3.1 Comparative statics: regeneration costs, interest rate and timber price
We derive here the comparative statics of the Hartman model. Substituting
T H = T H (p,r,c,τ) , defined implicitly by the first-order condition (6), for T in
WT = 0 and differentiating the resulting identity partially with respect to exogenous
parameters gives the comparative statics. The effects of parameters c, r and p on
private rotation age are derived in Appendix 2. It turns out that TcH > 0, which is
qualitatively the same as in the Faustmann model. Also in the Hartman model the
interest rate affects the private rotation age negatively, i.e., TrH < 0 . As for the
relationship between the private rotation age and the timber price p, it turns out to be
useful to characterize first how the relative size of the amenity benefits at the harvest
time and its opportunity cost depends on the precise type of amenity valuation. This is
given in the following
Lemma 1. F(T,τ) - rE
<=≥ 0 as FT (T, τ)
<!4 0.9
Proof. See Appendix 3.
According to Lemma 1 the site-specific amenity valuation of the private stand,
FT = 0, implies that F(T,τ) = rE, so that the Faustmann and the Hartman rotation
age are the same (see equation [6]). If the marginal valuation increases (decreases)
with the age of the private forest stand, then the valuation at the time of harvest
dominates (is dominated by) its opportunity cost over an infinite series of rotations.
Therefore, the Hartman rotation age is longer (shorter) than the Faustmann rotation
age.
As for timber price p we get TpH = (-WTT)-1WTp , and it can be shown that
9 The content of Lemma 1 can be found also in Bowes and Krutilla 1985, p. 539, and in
Johansson and Lofgren (1988).