Forest value and optimal rotations in continuous cover forestry

The Faustmann forest rotation model is a celebrated contribution in economics. The model provides a forest value expression and allows a solution to the optimal rotation problem valid for perpetual rotations of even-aged forest stands. However, continuous forest cover forest management systems imply uneven-aged dynamics, and while a number of numerical studies have analysed specific continuous cover forest ecosystems in search of optimal management regimes, no one has tried to capture key dynamics of continuous cover forestry in simple mathematical models. In this paper we develop a simple, but rigorous mathematical model of the continuous cover forest, which strictly focuses on the area use dynamics that such an uneven-aged forest must have in equilibrium. This implies explicitly accounting for area reallocation and for weighting the productivity of each age class by the area occupied. The model allows for a simple expression for forest value and the derivation of conditions for the optimal rotation age. The model also makes straightforward comparisons with the well-known Faustmann model possible. We present results for unrestricted as well as area-restricted versions of the models. We find that land values are unambiguously higher in the continuous cover forest models compared with the even-aged models. Under area restrictions, the optimal rotation age in a continuous cover forest model is unambiguously lower than the corresponding area restricted Faustmann solution, while the result for the area unrestricted model is ambiguous.