acre. The optimal lump sum payment per rotation period is a subsidy of $8,891. Before taxes,
the firm makes a gross profit of $22,822 per acre. The firm makes an after tax net profit of
$20,302 per acre.
As predicted by the general theoretical model, it is possible, if not likely, that the lump sum
licensing fee will take the form of a subsidy in order to correct for the heavy clear-cut tax
necessary to reach the optimal percentage commercial use per acre. In the case above, the firm is
charged a clear-cut penalty that is nearly half of their gross margins on timber. Furthermore, the
firm is harvesting half of the lumber it would harvest in the absence of the tax. Therefore, to
reach the optimal rotation time and make up for the clear-cut penalty that induces the optimal
harvest percentage but misses the optimal rotation time, the firm must be subsidized each
rotation period.
To better illustrate this point, the model is run under the previous parameter settings with the
tax rates held constant at incorrect values. The lump sum tax is set to zero and the clear-cut tax
rate is held at what optimal in the previous example ($37,444 per acre). Under this tax schedule,
the firm will choose a rotation period of 46 years and a harvest percentage of 61%. The firm lets
the trees grow for four years longer than is socially optimal, and because of the longer rotation
period, the firm harvests 11% more trees than is socially optimal in order to maximize net
profits. Without the corrective lump sum subsidy, the logging firm will harvest too much, too
late.
To evaluate the sensitivity of the model to the assumptions about r and γ, the model is run
with a range of values for these parameters. The effects of changing the discount rate, holding γ
constant, on the optimal rotation period and harvest percentage are shown in Figure II. As
shown in the figure, the optimal commercial use percentage decreases fairly rapidly as the
24
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