On the Mitra–Wan forest management problem in continuous time

The paper provides a continuous-time version of the discrete-time Mitra–Wan model of optimal forest management, where trees are harvested to maximize the utility of timber flow over an infinite time horizon. The available trees and the other parameters of the problem vary continuously with respect to both time and age of the trees, so that the system is ruled by a partial differential equation. The behavior of optimal or maximal couples is classified in the cases of linear, concave or strictly concave utility, and positive or null discount rate. All sets of data share the common feature that optimal controls need to be more general than functions, i.e. positive measures. Formulas are provided for golden-rule configurations (uniform density functions with cutting at the ages that solve a Faustmann problem) and for Faustmann policies, and their optimality/maximality is discussed. The results do not always confirm the corresponding ones in discrete time.