18
Proposition 5 provides an interesting qualification to Proposition 4. Consider part (a)
of Proposition 5. Increasing temporal interdependence between stands implies a
longer private rotation period when the marginal amenity valuation of a private stand
increases with its age. A longer private rotation age benefits recreators provided that
the private stand enters into their marginal valuation of the public stand as an
independent or complement. Hence public rotation age will increase. Likewise
decreasing marginal valuation of a private stand with age implies a shorter private
rotation period. This benefits recreators if they regard the private stand as a substitute
or independent in the marginal valuation of the public stand. Then the Forest Service
promotes a beneficial change in the private rotation age by decreasing the public
rotation age compared with the temporal independence.15
4.2 No Access to Private Forest
Thus far we have assumed that citizens have full access to private forests for
recreation, which is the case e.g. in Finland and Sweden. One may ask how the lack of
access to private forests, as is the case in many parts of the United States, affects the
socially optimal public harvesting? Given no access to private forests for recreation,
the term (n - 1)E is no longer relevant and the social welfare function can now be
written as
[18] SW = W * (τ,..) +V4 2nE3 ,
private forests public forests
The first-order condition for the social optimum is given by
[19] SWτ = Wτ* + Vτg + nEg + nETTτH .
Assume first that the stands are independent. Then the last term in [19] is zero, and
comparing the first-order conditions [13] and [19] allows one to conclude, in
comparison with the case of free and no access, that
15 Proposition 5 does not exhaust the possibilities inherent in equation (17). One can provide
an analogous characterization of sufficient conditions for the case of decreasing temporal