Two-Part Tax Controls for Forest Density and Rotation Time

Note that while the clear-cut tax affects both PC and T, the licensing fee only affects T.
This is both an interesting and useful result. A planner wanting to control for commercial
harvest percentage can set τ^CC to arrive at the optimal PC, then use τ^LS to fine tune the timing
of each harvest. If the effect of PC on the externality is sufficiently large to produce the need
for a large clear-cut tax, inducing an inefficiently long rotation period, τ^LS can take the form of a
subsidy to reduce the rotation period by the optimal amount.

Setting private first-order conditions equal to social first-order conditions to solve for the
optimal tax rates yields:

T

τ^LS =∫(F(t,PC)-F(T,PC))e^-rt-τ^CCθ(PC)
0

These tax rates make the private first order conditions match the socially optimal first order
conditions. From equation (7) we know the social value function is maximized where F(t,PC) is
decreasing in PC, whether F(t,PC) is monotonically decreasing in PC as in Case 1, or inverse U
shaped in PC as in Case 2. Thus, since the tax penalty is constant or graduated by definition,
the optimal clear cut tax rate is positive in either case. The optimal tax rate increases as the effect
of PC on the externality increases. For example, if the externality were erosion control, the
clear-cut tax would necessarily be higher for firms harvesting on sloped landscapes, or above a

¹⁴ This is true only when there is an interior solution for the maximization problem relative to rotation time. If the
forest is unprofitable to the private firm, a lump sum subsidy could be used to induce harvest of PC >0. However,

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