Homework #3
Due
4/21/2010
Environmental Economics
This homework focuses on natural resource economics. You can answer these questions
using calculus, or plug in values to find the solution using Microsoft Excel (or Matlab)
Hint #1:
The Present Discounted Value (PDV) of a payoff of $X in two years =
X/(1+r)
2
where r is the market rate of interest.
Hint #2:
Expected Present Discounted Value =
probability that a payout takes
place*PDV
The Setup:
You own one tree.
Its height measured in feet is a function of the tree’s age
measured in years.
Here is the production function.
Feet =
*
44 Age
Assume that the real price per foot of wood always equals $30.
Suppose that the cost of
cutting down your tree is $20 (note: not per foot, this is a fixed cost).
Assume the interest
rate always equals 8%.
1.
If your goal is to maximize the present discounted value of your profits, what age
will you cut this tree down?
Profit=revenue – cost
=P*Qcost
=30*feet20
=30*44*age
1/2
 20
=1320*age
1/2
– 20
PDV of profit=
(1320*age
1/2
– 20)/(1+0.08)
age
Solution from excel:
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 Spring '08
 BRESNOCK
 Economics, Environmental Economics, Opportunity Cost, Time Value Of Money, Interest, Probability theory, present discounted value

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