A generalized Faustmann model for the determination of optimal harvest age

Abstract

This paper presents a generalization of the classic Faustmann formula for land expectation value. The generalized Faustmann formula allows the harvest age to vary from timber crop to timber crop by letting the stumpage price, timber yield, regeneration cost, and interest rate vary from timber crop to timber crop. The generalized Faustmann formula is then shown to be a dynamic programming problem that could theoretically be solved by the forward recursive solution method. To solve the problem analytically, the first-order condition for reaching the optimal harvest age is derived. The derivation yields a compact and tidy result similar to that derived from the classic Faustmann formula. This analytical result also provides a simple solution for obtaining the optimal harvest age of any particular timber crop. In addition to presenting two empirical examples, one of a southern pine pulpwood plantation for short harvest age and one of a Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) sawtimber stand for long harvest age, the paper also examines analytically the impact of changes in both the current and future stumpage price, regeneration cost, and interest rate on the optimal harvest age. The impacts are then contrasted with those obtained under the classic Faustmann formula. The paper concludes by pointing out that it would be a rewarding endeavor to examine many topics in the timber management literature under the generalized Faustmann formula.