Optimal forest stock and harvest with valuing non-timber benefits: a case of US coniferous forests
Introduction
Many studies have been undertaken to determine the optimal forest rotation length under different scenarios since the advent of the Faustmann formula. Some were focused on the optimal rotation age with the consideration of only timber value (Hyde, 1980, Chang, 1983, McConnell et al., 1983, Newman et al., 1985). Others searched for the optimal rotation age with the inclusion of both timber and non-timber benefits (Calish et al., 1978, Hartman, 1976, van Kooten et al., 1995). These studies have provided important guidelines on when to cut trees in the even-aged plantations. However, their applications in uneven-aged, or natural forests, are limited because age is no longer an appropriate variable under such circumstances. Also, in formulating a forest management plan/policy, particularly in the management of a large-scale (such as a regional or national scale) forest resources, it may be more relevant to determine how much timber should be harvested and what level of the forest stock should be maintained than to know when trees should be cut. This will become increasingly important if non-timber benefits that largely depend on forest stock are valued, and if sustainability needs to be addressed in forest resource management and utilization. Moreover, to analyze how forest stock and harvest respond to changes in the discount rate, timber price, non-timber benefit, and silvicultural cost would also be helpful in better understanding some of the emerging issues in forest management such as deforestation, and sustainable and multiple-use management. Finally, the optimal steady state harvest level, unlike the optimal rotation age, can directly provide information on the long-run potential timber supply from a forest.
To this end, this article investigates the optimal forest stock and harvest with and without addition of non-timber benefits to timber value, and the impact of some economic and financial factors (discount rate, timber prices, non-timber benefits, and silvicultural costs) on the optimal stock and harvest. A theoretical optimal control model of forest management will be formulated. The model will then be solved to find the optimal steady state forest stock and harvest. The impact of the economic and financial factors on the optimal steady state forest stock and harvest will also be analyzed, followed by discussion on policy implications. Finally, the western and eastern US coniferous forests will be used as an empirical example to illustrate our theoretical results.
Section snippets
Methodology and theoretic approach
Forest production is a joint production process, in which inputs are transferred into multi-outputs. The outputs derived from forests may consist of timber and non-timber benefits. Assume that the timber benefit is a function of the amount of the timber harvested (h), denoted by U(h), and that the non-timber benefits depend on the level of the forest stock (x), denoted by V(x). It is also assumed that only two inputs are involved in the forest production. One is a composite input, silvicultural
Optimal steady state forest stock and harvest
From the theoretical model presented previously, the optimal equilibrium levels of the forest stock and harvest can be derived. In addition to maximizing the present value of the net timber and non-timber benefits, the solution from the above model also represents a sustainable level of the forest stock and harvest because the optimal equilibrium is a steady state solution. Therefore, the optimal steady state forest stock and harvest are efficient and sustainable. Here we discuss two scenarios
Conclusions
Forest management often involves making decisions on how much to cut (harvest) and remain (stock) as well as when to cut (rotation age). Using forest stock and harvest levels as decision variables is applicable to the management of both plantations and natural forests. This paper describes an approach to determining the optimal forest stock and harvest and demonstrates the applicability of this approach in empirical forest management using the example of the US coniferous forests. Our results
Acknowledgements
We wish to thank Sun Joseph Chang, J.E. de Steiguer, anonymous reviewers, the associate editor and the editor for their valuable comments and suggestions. Of course, opinions and errors are ours.
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