Optimal Harvesting of a Renewable Resource : A Mathematical Model

This paper derives the optimal harvesting policy for a renewable natural resource using a real-option model. The harvesting policy is illustrated using the well-known “tree-cutting” or “optimal rotation” problem from Forest Economics. We show how to identify the optimal tree size at which to harvest (or the optimal harvesting trigger), and also the resulting expected rotation period. The optimal trigger depends on (i) the growth dynamics of the tree, (ii) the interest rate, (iii) the harvesting cost, and (iv) size of the replacement seedling. With reasonable input parameters, it is shown that tree size must increase to 4½ times the original size before it is optimal to harvest it, which gives an expected rotation period of 51 years. The model is flexible enough to accommodate various adjustments if necessary