Optimal Private and Public Harvesting under Spatial and Temporal Interdependence

Applying integration by parts yields

T

Fτ(0,τ)-Fτ(T,τ)e^-rT+∫FτT(s,τ)e^-rsds

0

so that equation [9] can be re-expressed as

T

)-^- Fτ(0,τ)-Fτ(T,T)e-^rT +∫Ftt(s,T)e^-rsds

_                                         0

The terms in equation [-0] have a natural interpretation. The first term describes the
effect of the adjacent stand on the amenity valuation of the private stand at the time of
the first harvest. The first and the second RHS bracket terms give the present value
effect over all rotations of τ on the marginal amenity valuation of private bare land
and of the stand during the harvesting period. Finally, the third RHS (integral) term
captures the present value effect of the temporal interdependence of private and
adjacent forests. It describes whether the complementarity or substitutability of the
stands becomes stronger, weaker or remains unchanged when the private rotation
period changes.

The response in the focal private rotation age to a change in τ is given by the
following theorem:

Proof. See Appendix 4.

According to the Theorem the response of the private rotation age will depend only on
how the temporal dependence between the stands in the amenity valuation will be
affected by the change in the private rotation age. Therefore, unlike for the single

(2000), respectively.

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