The private landowner who does not internalize the externality will not choose the socially
optimal rotation period. Thus the need for corrective regulation or tax instruments arises.
Allowing for Choice in Percent Commercial Use and Rotation Timing
To capture the effects of the density of trees left standing, as well as the rotation period on
forest amenities, two major features are added to the previous model. First the forest planner or
the private landowner chooses not only when to cut, but also what percentage per acre to use
commercially. This additional choice is important, since many forest amenities such as erosion
control are directly related to the remaining density of the forest. It may not be optimal to let the
external benefit reach zero, as might be the case with a clear-cut. This is especially true when
the positive externality is control of a potential disaster, such as a flood, massive erosion, or fire.
The firm in this case, before harvesting the first rotation, chooses once and for all what
percentage of each acre of forest to use commercial harvest.4 The remaining trees, the ones not
within the commercial portion of each acre, are “tagged” to remain uncut for as long as they
live.5,6 Second, the externality function and the private gross revenues and costs, the timber
value of the forest, are allowed to be functions of the percentage commercial use, as well as the
forest’s age.
The forest planner again maximizes the sum of the timber and non-timber benefits of the
4 Interesting papers have been written addressing optimal forest thinning (Cawrse, et al (1984), Betters et. al.
(1991)). The choice of commercial use percentage is not identical to the thinning choice, however. Because we are
concerned primarily with externalities associated with clear cuts, this paper focuses on controlling the timing and the
number of trees cut during the final harvest decision. For simplicity and to center attention on the final harvesting
decision, within rotation thinning decisions on the commercial portion of the forest are left out of the model.
5 The trees may be left in different patterns depending on the externality in question. For instance, if the externality
is silt flow into a salmon habitat, a band of trees never-cut lining separating the stream and the commercially
harvested portion of the land would be desirable. If the externality is erosion on the side of a hill, fire control, or
viewing pleasure, the trees left uncut might be spread evenly throughout each acre.
6 This restriction, that trees that are not harvested in the first period are left uncut once and for all, implies that the
commercial use portion of the forest can be modeled as an even age forest.