Optimal Private and Public Harvesting under Spatial and Temporal Interdependence



forest management. In this paper we show, however, that this analysis does not hold
for the more complex case of even-aged forests with an infinite series of rotations.

We use the Hartman model to re-examine the existing literature on stand
interdependence and extend it in several directions. We draw on Swallow and Wear
(1993), but formalize spatial interdependence so as to fit a characterization of
substitutes and complements suggested in the economics literature. In the same vein
as Swallow and Wear (1993) and Vincent and Binkley (1993) we start by considering
a forest landowner who owns one focal stand and faces an exogenous adjacent stand
which affects the amenity production of his stand. In the case of a single rotation the
effect of the exogenous stand on the private rotation age depends on the spatial
interdependence between the stands, i.e., on whether they are substitutes,
independents or complements in the valuation of amenity services. For ongoing
rotations we show that the rotation age of the focal private stand does not react to
changes in exogenous stand if the amenity services are either independent or if the
temporal interdependence does not change with the private rotation age, even though
the stands were substitutes or complements. Private rotation age reacts negatively
(positively) to the harvesting change of the exogenous stand under temporal
dependence, when rotation age substitutability or rotation age complementarity
increases (decreases) with private rotation age.

After having analyzed the private rotation age, we apply this generalized Hartman
model to the determination of public rotation age. The interaction between private and
public agents is described as a two-stage game.

In the first stage the Forest Service acts as a Stackelberg leader and decides about its
harvesting, and private harvesting is chosen in the second stage. In our social welfare
analysis we take into account the fact that the economy also consists of non-forest
owners (recreators), who value amenities from private and public forests. Amenity
services of public forest stands are a public good, while those of private forest stands
may or may not be, depending on whether recreators have access to private forests or
not. For socially optimal public harvesting, several new rules are derived depending

stand solution of the traditional Hartman-type forest management models.



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