[8]
Th J
tp
as
rc(1-e-rT)-1 +F(T,τ) -rE
J = ^ 0.
To summarize, we have
Proposition 2.
In the Hartman model, regeneration cost affects positively and interest rate
negatively optimal rotation age, while the effect of the timber price is
ambiguous a priori.
Proposition 2 is new and shows that the timber price effect may differ from that given
in the Faustmann model, in which TpF < 0 .10 Under positive regeneration costs the
effect of the timber price on rotation age depends both on the discounted regeneration
costs and on the sign of FT(T,τ). Since private rotation age and timber price can now
be also positively related, the effects of forest taxes on private rotation age may
change qualitatively when we allow for non-timber services.11
3.2 The Response of Private Rotation Age to a Change in the Age of the
Exogenous Stand
What happens to the focal private rotation age when the age of the exogenous
adjacent stand changes? Using the similar procedure as above we get
TτH =-(WTT)-1WTτ, where
T
[9] WTτ = Fτ(T,τ)-r(1-e-rT)-1∫Fτ(s,τ)e-rsds.
0
10 Bowes and Krutilla (1985, p. 540-541) present a part of this result when they say that
under zero regeneration costs, TpH < 0 if the Hartman solution is above the Faustmann
solution, i.e., if FT (T,τ) > 0 .
11 For the effects of forest taxes on the optimal private rotation age in the Faustmann and
Hartman models, see Johansson and Lofgren (1985, Chapter 5), and Koskela and Ollikainen
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