Optimal forest rotation with multiple product classes

We develop and analyze a multiple products model that extends the optimal rotation Faustmann Model, including necessary and sufficient conditions for the optimal harvest age. Comparative statics results are derived by shifting prices of product classes, regeneration costs, and the discount rate. Comparative statics results for regeneration costs and the discount rate are qualitatively identical to those for the standard Faustmann Model. Based on the comparative statics results for product class prices, we prove that although the optimal harvest age must vary inversely with at least one product class price, the optimal harvest age may vary directly with some product class prices, which is in contrast to the comparative statics result for the standard Faustmann Model and a previous multiple product analysis. A theoretical analysis of a stylized volume function demonstrates that the optimal rotation age will vary directly with products that require larger minimum diameter sizes. A numerical simulation based on an observed US southern pine three-product volume function determines the optimal harvest age. Simulated sensitivity results illustrate the possible impacts of each theoretical result and suggest that the optimal rotation age may vary directly with sawtimber price but inversely with pulpwood and chip-n-saw prices.