On Equilibrium Cycles and Normal Forests in Optimal Harvesting of Tree Vintages

A normal forest that has an even land allocation between tree vintages has traditionally been taken as a desirable long-run goal in forestry. In contrast, the presently favored economic hypothesis suggests that under positive discounting the optimal forest vintage structure typically evolves to a cycle without convergence toward the normal forest. This paper proves the existence of the cyclical solution and its global stability properties using elementary methods. The occurrence of cycles in forest harvesting is given a resource economics interpretation. A numerical example that was previously analyzed incorrectly is clarified. In the existing vintage model, forest land has no competing uses. In an extension with competitive land use, the stationary cycles are shown to be replaced by a saddle point path with damped oscillations and convergence toward the normal forest.