Two-Part Tax Controls for Forest Density and Rotation Time

forever. Initially, the land is bare with timber production as its only use. The landowner chooses
the rotation period T to maximize the following private value function:

V (T) = G^(T)^e _τ                                         (1)

1 -e ^-rT

where G(T) is the net timber value of the stand at time T. The numerator is the present net
value of the stand that will be harvested at T . The denominator is simply the result of summing
over an infinite series of identical rotations.

Taking the derivative with respect to the rotation length and rearranging, the following first
order condition is derived:

G (T) =   r

G (T)   1 - e -^rT

where the left hand side of the equation is the growth rate of the forest in terms of net value. So
a rational landowner will cut down all the trees and replant when the growth rate equals the
interest rate multiplied by a discount factor.

Hartman: Forest Planner Problem, Externalities Included

Following Hartman (1976), an externalities function that varies with the age of the forest is
introduced into the forest planner’s problem. The social value (SV) function can now be written

The trees that are not part of the commercial use portion of each acre will never be harvested.

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