Problem And Solution

Maximum Points: 60
Grade:
Let G be the smaller number between 6 and
(achieved points+10)/10
Round G exactly to quarters of a grade to get your grade.
Examples:
32 points give a 4.25,
31 points give a 4

Solution to Homework Set 1
Managerial Economics Fall 2011

Conceptual and Computational Questions
4 points 2. What is the maximum amount you would pay for an asset that gen- 2 pt for a erates an income of $150,000 at the end of each of five years if the reasonable formula, opportunity cost of using funds is 9 percent?
The maximum you would be willing to pay for this asset is the present 2 points for the value, which is correct result
150, 000
150, 000
150, 000
150, 000
150, 000
+
+
+
+
2
3
4
1 + 0.09 (1 + 0.09)
(1 + 0.09)
(1 + 0.09)
(1 + 0.09)5
= $583, 447.69.

PV =

6 points

3. Suppose that the total benefit and total cost from an activity are, respectively, given by the following equations: B(Q) = 150 + 28Q − 5Q2 and C(Q) = 100 + 8Q.
(a) Write out the equation for the net benefits.
Net benefits are N (Q) = 50 + 20Q − 5Q2 .
(b) What are the net benefits when Q = 1? Q = 5?
Net benefits when Q = 1 are N (1) = 50 + 20 − 5 = 65 and when
Q = 5 they are N (5) = 50 + 20 · 5 − 5(5)2 = 25.
(c) Write out the equation for the marginal net benefits.
Marginal net benefits are MNB(Q) = 20 − 10Q.
(d) What are the marginal net benefits when Q = 1? Q = 5?
Marginal net benefits when Q = 1 are MNB(1) = 20 − 10 = 10 and when Q = 5 they are MNB(5) = 20 − 10 · 5 = −30.
(e) What level of Q maximizes net benefits?
Setting MNB(Q) = 20 − 10Q = 0 and solving for Q, we see that net benefits are maximized when Q = 2.
(f) At the value of Q that maximizes net benefits, what is the value of marginal net benefits?
When net benefits are maximized at Q = 2 , marginal net benefits are zero. That is, MNB(2) = 20 − 10 · 2 = 0.

1

1 point per correct result 4 points

4. A firm’s current profits are $550,000. These profits are expected to 2 points (1 for a grow indefinitely at a constant annual rate