Differentiating equation (14) with respect to τLS yields the effect of the lump sum licensing
fee on PC*:
dPc * λ
(17)
—— = 0
dτL
Differentiating equation (14) with respect to τCC yields the effect of the clear-cut tax on
PC*:
dPc *
dτCC
dθ(Pc)
dPc
<0
(18)
The licensing fee has no effect on the optimal commercial use percentage. This is expected.
The licensing fee penalizes the firm a fixed amount every rotation, but does not penalize it based
on how much of each acre it allocates for harvest. Therefore the firm’s profit maximizing
commercial use percentage is not influenced by the lump-sum licensing fee.14 The effect of the
clear-cut tax depends upon the marginal penalty received for cutting Pc. Since by definition
θ(Pc) is increasing in Pc, the tax decreases the optimal commercial use percentage. Further, the
net effect of the two-tax instrument on Pc is negative when both taxes are positive. The policy
will always serves to decreases the optimal density of the harvest.
17
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