Download Answers to Version A - Midterm Test #1 - October 19, 2009

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ECMC02H
Intermediate Microeconomics - Topics in Price Theory
Term Test – October 19, 2009
Professor Gordon Cleveland
Time: 80 minutes
ANSWERS TO THE TEST QUESTIONS ARE SHOWN BELOW EACH
QUESTION. DIFFERENT VERSIONS OF THE TEST HAD THE SAME
QUESTIONS BUT IN A DIFFERENT ORDER
______________________________________ ____________________
PART I - 15 Multiple Choice Questions - 75 marks
1-5. A firm in a perfectly competitive constant cost industry has total costs in the short run given
by:
TC = 2.5q2 + 5q + 40
where q is output per day and TC is the total cost per day in dollars. The firm has fixed costs of
$30 (already included in the TC equation above). The TC equation generates minimum average
costs of $25 (per unit) at q = 4. You are also told that this size firm generates minimum long run
average costs (that is, minimum LRAC occurs at q = 4, with min LRAC = $25). In the short run,
there are 200 firms in this industry. Questions 1 through 5 concern this firm and this industry.
1. In the short run there are 200 firms in the industry, all with the same cost curves described
above. Suppose that the demand curve facing the industry is given by the equation P = 125 .075Q where P is the price per unit and Q is the number of units demanded per day. The
equilibrium price in the short run is:
A) $25
B) $30
C) $35
D) $40
E) $45
F) $50
G) $55
H) $60
I) $65
J) none of the above
MC = dTC/dq = 5 + 5q. Since the PC firm sets MC = P, we have P = 5 + 5q, which is the
equation of the firm’s supply curve (above min AVC). 200q = Q, so q = .005Q. Substituting, we
can find the industry supply curve for this group of 200 firms. P = 5 + 5(.005Q) = 5 + .025Q.
Since demand is P = 125 - .075Q, we have 125 - .075Q = 5 + .025Q or Q0*= 1200 and P0* = $35.
The correct answer is (C).
2. Continuing the situation described in question 1 (the short run, with 200 firms and demand given
by P = 125 - .075Q), the profit earned by an individual firm per day in the short run is:
A) $0
B) -$50
C) -$30
D) -$20
E) $20
F) $30
G) $50
H) $70
I) $90
J) none of the above
Profit = 35 x 6 – (2.5[6 x 6] + 30 +40) = 210 – 160 = $50. The correct answer is (G).
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3. How much is sum of consumer surplus and producer surplus in this industry in the short run?
A) $0
B) -$5000
C) -$3000
D) -$2000
E) $2000
F) $4,500
G) $13,500
H) $18,000
I) $21,000
J) $24,000
K) $30,000 L) $36,000
M) $44,000
N) $54,000
O) $60,000
P) $66,000
Q) $70,000
R) $72,000
S) $76,000
T) $80,000
U) $88,000 V) $96,000
W) $100,000
X) $102,000
Y) $108,000
Z) none of the above
The sum of consumer surplus and producer surplus is the whole area between the demand and
supply curves up to the equilibrium quantity. This is:([125 – 5] x 1200)/2 = $72,000. The
correct answer is (R).
4. Imagine that, somehow or other, the amount of output traded in this industry is not at its
equilibrium level, but is artificially held down to 600 units of output, so that 600 units are
consumed and 600 units are produced in this industry. What now would be the sum of consumer
surplus and producer surplus in this industry?
A) $0
B) -$5000
C) -$3000
D) -$2000
E) $2000
F) $4,500
G) $13,500
H) $18,000
I) $21,000
J) $24,000
K) $30,000 L) $36,000
M) $44,000
N) $54,000
O) $60,000
P) $66,000
Q) $70,000
R) $72,000
S) $76,000
T) $80,000
U) $88,000 V) $96,000
W) $100,000
X) $102,000
Y) $108,000
Z) none of the above
If output is 600, then the demand price is $80 and the supply price is $20. The sum of CS and
PS is [(125 – 80) x 600]/2 + [60 x 600] + [(20-5) x 600]/2 = $54,000. The correct answer is (N).
5. Continuing the situation described in question 1 (demand given by P = 125 - .075Q, 200 firms in
the short run), suppose now that we move into the long run (you are reminded that information on
long run costs was given at the beginning of the problem). The number of firms in the industry,
rounding to the nearest integer, is:
A) 0
B) 20
C) 100
D) 133
E) 146
F) 200
G) 233
H) 283
I) 333
J) none of the above
Since we have constant costs and the min LRAC occurs at $25, the long run supply curve will be
horizontal at P = 25. Therefore, LR equilibrium will be where 25 = 125 - .075Q or Q = 1333.33.
Since the minimum cost size of an individual firm is at q = 4, n = 1333.33/4 = 333.33 firms. The
correct answer is (I).
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6-10. A monopoly producer of a particular well-known economics textbook is able to sell
them to consumers in North America and also to consumers in South America. Because
the markets are geographically separated, producers are able to separate these two types
of consumers and sell them the same product at two different prices. You are given the
following demand curves per year for these distinct markets:
North America:
P1 = 100 - .01Q1
South America:
P2 = 80 - .04Q2
where P refers to prices charged to each group and Q refers to quantities demanded by each
group. The variable cost of producing textbooks is constant at $16 per textbook. In addition
there are sunk fixed costs of $100,000 per period. Questions 6 through 10 concern this case.
6. If the producer of this textbook can price discriminate by charging different prices to each
group, the profit-maximizing price charged to North American consumers will be:
A) $0
B) $38
C) $40
D) $42
E) $44
F) $46
G) $48
H) $50
I) $52
J) $54
K) $56
L) $58
M) $60
N) $62
O) $64
P) $66
Q) $68
R) $70
S) $72
T) $74
U) $76
V) $78
W) $80
X) $82
Y) $84
Z) none of the above
MR1= 100 - .02Q = 16, so Q1* = 4200 and P1* = $58. The correct answer is (L).
7. If the producer of this textbook can price discriminate by charging different prices to
each group, the profit-maximizing price charged to South American consumers will be:
A) $0
B) $38
C) $40
D) $42
E) $44
F) $46
G) $48
H) $50
I) $52
J) $54
K) $56
L) $58
M) $60
N) $62
O) $64
P) $66
Q) $68
R) $70
S) $72
T) $74
U) $76
V) $78
W) $80
X) $82
Y) $84
Z) none of the above
MR2= 80 - .08Q = 16, so Q2* = 800 and P2* = $48. The correct answer is (G).
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8. Assume now that the monopoly producer of textbooks is unable to discriminate between
these groups but must sell at a uniform price. What price will now be charged?
A) $0
B) $38
C) $40
D) $42
E) $44
F) $46
G) $48
H) $50
I) $52
J) $54
K) $56
L) $58
M) $60
N) $62
O) $64
P) $66
Q) $68
R) $70
S) $72
T) $74
U) $76
V) $78
W) $80
X) $82
Y) $84
Z) none of the above
Q1 = 10,000 – 100 P and Q2 = 2000 – 25P, so the sum of these is Q = 12,000 – 125P.
Putting P on the left-hand side, we have P = 96 - .008Q as the equation of the (bottom
part of the) sum of the demand curves. MR = 96 - .016Q = 16, so Q3* = 5,000 and P3* =
$56. The correct answer is (K).
9.
By how much has total profit risen when the monopolist moves from charging a
single price to both markets to charging two different prices in North America and South
America?
A) $0
B) -$5000
C) -$3000
D) -$2000
E) $2000
F) $4,500
G) $13,500
H) $18,000
I) $21,000
J) $24,000
K) $30,000 L) $36,000
M) $44,000
N) $54,000
O) $60,000
P) $66,000
Q) $70,000
R) $72,000
S) $76,000
T) $80,000
U) $88,000 V) $96,000
W) $100,000
X) $102,000
Y) $108,000
Z) none of the above
Profit for the single-price monopolist is (56 x 5000) – (100,000 + [16 x 5000]) = $100,000. The
profit for the monopolist who is able to price-discriminate between the two markets is: (58 x
4200) + (48 x 800) – (100,000 + [16 x 5000]) = $102,000. The price-discriminating profit is
higher by $2,000. The correct answer is (E).
10.
For North America only, by how much has consumer surplus fallen (-) or risen (+)
in moving from the price discrimination situation to the normal monopoly situation with no
price discrimination?
A) -$18,000 B) -$12,800 C) -$10,600 D) -$9,800 E) -$8,600 F) -$7,900
G) -$6,400 H) -$5,200 I) -$4,800
J) -$4,200 K) -$3,200 L) +$0
M) +$3,200 N) +$4,200 O) +$4,800 P) +$5,200 Q) +$6,400 R) +$7,900
S) +$8,600 T) +$9,800 U) +$10,600 V) +$12,800 W) +$18,000 X) +$19,600
Y) +$21,200 Z) none of the above
The consumer surplus in North American under price discrimination is [(100 – 58) x
4,200]/2 = $88,200. The consumer surplus under a single-price monopoly is [(100 – 56)
x 4,400]/2 = $96,800. The difference is + $8,600. The correct answer is (S).
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11-14. The province of Prince Edward Island specializes in the growing of potatoes. The
government of Prince Edward Island is anxious to keep the potato farmers happy, and does
not want the price of potatoes to fall too low. The current demand for potatoes is given by P
= 100 - .005Q, with P representing the price in dollars per bushel of potatoes and Q
representing the annual quantity in bushels of potatoes. The supply of potatoes is given by
P = 20 + .005Q. The questions below refer to this potato-growing industry.
This information can be used in answering questions 11-14.
11.
If there is no government intervention in this perfectly competitive potato industry,
what will be the total amount of consumer and producer surpluses?
A) $0
B) $6000
C) $8000
D) $10,000
E) $20,000
F) $30,000
G) $40,000 H) $50,000 I) $60,000
J) $70,000
K) $80,000
L) $90,000
M) $100,000 N) $120,000 O) $140,000 P) $160,000 Q) $180,000
R) $200,000
S) $220,000 T) $240,000 U) $260,000 V) $280,000 W) $300,000 X) $320,000
Y) $340,000 Z) none of the above
The equilibrium will be where 100 - .005Q = 20 + .005Q or where Q0* = 8,000 and P0* =
$60. The sum of CS and PS will be [(100 – 20) x 8000]/2 = $320,000. The correct
answer is (X).
12. Now, imagine that the government of Prince Edward Island decides to support the
price of potatoes by establishing a price floor of $70 per bushel. Imagine that the potato
farmers ignore the reduced demand for potatoes at this higher price, and decide to plant
potatoes imagining they can sell as much as they want to at this new price. What will be
the deadweight loss due to this system of price supports?
A) $0
B) $6000
C) $8000
D) $10,000
E) $20,000
F) $30,000
G) $40,000 H) $50,000 I) $60,000
J) $70,000
K) $80,000
L) $90,000
M) $100,000 N) $120,000 O) $140,000 P) $160,000 Q) $180,000
R) $200,000
S) $220,000 T) $240,000 U) $260,000 V) $280,000 W) $300,000 X) $320,000
Y) $340,000 Z) none of the above
At P = $70, the quantity demanded is 6,000 and the quantity supplied would be 10,000.
The deadweight loss = (70 x [10,000 – 6,000]) – ([70 – 60] x 4000)/2 = $260,000. The
correct answer is (U).
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13. Now, instead of this legislated price floor, the PEI government decides to enforce a
quota that will keep the price up at $70. What is the amount of the deadweight loss as a
result of this quota?
A) $0
B) $6000
C) $8000
D) $10,000
E) $20,000
F) $30,000
G) $40,000 H) $50,000 I) $60,000
J) $70,000
K) $80,000
L) $90,000
M) $100,000 N) $120,000 O) $140,000 P) $160,000 Q) $180,000
R) $200,000
S) $220,000 T) $240,000 U) $260,000 V) $280,000 W) $300,000 X) $320,000
Y) $340,000 Z) none of the above
With a quota, the supply is restricted to 6,000 units. The demand price is $70 at 6,000
units and the supply price is $50. The deadweight loss would be [(70 – 50) x (8000 –
6000)]/2 = $20,000. The correct answer is (E).
14. Now, instead of the price floor or the quota (discussed in questions 12 and 13), the
government of Prince Edward Island decides to pay farmers not to produce potatoes until it
reduces the quantity of output sufficient to keep the price at $70. How much will the
government have to pay farmers in order to achieve its objectives?
A) $0
B) $6000
C) $8000
D) $10,000
E) $20,000
F) $30,000
G) $40,000 H) $50,000 I) $60,000
J) $70,000
K) $80,000
L) $90,000
M) $100,000 N) $120,000 O) $140,000 P) $160,000 Q) $180,000
R) $200,000
S) $220,000 T) $240,000 U) $260,000 V) $280,000 W) $300,000 X) $320,000
Y) $340,000 Z) none of the above
In order to encourage the farmers to reduce their output, the government would have to
pay them the amount of producer surplus they would give up by reducing production.
That would be [(70 – 50) x (10,000 – 6,000)]/2 = $40,000. The correct answer is (G).
15. Imagine a (different) situation in which a monopolist is serving two distinct markets. It
is able to produce output from a single factory with a constant marginal cost. Imagine that
you know that the elasticity of demand in the first market is –15. In the second market, the
elasticity of demand is –3. The price in the first market is $60. Assuming the monopolist
engages in third-degree price discrimination, what is the price in the second market?
A) $0
B) $38
C) $40
D) $42
E) $44
F) $46
G) $48
H) $50
I) $52
J) $54
K) $56
L) $58
M) $60
N) $62
O) $64
P) $66
Q) $68
R) $70
S) $72
T) $74
U) $76
V) $78
W) $80
X) $82
Y) $84
Z) none of the above
MR = P(1 + [1/ED]) = 60(1 – [1/15]) = $56. The producer will profit maximize by making
MR equal in the second market, so 56 = P(1 – [1/3]) = (2/3)P. Therefore, P in the second
market = $84.
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PART II - Graphical and Short Answer Questions - 25 marks
Price
Short-run Supply
100
70
Demand
10
0
3000
10,000
16(a) Assume that the graph above refers to a perfectly competitive industry that produces
hula hoops. In this industry there is no international trade. Now imagine that international
trade is possible…in fact, hula hoops are perfectly elastically supplied from international
producers at a price of $30. What is the extra amount of economic welfare or economic
well-being due to opening up international trade and who receives it?
The demand curve is P = 100 - .01Q and the supply curve is P = 10 + .02Q. This
generates an equilibrium price of $70 and equilibrium quantity of 3000 units. At a price
of $30, we can calculate that 7,000 hula hoops will be demanded and 1,000 hula hoops
will be domestically supplied. The extra well-being = ([70 – 30] x [7000 – 1000])/2 =
$120,000
(b) How many hula hoops will be imported?
From the calculations above, 7,000 – 1,000 = 6,000 hula hoops will be imported.
(c) If a tariff of $10 per hula hoop is placed on imports, what will be the amount of
deadweight loss due to the tariff?
A tariff of $10 will drive the equilibrium price up to $40. At $40, the quantity demanded
will be 6,000 units and the quantity supplied domestically will be 1,500 units. There will
be three areas of loss of consumer surplus compared to the situation without a tariff.
There are two areas of deadweight loss: (10 x 500)/2 = $2,500 and (10 x 1000)/2 = $5,000
Quantity
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for a total deadweight loss of $7,500. There is also the tariff revenue, which, on 4,500
units of imports = 4500 x 10 = $45,000. The tariff revenue is not part of deadweight loss
(and you don’t need to calculate it for this question… ).
(d) Imagine now that the curve labelled “short run supply” is actually a long-run supply
curve in this industry (and international trade still happens and there is a tariff of $10).
How much is the producer surplus? Who gets this producer surplus? Invent an example to
give an illustration of who might get this producer surplus.
The producer surplus is ([40 – 10] x 1500)/2 = $22,500. The producer surplus in the
long run is received by the owners of scarce productive inputs whose input prices rise as
the industry expands (as Q rises). The scarce input could be labour. If there was some
kind of scarce specialized labour required in the production of hula hoops, its price
might rise as the industry expands. Or, it could be some material used in the production
of hula hoops (a rare mineral or metal) whose price would rise as output in this industry
expands. For this to happen, the hula hoop industry would have to be a major consumer
of this mineral or metal.
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17. There are two types of consumers in the market for hand-held digital devices. Type
A consumers are wary and uncertain, Type B consumers are enthusiastic. The demand
per week by each Type A consumer is given on the graph below (labelled “Type A
Demand”). The demand per week by each Type B consumer is given on the graph
below (labelled “Type B Demand”). You can assume that the cost of producing digital
devices is zero. The monopoly producer of digital devices is trying to figure out how to
price digital devices so that each type of consumer will pay a different price, so that the
monopolist can price discriminate. Since the consumers are not distinguished by any
obvious characteristic, the monopolist will have to design different price-quantity
packages that encourage consumers to self-select into the two types. For the purposes
of this question, you can assume that there is one Type A consumer and one Type B
consumer in the market. The questions on the next page refer to this diagram.
$ per
device
1200
800
Type B Demand
Type A
Demand
0
15
20
30
40
50
60
Number of digital
devices
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17 (a) Assume that 20 digital devices is the optimum quantity to sell to the Type A
consumer to allow self-selection by consumers and to maximize profit for the producer.
Show on the diagram (i.e., shade in the area or colour it in and indicate with arrows
etc.) the area that corresponds to the price charged to the Type A consumer. What is the
dollar value of the price charged to the Type A consumer?
The self-selecting price to charge to the Type A consumer will be ([800 – 400] x20)/2
+ (400 x 20) = $12,000. The area is coloured in red on the graph above.
(b) Using a different colour or a different pattern of cross-hatching, indicate on the
diagram the area that corresponds to the amount of consumer surplus that the Type B
consumer will receive. What is the dollar value of this amount of consumer surplus?
The consumer surplus received by the Type B consumer is shown in blue with a
pattern of small squares on the diagram above. The amount of consumer surplus will
be 400 x 20 = $8,000.
(c) What price will the Type B consumer have to pay?
The type B consumer will have to pay a price that exactly leaves the amount of
consumer surplus calculated in part (b). That price is $12,000 (i.e., the Type A price)
+ ([800 x 40]/2) which is another $16,000. The total price for the Type B package will
be $28,000.