Optimal Private and Public Harvesting under Spatial and Temporal Interdependence

19

Proposition 3’. If private and public forest stands are independent, denying access to
private forests will have no effect on optimal public harvesting relative to open
access to them.

If there is no link between private and public stands in the valuation of amenities, or if
a change in private rotation age does not affect the marginal valuation of amenities
from public stands, then accessibility to private stands affects neither recreators’ nor
forest owner’s utility. Therefore optimal public harvesting remains unaffected as well.

Assume next that forest stands depend on each other, but the degree of this
dependence does not change in time, i.e., they are temporally independent (F_τ ≠ 0,
but F_τT = 0). Noting that [19] will be identical to equation [16], when we set n = 1
due to access restriction, we have

Proposition 4’. If the relationship between private and public forest stands is
temporally independent, denying access to private forest will shift the optimal
public rotation age up to that of independent stands from below
(complements) or down from above (substitutes).

The interpretation is straightforward. Denying recreators’ access to private forests
reduces the size of the externality caused by public harvesting through the marginal
valuation of private forests from (n-1) to 1. Therefore, compared to the open access
case, the optimal public rotation age will be closer to the age in the absence of
externalities, i.e., the age of independent stands.

Finally, in the general case, where F_τ ≠ 0 and F_τT ≠ 0 , we get from [19]

τ

[20]   SWτ_l Fτ ≠,,Fττ ≠,,n >1= 0 ⇔   SW,_l Fτ ≠o Ft =,, >ι + THe - r^τ » ∫ Ff (T. » ) e ~ rxdx = 0.

0

dependence (F_τT < 0).

<<   18   19   20   21   22   23   24   >>

More intriguing information