anderson (1976), in comparing the net present value (NPV) model of forest rotation and the optimal control approach to resource management, generated a rotation rule comparable to the Faustmann rule (1968). But both of these approaches assume that timber production is the sole objective of forest management and abstract from multiple forest benefits. The purpose of the present paper is to provide such a comparison when a forest has, besides timber value, a flow of value of recreational services (a general term used to capture non-timber uses of a standing forest) when standing. Through this exercise it is shown that an optimal control model of a slightly different form than the one proposed by Anderson (1976) suffices to generate a rotation rule-comparable to a more general Faustmann rule derived by, e.g., Hartman (1976). The basic theoretical model employed in this paper uses the framework provided by Berck (1981) and Anderson (1976)