The owner of one acre of ponderosa pine (Pinus ponderosa) needs to plan a forest rotation length. Unless the owner chooses to sell the forest land, it will be kept in forestry and the chosen rotation will be maintained indefinitely. Assume that the stumpage price is p = $2.50 per cubic feet and the fixed cost of harvest is C = $4,350.90. The volume (in cubic feet) of the stand at any point in time is given by W(t) = at – bt2 = 141.2t - 0.2824t 2 , where t is measured in years. Assume that the forest owner uses an annual discount rate of r = .01 and that the present value of bare land is S = $17,912.46 per acre.
a. Write down a condition the forest owner may use to choose a rotation length that maximizes the net present value of profits from timber harvest. In a few sentences, interpret the condition.
b. What is the forest owner’s efficient rotation length, rounded to the nearest year? Show your work, and plot your solution using a figure.