Optimal Private and Public Harvesting under Spatial and Temporal Interdependence

1. Introduction

Conventionally, the rotation period of a forest stand has been analyzed independently
of that of other adjacent stands. Current focus on ecosystem management in forestry
has put the possibility of stand interdependence on the research agenda. A typical
example of spatial interdependence between stands is a forest area, comprising many
stands, which sustains a given ecosystem, so that harvesting a stand would have a
considerable impact on the whole ecosystem. To give another example, consider a
private landowner producing timber and amenity services. Amenity services,
however, can be produced either jointly by his own stand and the adjacent stand, or in
either of them, while the adjacent stands may be owned by the forest landowner
himself or by another landowner (private or public).

Both examples open a number of questions, the most crucial one being how the
rotation age of a stand should be adjusted to those of adjacent stands when the stands
are interdependent in the production of amenity services? If the landowner owns all
spatially relevant stands the optimization problem is different from the case in which
the adjacent stands are owned by other agents. The former case is often plausible in
the management of public forests, while the latter is more typical of dispersed,
private, nonindustrial land ownership.

The first analysts to point out the problem of potential interdependency between
adjacent forest stands and its implications for forest management were Bowes and
Krutilla (1985, 1989), who extended the standard single stand analysis to account for
the age class distribution of the forest. Swallow and Wear (1993, 1997) reformulated
the Hartman model for spatial interactions by defining the cases of substitutability and
complementarity both for a forest landowner who does not own the adjacent stand and
for a forest landowner who owns all stands. They concentrated, however, mostly on
numerical simulations and did not fully develop the analytics of stand
interdependence.¹ Koskela and Ollikainen (1999) offers an analysis of the
interdependence in a two-period framework which suits to the case of uneven-aged

¹ Interestingly enough, their numerical simulations show that the optimal harvest schedule in the
multiple stand ecosystem management problem does not necessarily converge to a single

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