A simple generalization of the Faustmann formula to tree level

The economic decision model serving as an objective function in forest economics was conceived originally by Faustmann at the stand level. Nevertheless, the tree level seems to be an appropriate scale for analysis, especially for harvesting decisions and certain estimations both at tree and stand levels. However, the Faustmann formula cannot be directly applied to the tree level. The present research has provided certain tree-level formulations of the Faustmann formula, including, in particular, tree expectation value (TEV) and land expectation value (LEV). TEV and tree-level LEV formulas were developed by analyzing the Faustmann formula under deterministic conditions. Unlike previous tree-level decision models presented in the forest economics literature, TEV and tree-level LEV formulas incorporate the expectation value of the land occupied by trees and its variability over time as well as the interaction between trees and their trajectories (cutting age). The proposed formulas were then compared with the Faustmann formula using the first-order condition of optimal harvest age. The TEV and tree-level LEV formulas appeared to be absolutely compatible with the Faustmann formula. The utility of the proposed formulas was then illustrated with application examples, including target diameter, stand expectation value, TEV, LEV, and the value of damage to beech trees or stands in northeastern France.