Download Principles of Microeconomics Problem Set 11 Model Answers

FRAMINGHAM STATE COLLEGE
PRINCIPLES OF MICROECONOMICS
PROBLEM SET NUMBER 11
My Name is? ________________________________________
Using the material covered in CHAPTER 15.
3. A publisher faces the following demand schedule for the next novel of one of its popular authors:
Price
Quantity
Demanded
Total
Revenue
Total Cost
Profit
Marginal
Revenue
$0
$2
$ -2
----
$100
0
$ 90
100,000
9
3
6
$9
$ 80
200,000
16
4
12
7
$ 70
300,000
21
5
16
5
$ 60
400,000
24
6
18
3
$ 50
500,000
25
7
18
1
$ 40
600,000
24
8
16
-1
$ 30
700,000
21
9
12
-3
$ 20
800,000
16
10
6
-5
$ 10
900,000
9
11
-2
-7
$ 0
1,000,000
0
12
-12
-9
The author is paid $2 million to write the book, and the marginal cost of publishing the book is a
constant $10 per book.
a.
Compute total revenue, total cost, and profit at each quantity.
What quantity would a profit-maximizing publisher choose? What price would it charge?
A profit-maximizing publisher would choose a quantity of 400,000 at a price of $60 or a quantity of 500,000
at a price of $50; both combinations would lead to profits of $18 million.
b.
Compute marginal revenue. (Recall that MR = ATR/AQ.)
How does marginal revenue compare to the price? Explain.
Marginal revenue is always less than price. Price falls when quantity rises because the demand curve
slopes downward, but marginal revenue falls even more than price because the firm loses revenue on all
the units of the good sold when it lowers the price.
Principles of Microeconomics
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Problem Set Number 11
c.
Graph the marginal-revenue, marginal-cost, and demand curves. At what quantity do the
marginal-revenue and marginal-cost curves cross? What does this signify?
Figure 1 shows the marginal-revenue, marginal-cost, and demand curves. The marginal-revenue and
marginal-cost curves cross between quantities of 400,000 and 500,000. This signifies that the firm
maximizes profits in that region.
Figure 1
d.
In your graph, shade in and label the deadweight loss.
Explain in words what this means.
The area of deadweight loss is marked “DWL” in the figure. Deadweight loss means that the total surplus
in the economy is less than it would be if the market were competitive, since the monopolist produces less
than the socially efficient level of output.
e.
If the author were paid $3 million instead of $2 million to write the book, how would this
affect the publisher's decision regarding the price to charge? Explain.
If the author were paid $3 million instead of $2 million, the publisher wouldn’t change the price, since there
would be no change in marginal cost or marginal revenue. The only thing that would be affected would be
the firm’s profit, which would fall.
f.
Suppose the publisher was not profit-maximizing but was concerned with maximizing
economic efficiency.
What price would it charge for the book? How much profit would it make at this price?
To maximize economic efficiency, the publisher would set the price at $10 per book, since that’s the
marginal cost of the book. At that price, the publisher would have negative profits equal to the amount paid
to the author.
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Problem Set Number 11
4.
The Placebo Drug Company holds a patent on one of its discoveries.
a.
Assuming that the production of the drug involves rising marginal cost, draw a diagram to
illustrate Placebo's profit-maximizing price and quantity. Also show Placebo's profits.
Figure 2 illustrates the drug company's situation. They will produce quantity Q1 at price P1. Profits are
equal to (P1 - AC1) x Q1.
Figure 2
b.
Now suppose that the government imposes a tax on each bottle of the drug produced. On a
new diagram, illustrate Placebo's new price and quantity. How does each compare to your
answer in part (a)?
The tax on the drug increases both marginal cost and average cost by the amount of the tax. As a result,
as shown in Figure 3, quantity is reduced to Q2, price rises to P2, and average cost plus tax rises to AC2.
Figure 3
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Problem Set Number 11
c.
Although it is not easy to see in your diagrams, the tax reduces Placebo's profit. Explain
why this must be true.
The tax definitely reduces profits. After all, the firm could have produced quantity Q2 at price P2 before the
tax was imposed, but it chose not to because this level did not maximize profit before the tax occurred.
d.
Instead of the tax per bottle, suppose that the government imposes a tax on Placebo of
$10,000 regardless of how many bottles are produced. How does this tax affect Placebo's
price, quantity, and profits? Explain.
A tax of $10,000 regardless of how many bottles of the drug are produced would result in the quantity
produced at Q1 and the price at P1 in Figure 8 because such a tax does not affect marginal cost or marginal
revenue. It does, however, raise average cost; in fact, profits decline by exactly $10,000.
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Problem Set Number 11