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Problem Set 7
1. (10%) At the monopoly price the price elasticity of demand is -2 and the
ratio of price to the firm’s average cost is 1.3. Can you tell from this
information whether the firm is operating in the region where there are
economies of diseconomies of scale?
2. (10%) Before a monopolist introduces a new process innovation, it
produces Qo. Units. After a new process innovation is introduced the
monopolist increases output to Q1 and lowers the price. The monopolist
produces Q1-Q0 units in new plants that use the new technology since the
average variable cost of the old plant is less than the long run average
cost of a new plant? Is the monopolist maximizing profits? With the use
of graphs explain why or why not.
3. (10%) Suppose the price a monopolist can charge is regulated by the
government. Find the regulated price that maximizes the total number of
units sold. Hint. At the regulated price, the firm’s marginal revenue
equals price up to the quantity demanded on the demand function.
a) Assume the government sets the price ceiling to that the regulated
monopolist sell the maximum quantity. Then a regulator allows
competitive bidding for the right to be a monopolist.
b) With the aid of graphs, determine how much a firm will pay for the
right to be a monopolist under these circumstances.
c) Does the amount the regulated monopolist pays tell you whether
long run average cost is increasing or decreasing?
4. (10%) A monopolist produced 1 million units last year. If a $10 per unit tax
is imposed, the profits of the monopolist will decrease by $10 million.
Explain why you agree or disagree with this statement.
5. (20%) A monopolist has a demand curve
Q = 200 - 5 P
He has one – and only one- plant. Its cost function is given by the
following table:
Q
C
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
22
28
31
33
37
42
48
55
63
72
84
98
113
130
149
170
193
218
245
274
305
339
378
a) How many units of the product should he make? What should he
charge for the product?
Now it he opens a second plant, whose cost function is given by the
following table:
6. (10%) In monopolistic competition, firms compete to establish a monopoly.
Explain whether you agree or disagree with this statement.
Q
C
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
1
3
6
10
15
21
28
36
45
55
66
78
91
105
120
136
153
171
190
210
231
253
276
a) How many units of the product should he make? How should he
divide output between the two plants? What should he charge for
the product?
7. (10%) If members of your class tried to form a study-reduction cartel, what
problems would such a cartel have?
8. (10%) A cartel includes large and small companies, each with different
long-run average and marginal cost curves. A cartel requires each
member to reduce output by 15% in the short run from the total output
produced. The authority assigns a quota to each firm that is 15% less
than the output produced by the firm in long-run competitive equilibrium.
a) Explain why the 15% reduction rule will or will not maximize total
profits of the cartel.
b) How would you assign the quota of each firm to maximize total
cartel profits?
c) Can you explain why the cartel, your insight notwithstanding, might
adopt the 15% rule?
9. (10%) If a firm wants to stop bidders from colluding on a construction
project, it should require written bids, and open them all at once in public.
Explain whether you agree or disagree with this statement.