Optimal Private and Public Harvesting under Spatial and Temporal Interdependence

11

rotation, the sign of the term F_τT alone, not the notion of ALEP independence,
substitutability and complementarity per se, is crucial. In the following three
corollaries we apply the notion of temporal interdependence developed in Definition 2
to provide interpretation of the theorem.

Note first that if F_τ = 0, we have the case of ALEP independence, so that a change in
the rotation of the exogenous stand has no effect on private rotation age, as ALEP
independence implies that F_τT = 0. Consider next the case of F_τ ≠ 0, for which there
are three possibilities. The first one is presented in

Corollary 1. If the ALEP substitutability or complementarity is temporally
independent, i.e., if F_τT = 0, then a change in the adjacent stand will have no
effect on the focal private rotation age.

Temporal independence between stands means that the complementarity or
substitutability relationship is merely due to their site-specific characteristics. Since a
change in the exogenous harvesting will affect neither the marginal valuation nor
opportunity costs, the private forest owner has no reason to change the privately
optimal rotation age.

If the relationship between private and exogenous stands is temporally dependent, we
have for increasing dependence

Corollary 2. If the temporal interdependence increases, i.e., if F_τT > 0, implying
that either ALEP complementarity becomes stronger or that ALEP
substitutability becomes weaker, then a rise in the exogenous adjacent stand
lengthens the focal private rotation age.

Increasing temporal interdependence means that for ALEP complements a rise in the
rotation age of the exogenous stand increases both the marginal valuation at harvest
time and the opportunity cost effect of the future amenity valuation, the former effect
being stronger. For ALEP substitutes, a rise in the rotation age of the exogenous stand
decreases both the marginal valuation and the opportunity cost of amenity services,

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