Convergence of Optimal Harvesting Policies to a Normal Forest

This paper extends the forestry maximum principle of Heaps (1984) to allow the benefits of harvesting to be the utility of the volume of wood harvested as in Mitra - Wan (1985, 1986). Unlike those authors, however, time is treated as a continuous rather than as a discrete variable. Existence of an optimal harvesting policy is established. Then necessary conditions are derived for the extended model which are also sufficient. The conditions are used to show that uniformly bounded sequences of optimal harvesting policies contain subsequences which converge pointwise a.e. and in net present value to an optimal harvesting policy. This result is then used to show that any optimal logging policy must converge in harvesting age to a constant rotation period given by modified Faustmann formula. The associated age class distribution converges to a normal forest.