Fuelwood harvesting in Niger and a generalization of Faustmann's formula

In some forests of Niger where ‘controlled rural markets’ have been organized, fuelwood is harvested following a policy of the form: every T year, cut the dead trees and those live trees which have a diameter greater than D . Dead trees generally form the main part of the harvest. In this paper, we present a simple continuous time model for the management of these uneven-aged stands subject to a high natural death rate α , and we derive a formula for the cycle length and the diameter optimizing the discounted income over an infinite horizon. Faustmann's classical formula for even-aged stands corresponds to the limit α → 0 and D = 0 (clear-cut).