Two-Part Tax Controls for Forest Density and Rotation Time

populated area or water source. Intuitively, the clear-cut tax rate decreases as the tax penalty
becomes increasingly graduated.

The sign and magnitude of the lump sum licensing fee depends upon the growth rate of the
value of the externality and τ^CC. The lump sum fee is positive if:

T

∫(F(t,PC)-F(T,PC))e^-rt >τ^CCθ(PC)
0

CC
or, plugging in the optimal τ^CC:

^τ_f∂≤4ir5^ e - rtdt(ΘP1 e - rτ T θ(p

∂P         dP          ^C

0   ^dPC         ∖ ^dPC J

In Case 1, F(t,PC) is strictly increasing over T, for all t<T, so the externalities balance is
negative. Therefore the optimal licensing fee is negative and takes the form of a subsidy. If the
value of the externality grows slowly throughout the rotation, the lump sum subsidy will be
larger. Furthermore, if the social value of the forest is very sensitive to the density of the trees,
requiring a large clear-cut tax, the planner will need to pay a larger subsidy. A large τ^CC may
give the firm incentive to wait longer to harvest than is optimal. The proper lump sum subsidy
corrects this inefficiency.

In Case 2, the amenity is fire control, so F(t,PC) is decreasing over all or some of t<T,
such that the externalities balance is positive. Thus it seems possible that equations (21) and (22)
could hold. However, since the planner is attempting to induce harvest in an otherwise

once the firm decides to harvest, the lump sum fee cannot control P_C.

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