Two-Part Tax Controls for Forest Density and Rotation Time

decrease a firm’s commercial use percentage and rotation period under fairly general conditions.

Two Part Instrument: Clear-cut and Lump Sum Licensing Fee

Differentiating equation (13) with respect to τ^LS yields the effect of the yield tax on the
optimal private rotation period:

dT_

dτ^LS

>0

(15)

Differentiating equation (13) with respect to τ^CC yields the effect of the clear-cut tax on T*:

A positive lump sum tax lengthens the rotation period. With a lump sum licensing fee paid
every rotation, the competitive private owner must let the trees mature longer in order to
maximize profits. The effect of the clear-cut tax on T* is the present value of the marginal clear
cut tax penalty. This is unambiguously positive. When a logging company is persuaded to
harvest fewer trees than is privately optimal, it must let the trees grow longer to maximize
profits. Since both taxes serve to lengthen the optimal rotation period, the effect of the two-part
instrument, where both taxes are positive, is to unambiguously lengthen rotation time. It is also
possible that a properly set subsidy tax instrument could be used to arrive at the optimal T.

¹³ Of course if the threat of fire were severe enough to outweigh the marginal alternate amenity value of even the last
tree, F(t, PC) would be monotonically increasing in PC. In this case, the result is a corner solution. The forest
planner subsidizes the firm to induce profits ≥ 0, and sets τ^CC = 0, allowing a clear-cut.

16

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