dπ(T, Pc - = 0
dPc
(12)
Equation (11) shows the firm will harvest when the benefit of a marginal increase in T
equals the discounted net profit gained by harvesting at time T. If pPCb(T) < c, the firm will
never harvest unless subsidized. Equation (12) shows the firm will choose PC such that the net
gains in increasing the commercial use percentage equals zero. With fixed costs and no taxes
the firm will arrive at a corner solution, where PC = 1.
Plugging the profit function and the proper partial derivates into 11 and 12 yields:
PPc ~T = I / |(PPcb(T) - c - TLS - τccθ(Pc ))
(13)
dT I1-e J
pb(T) = τcc
-θ( Pc -
dPc
(14
The intuition for equations (13- and (14- are similar to the previous two equations, though it
is clear now, from equation (14- that with constant costs and no tax, an internal solution for Pc
does not exist.
The Growth Function, Externalities, and the Effect of clear-cutting: Two cases
Before launching into analysis of the implementation of clear-cut tax, lump sum licensing fee
combination, it will be helpful again to examine the possible forest characteristics that might
influence the optimal tax combinations as well as the magnitude of their actual effect..
14