Optimal Private and Public Harvesting under Spatial and Temporal Interdependence



holds. Finally, when the forest stands are independents in terms of amenity valuation,
changes in exogenous harvesting will have no effect on private harvesting.
6

2.2. Temporal Interdependence between Private and Exogenous Forest Stands

Next we characterize how the spatial interdependence between the private and
exogenous adjacent stands might evolve over time. The following definition turns out
to be the key element in interpreting the results for the response of the focal private
rotation age to changes in the age of the exogenous adjacent stand in the Hartman
model for ongoing rotations.

Definition 2. Temporal interdependence

Temporal interdependence between two stands is constant, increases or
decreases when substitutability or complementarity between the stands
remains unchanged, increases or decreases with a higher private rotation age,
i.e., when F
τT = 0, FτT0 or FτT0.

Constant temporal dependence holds when substitutability or complementarity is
merely associated with site-specific properties, which remain the same regardless of
the age of the endogenous private forest stand.
7 Increasing temporal dependence
between the stands means that for ALEP complements the complementarity between
stands increases with private rotation age, while for ALEP substitutes the
substitutability decreases. Decreasing temporal dependence implies just the opposite:
complementarity weakens, while substitutability becomes stronger. In Appendix 1 we

6 As for examples of substitutes and complements, we can offer the case on which Swallow
and Wear (1993) base their simulations. They assume that a landowner values forage
production consistently with big game production, where big game requires both forage and
cover. The focal stand and the exogenous adjacent stand function as substitutes in their
production by providing simultaneously both. The stands become complements if the focal
stand provides forage, and the adjacent stand provides cover.

7 See the discussion about this and several other cases in Calish, Fight and Teeguarden (1978)
and in Swallow, Parks and Wear (1990). One should also note that if the amenity valuation is
site-specific in the sense of
Fτ = 0 , it is also temporally independent in the sense of
FτT = 0 , but not necessarily the other way round.



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