discount rate increases. If the discount rate is high, the present value of the amenities a tree
generates (which begin flowing immediately) will outweigh the present value of harvesting the
tree at the end of each period. The amenity is worth relatively more when the discount rate is
higher. Although T is not affected by the externality, it is affected by the discount rate. It is
apparent from Figure II that the higher the discount rate, the shorter the rotation period. If the
firm’s revenue stream is discounted at a higher rate, it will harvest sooner. The decision of PC
seems to be more sensitive to changes in the assumed discount rate than does the decision of the
optimal rotation period. With a discount rate of 7%, the optimal rotation period is 37.7 years
and the optimal commercial use percentage is 18%. Thus the optimal rotation period decreased
less than 12% from the previous example, where r = 3%, but the optimal commercial use
percentage decreases by 37%.
The effect of changing the marginal amenity value, γ, holding r constant, on the optimal
rotation period and commercial use percentage are shown in Figure III. As predicted, the
optimal rotation period is unaffected by the marginal value of the amenity. The optimal PC,
decreases as γ gets larger. As the units on x-axis double, the optimal PC decreases by one
half. There is a seemingly linear inverse relationship between commercial use percentage and
marginal amenity value. At γ = $2.56/board foot, the optimal becomes no harvest at all. This is
analogous to the case where each tree cut might drastically increase the chance of a landslide or
damaging erosion. And although not shown on the figure, values of γ near $0.01 produce a
corner solution , where it is best to clear-cut. The marginal amenity value of each tree is so low
that it is better to chop all of the trees down to reap the timber value.
The different optimal tax rates for changing values of r and γ, are shown in Table I. As
expected, the clear-cut tax rate increases as the interest rate or γ increases. However, the actual
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