the following way:
T
∫e-rtF(t)dt+G(T)e-rT
SV (T ) = 0-----------=-------
(3)
1 - e-rT
where G(T) is again the net timber value at age T , r is the interest rate, and F(t) is a function
giving the externalities generated by the forest at each point in time. The integral gives the
present value of a stream of non-timber benefits coming from the standing forest. Thus SV(T)
describes society’s total benefit from the forest, summed over an infinite series of rotations of
length T.
The time path of the benefits flowing from a standing forest is controversial. Hartman (1976),
Strang (1983), Snyder and Bhattacharyya (1990), Max and Lehman (1988),and Reed (1984),
assume F(t) increases with the age of the trees at a decreasing rate. If this is the case, the
externality function is monotonically increasing, and it is always optimal, disregarding the timber
value, to let the forest grow. Even though this case may be the most likely, it is not the most
general case. Calish et. al. (1978) show that, depending on the forest, the externality function
could take any number of shapes, including a non-monotonic one. Englin and Klan (1990)
assume only that F(t) is either increasing at a decreasing rate or increasing and then, at some
point, decreasing. In this case, the externality function, at some time tFmax, begins to decrease
and it is optimal (again disregarding timber value) to harvest the forest at some time less than
infinity. Therefore, conceptually, the externality may “favor” either older trees or younger trees.
This paper follows Englin and Klan’s model in this regard.
Maximizing equation (3) with respect to the rotation length and rearranging, the first order