FINAL EXAM ECONOMICS OF MARKETS AND
ORGANISATIONS MAY 2019
1.
Consider a market in which demand equals 𝐷 (𝑝) = 202 – 𝑝, where 𝑝 denotes the price. Two
companies compete on quantity à la Stackelberg. The leader produces with constant marginal
costs equal to 10. The follower produces with constant marginal costs equal to 2. Assuming
that the follower will enter the market, what is the outcome in the subgame perfect Nash
equilibrium?
a.
b.
c.
d.
2.
Two ice cream sellers are located at two extreme ends of a beach which is 1000 meters long.
1000 customers are uniformly distributed along the length of the beach. These customers do
not like to walk and therefore incur a total travel cost of 𝑡 = 0.002 for each meter of distance
from the shop where they buy. Assume that each customer will buy exactly one ice cream.
The marginal cost of an ice cream is zero. What price will the sellers charge for the ice cream?
a.
b.
c.
d.
3.
The market leader produces 50, the follower 25
The market leader produces 102, the follower 40
The market leader produces 80, the follower 40
The market leader produces 92, the follower 54
2
5
7
10
(Risk-neutral) agent Antonio directs a movie on behalf of (risk-neutral) principal Penélope.
Antonio can exert effort 𝑒 at cost 𝐶(𝑒) = 25𝑒7. There are no costs other than the costs of
effort. Each unit of Antonio’s effort yields one additional movie theatre ticket sold, i.e.,
Antonio’s output equals 𝑄 = 𝑒. Suppose that Penélope obtains a price of 10 per movie
ticket. Penélope offers Antonio a linear contract which specifies that Antonio will receive a
base wage 𝑤 plus a bonus 𝛽 for each movie theatre ticket sold. Antonio has an outside
utility of 𝑈OPQ = 0. In the contract that maximizes Penelope’s profit, how high is the base
wage 𝑤? (Assume that Antonio accepts the job if he is indifferent).
a. 𝑤 = −1
6
b. 𝑤 = − 7
6
c. 𝑤 = T
6
d. 𝑤 = 7
4.
Two firms operate in a market with demand 𝐷(𝑝) = 100 − 2𝑝. Assume that the firms will
interact for an infinite number of periods and that no other firms will enter the market in the
future. Each firm has marginal costs 𝑀𝐶 = 10. The firms can either form a cartel, in which
case they charge the monopoly price and share profits equally, or compete a la Bertrand. In
case they form a cartel, they each play a trigger strategy whereby if the other firm does not
stick to the agreement, no cartel will be formed in the future. Suppose that the firms do not
discount the future. However, forming a cartel is illegal and in each round with probability P,
the cartel is detected by the authorities. If the cartel is detected, the firms will not be able to
form a cartel again. What is the maximum P for which it is still attractive to form a cartel?
a. A cartel can be formed if 𝑃 ≤
b. A cartel can be formed if 𝑃 ≤
c. A cartel can be formed if 𝑃 ≤
d. A cartel can be formed if 𝑃 ≤
5.
6
T
6
Z
6
2
Z
T
Consider a used-car market where two types of cars are sold, low-quality cars and high-quality
cars. Potential car buyers value low-quality used cars at €1,000 and high-quality used cars at
€2,500. Low-quality car owners value their car at €750, while owners of a high-quality used
car value it at €2,000. The fraction of current owners who have lemons is λ<1. For what values
of λ do all potential sellers sell their used cars?
a. 𝜆 ≤
b. 𝜆 ≤
6
T
6
3
6
c. 𝜆 ≤ 7
Z
d. 𝜆 ≤ T
6.
Two firms operate in a market with demand 𝐷(𝑝) = 100 − 4𝑝. Each firm has marginal costs
𝑀𝐶 = 9. The firms can either form a cartel, in which case they charge the monopoly price
and share profits equally, or compete a la Bertrand. What is the welfare loss (deadweight loss)
in this market if the firms form a cartel?
a.
b.
c.
d.
0
50
78
128
iE
7.
Two workers work in a team. They both have effort costs of 𝐶(𝑒) = 7 . The team output is
given by 𝑄 = 10(𝑒6 + 𝑒7 ). The workers receive a fixed wage w and a bonus of 10 per unit of
output. What is the quantity produced by each worker?
a.
b.
c.
d.
100
200
500
1000
A restaurant is looking for a new cook. It offers a contract consisting of a base wage w and a
bonus 𝛽 per meal produced. Meals are sold at price 𝑝 = 10. The only applicant is Linda. She
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produces one meal per unit of effort she exerts and her effort costs are 𝐶(𝑒) =
. Her 7
outside utility is 50𝛼 (that is, her outside utility depends on her productivity). Assuming that
k
Linda gets the job, how does the optimal contract for the restaurant change if 𝛼 increases?
a.
b.
c.
d.
9.
w stays the same and 𝛽 stays the same
w decreases and 𝛽 stays the same
w increases and 𝛽 decreases
w decreases and 𝛽 increases
Imagine a market with 𝑛 firms who can either compete à la Cournot or form a cartel.
Everything else equal, if the government increases the fine that companies have to pay if the
cartel is discovered by the authorities…
a.
b.
c.
d.
… the firms’ discount factors decrease
… the firms’ discount factors increase
… the critical (cutoff) discount factor decreases
… the critical (cutoff) discount factor increases
10. Consider the following prisoner’s dilemma game that is repeated an infinite number of times:
Prisoner 2
Prisoner 1
Deny
Confess
Deny
6,6
8,1
Confess
1,8
5,5
The players have discount rates of 𝛿6 = 0.8 and 𝛿7 , respectively. For what values of 𝛿7 can
cooperation be sustained in a subgame perfect Nash equilibrium?
a.
b.
c.
d.
𝛿7 ≥ 1/2
𝛿7 ≥ 2/3
𝛿7 ≥ 3/4
There is no 𝛿7 for which a cooperative equilibrium can be achieved.
11. Which of the following statements are true?
I. Allowing firms to sell so-called “damaged goods” (goods whose performance is artificially
lowered) may be beneficial for consumer surplus.
II. Perfect first-degree price discrimination may enhance the consumer surplus of some
types of consumers
a.
b.
c.
d.
Both I and II are true
I is true and II is false
I is false and II is true
Both I and II are false
12. Consider the following dynamic game. Which of the following statements are true? (Note:
the upper number denotes the payoff of player 1 and the lower number denotes the payoff
of player 2).
I. The Nash equilibrium of the game is efficient according to the value-maximization
principle.
II. If Player 2 signs a binding contract forcing her to play Left if Player 1 plays Left, her payoff
increases by 1 relative to the payoff she receives under the Nash equilibrium.
a.
b.
c.
d.
Both I and II are true
I is true and II is false
I is false and II is true
Both I and II are false
NB: see game on next page
1
Left
Right
2
Left
2
Right
5
5
-5
10
Left
Right
0
2
2
4
13. Consider the following game between a worker (player 1) and a manager (player 2). Player
1’s payoff appears above player 2’s in the diagram below. Suppose this game is repeated an
infinite number of times. Player 2 discounts the future with discount factor 𝛿. For which
discount factor 𝛿 does the game have a subgame-perfect Nash equilibrium in which player 1
chooses Trust in every period? (Assume that the worker plays a trigger strategy according to
which he starts playing Trust and continues to do so until the manager chooses Betray once.
Also assume that when indifferent, player 2 chooses Honor).
1
Trust
Not trust
2
Honor
5
5
T
a. 𝛿 ≥ U
Z
b. 𝛿 ≥ T
7
c. 𝛿 ≥ Z
1
d. 𝛿 ≥ 2
Betray
-5
10
0
0
14. In a vertical chain, upstream producers may free ride on efforts of competing producers
upstream to improve in-store customer service. Which of the following contractual
agreements could alleviate the resulting free-riding problem?
a.
b.
c.
d.
An exclusive dealing contract
Resale price maintenance
An exclusive territories contract
A most-favored-customer clause
15. A new swimming pool opens in a small town. All residents of the town have the same yearly
individual demand function: 𝑄• = 300 − 100𝑝. Suppose the pool has zero marginal cost and
is the only pool in town. The pool operates a membership system whereby individuals who
want to use the pool have to buy a yearly subscription that gives them unlimited access. What
is the price for the subscription that maximizes the profit of the pool? (Assume that when
indifferent, the consumers will buy the subscription).
a.
b.
c.
d.
0
300
450
900
16. Consider a market in which demand equals 𝑄 = 𝐷(𝑝) = 94 − 𝑝, where 𝑝 denotes the price
and 𝑄 total quantity. Two firms are active in the market. Each firm has marginal costs 𝑀𝐶 =
10 and fixed costs 𝐹 = 0. Assume that the market is characterized by Cournot competition.
How much higher is the combined profit of the two firms under the optimal cartel agreement
compared to the Cournot equilibrium?
a.
b.
c.
d.
82
196
1000
1762
17. Which of the following statements are true?
I. In two-sided markets, it may be optimal for the platform to offer a price below marginal
cost on the less price-elastic side of the market.
II. In two-sided markets, if consumers on one side use only a single platform, a platform may
be able to charge monopoly prices on the other side of the market even if they only control
a modest share of consumers.
a.
b.
c.
d.
Both I and II are true
I is true and II is false
I is false and II is true
Both I and II are false
18. How many Nash equilibria in pure strategies does the following game have?
Column
Row
a.
b.
c.
d.
Left
Center
Right
Top
1,1
1,3
2,4
Middle
1,1
0,1
1,2
Bottom
9,2
9,0
0,0
0
1
2
3
19. Which of the following statements are true?
I. For probation to work as a screening device, the salary under probation must be above
the market salary for unskilled workers
II. For probation to work as a screening device, the salary after probation must be below the
market salary for skilled workers
a.
b.
c.
d.
Both I and II are true
I is true and II is false
I is false and II is true
Both I and II are false
20. Two fruit pickers harvest oranges for a farmer. The farmer pays them a base wage of 500. The
fruit picker who harvests the higher number of oranges obtains a bonus of 2 for every orange
she harvests more than the other worker. The other fruit picker pays a penalty of 2 for every
orange she harvests less than the other worker. The fruit pickers harvest 10 oranges per unit
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of effort they expend and have an effort cost of . How much effort will they put in if they
7
collude with each other?
a. 0
b. 10
c. 20
d. 30
21. A monopoly has the following cost function: 𝐶(𝑄) = 20𝑄 + 20. The market the monopoly
operates in is characterized by a price elasticity of demand of 2. Find the profit-maximizing
price the monopoly will choose. (Hint: use the inverse elasticity rule.)
a.
b.
c.
d.
p=10
p=20
p=30
p=40
22. Which of the following is a condition that must be satisfied for third-degree price
discrimination to work?
a.
b.
c.
d.
The firm must be able to observe each individual’s demand curve
The firm must be able to offer the good in different qualities
The firm has market power
Arbitrage is easy
23. Macrosoft considers creating a student version of its spreadsheet MS Accel. The only
difference between the student version and the original version is that in the student version,
Macrosoft has disabled certain features of the original spreadsheet. Macrosoft has two types
of customers: business people and students. The table below indicates the willingness-to-pay
for the normal version (N) and for the student version (S) for business people (2 million in
total) and for students (1 million in total).
Business people
Students
Number
(in millions)
2
1
Willingness-to-pay
Normal version (N)
Student version (S)
160
50
60
40
Macrosoft does not know whether someone who buys its spreadsheet is a business
person or a student. What is the revenue-maximizing menu of price/quality pairs?
(Assume that clients, when indifferent, pick the most expensive item from the menu.)
a.
b.
c.
d.
Price N = 160; price S = 160
Price N = 60; price S = 50
Price N = 160; price S = 40
Price N = 150; price S = 40
24. The city of London wishes to improve competition in the market for magic wands. To reach
this target, the city sells a new market license using the English auction. If incumbent
Ollivanders Wand Shop obtains the license in the auction, it will realize monopoly profits
equal to 5. If potential entrant The Wizard of Oz wins, Ollivanders’ duopoly profits will be 2
while The Wizard’s duopoly profits will also be 2. Who will win the auction at what price?
(Assume that when indifferent, the companies do not bid).
a.
b.
c.
d.
The Wizard of Oz will win at a price of 2
Ollivanders Wand Shop will win at a price of 2
Ollivanders Wand Shop will win at a price of 3
Ollivanders Wand Shop will win at a price of 5
25. Orange has a monopoly in the mobile operating systems market with its software, the y-OS.
Orange has a constant marginal cost of production equal to 5 and charges a unit price of 𝑤
for the y-OS. Apple is the only firm that designs and sells smartphones that are compatible
with the y-OS. Every smartphone is equipped with Orange’s operating system. Apple incurs a
cost of 4 per smartphone for the design, parts, and assembly of its smartphone. Both firms’
fixed costs are assumed to be sunk. Demand for Apple’s smartphones is given by 𝐷(𝑝) =
25 − 𝑝, where 𝑝 is the price. Orange writes a franchise contract that specifies a fixed fee 𝑓
that Apple has to pay Orange as well as a price of 𝑤 for each unit of y-OS. What contract
maximizes Orange’s profits?
a.
b.
c.
d.
𝑤 = 4; 𝑓 = 25
𝑤 = 5; 𝑓 = 0
𝑤 = 4; 𝑓 = 64
𝑤 = 13; 𝑓 = 16
26. Frequent interaction facilitates collusion. The reason is that the more frequently firms
interact, …
a. … the lower the discount factor
b. … the higher the discount factor
c. … the lower the critical discount factor
d. … the higher the critical discount factor
27. Consider a market in which demand equals 𝐷 (𝑝) = 117 – 𝑝, where 𝑝 denotes the price.
There is currently one company in the market (the leader). A second company is considering
whether to enter the market (the follower). Both companies produce with constant marginal
costs equal to 9. If the follower company wants to enter the market, it has to pay a fixed cost
of 400. What is the minimum quantity the leader needs to produce to keep the follower from
entering the market?
a.
54
b.
c.
d.
68
96
108
28. Which of the following statements are true?
I. A higher Nash payoff 𝜋 Œ decreases the critical (cutoff) discount factor
II. Dan Ariely and his colleagues ran experiments to test the effect of high bonuses on
performance. Their main conclusion is that very high bonuses may decrease performance in
some tasks.
a.
b.
c.
d.
Both I and II are true
I is true and II is false
I is false and II is true
Both I and II are false
29. Often, the same book is available as a hardcover and as a paperback. This is an example of:
a.
b.
c.
d.
first degree price discrimination
second degree price discrimination
third degree price discrimination
arbitrage
30. Which of the following is a threat to a first-mover’s ability to profit from technological
leadership?
a.
b.
c.
d.
Imitation
Preemption of assets
Patents
Switching costs
1.
Consider a market in which demand equals 𝐷 (𝑝) = 202 – 𝑝, where 𝑝 denotes the price. Two
companies compete on quantity à la Stackelberg. The leader produces with constant marginal
costs equal to 10. The follower produces with constant marginal costs equal to 2. Assuming
that the follower will enter the market, what is the outcome in the subgame perfect Nash
equilibrium?
a.
b.
c.
d.
The market leader produces 50, the follower 25
The market leader produces 102, the follower 40
The market leader produces 80, the follower 40
The market leader produces 92, the follower 54
You can find the equilibrium using backward induction. First, solve the follower’s maximization
problem: 𝑚𝑎𝑥 𝜋0 = (𝑝 − 2) 𝑞0 = (200 − 𝑞0 − 𝑞3 )𝑞0 . The FOC yields: 200 − 2𝑞0 − 𝑞3 =
-.
6
0 ⇒ 𝑞0 = 100 − 𝑞3 , which represents the follower’s best response function. Now, the
7
6
leader’s maximization problem writes: 𝑚𝑎𝑥 𝜋3 = (𝑝 − 10) 𝑞3 = 9202 − 100 + 7 𝑞3 − 𝑞3 −
-8
6
10; 𝑞3 = 992 − 𝑞3 ; 𝑞3 . The FOC yields 𝑞3∗ = 92. By substitution, the follower’s quantity is
7
𝑞0∗ = 54.
2.
Two ice cream sellers are located at two extreme ends of a beach which is 1000 meters long.
1000 customers are uniformly distributed along the length of the beach. These customers do
not like to walk and therefore incur a total travel cost of 𝑡 = 0.002 for each meter of distance
from the shop where they buy. Assume that each customer will buy exactly one ice cream.
The marginal cost of an ice cream is zero. What price will the sellers charge for the ice cream?
a.
b.
c.
d.
𝟐
5
7
10
The location of the indifferent consumer is 𝑙 = 500 +
The profit of seller 1 is then 𝜋6 = 9500 +
D F7D
DE FDG
7H
DE FDG
7H
; 𝑝6
FOC: 500 + E 7H G = 0
Because of symmetry, in equilibrium 𝑝7 = 𝑝6 and therefore 𝑝 = 1000𝑡 = 2
3.
(Risk-neutral) agent Antonio directs a movie on behalf of (risk-neutral) principal Penélope.
Antonio can exert effort 𝑒 at cost 𝐶(𝑒) = 25𝑒 7 . There are no costs other than the costs of
effort. Each unit of Antonio’s effort yields one additional movie theatre ticket sold, i.e.,
Antonio’s output equals 𝑄 = 𝑒. Suppose that Penélope obtains a price of 10 per movie
ticket. Penélope offers Antonio a linear contract which specifies that Antonio will receive a
base wage 𝑤 plus a bonus 𝛽 for each movie theatre ticket sold. Antonio has an outside
utility of 𝑈OPQ = 0. In the contract that maximizes Penelope’s profit, how high is the base
wage 𝑤? (Assume that Antonio accepts the job if he is indifferent).
a. 𝒘 = −𝟏
6
b. 𝑤 = − 7
6
c. 𝑤 = T
6
d. 𝑤 = 7
The optimal bonus guarantees that Antonio becomes the residual claimant of the fruits of his
efforts. Therefore, 𝛽 = 𝑝 = 10. The effort that maximizes Antonio’s utility is obtained by
6
6
maximising 𝑈 = 10𝑒 + 𝑤 − 25𝑒 7 and therefore 𝑒 = and Antonio’s utility is 𝑈 = 10 +
U
6
25(U)7
U
= 1 + 𝑤. Antonio accepts the job as long as 𝑈 = 1 + 𝑤 ≥ 0 and the minimum
𝑤−
wage he is willing to accept is therefore 𝑤 = −1.
4.
Two firms operate in a market with demand 𝐷(𝑝) = 100 − 2𝑝. Assume that the firms will
interact for an infinite number of periods and that no other firms will enter the market in the
future. Each firm has marginal costs 𝑀𝐶 = 10. The firms can either form a cartel, in which
case they charge the monopoly price and share profits equally, or compete a la Bertrand. In
case they form a cartel, they each play a trigger strategy whereby if the other firm does not
stick to the agreement, no cartel will be formed in the future. Suppose that the firms do not
discount the future. However, forming a cartel is illegal and in each round with probability P,
the cartel is detected by the authorities. If the cartel is detected, the firms will not be able to
form a cartel again. What is the maximum P for which it is still attractive to form a cartel?
6
a. A cartel can be formed if 𝑃 ≤
T
6
b. A cartel can be formed if 𝑃 ≤ Z
𝟏
c. A cartel can be formed if 𝑷 ≤ 𝟐
Z
d. A cartel can be formed if 𝑃 ≤ T
6
If the firms form a cartel, they will act as a monopolist. 𝑝 = 50 − 𝑄. 𝑀𝑅 = 50 − 𝑄. Setting
7
𝑀𝑅 = 𝑀𝐶 leads to 𝑄 = 40, 𝑝 = 30 and 𝜋 = 40(30 − 10) = 800, so each firm makes a
profit of 400. In case a firm reneges on the cartel agreement, it would lower its price by the
smallest possible amount, capture the whole market, and therefore make a profit close to
the monopoly profit of 800. It is profitable for each firm to form a cartel if 800 <
6
6
400, that is if 𝑃 < 7.
6F(6F`)
5.
Consider a used-car market where two types of cars are sold, low-quality cars and high-quality
cars. Potential car buyers value low-quality used cars at €1,000 and high-quality used cars at
€2,500. Low-quality car owners value their car at €750, while owners of a high-quality used
car value it at €2,000. The fraction of current owners who have lemons is λ<1. For what values
of λ do all potential sellers sell their used cars?
6
a. 𝜆 ≤
T
𝟏
b. 𝝀 ≤ 𝟑
6
c. 𝜆 ≤
7
Z
d. 𝜆 ≤ T
A buyer is willing to pay at most 𝑝 = 2500(1 − 𝜆) + 1000𝜆 = 2500 − 1500𝜆.
Moreover, owners of high-quality cars only sell if the price is at least 2,000.
6
Thus, 𝑝 ≥ 2000 ⇒ 2500 − 1500𝜆 ≥ 2000 ⇒ 𝜆 ≤ Z.
6.
Two firms operate in a market with demand 𝐷(𝑝) = 100 − 4𝑝. Each firm has marginal costs
𝑀𝐶 = 9. The firms can either form a cartel, in which case they charge the monopoly price
and share profits equally, or compete a la Bertrand. What is the welfare loss (deadweight loss)
in this market if the firms form a cartel?
a.
b.
c.
d.
0
50
78
𝟏𝟐𝟖
6
6
If the firms form a cartel, they will act as a monopolist. 𝑝 = 25 − T 𝑄. 𝑀𝑅 = 25 − 7 𝑄.
Setting 𝑀𝑅 = 𝑀𝐶 leads to 𝑄 = 32, 𝑝 = 17. In case of Bertrand competition, 𝑝 = 𝑀𝐶 = 9
6
and 𝑄 = 64. 𝐷𝑊𝐿 = (17 − 9)(64 − 32) = 128
7
7.
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Two workers work in a team. They both have effort costs of 𝐶(𝑒) = 7 . The team output is
given by 𝑄 = 10(𝑒6 + 𝑒7 ). The workers receive a fixed wage w and a bonus of 10 per unit of
output. What is the quantity produced by each worker?
a.
b.
c.
d.
100
200
500
1000
𝑒67
𝑈6 = 10 ∗ 10(𝑒6 + 𝑒7 ) − + 𝑤
2
𝜕𝑈6
= 100 − 𝑒6 = 0
𝜕𝑒6
𝑒6 = 100 = 𝑒7 (by symmetry). Each worker produces 10 units of output per unit of effort:
𝑞6 = 𝑞7 = 1000
8.
A restaurant is looking for a new cook. It offers a contract consisting of a base wage w and a
bonus 𝛽 per meal produced. Meals are sold at price 𝑝 = 10. The only applicant is Linda. She
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produces one meal per unit of effort she exerts and her effort costs are 𝐶(𝑒) = 7 k . Her
outside utility is 50𝛼 (that is, her outside utility depends on her productivity). Assuming that
Linda gets the job, how does the optimal contract for the restaurant change if 𝛼 increases?
a.
b.
c.
d.
w stays the same and 𝜷 stays the same
w decreases and 𝛽 stays the same
w increases and 𝛽 decreases
w decreases and 𝛽 increases
Solve by backward induction:
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1. 𝑈 = 𝑤 + 𝛽𝑒 − 7 k . ; maximizing U with respect to e leads to 𝑒 = 𝛽𝛼; plugging this back
6
into U yields 𝑈 = 𝑤 + 7 𝛽 7 𝛼
2. The restaurant will set the wage as low as possible given 𝑈 noH = 50𝛼 which leads to 50𝛼 =
6
6
𝑈 = 𝑤 + 7 𝛽 7 𝛼 → 𝑤 = 50𝛼 − 7 𝛽 7 𝛼.
3. The optimal bonus does not depend on the cost of effort and is simply equal to the price:
𝛽 = 10 (see the book, chapter 2.2).
6
6
4. 𝑤 = 50𝛼 − 7 𝛽 7 𝛼 = 50𝛼 − 7 107 𝛼 = 0. The optimal w is zero no matter how high 𝛼 is.
9.
Imagine a market with 𝑛 firms who can either compete à la Cournot or form a cartel.
Everything else equal, if the government increases the fine that companies have to pay if the
cartel is discovered by the authorities…
a.
b.
c.
d.
… the firms’ discount factors decrease
… the firms’ discount factors increase
… the critical (cutoff) discount factor decreases
… the critical (cutoff) discount factor increases
The fine does not have an impact on a firm’s discount factor. The fine makes collusion less
attractive, that is, it increases the critical (cutoff) discount factor.
10. Consider the following prisoner’s dilemma game that is repeated an infinite number of times:
Prisoner 2
Prisoner 1
Deny
Confess
Deny
6,6
8,1
Confess
1,8
5,5
The players have discount rates of 𝛿6 = 0.8 and 𝛿7 , respectively. For what values of 𝛿7 can
cooperation be sustained in a subgame perfect Nash equilibrium?
a.
b.
c.
d.
𝛿7 ≥ 1/2
𝜹𝟐 ≥ 𝟐/𝟑
𝛿7 ≥ 3/4
There is no 𝛿7 for which a cooperative equilibrium can be achieved.
uv Fuw
Use the trigger strategy stability condition to find 𝛿 ≥ v x =
u Fu
7
yFz
yFU
7
= Z for both players.
7
Since the game is symmetric and 𝛿6 = 0.8 > Z, cooperation is possible if 𝛿7 ≥ Z .
11. Which of the following statements are true?
I. Allowing firms to sell so-called “damaged goods” (goods whose performance is artificially
lowered) may be beneficial for consumer surplus.
II. Perfect first-degree price discrimination may enhance the consumer surplus of some
types of consumers
a.
b.
c.
d.
Both I and II are true
I is true and II is false
I is false and II is true
Both I and II are false
I.
See chapter 15.5
II.
First-degree price discrimination allows the firm to capture the entire consumer
surplus of all consumers.
12. Consider the following dynamic game. Which of the following statements are true? (Note:
the upper number denotes the payoff of player 1 and the lower number denotes the payoff
of player 2).
I. The Nash equilibrium of the game is efficient according to the value-maximization
principle.
II. If Player 2 signs a binding contract forcing her to play Left if Player 1 plays Left, her payoff
increases by 1 relative to the payoff she receives under the Nash equilibrium.
a.
b.
c.
d.
Both I and II are true
I is true and II is false
I is false and II is true
Both I and II are false
1
Left
Right
2
Left
5
5
2
Right
-5
10
Left
Right
0
2
2
4
13. Consider the following game between a worker (player 1) and a manager (player 2). Player
1’s payoff appears above player 2’s in the diagram below. Suppose this game is repeated an
infinite number of times. Player 2 discounts the future with discount factor 𝛿. For which
discount factor 𝛿 does the game have a subgame-perfect Nash equilibrium in which player 1
chooses Trust in every period? (Assume that the worker plays a trigger strategy according to
which he starts playing Trust and continues to do so until the manager chooses Betray once.
Also assume that when indifferent, player 2 chooses Honor).
1
Trust
Not trust
2
Honor
5
5
Betray
0
0
-5
10
T
a. 𝛿 ≥ U
Z
b. 𝛿 ≥
T
7
c. 𝛿 ≥ Z
𝟏
d. 𝜹 ≥ 𝟐
The manager prefers to choose Honor in all periods rather than Betray (only) if
5 + 5𝛿 + 5𝛿 7 + 5𝛿 Z + ⋯ ≥ 10
U
⟺ 6F~ ≥ 10 ⟺ 5 ≥ 10(1 − 𝛿)
5
1
⟺1−𝛿 ≤
⟺ 𝛿 ≥1−
10
2
⟺ 𝛿 ≥ 1/2.
14. In a vertical chain, upstream producers may free ride on efforts of competing producers
upstream to improve in-store customer service. Which of the following contractual
agreements could alleviate the resulting free-riding problem?
a.
b.
c.
d.
An exclusive dealing contract
Resale price maintenance
An exclusive territories contract
A most-favored-customer clause
See the book, chapter 17.2.
15. A new swimming pool opens in a small town. All residents of the town have the same yearly
individual demand function: 𝑄• = 300 − 100𝑝. Suppose the pool has zero marginal cost and
is the only pool in town. The pool operates a membership system whereby individuals who
want to use the pool have to buy a yearly subscription that gives them unlimited access. What
is the price for the subscription that maximizes the profit of the pool? (Assume that when
indifferent, the consumers will buy the subscription).
a.
b.
c.
d.
0
300
450
900
The highest price consumers are willing to pay is equal to their entire consumer surplus at
Z€€
𝑝 = 0: 3 ∗ 7 = 450.
16. Consider a market in which demand equals 𝑄 = 𝐷(𝑝) = 94 − 𝑝, where 𝑝 denotes the price
and 𝑄 total quantity. Two firms are active in the market. Each firm has marginal costs 𝑀𝐶 =
10 and fixed costs 𝐹 = 0. Assume that the market is characterized by Cournot competition.
How much higher is the combined profit of the two firms under the optimal cartel agreement
compared to the Cournot equilibrium?
a.
b.
c.
d.
82
𝟏𝟗𝟔
1000
1762
Cournot: each firm maximizes the following profit function
𝜋6 = 𝑞6 (94 − 𝑞6 − 𝑞7 − 10)
The resulting first-order condition is:
𝑞6 = 42 − 𝑞7 /2.
This leads to 𝑞∗ = 28 and 𝜋6 = 28(94 − 28 − 28 − 10) = 784. Combined profit is then
equal to 2*784 = 1568.
If they form a cartel and charge the monopoly price, we get 𝜋 = 𝑄(94 − 𝑄 − 10)
The resulting first-order condition is:
94 − 2𝑄 = 10
This leads to 𝑄 = 42 and 𝜋 = 42(94 − 42 − 10) = 1764
The difference in combined profits is then 1764 − 1568 = 196
17. Which of the following statements are true?
I. In two-sided markets, it may be optimal for the platform to offer a price below marginal
cost on the less price-elastic side of the market.
II. In two-sided markets, if consumers on one side use only a single platform, a platform may
be able to charge monopoly prices on the other side of the market even if they only control
a modest share of consumers.
a.
b.
c.
d.
Both I and II are true
I is true and II is false
I is false and II is true
Both I and II are false
See slides week 3.
18. How many Nash equilibria in pure strategies does the following game have?
Column
Row
a.
b.
c.
d.
Left
Center
Right
Top
1,1
1,3
2,4
Middle
1,1
0,1
1,2
Bottom
9,2
9,0
0,0
0
1
2
3
The best responses of both players are in bold.
19. Which of the following statements are true?
I. For probation to work as a screening device, the salary under probation must be above
the market salary for unskilled workers
II. For probation to work as a screening device, the salary after probation must be below the
market salary for skilled workers
a.
b.
c.
d.
Both I and II are true
I is true and II is false
I is false and II is true
Both I and II are false
See chapter 14.3
20. Two fruit pickers harvest oranges for a farmer. The farmer pays them a base wage of 500. The
fruit picker who harvests the higher number of oranges obtains a bonus of 2 for every orange
she harvests more than the other worker. The other fruit picker pays a penalty of 2 for every
orange she harvests less than the other worker. The fruit pickers harvest 10 oranges per unit
of effort they expend and have an effort cost of
iE
7
. How much effort will they put in if they
collude with each other?
a.
b.
c.
d.
0
10
20
30
The two fruit pickers’ joint payoffs are 1,000 regardless of the number of oranges harvested.
As effort is costly, it is optimal for the fruit pickers to harvest zero oranges.
21. A monopoly has the following cost function: 𝐶(𝑄) = 20𝑄 + 20. The market the monopoly
operates in is characterized by a price elasticity of demand of 2. Find the profit-maximizing
price the monopoly will choose. (Hint: use the inverse elasticity rule.)
a.
b.
c.
d.
p=10
p=20
p=30
p=40
The inverse elasticity rule states that 𝐿 = 1/𝜀 for monopolies. Since 𝐿 = (𝑝 − 𝑀𝐶)/𝑝 and
𝑀𝐶 = 20, we get (𝑝 − 20)/𝑝 = 1/2 ⟺ 𝑝 = 40.
22. Which of the following is a condition that must be satisfied for third-degree price
discrimination to work?
a. The firm must be able to observe each individual’s demand curve
b. The firm must be able to offer the good in different qualities
c. The firm has market power
d. Arbitrage is easy
See Chapter 15.2.
23. Macrosoft considers creating a student version of its spreadsheet MS Accel. The only
difference between the student version and the original version is that in the student version,
Macrosoft has disabled certain features of the original spreadsheet. Macrosoft has two types
of customers: business people and students. The table below indicates the willingness-to-pay
for the normal version (N) and for the student version (S) for business people (2 million in
total) and for students (1 million in total).
Number
(in millions)
2
1
Business people
Students
Willingness-to-pay
Normal version (N)
Student version (S)
160
50
60
40
Macrosoft does not know whether someone who buys its spreadsheet is a business
person or a student. What is the revenue-maximizing menu of price/quality pairs?
(Assume that clients, when indifferent, pick the most expensive item from the menu.)
a.
b.
c.
d.
Price N = 160; price S = 160
Price N = 60; price S = 50
Price N = 160; price S = 40
Price N = 150; price S = 40
Consider the following table which represents who will buy which product. Option d. results in
the highest revenue.
Pricing
scheme
Normal
(N)
version Student
(S)
version Profits
(millions)
a.
b.
Business people
Business people
Students
-
320
180
c.
-
120
d.
Business people
Business people
Students
Students
340
24. The city of London wishes to improve competition in the market for magic wands. To reach
this target, the city sells a new market license using the English auction. If incumbent
Ollivanders Wand Shop obtains the license in the auction, it will realize monopoly profits
equal to 5. If potential entrant The Wizard of Oz wins, Ollivanders’ duopoly profits will be 2
while The Wizard’s duopoly profits will also be 2. Who will win the auction at what price?
(Assume that when indifferent, the companies do not bid).
a.
b.
c.
d.
The Wizard of Oz will win at a price of 2
Ollivanders Wand Shop will win at a price of 2
Ollivanders Wand Shop will win at a price of 3
Ollivanders Wand Shop will win at a price of 5
In the English auction, both firms bid up to their value for the license in equilibrium. The
Wizard’s value equals its duopoly profits, i.e., 2. Ollivanders Wand Shop’s value equals the
difference between its monopoly profits and its duopoly profits, i.e., 3. So, Ollivanders will
win and in equilibrium it will pay a price equal to Wizard’s value, i.e., 2.
25. Orange has a monopoly in the mobile operating systems market with its software, the y-OS.
Orange has a constant marginal cost of production equal to 5 and charges a unit price of 𝑤
for the y-OS. Apple is the only firm that designs and sells smartphones that are compatible
with the y-OS. Every smartphone is equipped with Orange’s operating system. Apple incurs a
cost of 4 per smartphone for the design, parts, and assembly of its smartphone. Both firms’
fixed costs are assumed to be sunk. Demand for Apple’s smartphones is given by 𝐷(𝑝) =
25 − 𝑝, where 𝑝 is the price. Orange writes a franchise contract that specifies a fixed fee 𝑓
that Apple has to pay Orange as well as a price of 𝑤 for each unit of y-OS. What contract
maximizes Orange’s profits?
a.
b.
c.
d.
𝑤 = 4; 𝑓 = 25
𝑤 = 5; 𝑓 = 0
𝒘 = 𝟓; 𝒇 = 𝟔𝟒
𝑤 = 13; 𝑓 = 16
Orange wishes to maximize the profits in the vertical chain and use the fixed fee to extract as
much rent as possible from Apple. Apple has the right incentive to maximize the vertical
chain’s profits if it buys Orange’s inputs at marginal cost price (i.e., 𝑤 = 𝑀𝐶P = 5). Its
profits will be 64, so that the profit-maximizing fee equals 64.
26. Frequent interaction facilitates collusion. The reason is that the more frequently firms
interact, …
a. … the lower the discount factor
b. … the higher the discount factor
c. … the lower the critical discount factor
d. … the higher the critical discount factor
See the book, page 169 and exercise 12.4.
27. Consider a market in which demand equals 𝐷 (𝑝) = 117 – 𝑝, where 𝑝 denotes the price.
There is currently one company in the market (the leader). A second company is considering
whether to enter the market (the follower). Both companies produce with constant marginal
costs equal to 9. If the follower company wants to enter the market, it has to pay a fixed cost
of 400. What is the minimum quantity the leader needs to produce to keep the follower from
entering the market?
a.
b.
c.
d.
54
68
96
108
Solve the follower’s maximization problem: 𝑚𝑎𝑥 𝜋0 = (𝑝 − 9) 𝑞0 = (108 − 𝑞0 − 𝑞3 )𝑞0 . The
-.
6
FOC yields: 108 − 2𝑞0 − 𝑞3 = 0 ⇒ 𝑞0 = 54 − 7 𝑞3 , which represents the follower’s best
response function. The follower’s profit is then:
1
1
𝜋0 = (𝑝 − 9) 𝑞0 = (108 − 𝑞0 − 𝑞3 )𝑞0 = Š108 − 54 + 𝑞3 − 𝑞3 ‹ Š54 − 𝑞3 ‹
2
2
1
= (54 − 𝑞3 )7
2
6
The follower will enter as long as 𝜋0 = (54 − 7 𝑞3 )7 > 400 or 𝑞3 < 68
28. Which of the following statements are true?
I. A higher Nash payoff 𝜋 Œ decreases the critical (cutoff) discount factor
II. Dan Ariely and his colleagues ran experiments to test the effect of high bonuses on
performance. Their main conclusion is that very high bonuses may decrease performance in
some tasks.
a.
b.
c.
d.
Both I and II are true
I is true and II is false
I is false and II is true
Both I and II are false
uv Fuw
I. 𝛿 = uv Fux
II. See case study chapter 11.
29. Often, the same book is available as a hardcover and as a paperback. This is an example of:
a.
b.
c.
d.
first degree price discrimination
second degree price discrimination
third degree price discrimination
arbitrage
See chapter 15.
30. Which of the following is a threat to a first-mover’s ability to profit from technological
leadership?
a. Imitation
b. Preemption of assets
c. Patents
d. Switching costs
See chapter 16.2.