Optimum Forest Rotations of Alternative Tree Species

We solve Faustmann's problem when two tree species are available for planting. The analysis also applies to optimal forest exploitation before an endogenous switch to some alternative land use such as agriculture, housing, or preservation, and vice versa. Each species has its own deterministic growth function and commands a timber price that grows exponentially at a constant rate. Therefore, it may be optimal to first exploit the species whose price is high but grows slowly, and then switch to the alternative species once its price has sufficiently increased relative to the price of the first one. When the land is bare, there exists a threshold of the relative price at which the investor is indifferent between planting either species. When the relative price lies below this switching threshold, it is optimal to plant and harvest the high-price low-rate species repeatedly until the value of the other species warrants its introduction; it is then repeatedly harvested and replanted indefinitely according to the standard Faustmann rule; the rotation does not depend on timber price. Before the switch, the optimal harvest age depends on the relative price; it defines a replanting boundary for relative prices below the switching threshold and a switching boundary for relative prices above the switching threshold. We show that the replanting boundary is a sequence of continuous segments giving the harvest age as function of the relative price; these segments differ depending on the number of harvests of the initial species that remain before the switch. Each segment is first decreasing, then increasing, and crosses Faustmann's rotation twice. On an optimal sequence of harvests, successive rotations are increasingly higher or decreasingly lower than Faustmann's rotation; they may also be constant and equal to Fausmann's rotation.