Alternative methods of calculating optimal timber rotations: a critique of the Stokey/Lucas/Prescott tree-cutting problem

Abstract

The traditional question of optimally deciding when to cut down a tree is among the most commonly posed questions asked of students learning the technique of dynamic programming. This paper shows that the traditional tree-cutting example is improperly formulated when the question of replanting is addressed, derives the proper method of finding optimal harvest length, and applies this method to an empirical forest growth function.

Notes

¹Alvarez and Koskela (2003) examine the tree cutting problem while relaxing the assumption of constant interest rates.

² It should be noted that in general, all types of trees follow a similar growth path. In percentage terms the most rapid growth occurs when the trees are young. In terms of gross amount of growth in volume per year, trees add the most volume to their mass when middle-aged. The growth then slows, and eventually the trees stop growing or may even die back as they enter their final stages of life.