unprofitable forest, the lump sum transfer must be a subsidy. Though F(t,PC) is inverse U
shaped in PC, equation (7), as discussed above, shows that the forest planner must choose a
percentage commercial use on the decreasing part of the amenity function. If the fire control
amenity is more sensitive to the age of the forest, rather the density, the externalities balance will
be relatively large, and F(t,PC) will begin decreasing in PC at a relatively low percentage
commercial use. In this case, the planner will offer the firm a large subsidy to induce shorter
rotation period, but will also tax the percentage commercial use relatively heavily. This results
in more never-cut trees, with less time between “maintenance” harvests. If the fire control
amenity is more sensitive to the density of the forest, rather than the age, the externalities balance
will be smaller, and F(t,PC) will begin decreasing in PC at a relatively high percentage
commercial use per acre. In this case, the planner will offer the firm a smaller subsidy to induce
harvest, but will also tax the percentage commercial use less heavily. This will result in more
trees per acre cleared during harvest, but with slightly longer rotations.
In summary, the clear-cut tax affects both commercial use percentage per acre and rotation
timing. However, in all except a unique case, the tax causes the firm’s rotation period to be too
short or too long. Furthermore, the clear-cut tax cannot induce harvest when the forest is not
privately profitable. Therefore the second part of the two-part instrument, the lump sum
licensing subsidy, is needed to correct for the inefficient rotation period.
4. A SIMPLE NUMERICAL EXAMPLE
So far the model has been very general and has been applicable to a wide range of cases. A
numerical model will illustrate what the optimal tax rates are under different conditions. This
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