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ANSWERS TO FINAL EXAM - ECMC02H3
Final Exam – August 11, 2007
Professor Gordon Cleveland
Time: 3 hours
______________________________________
Your name (Print clearly and underline your last name)
____________________
Your student number
This exam consists of multiple choice questions and short answer questions. There
are 20 multiple choice questions, each worth 3 marks, which are to be answered on
the front sheet of this exam in the spaces provided. If two multiple choice
answers seem reasonable, choose the best possible answer. There are four short
answer questions at the end of this exam paper. Space is provided to answer those
questions directly on this exam paper.
Your exam consists of 17 pages (counting this first page). Please count your exam's
pages immediately and report any problems. FILL IN YOUR NAME NOW.
1. __H_____
6. ___K____
11. __F______
16. __M_____
2. ___N____
7. ___A____
12. __I______
17. __G_____
3. ___C____
8. ___G____
13. __F______
18. ___S____
4. __G_____
9. ___X____
14. __T______
19. ___N____
5. __C_____
10. __Y_____
15. ___S_____
20. ___K____
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PART I - 20 Multiple Choice Questions – 3 marks each.
1 - 4 You are given the following 5 strategic games involving two firms. Firm I can adopt
either strategy A or strategy B. Firm II can adopt either strategy Y or strategy Z. Payoffs
to the firms appear in the matrix. Questions 1 through 3 concern these five games.
Firm II
Game #1:
Firm I
Strategy Y
Strategy Z
Strategy A
(3, 4)
(4, 5)
Strategy B
(4, 5)
(5, 6)
Firm II
Game #2:
Firm I
Strategy Y
Strategy Z
Strategy A
(3, 4)
(4, 5)
Strategy B
(4, 5)
(3, 4)
Firm II
Game #3:
Firm I
Strategy Y
Strategy Z
Strategy A
(3, 4)
(4, 5)
Strategy B
(2, 3)
(6, 2)
Firm II
Game #4:
Firm I
Strategy Y
Strategy Z
Strategy A
(3, 4)
(-4, -5)
Strategy B
(4, -3)
(-1, -2)
Firm II
Game #5:
Firm I
Strategy Y
Strategy Z
Strategy A
(3, 4)
(4, 5)
Strategy B
(2, 3)
(5, 2)
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1. Assume that these are sequential games in which Firm II moves first and Firm I moves
second. In which of these five games is “Strategy B – Strategy Z” a Nash equilibrium?:
A) only #1 B) only #2
F) only #1 and #2
I) only #1 and #5
L) only #2 and #5
O) only #4 and #5
R) only #1, #2, and #5
U) only #1, #4, and #5
X) only #2, #4, and #5
C) only #3 D) only #4
G) only #1 and #3
J) only #2 and #3
M) only #3 and #4
P) only #1, #2, and #3
S) only #1, #3, and #4
V) only #2, #3, and #4
Y) only #3, #4, and #5
E) only #5
H) only #1 and #4
K) only #2 and #4
N) only #3 and #5
Q) only #1, #2, and #4
T) only #1, #3, and #5
W) only #2, #3, and #5
Z) all of the games
2. Now, assume each firm is trying to maximize its individual benefit, and that the firms
must move simultaneously (rather than sequentially). If all five of the games are
simultaneous, rather than sequential, in which of these games would the Nash
equilibrium be different than before? (Note: If there is no equilibrium in one case but
an equilibrium in the other, count that as different. If there is one equilibrium in one
case, but two equilibria in the other case, count that as different).
A) only #1 B) only #2
F) only #1 and #2
I) only #1 and #5
L) only #2 and #5
O) only #4 and #5
R) only #1, #2, and #5
U) only #1, #4, and #5
X) only #2, #4, and #5
C) only #3 D) only #4
G) only #1 and #3
J) only #2 and #3
M) only #3 and #4
P) only #1, #2, and #3
S) only #1, #3, and #4
V) only #2, #3, and #4
Y) only #3, #4, and #5
E) only #5
H) only #1 and #4
K) only #2 and #4
N) only #3 and #5
Q) only #1, #2, and #4
T) only #1, #3, and #5
W) only #2, #3, and #5
Z) all of the games
3. If Game #4 is a simultaneous game, but if both players are risk-averse, what is the
Nash Equilibrium?
A)
B)
C)
D)
E)
F)
Strategy A/Strategy Y is the Nash equilibrium
Strategy A/Strategy Z is the Nash equilibrium
Strategy B/Strategy Y is the Nash equilibrium
Strategy B/Strategy Z is the Nash equilibrium
There is no Nash equilibrium
There are two Nash equilbria to this game.
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4. Bert has an initial endowment of 10 units of clothing and 5 units of food. Ernie’s initial
endowment is 5 units of food and 10 units of clothing. Bert regards food and clothing as
perfect one-for-one substitutes. Ernie regards food and clothing as perfect one-for-two
substitutes (one unit of food equals two units of clothing). What is the best description of
the contract curve (assuming Bert’s origin is in the bottom left hand corner of the
Edgeworth Exchange Box, and that food is measured on the vertical axis)?
(A) The contract curve is a straight line that joins the top left-hand corner of the
box to the bottom right-hand corner of the box
(B) The contract curve is a straight line that joins the mid-point of the bottom of
the box to Ernie’s origin at the top right-hand corner of the box
(C) The contract curve is a straight line that joins the mid-point of the top of the
box to Bert’s origin at the bottom left-hand corner of the box.
(D) The contract curve is bowed upwards and joins Bert and Ernie’s origins
(E) The contract curve is bowed downwards and joins Bert and Ernie’s origins
(F) The contract curve is a straight line joining Bert and Ernie’s origins
(G) The contract curve is a straight line along the right side of the box from top to
bottom and then along the bottom of the box to Bert’s origin.
(H) The contract curve goes along the top of the box from right to left and then
down the left side of the box to Bert’s origin.
(I) There is no contract curve because there are no points of tangency
(J) The initial endowment point is the only point on the contract curve.
5. Using the information given in Question 4 about Bert and Ernie, if Ernie trades one
unit of food to Bert in exchange for one unit of clothing, will the result be Pareto
superior?
(A) Yes
(B) No, the original equilibrium was Pareto Optimal
(C) No
(D) Can’t tell from the information given
(E) It depends upon the prices of food and clothing
(F) None of the above
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6-7. Suppose that Pat is endowed with 5 units of X and 20 units of Y. Pat’s
utility function for X and Y is given by U = X2Y. At the same time, Mike is
endowed with 15 units of X and 30 units of Y. Mike’s utility function for X and Y is
given by U = XY2. Assume that the price of X and Y is given by PX = 2 and PY = 1.
Use this information to answer questions 6 and 7.
6. At this set of prices of good X and good Y, how many units of good Y will Pat
want to consume?
A) 0
G) 6
M) 12
S) 18
Y) 24
B) 1
C) 2
H) 7
I) 8
N) 13
O) 14
T) 19
U) 20
Z) none of the above
D) 3
J) 9
P) 15
V) 21
E) 4
K) 10
Q) 16
W) 22
F) 5
L) 11
R) 17
X) 23
7. Will the set of prices shown above lead Pat and Mike towards a competitive
equilibrium that is Pareto Optimal?
(A) Yes
(B) No, the price of X needs to rise relative to the price of Y
(C) No, the price of Y needs to rise relative to the price of X.
(D) Yes, they will lead to an equilibrium, but it is not Pareto Optimal
(E) Yes, they will lead to pareto optimality, but it is not a competitive equilibrium
(F) The initial endowments were already pareto optimal
(G) None of the above
8 -10. In the competitive market for cut flowers, demand is given by P = 100 – Q and
supply is given by P = 10 + 0.5Q. The government considers the equilibrium price ($40)
too low to support farmers continuing to produce this product. They would like the
price of cut flowers to be $70 per unit. They are considering a number of alternative
policies to keep prices high. You can use this information to answer questions 8 – 10.
8. Assume that the government legislates a minimum price of $70 and credibly
enforces this minimum price, so that producers restrict their output to the amount
that can be sold. What is the amount of increase in producer surplus, compared
to the competitive equilibrium?
A) $0
B) $100
C) $225
D) $350
E) $400
F) $525
G) $675
H) $750
I) $800
J) $925
K) $1000
L) $1150
M) $1275
N) $1300
O) $1450
P) $1575
Q) $1625
R) $1750
S) $1800
T) $1950
U) $2000
V) $2250
W) $2500
X) $2700
Y) $3600
Z) none of the above
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9. Assume now that the government implements a minimum price (as above), but
now producers do not restrict their output to the amount that can be sold at a price
of $70. Further, output is not storable (it is perishable), so this excess output will
be wasted. What now is the amount of deadweight loss?
A) $0
B) $675
C) $750
D) $800
E) $925
F) $1000
G) $1150
H) $1275
I) $1300
J) $1450
K) $1575
L) $1625
M) $1750
N) $1800
O) $1950
P) $2000
Q) $2250
R) $2500
S) $2700
T) $3600
U) $3900
V) $4250
W) $4775
X) $4950
Y) $6975
Z) none of the above
10. Assume now, instead, that the government restricts production by paying farmers
not to grow cut flowers. Assume that the government pays farmers just the right
amount to just drop production to the exact level necessary to establish a price of
$70. What now is the total amount of producer surplus?
A) $0
B) $100
C) $225
D) $350
E) $400
F) $525
G) $675
H) $750
I) $800
J) $925
K) $1000
L) $1150
M) $1275
N) $1300
O) $1450
P) $1575
Q) $1625
R) $1750
S) $1800
T) $1950
U) $2000
V) $2250
W) $2500
X) $2700
Y) $3600
Z) none of the above
11.
Frank and Harry have the following utility functions: for Harry U = X0.5Y0.5; for
Frank U = X + 2Y. Between them, Frank and Harry have 100 units of X and 60
units of Y. Below are listed a number of possible allocations of goods X and Y to
Harry (the remainder would go to Frank). Which one of these allocations is on the
contract curve?
(A) 95 units of X and 5 units of Y
(B) 80 units of X and 10 units of Y
(C) 60 units of X and 20 units of Y
(D) 40 units of X and 40 units of Y
(E) 50 units of X and 45 units of Y
(F) 60 units of X and 30 units of Y
(G) 30 units of X and 20 units of Y
(H)20 units of X and 40 units of Y
(I) 10 units of X and 40 units of Y
(J) 0 units of X and 50 units of Y
(K) none of the above
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12-13. An industry consists of two mineral springs, each of which have variable costs of
$20 per unit of water produced and no fixed costs. The industry demand curve is:
P = 164 - 2Q. Questions 12 and 13 concern this industry.
12. If the firms compete under the Cournot assumptions (that is, each firm assumes that
the other firm will not change its output), then the price that will result in the Nash
equilibrium is:
A) $0
B) $20
C) $34
D) $40
G) $58
H) $64
I) $68
J) $72
M) $104
N) $108
O) $116
P) $122
S) $128
T) $130
U) $131
V) $132
Y) more information is needed to answer
E) $46
F) $56
K) $82
L) $96
Q) $124
R) $126
W) $133
X) $134
Z) none of the above
13. Now suppose that one firm is a Stackelberg leader while other firm is a follower.
Assume, as usual, that the follower behaves like a Cournot duopolist (that is, assumes that
the leader's output is fixed). Then the price that will result is:
A) $0
B) $20
C) $34
D) $40
G) $58
H) $64
I) $68
J) $72
M) $104
N) $108
O) $116
P) $122
S) $128
T) $130
U) $131
V) $132
Y) more information is needed to answer
E) $46
F) $56
K) $82
L) $96
Q) $124
R) $126
W) $133
X) $134
Z) none of the above
14-15. Suppose there are twenty people in society. Each person has utility for mosquito
control given by U = 200X – 4X2, where X is the number of units of mosquito control, and
where utility is measured in dollars. Mosquito control is a non-excludable and non-rival
good.
14. What would be the optimal level of this activity (units of mosquito control produced)
if the total cost of mosquito control is given by TC = 200X + 20X2?
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A) 0
G) 6
M) 12
S) 18
Y) 24
B) 1
C) 2
H) 7
I) 8
N) 13
O) 14
T) 19
U) 20
Z) none of the above
D) 3
J) 9
P) 15
V) 21
E) 4
K) 10
Q) 16
W) 22
F) 5
L) 11
R) 17
X) 23
15. If the government were to produce the optimal amount of mosquito control, what
would be the total value to citizens of the mosquito control they were receiving?
A) $0
G) $1620
M) $11240
S) $47120
Y) $75400
B) $19
C) $200
H) $1740
I) $1968
N) $13700 O) $14300
T) $51920 U) $52040
Z) none of the above
D) $327
J) $2196
P) $21540
V) $52660
E) $438
K) $2356
Q) $31680
W) $63000
F) $960
L) $2874
R) $41720
X) $64080
16-18.There is a group of 20 citizens, equally distributed by age from 5 to 100. In other
words, there is one person who is five years of age, a second person is ten years of age,
and so on right up to the oldest who is 100 years of age. A monopoly firm has invented a
marvellous new medical technology that is capable of making citizens young again after
just one treatment. Each citizen is willing to pay two times the number of dollars equal to
his or her age to gain access to this technology (the five-year old is willing to pay $10, the
ten-year old is willing to pay $20, and so on). Each treatment with this new medical
technology uses up resources worth $40 per person (i.e. the marginal cost and average
cost is $40 per treatment). You can use this information to answer questions 16-18.
16. If this is a single-price monopolist, what is the maximum profit that this monopolist
will make?
A) $0
B) $160
C) $200
D) $240
E) $280
F) $300
G) $360
H) $400
I) $450
J) $480
K) $500
L) $630
M) $720
N) $880
O) $900
P) $1020
Q) $1100
R) $1280
S) $1360
T) $1460
U) $1500
V) $1620
W) $1710
X) $1840
Y) $1950
Z) none of the above
17. What is the largest amount of consumer surplus that can be provided by the singleprice monopolist when charging a price that will maximize profit?
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A) $0
G) $360
M) $720
S) $1360
Y) $1950
B) $160
C) $200
H) $400
I) $450
N) $880
O) $900
T) $1460
U) $1500
Z) none of the above
D) $240
J) $480
P) $1020
V) $1620
E) $280
K) $500
Q) $1100
W) $1710
F) $300
L) $630
R) $1280
X) $1840
18. If the monopolist is able to perfectly price discriminate, how much profit will this
producer make?
A) $0
B) $160
C) $200
D) $240
E) $280
F) $300
G) $360
H) $400
I) $450
J) $480
K) $500
L) $630
M) $720
N) $880
O) $900
P) $1020
Q) $1100
R) $1280
S) $1360
T) $1460
U) $1500
V) $1620
W) $1710
X) $1840
Y) $1950
Z) none of the above
19-20. There are six sellers of ice-cream evenly spaced along a beach that is 600 metres
long. There are 600 people evenly spaced along the beach every day and each one of
them buys one ice-cream cone from the seller who offers the lowest delivered price. The
lowest delivered price consists of the price that consumers pay for the ice-cream plus one
penny for each metre of distance they have to walk towards the ice-cream vendor from
where their towels are (you can ignore the return walk distance). The currently located
six vendors are ideally placed to split the market evenly. Each one of them charges $3 for
an ice-cream cone. This information can be used to answer questions 19 and 20.
19. With the six ice-cream vendors, what is the average delivered price of ice-cream for
customers on this beach?
A) $0
B) $0.25
C) $0.50
D) $0.75
E) $1.00
F) $1.25
G) $1.50
H) $1.75
I) $2.00
J) $2.25
K) $2.50
L) $2.75
M) $3.00
N) $3.25
O) $3.50
P) $3.75
Q) $4.00
R) $4.25
S) $4.50
T) $4.75
U) $5.00
V) $5.25
W) $5.50
X) $5.75
Y) $6.00
Z) none of the above
20. Assume that another ice-cream vendor comes along. The other vendors will not move
their carts, so this vendor must choose the best possible location given the locations
already chosen by the other vendors. If this vendor wants to have 100 customers, and the
other vendors do not change their selling price for ice-cream, what price will he have to
charge for an ice-cream cone?
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A) $0
G) $1.50
M) $3.00
S) $4.50
Y) $6.00
B) $0.25
C) $0.50
H) $1.75
I) $2.00
N) $3.25
O) $3.50
T) $4.75
U) $5.00
Z) none of the above
D) $0.75
J) $2.25
P) $3.75
V) $5.25
E) $1.00
K) $2.50
Q) $4.00
W) $5.50
F) $1.25
L) $2.75
R) $4.25
X) $5.75
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Short answer questions (40 marks in total)
21. There are two bus companies in the Land of Oz. Both bus companies have buses that
produce considerable amounts of pollution; in fact, with no government intervention,
each bus company will produce 100 tonnes of carbon monoxide emissions, creating 200
tonnes of emissions in total. Because one company has old buses and one company has
newer buses, the marginal cost of reducing this pollution is different for these two
companies. For Firm #1, the marginal cost of abatement is given by MCA1 = 200 – 2Q1.
For the company with the newer buses (Firm #2), the marginal cost of abatement is given
by MCA2 = 50 – 0.5Q2. In each case, MCA is measured in dollars per tonne of pollution
and Q measures the amount of pollution. You may assume there are no “fixed” costs of
abatement, so the marginal costs can be summed to find total costs of abatement. The
total reduction of pollution in society is the sum of the reduction by the two companies.
The cost to society caused by this carbon monoxide pollution is given by MSC = 0.6Q,
where MSC (marginal social cost) is measured in dollars per tonne of pollution.
(a)
What is the optimal number of tonnes by which emissions of carbon monoxide
should be reduced in the Land of Oz? Optimally, how much will pollution be
reduced by each of these companies?
Since MCA1 = 200 – 2Q1, Q1 = 100 - .5 MCA1 .
Since MCA2 = 50 – 0.5Q2 , Q2 = 100 2 MCA2. The sum of these two is Q = 200 – 2.5MCA, which is the equation for the overall
marginal cost of abatement function. Alternatively, it is MCA = 80 - .4Q. The optimal
solution occurs where MCA = MSC, so 80 - .4Q = .6Q, or Q = 80. This Q refers to the
amount of pollution, so the reduction of pollution is 200 – 80 or 120 tonnes of emissions
reduction. At this optimum, the MCA = 80 - .4(80) = $48. The optimum for each firm will be
for each firm to reduce pollution until its own MCA is equal to $48, so we can find 48 = 200 –
2Q1 or Q1 = 76 tonnes of emissions. Therefore, emissions reduction by Company #1 would be
100 – 76 = 24 tonnes. For Company #2, we can find 48 = 50 – 0.5Q2 or Q2 = 4 tonnes of
emissions. Therefore, emissions reduction by Company #2 is 100 – 4 or 96 tonnes of
emissions.
(b)
If the Land of Oz passes a law ordering each of these two firms to reduce its
pollution by half of the optimal amount of pollution reduction calculated in part
(a) (i.e., each company does its “fair” share of total pollution reduction), what will
be the total cost of reducing (i.e., abating) pollution to this level in Oz?
The optimal reduction is 120 tonnes, so equal shares would be 60 tonnes. In other words, the
quantity of emissions would be 40 (i.e., 100 – 60) for each firm. At these quantities, MCA1 = 200
– 2(40) = $120, and MCA2 = 50 – 0.5(40) = $30. The total cost of emissions reduction will be the
sum of the area of the triangle under each MCA curve up to 60 tonnes of emissions. This is [(120
x 60)/2] + [(30 x 60)/2] = $3600 + $900 = $4500.
(c)
Imagine that instead of passing a law that dictates the amount of pollution that
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should be reduced, the land of Oz sets a fine (or fee) for polluting (which will have
the same effect as a tax on emissions). What would be the optimal fee per tonne of
pollution?
The optimal fee would be $48, which is the MCA when emissions reduction is at the
optimal amount.
(d)
If the land of Oz sets the fee at the optimal level, what will be the total cost of
reducing pollution to the optimal level in Oz?
If pollution reduction is optimal, then the first company will reduce by 24 tonnes and the second
by 96 tonnes. The total cost, using the technique described in part (b) will be: [(48 x 24)/2] + [(48
x 96)/2] = $576 + $2304 = $2880.
22. You are given the following Production Possibilities Frontier:
X2 + Y = 400
(a) If there is no international trade (autarchy), and if the competitive equilibrium price of
good X is 36 and the price of good Y is 1, how much of good X and Y will be produced in
this country? How much of good X and good Y will be consumed?
In competitive equilibrium, the slope of the PPF will be equal to the slope of the price line, so
dY/dX = -(PX/PY). Since Y = 400 – X2, dY/dX = -2X, and we are given that –(PX/PY) = -36/1.
Therefore, X* = 18 and Y* = 400 – (18)2 = 76.
(a)
Now assume that we have the same PPF as above, and that the international price
of good X is 6 and the international price of good Y is 1, and this country now opens itself
up to international trade. Therefore, the international trade line will obey the equation
6(XC – XP ) = (YP – YC ). The utility function of all consumers in this society is U = XY.
How much of good X and good Y will be produced in this country and how much of
good X and good Y will be consumed?
The Lagrangean function (£) is XCYC + (400 – XP2 – YP) + (6XC – 6XP – YP + YC).
Therefore, ∂£/∂XC = YC + 6 = 0
∂£/∂YC = XC +  = 0
∂£/∂XP = -2XP - 6 = 0
∂£/∂YP = - -  = 0
∂£/∂ = 400 – XP2 – YP = 0
∂£/∂ = 6XC – 6XP – YP + YC = 0
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We can manipulate the first two equations to find that YC = 6XC. We can manipulate the second
two equations to find that XP = 3. Substituting this value into the first constraint (fifth equation),
we can find that YP = 391. Substituting these values for XP and YP into the sixth equation and
using the result from above that YC = 6XC , we can find that XC = 34.1 and YC = 204.5.
(b)
How much of good X is traded with other countries and how much of good Y?
Which one is imported and which one is exported? What is the utility level after trade?
From the results in part (a), we can see that the gap between production of X and consumption of
X is 31.1 units. In other words, 31.1 units of X will be imported. The gap between production
and consumption of Y is 186.5 units, so that this number of units of Y will be exported to other
countries. Inserting the consumption values of X and Y into the utility function, we find that
after trade utility = 6969.36 utils.
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27. A monopoly producer of a miracle cure for baldness has demand for the product
given by P = 40 – 0.5Q. The total costs of the monopolist are given by TC = 2Q2. The
graph below shows dollars on the vertical axis and quantity on the horizontal axis. Fill in
the table below, calculating the Total Revenue and Total Cost and Profit of a single-price
monopolist at different levels of output. Label the diagram below, put numbers on the
axes, and show the Total Revenue and Total Cost functions on this graph. Show on the
diagram the profit-maximizing quantity of output (Q*), and indicate with a two-headed
arrow (
) the amount of profit earned at this output.
Draw the diagram yourself using the data below
Quantity
TR
TC
Profit
2
78
8
70
4
152
32
120
6
222
72
150
8
288
128
160
10
350
200
150
12
408
288
120
14
462
392
70
16
512
512
0
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22. There are two types of consumers in the market for digital books: 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 books is zero. The monopoly producer of
digital books is trying to figure out how to price digital books 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 book
120
Type B Demand
Type A
Demand
0
15
20
25
40
60
Number of digital
books
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22 (a). If the monopolist were able to completely separate the Type A consumer from
the Type B consumer (so that no resale was possible, and so that the Type A consumer
could only buy the Type A package and the Type B consumer could only buy the
Type B package), what would be the price and quantity of the “take-it-or-leave-it”
package offered to the Type A consumer? What would be the price and quantity of
the package offered to the Type B consumer?
The equation of the demand curve for the Type B consumers is P = 120 – 2Q. For the Type A
consumers, it is P = 120 – 3Q. If segmentation of these markets were possible, the maximum
price that Type A consumers would pay is the whole area under the demand curve, which is
120 x 40/2 = $2,400. Under the Type B demand curve, the area is 120 x 60/2 = $3,600.
(b) Now assume that it is not possible to completely separate the market into two
sections. Instead, both the Type A consumer and the Type B consumer can purchase
either package. Now, the monopolist must try to design price-quantity packages that
will encourage the two types of consumers to self-select the package designed for
each. Assuming now that the Type A package will contain 40 digital books and the
Type B package will contain 60 digital books, what would be the price charged for the
Type A package and the price charged for the Type B package to encourage selfselection (but provide as much revenue for the monopolist as is possible from these
packages)?
If the price of the Type A package were $2,400, and the Type B consumer bought this package,
he would receive consumer surplus = 3600 – [2400 + (40 x 20/2)] = $800. Therefore, in order
to encourage self-selection, the Type B consumer must be given at least this much consumer
surplus. Therefore, the maximum price that can be charged for 60 books is 3600 – 800 =
$2,800. A price of $2,400 would be charged for the Type A package of 40 books.
(c) Now assume that the monopolist can change the size of the Type A package. It no
longer has to contain 40 digital books. Instead it could contain 15 or 20 or 25 books.
Of these four possibilities (i.e., 15 books, 20 books, 25 books, or 40 books), what is the
profit-maximizing amount of books for the monopolist to include in the Type A
package (given that this might affect the sale price of the Type B package)? What
price should the monopolist charge to the Type A consumer for this package?
Different numbers of books will imply different prices for the Type A package and different
amounts of consumer surplus for the Type B consumer if he should buy this Type A package.
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This then affects the price that can be charged for the package of 60 books. With 15 books, the
Type A package will cost $1462.50. The Type B package will cost $3487.50. With one of each
type of consumer, total revenue/profit will be $4,950.00. With 20 books, the Type A package
will cost $1800.00. The Type B package will cost $3400.00. With one of each type of
consumer, total revenue/profit will be $5,200.00. With 25 books, the Type A package will cost
$2062.50. The Type B package will cost $3287.50. With one of each type of consumer, total
revenue/profit will be $5,350.00. With 40 books, the Type A package will cost $2,400.00. The
Type B package will cost $2,800.00. With one of each type of consumer, total revenue/profit
will be $5,200.00. Therefore, it is profit-maximizing to include 25 books in the Type A
package. A price of $2062.50 would be charged for the Type A package.
(d) If the monopolist offers the Type A consumer the profit-maximizing package from
amongst the choices described in part (c) of this question, what price will be offered to
the Type B consumer for 60 digital books? How much consumer surplus will the
Type B consumer get?
From above, a price of $3287.50 would be charged for the Type B package. The Type B
consumer would get consumer surplus of $3,600 - $3,287.50 = $312.50.
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