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AEC 3511of 2Homework 41

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AEC 3511of 2Homework 41.The owner of oneacre of ponderosapine (Pinus ponderosa) needs to plan a forest rotationlength. Unless the owner chooses to sell the forest land, itwill be kept in forestry and the chosen rotation will be maintained indefinitely. Assume that the stumpage price is p= $2.50 per cubic feetand the fixed costof harvest isC= $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 -0.2824t2, where tis measured in years. Assume that the forest owner usesan annualdiscount rate of r= 0.01 and that the present value of bare land is S= $17,912.46per acre.1.a.Write down a condition (i.e., a mathematical relationship) 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 thecondition.1.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.2.Return to the set-up of problem #1. Now assume that the forest owner faces the risk of severe fire that requires replantingof the stand. Such a fire occurs on average once roughly every 38 years. Specifically, assume that the forest owner’s fire risk parameter is λ= 0.02637. This risk is reflected in the value of bare forest land in the area, which in this scenario is S= $2,917.92 per acre. Assume all other parameters from problem #1 remain the same.2.a. Write down a condition the forest owner may useto choose a rotation length that maximizes the (expected) net present value of profits from timber harvest in this scenario. In a few sentences, interpret the condition.2.b. What is the forest owner’s efficient rotation lengthgiven the risk of fire, rounded to the nearest year? 2.c. Using a figure, compare your solution fromproblem #2.b with your solution from problem #1.b. In a few sentences, interpret your results.3.Return once again to the set-up of problem #1. Consider an alternative scenario wherein the forest owner’s stand provides wildlife habitat that society values. Assume that the annual value of this non-timber benefit is fixed at Ht= $12.77 per acre per year. Assume further all other parameters from problem #1 remain the same.3.a. Write down a condition that characterizes thesocially-efficient rotation length. In a few sentences, interpret the condition.

2of 23.b. What is the socially-optimal rotation length, rounded to the nearest year? Show your work.3.c. Using a figure, compare your solution fromproblem #3.b with your solution from problem #1.b. In a few sentences, interpret your results.