Suppose the inverse demand for redwood trees is given by P(Q) = 100 - Q: Conside
ID: 1192731 • Letter: S
Question
Suppose the inverse demand for redwood trees is given by
P(Q) = 100 - Q:
Consider a rm who takes demand as given, whose marginal cost of cutting down redwood trees is a constant
marginal cost,
MC(Q) = 10:
Suppose there are only 42 redwood trees left, all owned by this rm, and the rm's discount rate is 7%.
1. If there is an unlimited number of redwood trees, how many trees will the rm cut down in each period?
2. Suppose instead the rm must choose how many trees to harvest this year and next year because the
rm knows in the following year legislation will be passed preventing it from cutting any more trees.
How many trees will the rm cut down in total?
3. According to Hotelling's rule, how many trees should the rm harvest this year and how many should
they harvest next year? For this exercise, assume the rm is able to harvest fractions of a tree.
Explanation / Answer
Profit is Q(100 - Q) - 10Q
Differentiating it w.r.t Q,
100 - 2Q - 10 = 0
Q =45
1) It will cut 45 trees.
2)net profit of the trees must grow at the rate of interest.
90 - 2Q / 100Q -Q2-10Q = 0.07
90 - 2Q = 7Q - 0.07Q2-0.7Q
Q = 106 OR 12
Q can thus be 12 as we have constraint of Q <=42
3) He will cut 12 trees now and rest 30 next year
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