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Oregon State University Department of Applied Economics AEC 351 Homework 4  The owner of one acre of ponderosa pine (Pinus ponderosa) needs to plan a forest rotation length

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Oregon State University

Department of Applied Economics

AEC 351

Homework 4 

1. 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 = 142t - 0.2824t², where t is measured in years. Assume that the forest owner uses an annual discount rate of r = 0.01 and that the present value of bare land is S = $17,912.46 per acre.

 

1. 1. 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 the condition.

 

1. 2. 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 replanting of 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.

 

1. 1. Write down a condition the forest owner may use to 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. What is the forest owner’s efficient rotation length given the risk of fire, rounded to the nearest year? 

 

1. 3. Using a figure, compare your solution from problem #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 H_t = $12.77 per acre per year. Assume further all other parameters from problem #1 remain the same.

 

1. 1. Write down a condition that characterizes the socially-efficient rotation length. In a few sentences, interpret the condition.

1 of 2

 

 

1. 2. What is the socially-optimal rotation length, rounded to the nearest year? Show your work.

 

1. 3. Using a figure, compare your solution from problem #3.b with your solution from problem #1.b. In a few sentences, interpret your results.