Two-Part Tax Controls for Forest Density and Rotation Time

condition can be written as: ²

The social planner will allow cutting when the growth rate of the forest in net timber value is
equal to a discount factor plus the “externalities balance”, as dubbed by Englin and Klan (1990),
divided by G(T), the timber value at T. ³ Think of the externalities balance as the present value
of the difference between the forest benefits available at the end of the rotation period, F(T) ,
and the stream of benefits available from the growing forest throughout the rotation period.
Whether the optimal rotation time is shorter or longer than it would be without externalities
depends on the sign of the second term on the right hand side. Furthermore, the sign of this term
depends on the time path of the externality function. The externality, or amenity, favors old trees
for example, when there is a positive difference between the amenity value at T and the amenity
value at t, for all t, summed over the rotation period. This paper examines two cases. In the first
case, it is assumed that for all t < T, F(T) >F(t). This implies that consideration of the externality
increases the optimal rotation time. This would be the case if the amenity were erosions control.
In the second case, analogous to a fire prevention amenity, F(t)>F(T) for some or all t, such that
the sum of the differences, the externalities balance, over the optimal rotation period is negative.
This implies that consideration of the amenity decreases the optimal rotation time.

•           ••               •

² The second order condition can be written as:              F(T)+ G(T) < rG(T)

³ Note, at this point, as in previous literature, clear-cutting is assumed.

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