Planning Timber Production with Evolving Prices and Costs

The traditional Faustmann solution to the timber harvesting problem was developed for an environment in which prices, costs, and technology were constant. Recent contributions, recognizing the evolution of economic institutions, have developed solutions to optimal harvesting problems under a variety of more realistic assumptions. Nautiyal and Fowler (1980) show that "The socially desirable rotation in a monopolistic situation is longer than that which maximizes the monopolist's present worth, but is shorter than the atomistic rotation...." (p. 213). Heaps and Neher (1979) derive the optimal rotation when the rate of harvest is constrained. Bare and Waggener (1980) investigate the value of timberland when timber prices change, using a traditional Faustmann model. Murphy, Fortson, and Bethune (1977) deal with an imperfect capital market. One problem not addressed by recent contributions concerns the violation of the assumption of constant price and cost functions for timber production. This assumption clearly does not hold. Stumpage prices exhibit substantial short-run fluctuations and systematic long-run trends. For Southern pine and Douglas fir, two species that are potential crops for timber plantations, historical evidence demonstrates that stumpage prices relative to other price have grown steadily. For the period 1913-1978, the ratio of Southern pine stumpage price to prices paid by farmers increased at a 4% annual rate, while the same ratio for Douglas fir increased at an annual rate of 5.7%.1 For Douglas fir and Southern pine, forecasts of prices and costs based on his-