Applied Economics

1. Using complete sentences and, optionally, one or more relevant economic graphs,
   respond to “Questions for Further Discussion” #4 from chapter 12 of the course
   textbook.
2. This problem analyzes management of an acre of southern pine (Pinus taeda) forest.
   Table: Parameter values for problem 2
   𝒂 𝒃 𝒅 𝒑 𝑪 𝒓
   −𝟑𝟒. 𝟎𝟏 −𝟐𝟎. 𝟔𝟓 9.51 0.1 84 0.03
   Source: Amacher, Gregory, Markku Ollikainen, and Erkki Koskela. 2009. Economics of Forest Resources.
   Cambridge, Mass.: MIT Press. (p. 15, 23)
   The wood growth function (in board feet per acre) is given by:
   𝑊(𝑡) = exp (
   𝑎
   𝑡
   2 +
   𝑏
   𝑡

• 𝑑)
  The corresponding wood growth rate function is:1
  𝑊̇ (𝑡) = − (
  𝑏𝑥 + 2𝑎
  𝑥
  3
  ) 𝑊(𝑡)
  Assuming this forest land remains in use for timber production, the value of the land
  cleared of trees is the following function of the rotation length 𝑻:
  𝜋(𝑇) =
  𝑝𝑊(𝑇) − 𝐶
  𝑒
  𝑟𝑇 − 1
  Parameter values for this problem are provided in the table above.
  2.a. Suppose the owner approaches you and asks for your advice on how to best manage the
  forest land for timber production. What formula would you apply to choose the best
  rotation length? Using complete sentences and, optionally, one or more economic
  graphs, describe how you would explain the formula to the land owner.
  2.b. What rotation length would you recommend for this forest land? Justify your
  recommendation.2

1 Here the expression for 𝑊̇ (𝑡) makes use of the formula for 𝑊(𝑡) in the definition.
2
It is recommended that you try to find the solution for this problem using a graphical approach. You are free to
choose your own graphing tool. Options include a graphing calculator and computer graphical tools such as Excel,
Wolfram Alpha, or R.
2 of 2
2.c. Suppose that, in order to promote conservation, a harvest tax is imposed that increases
the fixed costs of harvest by 20% (so now 𝑪 =$100.8). Given this change, how would
you advise the land owner to adjust the rotation length for this forest land (if at all)?
Provide supporting calculations and, optionally, relevant economic graphs to justify
your response.