~~EC2066 ZA d0
This paper is not to be removed from the Examination Halls
UNIVERSITY OF LONDON
EC2066 ZA
BSc degrees and Diplomas for Graduates in Economics, Management, Finance and the
Social Sciences, the Diplomas in Economics and Social Sciences and Access Route
Microeconomics
Tuesday, 21 May 2013 : 10.00am to 1.00pm
Candidates should answer ELEVEN of the following SIXTEEN questions: EIGHT from
Section A (5 marks each) and THREE from Section B (20 marks each). Candidates are
strongly advised to divide their time accordingly.
A calculator may be used when answering questions on this paper and it must comply in all
respects with the specification given with your Admission Notice. The make and type of
machine must be clearly stated on the front cover of the answer book.
If more questions are answered than requested, only the first answers attempted will be counted.
PLEASE TURN OVER
© University of London 2013
UL13/0033
Page 1 of 8
D1
SECTION A
Answer eight questions from this section (5 marks each).
1. Mary’s demand curve for food is given by
Q = 10 − 2P
where Q is the quantity of food and P is the price of food. Calculate her price
elasticity of demand for food at P = 2.
2. Andy purchases only two goods, apples (A) and oranges (R). The price of apples is 2 and the price of oranges is 4. Andy has an income of 40 and his utility
function is
U ( A, R) = 3A + 5R
What bundle of apples and oranges should Andy purchase to maximize utility?
3. Under first-degree price discrimination, a monopolist’s marginal revenue is equal
to average revenue. Is this true or false? Explain your answer.
4. Consider the following game. For what values of x does each player have a
dominant strategy? Explain your answer.
Player 1
A1
B1
C1
Player 2
A2 B2 C2
3,3 3,0 1,2
2,3 1,2 0,1
0,1 2,0 x, x
5. If the long-run average cost is decreasing in output, the long-run marginal cost
must be decreasing in output as well. Is this true or false? Explain your answer.
6. As the rate of interest falls, a saver might save less but never becomes a borrower. Is this true or false? Explain your answer.
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7. Consider a competitive industry with several identical firms. The total cost
function of the representative firm is given by
C ( q ) = q − q2 +
q3
2
where q denotes the output of the representative firm. Derive the supply function of the representative firm, paying proper attention to the shut-down point.
8. If lenders cannot observe the quality of projects of borrowers, the usual competitive market supply logic of lending more at higher interest rates does not
always hold. Is this true or false? Explain your answer.
9. If market demand is infinitely elastic and market supply elasticity is finite, a per
unit tax on suppliers creates no deadweight loss. Is this true or false? Explain
your answer.
10. Suppose an agent borrows funds and invests in a project. His effort must be
monitored by lenders to ensure that the investment is successful, and monitoring is costly. If the agent borrows from several lenders, he is likely to be
monitored at an inefficient level. Is this true or false? Explain your answer.
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SECTION B
Answer three questions from this section (20 marks each).
11. Suppose there are two identical firms in an industry. The output of firm 1 is
denoted by q1 and that of firm 2 is denoted by q2 . The total cost of production
for firm i, i ∈ {1, 2}, is
C ( qi ) = 4 qi
Let Q denote total output, i.e. Q = q1 + q2 . The inverse demand curve in the
market is given by
P = 10 − Q
(a) Find the Cournot-Nash equilibrium quantity produced by each firm and
the market price.
[5 marks]
(b) Suppose the firms can collude, and maximize joint profit. Calculate the
deadweight loss arising under this scenario.
[5 marks]
(c) What would be the quantities produced by each firm and market price
under Stackelberg duopoly if firm 1 moves first?
[5 marks]
(d) Now suppose the production process in the industry pollutes the environment and generates a marginal social cost given by
MCE = 2Q
Calculate the deadweight loss arising from the Cournot-Nash equilibrium
in this case.
[5 marks]
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12. Consider a market for used cars. There are some low quality cars and some high
quality cars. Potential sellers have a car each, and there are many more buyers
than possible sellers in the market. A high quality car never breaks down. A
low quality car provides a poorer ride quality over longer journeys and also
breaks down with positive probability.
A seller values a high quality car at 9000 and a low quality car at 4000. A buyer
values a high quality car at 10,000 and a low quality car at 5000. All agents are
risk-neutral.
In answering the following questions, assume that the sellers get the entire surplus from trade.
(a) Suppose quality is observable to sellers but not to buyers. Buyers only
know that a fraction 3/5 of the cars in the market are high quality and the
rest are low quality. Would cars of both low and high qualities be traded
in equilibrium? Derive the equilibrium price(s) at which such trade takes
place.
[5 marks]
(b) Is the market outcome in part (a) efficient? Explain your answer.[5 marks]
(c) Now suppose low quality cars break down with probability 0.7. Recall that
high quality cars never break down. Suppose the sellers of high quality
cars announce a guarantee that promises a full refund if the car breaks
down. Show that with this guarantee, high quality cars sell for 10000 and
low quality cars sell for 5000.
[5 marks]
(d) Suppose, as in part (c), that low quality cars break down with probability
0.7. Suppose the government decides to force each seller to offer a full
refund if the car sold by the seller breaks down. How does this change the
market outcome? Is the market outcome efficient? Explain your answer.
[5 marks]
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13. (a) Find the pure and mixed strategy Nash equilibria of the following game.
[8 marks]
Player 2
A2 B2
Player 1 A1 2,7 3,2
B1 0,0 4,1
(b) Consider the following extensive-form game with two players. Player 2
moves after player 1. Each player can produce a high output or a low
output. Player 1’s payoff is additionally influenced by an exogenous event
which occurs with probability p ∈ [0, 1].
The payoffs are written as ((Payoff to 1), Payoff to 2).
1
L1
H1
2
L2
((4 − 2p), 1)
2
H2
L2
((3 − 2p), 4)
((2 + p), 2)
H2
((1 + p), 1)
i. Suppose p > 1/3. Find the subgame perfect Nash equilibrium of the
game above.
[6 marks]
ii. Suppose, before the start of the game, player 2 has the option of committing to produce a high output (H2 ). Making such a commitment
requires player 2 to incur a cost of 1. Find the range of values of p for
which it is optimal to make such a costly commitment.
[6 marks]
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14. (a) Jean spends her income on fuel for heating her house and other goods
(“other goods” represents a composite of all other goods). The price of
the composite of other goods is 1, and the price of heating fuel is p. The
government decides to put a tax of t per unit on heating fuel.
i. Suppose the government asked for a lump-sum tax that would leave
Jean with the same level of utility as after the per-unit tax. Would Jean
pay more or less tax under the lump-sum tax scheme compared to the
per-unit tax scheme? Explain using a diagram.
[5 marks]
ii. Suppose the per-unit tax has been imposed. The local council starts a
scheme to help certain residents with their fuel tax bill. Jean qualifies
for the scheme, and she receives extra income equal to the amount of
tax she pays. Would this make Jean’s utility as high as her pre-tax level
of utility? Explain using a diagram.
[5 marks]
(b) Jo has a wealth of 10,000, but faces the risk of losing 3600 with probability
0.2. An insurance company offers Jo the following scheme: in exchange for
a premium of X, the insurance company would pay out 5X in the event of
a loss.
i. Suppose Jo’s utility function is given by
u(w) = ln w
where w denotes wealth. What is the optimal choice of X for Jo?
[5 marks]
ii. Now suppose Jo’s utility function is given by
u(w ) = 1 −
1
w
where w denotes wealth. What is the optimal choice of X for Jo in this
case?
[5 marks]
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15. A society consists of 2 identical individuals who derive utility from a public
good. The public good can be provided at a constant marginal cost of 6. Let xi
denote the level of public good provision by i and let X denote the total provision of the public good. The net benefit enjoyed by individual i from providing
xi units of the public good is given by
1
Ui ( xi , X ) = − (10 − X )2 − 6xi
2
where i ∈ {1, 2}.
(a) Derive the socially optimal level of provision of the public good.[6 marks]
(b) If every individual optimally chooses how much public good to provide,
derive the total level of provision of the public good.
[7 marks]
(c) Suppose n > 1 new individuals arrive in the society. The net benefit enjoyed by new individual j from providing x j units of the public good is
given by
1
Vj ( x j , X ) = − (9 − X )2 − 6x j
3
Suppose every individual optimally chooses how much public good to
provide. Does the total level of public good provision change compared
to part (b) as a result of the new arrivals? Explain your answer. [7 marks]
16. (a) Explain the incentive properties of residual claimant contracts relative to
flat salaries in terms of reducing unobservable shirking by an employee.
[10 marks]
(b) Carefully explain why flat salaries are often observed, and residual claimant
contracts are rarely observed.
[10 marks]
END OF PAPER
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D1
~~EC2066 ZA d0
This paper is not to be removed from the Examination Halls
UNIVERSITY OF LONDON
EC2066 ZB
BSc degrees and Diplomas for Graduates in Economics, Management, Finance and the
Social Sciences, the Diplomas in Economics and Social Sciences and Access Route
Microeconomics
Tuesday, 21 May 2013 : 10.00am to 1.00pm
Candidates should answer ELEVEN of the following SIXTEEN questions: EIGHT from
Section A (5 marks each) and THREE from Section B (20 marks each). Candidates are
strongly advised to divide their time accordingly.
A calculator may be used when answering questions on this paper and it must comply in all
respects with the specification given with your Admission Notice. The make and type of
machine must be clearly stated on the front cover of the answer book.
If more questions are answered than requested, only the first answers attempted will be counted.
PLEASE TURN OVER
© University of London 2013
UL13/0034
Page 1 of 7
D1
SECTION A
Answer eight questions from this section (5 marks each).
1. Mary’s demand curve for food is given by
Q = 10 − 2P
where Q is the quantity of food and P is the price of food. Calculate her price
elasticity of demand for food at P = 2.
2. Andy purchases only two goods, apples (A) and oranges (R). The price of apples is 2 and the price of oranges is 4. Andy has an income of 40 and his utility
function is
U ( A, R) = 3A + 5R
What bundle of apples and oranges should Andy purchase to maximize utility?
3. Under first-degree price discrimination, a monopolist’s marginal revenue is equal
to average revenue. Is this true or false? Explain your answer.
4. Consider the following game. For what values of x does each player have a
dominant strategy? Explain your answer.
Player 1
A1
B1
C1
Player 2
A2 B2 C2
3,3 3,0 1,2
2,3 1,2 0,1
0,1 2,0 x, x
5. If the long-run average cost is decreasing in output, the long-run marginal cost
must be decreasing in output as well. Is this true or false? Explain your answer.
6. If leisure is a normal good, the demand for leisure rises as wage rises. Is this
true or false? Explain your answer.
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7. In an Edgeworth Box, a reallocation of resources from the initial endowment to
any point on the contract curve always constitutes a Pareto improvement. Is
this true or false? Explain your answer.
8. If consumption at all dates is a normal good, savers necessarily save less if the
rate of interest falls. Is this true or false? Explain your answer.
9. Private provision of goods that are non-excludable and non-rival leads to overprovision compared to the socially optimal level. Is this true or false? Explain
your answer.
10. The LSE requires mobile phones to be switched off in the library. Assuming
this is strictly enforced, does such a restriction enhance efficiency? Explain your
answer.
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D1
SECTION B
Answer three questions from this section (20 marks each).
11. Suppose there are two identical firms in an industry. The output of firm 1 is
denoted by q1 and that of firm 2 is denoted by q2 . The total cost of production
for firm i, i ∈ {1, 2}, is
C ( qi ) = 4 qi
Let Q denote total output, i.e. Q = q1 + q2 . The inverse demand curve in the
market is given by
P = 10 − Q
(a) Find the Cournot-Nash equilibrium quantity produced by each firm and
the market price.
[5 marks]
(b) Suppose the firms can collude, and maximize joint profit. Calculate the
deadweight loss arising under this scenario.
[5 marks]
(c) What would be the quantities produced by each firm and market price
under Stackelberg duopoly if firm 1 moves first?
[5 marks]
(d) Now suppose the production process in the industry pollutes the environment and generates a marginal social cost given by
MCE = 2Q
Calculate the deadweight loss arising from the Cournot-Nash equilibrium
in this case.
[5 marks]
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12. Consider a market for used cars. There are some low quality cars and some high
quality cars. Potential sellers have a car each, and there are many more buyers
than possible sellers in the market. A high quality car never breaks down. A
low quality car provides a poorer ride quality over longer journeys and also
breaks down with positive probability.
A seller values a high quality car at 9000 and a low quality car at 4000. A buyer
values a high quality car at 10,000 and a low quality car at 5000. All agents are
risk-neutral.
In answering the following questions, assume that the sellers get the entire surplus from trade.
(a) Suppose quality is observable to sellers but not to buyers. Buyers only
know that a fraction 3/5 of the cars in the market are high quality and the
rest are low quality. Would cars of both low and high qualities be traded
in equilibrium? Derive the equilibrium price(s) at which such trade takes
place.
[5 marks]
(b) Is the market outcome in part (a) efficient? Explain your answer.[5 marks]
(c) Now suppose low quality cars break down with probability 0.7. Recall that
high quality cars never break down. Suppose the sellers of high quality
cars announce a guarantee that promises a full refund if the car breaks
down. Show that with this guarantee, high quality cars sell for 10000 and
low quality cars sell for 5000.
[5 marks]
(d) Suppose, as in part (c), that low quality cars break down with probability
0.7. Suppose the government decides to force each seller to offer a full
refund if the car sold by the seller breaks down. How does this change the
market outcome? Is the market outcome efficient? Explain your answer.
[5 marks]
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13. (a) Find the pure and mixed-strategy Nash equilibria of the following game.
[8 marks]
Player 2
A2 B2
Player 1 A1 2,7 3,2
B1 0,0 4,1
(b) Consider the following extensive-form game with two players. Player 2
moves after player 1. Each player can produce a high output or a low
output. Player 1’s payoff is additionally influenced by an exogenous event
which occurs with probability p ∈ [0, 1].
The payoffs are written as ((Payoff to 1), Payoff to 2).
1
L1
H1
2
L2
((4 − 2p), 1)
2
H2
L2
((3 − 2p), 4)
((2 + p), 2)
H2
((1 + p), 1)
i. Suppose p > 1/3. Find the subgame perfect Nash equilibrium of the
game above.
[6 marks]
ii. Suppose, before the start of the game, player 2 has the option of committing to produce a high output (H2 ). Making such a commitment
requires player 2 to incur a cost of 1. Find the range of values of p for
which it is optimal to make such a costly commitment.
[6 marks]
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14. Consider a competitive industry with several identical firms. You are given the
following information about this industry
Q D = 320 − 2P
C(q) = 50 + 10q + 50q2
(Market demand)
(Total cost function of a firm)
Here P is the market price and q denotes the output of the representative firm.
(a) Derive the supply function of the representative firm, paying proper attention to the shut-down point.
[5 marks]
(b) Suppose there are 100 firms in the industry. Derive the market supply function and equilibrium market price and quantity.
[5 marks]
(c) Suppose a tax of 30 per unit of output is imposed on sellers. Calculate the
deadweight loss from the tax.
[5 marks]
(d) For the per-unit tax in part (c), calculate the burden of the tax on consumers, and the burden of the tax on sellers.
[5 marks]
15. (a) Explain the social cost arising from monopoly using a diagram. Suppose
a lump-sum tax is imposed on a monopolist and the revenue is redistributed among consumers. Would such a measure reduce the social cost
of monopoly? Explain your answer.
[5 marks]
(b) Write the monopolist’s profit maximization condition in terms of the priceelasticity of demand.
[5 marks]
(c) Assuming marginal cost is positive, show that demand must be elastic (i.e.
the absolute value of elasticity must be greater than 1) at the equilibrium
output level under monopoly.
[5 marks]
(d) Explain, using a diagram, why attaining the socially optimal level of output under a natural monopoly requires a government subsidy. [5 marks]
16. (a) Explain how private individuals can avoid inefficiencies arising from the
presence of externalities through (i) mergers and (ii) bargaining. [7 marks]
(b) Identify examples in which the problem of externalities cannot be solved
well by the methods discussed in part (a).
[6 marks]
(c) Briefly discuss how the government can address some types of externalities
by creating a market for trading of permits in the externality-generating
activity.
[7 marks]
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D1
Examiners’ commentaries 2013
Examiners’ commentaries 2013
EC2066 Microeconomics
Important note
This commentary reflects the examination and assessment arrangements for this course in the
academic year 2012–13. In 2014 the format of the examination will change as the element of choice
in Section A will be eliminated.
Section A will comprise EIGHT rathen than TEN questions, all of which must be answered.
The format and structure of the examination may change again in future years, and any such
changes will be publicised on the virtual learning environment (VLE).
Information about the subject guide
Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2011).
You should always attempt to use the most recent edition of any Essential reading textbook, even if
the commentary and/or online reading list and/or subject guide refers to an earlier edition. If
different editions of Essential reading are listed, please check the VLE for reading supplements – if
none are available, please use the contents list and index of the new edition to find the relevant
section.
General remarks
Learning outcomes
By the end of this course and having completed the Essential reading and activities you should:
• be able to define and describe:
• the determinants of consumer choices, including inter-temporal choicees and those
involving risk
• firms’ behaviour
• how firms’ behaviour differs in different market structures and may help to determine
those structures
• how firms and households determine factor prices.
• be able to analyse and assess:
• efficiency and welfare optimality of perfectly and imperfectly competitive markets
• the effects of externalities and public goods on efficiency
• government policies aimed at improving welfare.
• be prepared for further courses which require a knowledge of microeconomics.
1
EC2066 Microeconomics
Time management
Section A comprises 10 questions, eight of which must be answered (accounting for 40% of the total
marks). As noted above, from 2014 onwards the element of choice in Section A will be eliminated,
so that it will comprise eight questions, all of which must be answered. Section B comprises six
questions of which three must be answered (accounting for 60% of the total marks). Candidates are
strongly advised to divide their time accordingly. On average, only nine minutes should be
allocated to any individual Section A question. On average, only 36 minutes should be allocated to
any individual Section B question.
Key steps to improvement
• You need to be able to apply relevant microeconomic theory to questions that you may not
have encountered before. To prepare for this, you need not only to gain a thorough
understanding of microeconomic models but also (and importantly) to practise using
relevant models to answer specific questions. Practice is the key, not the learning of specific
answers.
• You should spend time planning your answers and make sure that you respond to all parts
of a question and to key words like define, explain and compare. Precise and concise
answers are to be preferred to vague and long-winded answers.
• You should be aware that, for most answers, diagrams and/or mathematical analysis are
essential. These should be correct and diagrams should be well-labelled. In addition, you
should always accompany them with appropriate explanations. Again, ‘practice makes
perfect’.
Essential reading: Important information
The subject guide refers to Morgan, Katz and Rosen as the principal text. In addition to this, you
should practice questions from other texts. Two ‘auxiliary’ texts that are good sources for practice
questions are listed below. Further, the auxiliary texts often develop applications not covered in the
principal text. You should study these to broaden, as well as deepen, your understanding. In some
cases, reading several treatments of the same topic might help to clarify the basic idea. You should
use the auxiliary texts for this purpose as well.
The coverage of game theory is often inadequate in texts. You should make sure that you
understand the key ideas covered in some detail in the subject guide.
Principal text
• Morgan, W., M.L. Katz and H.S. Rosen Microeconomics. (Boston, MA: Irwin/McGraw-Hill,
2009) second edition [ISBN 9780077121778]. Referred to as MKR throughout the Examiners’
commentaries.
Auxiliary texts
• Perloff, J.M. Microeconomics with Calculus. (Upper Saddle River, NJ: Pearson Education,
2011) second edition [ISBN 9781408264324]. Referred to as Perloff throughout the
Examiners’ commentaries.
• Pindyck, R.S. and D.L. Rubinfeld Microeconomics. (Upper Saddle River, NJ: Prentice
Hall/Pearson, 2012) eighth edition [ISBN 9780133041705 ].
2
Examiners’ commentaries 2013
Question spotting
Many candidates are disappointed to find that their examination performance is poorer
than they expected. This can be due to a number of different reasons and the Examiners’
commentaries suggest ways of addressing common problems and improving your performance. We want to draw your attention to one particular failing – ‘question spotting’, that is,
confining your examination preparation to a few question topics which have come up in past
papers for the course. This can have very serious consequences.
We recognise that candidates may not cover all topics in the syllabus in the same depth, but
you need to be aware that Examiners are free to set questions on any aspect of the syllabus.
This means that you need to study enough of the syllabus to enable you to answer the required
number of examination questions.
The syllabus can be found in the ‘Course information sheet’ in the section of the VLE dedicated to this course. You should read the syllabus very carefully and ensure that you cover
sufficient material in preparation for the examination.
Examiners will vary the topics and questions from year to year and may well set questions
that have not appeared in past papers – every topic on the syllabus is a legitimate examination
target. So although past papers can be helpful in revision, you cannot assume that topics or
specific questions that have come up in past examinations will occur again.
If you rely on a question spotting strategy, it is likely you will find yourself in difficulties
when you sit the examination paper. We strongly advise you not to adopt this strategy.
3
EC2066 Microeconomics
Examiners’ commentaries 2013
EC2066 Microeconomics
Important note
This commentary reflects the examination and assessment arrangements for this course in the
academic year 2012–13. In 2014 the format of the examination will change as the element of choice
in Section A will be eliminated.
Section A will comprise EIGHT rathen than TEN questions, all of which must be answered.
The format and structure of the examination may change again in future years, and any such
changes will be publicised on the virtual learning environment (VLE).
Information about the subject guide
Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2011).
You should always attempt to use the most recent edition of any Essential reading textbook, even if
the commentary and/or online reading list and/or subject guide refers to an earlier edition. If
different editions of Essential reading are listed, please check the VLE for reading supplements – if
none are available, please use the contents list and index of the new edition to find the relevant
section.
Comments on specific questions – Zone A
Candidates should answer ELEVEN of the following SIXTEEN questions: EIGHT from Section A
(5 marks each) and THREE from Section B (20 marks each). Candidates are strongly advised to
divide their time accordingly.
Section A
Answer eight questions from this section (5 marks each).
Question 1
Mary’s demand curve for food is given by
Q = 10 − 2P
where Q is the quantity of food and P is the price of food. Calculate her price elasticity of
demand for food at P = 2.
Reading for this question
MKR Chapter 3; Subject guide Chapter 3 (Consumer theory).
4
Examiners’ commentaries 2013
Approaching the question
It is straightforward to calculate the price elasticity of demand:
ε=−
dQ P
P
=2
dP Q
10 − 2P
At P = 2, ε = 4/6 = 2/3.
Question 2
Andy purchases only two goods, apples (A) and oranges (R). The price of apples is 2 and the
price of oranges is 4. Andy has an income of 40 and his utility function is
U ( A, R) = 3A + 5R
What bundle of apples and oranges should Andy purchase to maximize utility?
Reading for this question
MKR Chapter 2; Subject guide Chapter 3 (Consumer theory).
Approaching the question
Since the indifference curves are straight lines (3A + 5R = constant) and the budget line is also a
straight line, you should guess just by looking at the problem that it is likely to have a corner
3
6
MU A
solution. You can confirm this by calculating as follows. We have
= = and
PA
2
4
MUR
5
= . So Andy should simply consume apples. The optimal bundle is A = 20, R = 0.
PR
4
Question 3
Under first-degree price discrimination, a monopolist’s marginal revenue is equal to average
revenue. Is this true or false? Explain your answer.
Reading for this question
MKR Chapter 13; Subject guide Chapter 8 (Competition and monopoly).
Approaching the question
This is false. The monopolist extracts full surplus, so marginal revenue coincides with the
demand curve. But because of the surplus extraction, the average revenue curve is now higher
than the demand curve. To see this, consider the following example. Suppose demand is given
by Q = 10 − P. The revenue of a monopolist who produces Q units is Q times price at Q plus
the entire consumers’ surplus. Therefore the revenue of a first-degree price-discriminating
monopolist from producing Q units, denoted by R FD ( Q), is given by
R FD ( Q) = PQ +
(10 − P) Q
.
2
Since P = 10 − Q, we can rewrite this as
R FD ( Q) = (10 − Q) Q +
Q2
Q2
= 10Q −
.
2
2
5
EC2066 Microeconomics
It follows that marginal revenue is
MR( Q) =
dR FD ( Q)
= 10 − Q = P.
dQ
Thus marginal revenue coincides with the demand curve. However, the average revenue curve
is now higher than the demand curve:
AR( Q) =
Q
R FD ( Q)
= 10 − > P.
Q
2
Question 4
Consider the following game. For what values of x does each player have a dominant
strategy? Explain your answer.
Player 1
A1
B1
C1
A2
3,3
2,3
0,1
Player 2
B2
C2
3,0 1,2
1,2 0,1
2,0 x, x
Reading for this question
The coverage of game theory in MKR (Chapter 16) is not ideal. See Chapter 9 (Game theory: an
introduction) of the subject guide for a detailed discussion.
Approaching the question
This is an easy question. But you should be careful to ‘read’ the payoffs of players correctly.
Remember that the first number in each box is the payoff of the row player (player 1) and the
second number is the payoff of the column player (player 2). Once you look at the right set of
numbers for each player, it should be obvious that A1 and A2 are dominant strategies for 1 and 2
respectively if x < 1.
Question 5
If the long-run average cost is decreasing in output, the long-run marginal cost must be
decreasing in output as well. Is this true or false? Explain your answer.
Reading for this question
MKR Chapter 9; Subject guide Chapter 7 (The firm).
Approaching the question
This is false. Decreasing long-run average cost (LRAC) implies that long-run marginal cost
(LRMC) is below long-run average cost, but has no implication on whether the LRMC is
increasing or decreasing. As the picture below shows , LRMC can be increasing while still below
LRAC.
6
Examiners’ commentaries 2013
Cost
LRMC
LRAC
Quantity
Declining LRAC implies LRMC<LRAC, but as the picture shows,
LRMC need not be decreasing.
Question 6
As the rate of interest falls, a saver might save less but never becomes a borrower. Is this true
or false? Explain your answer.
Reading for this question
MKR Chapter 4; Subject guide Chapters 3 (Consumer theory) and 5 (Saving, investment and
choice over time).
Approaching the question
This is false. Many candidates attempt to answer this question by drawing a picture to start with.
This is not the right way to go about answering it. A picture is not very helpful here. You need
to know the logic of the answer first, and then you can show this in a picture to clarify your own
understanding, but you cannot simply draw a picture and try to guess the answer from that.
Let us try to identify the different effects arising from a change in the interest rate. A fall in the
interest rate has two effects.
• Substitution effect: The price of current consumption C0 has fallen relative to future
consumption C1 , so the agent will choose a higher C0 . This implies that the saver saves less.
• Income effect: The saver feels poorer as the interest rate decreases. If consumption today is
a normal good, the income effect implies the saver will reduce today’s consumption and
save more.
The two effects go in opposite direction. It is clear, however, that if the substitution effect is large
enough compared to the income effect, it is possible that the saver could become a borrower. Of
course, if current consumption is an inferior good, both effects would go in the same direction
(save less) and then it is even more likely that a saver becomes a borrower.
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EC2066 Microeconomics
Question 7
Consider a competitive industry with several identical firms. The total cost function of the
representative firm is given by
q3
C ( q ) = q − q2 +
2
where q denotes the output of the representative firm. Derive the supply function of the
representative firm, paying proper attention to the shut-down point.
Reading for this question
MKR Chapter 10.1; Subject guide Chapter 8 (Competition and monopoly).
Approaching the question
The supply function is given by the MC curve above the average cost (which is here the same as
average variable cost) curve. Now, MC = 1 − 2q + 3q2 /2, and AC = 1 − q + q2 /2. Therefore
MC > AC if
1 − 2q + 3q2 /2 > 1 − q + q2 /2
which implies
q2 > q
This happens when q > 1. Thus the (inverse) supply curve is given by
P = 1 − 2q + 3q2 /2
Cost
for q > 1
MC
AVC (here same as AC)
1
Quantity
The supply curve is the solid part of the MC curve, which
is the part above AVC (here same as AC).
Question 8
If lenders cannot observe the quality of projects of borrowers, the usual competitive market
supply logic of lending more at higher interest rates does not always hold. Is this true or
false? Explain your answer.
8
Examiners’ commentaries 2013
Reading for this question
MKR Chapter 17; Subject guide Chapter 12 (Asymmetric information).
Approaching the question
This is true. The key idea is adverse selection, combined with the fact that loan contracts are
typically limited liability contracts, so that if a project fails and gets a zero return (say), the
lender gets zero return as well. As rates increase the borrowers with less risky projects (which
typically earn a lower return) tend to drop out of the market. On the other hand, consider a
project that succeeds with a small probability but yields a very high return when it succeeds.
When it fails, the project returns zero. A borrower who invests in such a risky project is happy to
obtain a loan at a high rate because he only has to pay that rate when the project succeeds. So as
the rate of interest rises, the lender is faced with an increasingly worsening (i.e. riskier) pool of
borrowers. Therefore the lender’s profit might decrease as the interest rate increases. It follows
that the lender might want to lend less (or not at all) at higher rates.
Question 9
If market demand is infinitely elastic and market supply elasticity is finite, a per unit tax on
suppliers creates no deadweight loss. Is this true or false? Explain your answer.
Reading for this question
MKR Chapter 11; Subject guide Chapter 8 (Competition and monopoly).
Approaching the question
This is false. There is no deadweight loss on consumers, but there is a deadweight loss in
producer surplus. The picture below shows the loss. You should be careful to correctly identify
the area of loss. Many candidates draw the right supply-demand picture, but then fail to
identify the correct area of deadweight loss.
Price
Supply after tax of t per unit
Supply
t
Demand
P
Deadweight Loss
Q
1
Q
0
Quantity
With a flat demand curve, price does not change after tax, but
quatity falls, giving rise to a deadweight loss (shaded area).
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EC2066 Microeconomics
Question 10
Suppose an agent borrows funds and invests in a project. His effort must be monitored by
lenders to ensure that the investment is successful, and monitoring is costly. If the agent
borrows from several lenders, he is likely to be monitored at an inefficient level. Is this true
or false? Explain your answer.
Reading for this question
MKR Chapter 18; Subject guide Chapter 13 (Externalities and public goods).
Approaching the question
This is true. The key is to understand that monitoring is a public good. If one lender monitors
the borrower, all other lenders benefit as well. Once you realise the public good nature of
monitoring, it should be clear that free riding incentives exist. This, in turn, implies that the
overall level of monitoring would fall short of the socially efficient level.
Section B
Answer three questions from this section (20 marks each).
Question 11
Suppose there are two identical firms in an industry. The output of firm 1 is denoted by q1
and that of firm 2 is denoted by q2 . The total cost of production for firm i, i ∈ {1, 2}, is
C ( qi ) = 4 qi
Let Q denote total output, i.e. Q = q1 + q2 . The inverse demand curve in the market is given
by
P = 10 − Q
(a) Find the Cournot-Nash equilibrium quantity produced by each firm and the market
price.
[5 marks]
(b) Suppose the firms can collude, and maximize joint profit. Calculate the deadweight loss
arising under this scenario.
[5 marks]
(c) What would be the quantities produced by each firm and market price under Stackelberg
duopoly if firm 1 moves first?
[5 marks]
(d) Now suppose the production process in the industry pollutes the environment and
generates a marginal social cost given by
MCE = 2Q
Calculate the deadweight loss arising from the Cournot-Nash equilibrium in this case.
[5 marks]
Reading for this question
MKR Chapter 15; Subject guide Chapter 10 (Oligopoly and strategic behaviour).
10
Examiners’ commentaries 2013
Approaching the question
(a) Firm 1 maximises (10 − q1 − q2 )q1 − 4q1 . The first order condition is
6 − 2q1 − q2 = 0
implying that the reaction function of firm 1 is given by
q1 = 3 −
q2
2
Imposing symmetry, we have q1 = q2 = q where
q = 3−
q
2
which implies q = 2. Therefore the Cournot-Nash equilibrium quantities are given by
q1 = q2 = 2 and the market price is P = 10 − 4 = 6.
(b) If firms collude, together they maximise joint profit given by (10 − Q) Q − 4Q. The first
order condition is 10 − 2Q − 4 = 0 which gives us Q = 3 and therefore P = 7.
To calculate the deadweight loss, note that the efficient quantity is the quantity demanded
at price equal to MC. Here MC = 4, so the efficient quantity is Q = 6. Thus at the
price-quantity pair ( P∗ , Q∗ ), the deadweight loss is given by
1 ∗
( P − 4)(6 − Q∗ )
2
Thus the deadweight loss under collusion is 9/2 = 4.5.
Price
10
Q D = 10 - P
Deadweight Loss
7
MC = 4
3
6
Quantity
Calculating the deadweight loss from collusive equilibrium.
(c) Now firm 1 takes firm 2’s reaction function as given. Firm 2’s reaction function is
q2 = 3 − q1 /2. Therefore firm 1 maximises
q 10 − q1 + 3 − 1
q1 − 4q1
2
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EC2066 Microeconomics
which simplifies to
q1 q1
2
The first order condition is given by 3 − q1 = 0 implying that q1 = 3. It follows that
q2 = 3/2. The market price is 10 − 3 − 3/2 = 11/2 = 5.5.
3−
(d) The private marginal cost is 4, and the marginal externality cost is 2Q. Therefore the
socially optimal quantity is given by
4 + 2Q = P
which implies
4 + 2Q = 10 − Q
which implies that the socially optimal quantity is Q0 = 2 and the associated price is P0 = 8.
At the total Cournot quantity 4, the social marginal cost is 4 + 2 × 4 = 12, and the social
marginal benefit is simply the height of the demand curve given by 10 − 2 × 4 = 6.
Therefore the deadweight loss is given by
1
1
(4 − Q0 )(12 − 6) = (4 − 2)(12 − 6) = 6
2
2
Price,
Cost
MC = 4 + 2Q
12
10
Deadweight Loss
8
6
P = 10 - Q
4
2
4
Quantity
Calculating the deadweight loss from Cournot equilibrium with private
marginal cost of 4 and an additional social marginal cost of 2Q.
Question 12
Consider a market for used cars. There are some low quality cars and some high quality cars.
Potential sellers have a car each, and there are many more buyers than possible sellers in the
market. A high quality car never breaks down. A low quality car provides a poorer ride
quality over longer journeys and also breaks down with positive probability.
A seller values a high quality car at 9000 and a low quality car at 4000. A buyer values a high
quality car at 10,000 and a low quality car at 5000. All agents are risk-neutral.
12
Examiners’ commentaries 2013
In answering the following questions, assume that the sellers get the entire surplus from
trade.
(a) Suppose quality is observable to sellers but not to buyers. Buyers only know that a
fraction 3/5 of the cars in the market are high quality and the rest are low quality. Would
cars of both low and high qualities be traded in equilibrium? Derive the equilibrium
price(s) at which such trade takes place.
[5 marks]
(b) Is the market outcome in part (a) efficient? Explain your answer.
[5 marks]
(c) Now suppose low quality cars break down with probability 0.7. Recall that high quality
cars never break down. Suppose the sellers of high quality cars announce a guarantee
that promises a full refund if the car breaks down. Show that with this guarantee, high
quality cars sell for 10000 and low quality cars sell for 5000.
[5 marks]
(d) Suppose, as in part (c), that low quality cars break down with probability 0.7. Suppose
the government decides to force each seller to offer a full refund if the car sold by the
seller breaks down. How does this change the market outcome? Is the market outcome
efficient? Explain your answer.
[5 marks]
Reading for this question
MKR Chapter 17; Subject guide Chapter 12 (Asymmetric information).
Approaching the question
(a) If all cars are offered for sale, the average value of buyers is
2
3
10000 + 5000 = 8000.
5
5
Since buyers would not pay more than 8,000 for a car, high quality sellers would not sell.
Anticipating this, a buyer would know that any car being offered for sale must be a low
quality car and therefore buyers would be willing to pay at most 5,000 for a car. Since
sellers get the entire surplus, the equilibrium market price would be 5,000 and only low
quality cars would be traded in equilibrium.
(b) The market outcome is inefficient as there are gains from trade in high quality cars, but this
gain is left unexploited.
(c) The key idea you should understand is that to establish a separating equilibrium as
described in the question, we must show that the low quality sellers would not want to
mimic the behaviour of the high quality sellers.
The high quality sellers have no cost of offering a guarantee. So the crucial question is
whether low quality car sellers would also offer a guarantee. By offering a guarantee they
could mimic the high quality sellers and sell at 10,000. But the cars would break down with
probability 0.7, so that they would have to pay back 10,000 with probability 0.7. Thus the
payoff of low quality sellers from offering a guarantee is 0.3 × 10000 = 3000. But if a seller
sells without a guarantee, he reveals himself as a low quality seller and his car sells at 5,000
in equilibrium. Since 5000 > 3000, a low quality seller has no incentive to imitate a high
quality seller by offering a guarantee.
It follows that there is a separating equilibrium: high quality cars sell with a guarantee at
the buyers’ valuation of 10,000 and low quality cars sell at the buyers’ valuation of 5,000.
(d) If low quality sellers are forced to give a guarantee, the best they can hope for is to sell at
10,000 with a guarantee. But as calculated above, they get a payoff of 3,000 even if they
could sell at the maximum price of 10,000. But 3000 < 4000, which is their reservation value
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EC2066 Microeconomics
for their cars. So low quality sellers would quit the market, and only high quality sellers
would sell their cars with a guarantee at 10,000.
This outcome is inefficient since there are gains from trade in low quality cars, and this gain
is left unexploited.
Question 13
(a) Find the pure and mixed strategy Nash equilibria of the following game.
Player 1
A1
B1
Player 2
A2 B2
2,7 3,2
0,0 4,1
[8 marks]
(b) Consider the following extensive-form game with two players. Player 2 moves after
player 1. Each player can produce a high output or a low output. Player 1’s payoff is
additionally influenced by an exogenous event which occurs with probability p ∈ [0, 1].
The payoffs are written as ((Payoff to 1), Payoff to 2).
i. Suppose p > 1/3. Find the subgame perfect Nash equilibrium of the game above.
[6 marks]
ii. Suppose, before the start of the game, player 2 has the option of committing to
produce a high output (H2 ). Making such a commitment requires player 2 to incur a
cost of 1. Find the range of values of p for which it is optimal to make such a costly
commitment.
[6 marks]
Reading for this question
The coverage of game theory in MKR (Chapter 16) is not ideal. See Chapter 9 (Game theory: an
introduction) of the subject guide for a detailed discussion.
Approaching the question
(a) The pure NE are ( A1 , A2 ) and ( B1 , B2 ). The mixed NE is as follows.
14
Examiners’ commentaries 2013
Suppose 1 plays A1 with probability p and B1 with probability (1 − p). Then p must be
such that 2 is indifferent between A2 and B2 . This gives us
7p = 2p + (1 − p).
Solving, p = 1/6. Now suppose 2 plays A2 with probability q and B2 with probability
(1 − q). Then q must be such that 1 is indifferent between A1 and B1 . This gives us
2q + 3(1 − q) = 4(1 − q).
Solving, q = 1/3. Therefore the mixed NE is given by 1 playing A1 with probability 1/6 and
B1 with probability 5/6 and 2 playing A2 with probability 1/3 and B2 with probability 2/3.
Many candidates derive the mixed strategies correctly using the method above. Some use a
slightly different method: first write down the expected payoff of each player given that
each plays a mixed strategy. Let Eπ1 denote the expected payoff of player 1. Now
differentiate this with respect to p and set this equal to zero. What does this do? Well, this
should give us the value of q for which Eπ1 does not depend on p (i.e. the derivative of Eπ1
with respect to p is zero, so that the expected payoff of 1 does not change when p changes).
This is precisely the value of q for which 1 would be indifferent between A1 and B1 . For all
other values of q, the derivative is either positive or negative, so that the optimal choice of p
is either 1 (when the derivative is positive) or 0 (when the derivative is negative). Similarly
we can find the p for which 2 is indifferent.
1
However, it is very important to note that when you set dEπ
dp = 0, this is not a maximisation
exercise (i.e. this is not a first order condition). If you say you are maximising with respect
to p, this tells the Examiners that you have not understood the exercise you are carrying
out, and you are unlikely to get any credit for your answer. In general, we would encourage
you to adopt the first method discussed above for deriving mixed strategy Nash equilibria.
That method is the simplest, makes the underlying intuition clear and minimises the chance
of making a mistake.
(b) i. A subgame perfect Nash equilibrium (which is a formalisation of the notion of
credibility) is a Nash equilibrium of the whole game that also induces Nash equilibrium
play in every subgame. For games of perfect information, we can obtain subgame
perfect Nash equilibria using backward induction. (In more complicated games where a
player does not have perfect information about moves of previous players, backward
induction may not work, but such games are outside the scope of this course.)
Solving backwards, we see that if 1 plays L1 , 2’s optimal action is H2 (the payoff from H2
is 4, while that from L2 is 1), and if 1 plays H1 , 2’s optimal action is L2 . Therefore in any
subgame-perfect equilibrium, 2’s strategy must be (H2 if L1 and L2 if H1 ). Given this, 1
compares between L1 which yields a payoff of 3 − 2p and H1 which yields a payoff of
2 + p.
Now,
2 + p > 3 − 2p
implies
p>
1
.
3
Since this is the case given by the question, 1’s optimal choice is H1 .
Therefore the subgame perfect Nash equilibrium is given by the strategy combination
(H1 , (H2 if L1 and L2 if H1 )).
Many candidates answer this question by saying that the subgame perfect Nash
equilibrium is ( H1 , L2 ). It is very important for you to understand that this is not fully
correct. You should carefully study the notion of a strategy in a dynamic game and the
concept of subgame perfect Nash equilibrium from the subject guide. A strategy in a
dynamic game with sequential moves (also called an extensive-form game) is a
complete plan of actions, and therefore you need to specify an action for the second
mover after every action of the first mover. An incomplete specification would earn you
very little credit.
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EC2066 Microeconomics
ii. There are two crucial points to understand. First, if p < 1/3, 1 would optimally play L1
so that 2 would get 4 simply by playing the subgame-perfect equilibrium strategy as
above. In this case commitment is not useful, so the first condition is that p > 1/3.
The second point to understand is that if 1 plays H1 optimally, commitment would have
no value for 2 (indeed, he would get 1 minus the cost of commitment, giving 2 a payoff
of 0 – but he could get 2 as above by not getting into any such commitment). Thus for
commitment to have any value, it must be that without the commitment 1 would play
H1 , but the commitment makes it optimal for 1 to play L1 , so that player 2 can get 4
minus the cost of commitment, giving 2 a payoff of 3. If 2 commits to playing H2 after
both L1 and H1 , 1 plays L1 optimally if
3 − 2p > 1 + p
which implies p < 23 . Thus it is optimal to make a commitment to high output if
2
1
<p< .
3
3
Question 14
(a) Jean spends her income on fuel for heating her house and other goods (“other goods”
represents a composite of all other goods). The price of the composite of other goods is 1,
and the price of heating fuel is p. The government decides to put a tax of t per unit on
heating fuel.
i. Suppose the government asked for a lump-sum tax that would leave Jean with the
same level of utility as after the per-unit tax. Would Jean pay more or less tax under
the lump-sum tax scheme compared to the per-unit tax scheme? Explain using a
diagram.
[5 marks]
ii. Suppose the per-unit tax has been imposed. The local council starts a scheme to help
certain residents with their fuel tax bill. Jean qualifies for the scheme, and she
receives extra income equal to the amount of tax she pays. Would this make Jean’s
utility as high as her pre-tax level of utility? Explain using a diagram.
[5 marks]
(b) Jo has a wealth of 10,000, but faces the risk of losing 3600 with probability 0.2. An
insurance company offers Jo the following scheme: in exchange for a premium of X, the
insurance company would pay out 5X in the event of a loss.
i. Suppose Jo’s utility function is given by
u(w) = ln w
where w denotes wealth. What is the optimal choice of X for Jo?
[5 marks]
ii. Now suppose Jo’s utility function is given by
u(w) = 1 −
1
w
where w denotes wealth. What is the optimal choice of X for Jo in this case?
[5 marks]
(a) Reading for this question
MKR Chapter 4; Subject guide Chapter 3 (Consumer theory).
16
Examiners’ commentaries 2013
Approaching the question
i. As the picture shows, the lump-sum tax would raise more revenue. The
non-distortionary policy fares better. Another way of saying this is that the equivalent
variation of a per-unit tax exceeds the tax revenue.
Other
Goods
B
D
A
C
Budget line
after lump-sum
tax
Budget line
after per-unit tax
Heating Fuel
The dashed line is the original budget line.
Jean consumes at A after the per-unit tax is imposed.
Since the composite good has a price of 1, the vertical
distance between the budget lines (segment AB) shows
the amount of tax paid. An equivalent lump-sum tax
would move Jean’s consumption to C, implying
tax revenue of CD, which is larger than AB.
The non-distortionary policy raises more tax.
In other words, EV of a per-unit tax exceeds tax revenue.
ii. As the picture shows, Jean’s utility after the tax plus extra income would not be as high
as her pre-tax level of utility. The compensating variation of a per-unit tax scheme is
greater than the tax-revenue (since it must also compensate for the distortion caused by
the tax). So just giving back the tax-revenue is going to leave the consumer worse-off
compared to the before-tax situation.
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EC2066 Microeconomics
Other
Goods
Budget line
after tax plus
extra income
equal to tax paid
C
A
B
Budget line
before tax
Budget line
after tax
Heating Fuel
Jean’s consumption is initially at A, and moves to B after the
per-unit tax. Since the composite good has a price of 1, the
vertical distance between the budget lines (segment BC) is
the amount of tax paid. If Jean receives extra income equal to
tax paid, her budget line shifts up as shown, but her utility on
this line is clearly less than that at point A. In other words,
the CV of the per-unit tax is greater than tax revenue.
(b) Reading for this question
MKR Chapter 6; Subject guide Chapter 6 (Choice under uncertainty). For a good coverage
of the expected utility model, as well as the derivation of risk premium for a risk-averse
individual, see Perloff, Chapter 17.2.
Approaching the question
i. For any X, the insurance company’s profit is
0.8X + 0.2( X − 5X ) = 0
Therefore the scheme is a fair insurance scheme. Since Jo is risk averse, she would
choose complete insurance. This implies 10000 − X = 6400 + 5X − X which implies
5X = 3600, or X = 720.
ii. The utility function is different, but this is still concave, i.e. Jo is still risk averse.
Therefore, under fair insurance Jo will still choose full insurance, i.e. X = 720.
Question 15
A society consists of 2 identical individuals who derive utility from a public good. The public
good can be provided at a constant marginal cost of 6. Let xi denote the level of public good
provision by i and let X denote the total provision of the public good. The net benefit enjoyed
by individual i from providing xi units of the public good is given by
1
Ui ( xi , X ) = − (10 − X )2 − 6xi
2
where i ∈ {1, 2}.
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Examiners’ commentaries 2013
(a) Derive the socially optimal level of provision of the public good.
[6 marks]
(b) If every individual optimally chooses how much public good to provide, derive the total
level of provision of the public good.
[7 marks]
(c) Suppose n > 1 new individuals arrive in the society. The net benefit enjoyed by new
individual j from providing x j units of the public good is given by
1
Vj ( x j , X ) = − (9 − X )2 − 6x j
3
Suppose every individual optimally chooses how much public good to provide. Does the
total level of public good provision change compared to part (b) as a result of the new
arrivals? Explain your answer.
[7 marks]
Reading for this question
MKR Chapter 18.3; Subject guide Chapter 13 (Externalities and public goods).
Approaching the question
(a) The socially optimal level of provision of the public good can be found by maximising the
sum of utilities:
1
max − 2 (10 − X )2 − 6X
2
X
which gives us
2(10 − X ) − 6 = 0
or X = 7, which is the socially optimal level of provision of the public good.
(b) Individual 1 maximises − 12 (10 − ( x1 + x2 ))2 − 6x1 . The first order condition is
10 − x1 − x2 − 6 = 0,
which implies
x1 = 4 − x2 .
Imposing symmetry, x1 = x2 = x where x = 4 − x, or x = 2. Therefore the total level of
provision of the public good is 4.
(c) Each new individual j maximises
1
− (9 − X )2 − 6x j
3
where
X=
n
2
j =1
i =1
∑ x j + ∑ xi
so that
∂X
= 1.
∂x j
Differentiating with respect to x j , we get
∂Vj
2
= (9 − X ) − 6 = − X < 0.
∂x j
3
Therefore any new individual j optimally contributes 0. It follows that the total level of
public good provision does not change compared to part (b) as a result of the new arrivals.
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EC2066 Microeconomics
Question 16
(a) Explain the incentive properties of residual claimant contracts relative to flat salaries in
terms of reducing unobservable shirking by an employee.
[10 marks]
(b) Carefully explain why flat salaries are often observed, and residual claimant contracts
are rarely observed.
[10 marks]
Reading for this question
MKR Chapter 17 ; Subject guide Chapter 12 (Asymmetric information).
Approaching the question
The question is about a problem that arises in the employer–employee relationship when the
employer is unable to observe the employee’s effort, giving rise to a moral hazard problem.
The answer to part (a) should explain that residual claimant contracts put all risk on employees
– so that the incentive to take high effort is maximised. Flat salaries, on the other hand, provide
complete insurance to the employees which provides zero incentive to take high effort.
The answer to part (b) should point out, first, that even when an employee gets a flat salary, it
need not be riskless. This is because an employee who shirks might increase the chance of
getting fired (e.g. if the performance remains poor for a few periods). The fear of getting fired
might act as an incentive to work hard even though the actual salary is flat. Second, if employees
are more risk averse compared to employers, residual claimant contracts may not be optimal.
Such contracts put a high level of risk on risk-averse employees. This might lead employees to
either not participate, or require very high levels of compensation to induce participation. In this
case it is efficient for the employers to absorb risk, and generate incentives through by
combining flat salaries with the threat of firing for poor performance, as noted above.
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Examiners’ commentaries 2013
Examiners’ commentaries 2013
EC2066 Microeconomics
Important note
This commentary reflects the examination and assessment arrangements for this course in the
academic year 2012–13. In 2014 the format of the examination will change as the element of choice
in Section A will be eliminated.
Section A will comprise EIGHT rathen than TEN questions, all of which must be answered.
The format and structure of the examination may change again in future years, and any such
changes will be publicised on the virtual learning environment (VLE).
Information about the subject guide
Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2011).
You should always attempt to use the most recent edition of any Essential reading textbook, even if
the commentary and/or online reading list and/or subject guide refers to an earlier edition. If
different editions of Essential reading are listed, please check the VLE for reading supplements – if
none are available, please use the contents list and index of the new edition to find the relevant
section.
Comments on specific questions – Zone B
Candidates should answer ELEVEN of the following SIXTEEN questions: EIGHT from Section A
(5 marks each) and THREE from Section B (20 marks each). Candidates are strongly advised to
divide their time accordingly.
Section A
Answer eight questions from this section (5 marks each).
Question 1
Mary’s demand curve for food is given by
Q = 10 − 2P
where Q is the quantity of food and P is the price of food. Calculate her price elasticity of
demand for food at P = 2.
Reading for this question
MKR Chapter 3; Subject guide Chapter 3 (Consumer theory).
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EC2066 Microeconomics
Approaching the question
It is straightforward to calculate the price elasticity of demand:
ε=−
dQ P
P
=2
dP Q
10 − 2P
At P = 2, ε = 4/6 = 2/3.
Question 2
Andy purchases only two goods, apples (A) and oranges (R). The price of apples is 2 and the
price of oranges is 4. Andy has an income of 40 and his utility function is
U ( A, R) = 3A + 5R
What bundle of apples and oranges should Andy purchase to maximize utility?
Reading for this question
MKR Chapter 2; Subject guide Chapter 3 (Consumer theory).
Approaching the question
Since the indifference curves are straight lines (3A + 5R = constant) and the budget line is also a
straight line, you should guess just by looking at the problem that it is likely to have a corner
3
6
MU A
solution. You can confirm this by calculating as follows. We have
= = and
PA
2
4
MUR
5
= . So Andy should simply consume apples. The optimal bundle is A = 20, R = 0.
PR
4
Question 3
Under first-degree price discrimination, a monopolist’s marginal revenue is equal to average
revenue. Is this true or false? Explain your answer.
Reading for this question
MKR Chapter 13; Subject guide Chapter 8 (Competition and monopoly).
Approaching the question
This is false. The monopolist extracts full surplus, so marginal revenue coincides with the
demand curve. But because of the surplus extraction, the average revenue curve is now higher
than the demand curve. To see this, consider the following example. Suppose demand is given
by Q = 10 − P. The revenue of a monopolist who produces Q units is Q times price at Q plus
the entire consumers’ surplus. Therefore the revenue of a first-degree price-discriminating
monopolist from producing Q units, denoted by R FD ( Q), is given by
R FD ( Q) = PQ +
(10 − P) Q
.
2
Since P = 10 − Q, we can rewrite this as
R FD ( Q) = (10 − Q) Q +
22
Q2
Q2
= 10Q −
.
2
2
Examiners’ commentaries 2013
It follows that marginal revenue is
MR( Q) =
dR FD ( Q)
= 10 − Q = P.
dQ
Thus marginal revenue coincides with the demand curve. However, the average revenue curve
is now higher than the demand curve:
AR( Q) =
Q
R FD ( Q)
= 10 − > P.
Q
2
Question 4
Consider the following game. For what values of x does each player have a dominant
strategy? Explain your answer.
Player 1
A1
B1
C1
A2
3,3
2,3
0,1
Player 2
B2
C2
3,0 1,2
1,2 0,1
2,0 x, x
Reading for this question
The coverage of game theory in MKR (Chapter 16) is not ideal. See Chapter 9 (Game theory: an
introduction) of the subject guide for a detailed discussion.
Approaching the question
This is an easy question. But you should be careful to ‘read’ the payoffs of players correctly.
Remember that the first number in each box is the payoff of the row player (player 1) and the
second number is the payoff of the column player (player 2). Once you look at the right set of
numbers for each player, it should be obvious that A1 and A2 are dominant strategies for 1 and 2
respectively if x < 1.
Question 5
If the long-run average cost is decreasing in output, the long-run marginal cost must be
decreasing in output as well. Is this true or false? Explain your answer.
Reading for this question
MKR Chapter 9; Subject guide Chapter 7 (The firm).
Approaching the question
This is false. Decreasing long-run average cost (LRAC) implies that long-run marginal cost
(LRMC) is below long-run average cost, but has no implication on whether the LRMC is
increasing or decreasing. As the picture below shows , LRMC can be increasing while still below
LRAC.
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EC2066 Microeconomics
Cost
LRMC
LRAC
Quantity
Declining LRAC implies LRMC<LRAC, but as the picture shows,
LRMC need not be decreasing.
Question 6
If leisure is a normal good, the demand for leisure rises as wage rises. Is this true or false?
Explain your answer.
Reading for this question
MKR Chapter 5.1; Subject guide Chapter 4 (Labour supply and the effect of taxes).
Approaching the question
Many candidates attempt to answer this question by drawing a picture to start with. Note that a
picture is not very helpful here. What you need to do is to work through the logic of income and
substitution effects. In fact, the best strategy for answering questions of this sort is as follows.
Start by writing down ‘substitution effect’. Try to argue for the relevant price change, which
direction the relevant demand changes. Next, write down ‘income effect’ and clarify the
direction of this effect. The answer should be apparent from the two effects you have just
identified.
Let us try this here.
• Substitution effect: As wage rises (the price of leisure rises), the substitution effect implies
that an agent would consume less leisure.
• Income effect Since leisure is a normal good, the income effect (here the agent is richer)
implies the agent would consume more leisure.
The two effects go in opposite directions. Clearly, it is possible that the substitution effect
dominates, in which case the demand for leisure would fall as wage rises. Therefore the
statement is false.
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Examiners’ commentaries 2013
Question 7
In an Edgeworth Box, a reallocation of resources from the initial endowment to any point on
the contract curve always constitutes a Pareto improvement. Is this true or false? Explain your
answer.
Reading for this question
MKR Chapter 12; Subject guide Chapter 11 (General equilibrium and welfare economics).
Approaching the question
This is one of the simplest questions here. It should be fairly obvious that this is false. If the
endowment point is already on the contract curve, any reallocation will make one agent strictly
worse off. Now consider any endowment point that is not on the contract curve. Reallocations to
the part of the contract curve that is preferred by both agents compared to the endowment point
are Pareto improving. Reallocations to other points do not constitute a Pareto improvement.
Question 8
If consumption at all dates is a normal good, savers necessarily save less if the rate of interest
falls. Is this true or false? Explain your answer.
Reading for this question
MKR Chapter 4; Subject guide Chapters 3 (Consumer theory) and 5 (Saving, investment and
choice over time).
Approaching the question
This is false. This is another example where drawing a picture is not very helpful. If you try to
draw a picture and get your answer from that, it is very likely you will answer incorrectly. You
need to know the logic of the answer first, and then you can show this in a picture to clarify your
own understanding, but you cannot simply draw a picture and try to guess the answer from
that.
Let us try to identify the different effects arising from a change in the interest rate. A fall in the
interest rate has two effects.
• Substitution effect: The price of current consumption C0 has fallen relative to future
consumption C1 , so the agent will choose a higher C0 . This implies that the saver saves less.
• Income effect: The saver feels poorer as the interest rate decreases. Since consumption
today is a normal good, the income effect implies that the saver will reduce today’s
consumption and save more.
The two effects go in opposite directions. It is clear, however, that if the income effect is larger
than the substitution effect, savers would save more.
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EC2066 Microeconomics
Question 9
Private provision of goods that are non-excludable and non-rival leads to over-provision
compared to the socially optimal level. Is this true or false? Explain your answer.
Reading for this question
MKR Chapter 18; Subject guide Chapter 13 (Externalities and public goods).
Approaching the question
This is false. Goods that are non-excludable and non-rival are public goods. You should know
that private provision of public goods leads to under-provision relative to the social optimum.
Question 10
The LSE requires mobile phones to be switched off in the library. Assuming this is strictly
enforced, does such a restriction enhance efficiency? Explain your answer.
Reading for this question
MKR Chapter 18; Subject guide Chapter 13 (Externalities and public goods).
Approaching the question
The answer to this question depends on how you interpret the question. If you associate phones
with people talking, it is clear that the answer is yes since talking in a library generates negative
externality on other users. Since the social cost of talking in a library outstrips the private
benefit, the restriction enhances efficiency.
On the other hand, smart phones now are often used for purposes such as surfing the internet,
which generates no externalities, and there is no economic case for restricting such use. If you
associate these sort of uses with phones, you would have to conclude that asking users to switch
off phones reduces efficiency, and the correct policy would be to ask users to put their phones in
the silent mode.
Either answer is acceptable so long as you clarify your own interpretation of the question.
Section B
Answer three questions from this section (20 marks each).
Question 11
Suppose there are two identical firms in an industry. The output of firm 1 is denoted by q1
and that of firm 2 is denoted by q2 . The total cost of production for firm i, i ∈ {1, 2}, is
C ( qi ) = 4 qi
Let Q denote total output, i.e. Q = q1 + q2 . The inverse demand curve in the market is given
by
P = 10 − Q
(a) Find the Cournot-Nash equilibrium quantity produced by each firm and the market
price.
[5 marks]
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Examiners’ commentaries 2013
(b) Suppose the firms can collude, and maximize joint profit. Calculate the deadweight loss
arising under this scenario.
[5 marks]
(c) What would be the quantities produced by each firm and market price under Stackelberg
duopoly if firm 1 moves first?
[5 marks]
(d) Now suppose the production process in the industry pollutes the environment and
generates a marginal social cost given by
MCE = 2Q
Calculate the deadweight loss arising from the Cournot-Nash equilibrium in this case.
[5 marks]
Reading for this question
MKR Chapter 15; Subject guide Chapter 10 (Oligopoly and strategic behaviour).
Approaching the question
(a) Firm 1 maximises (10 − q1 − q2 )q1 − 4q1 . The first order condition is
6 − 2q1 − q2 = 0
implying that the reaction function of firm 1 is given by
q1 = 3 −
q2
2
Imposing symmetry, we have q1 = q2 = q where
q = 3−
q
2
which implies q = 2. Therefore the Cournot-Nash equilibrium quantities are given by
q1 = q2 = 2 and the market price is P = 10 − 4 = 6.
(b) If firms collude, together they maximise joint profit given by (10 − Q) Q − 4Q. The first
order condition is 10 − 2Q − 4 = 0 which gives us Q = 3 and therefore P = 7.
To calculate the deadweight loss, note that the efficient quantity is the quantity demanded
at price equal to MC. Here MC = 4, so the efficient quantity is Q = 6. Thus at the
price-quantity pair ( P∗ , Q∗ ), the deadweight loss is given by
1 ∗
( P − 4)(6 − Q∗ )
2
Thus the deadweight loss under collusion is 9/2 = 4.5.
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EC2066 Microeconomics
Price
10
Q D = 10 - P
Deadweight Loss
7
MC = 4
6
3
Quantity
Calculating the deadweight loss from collusive equilibrium.
(c) Now firm 1 takes firm 2’s reaction function as given. Firm 2’s reaction function is
q2 = 3 − q1 /2. Therefore firm 1 maximises
q q1 − 4q1
10 − q1 + 3 − 1
2
which simplifies to
3−
q1 q1
2
The first order condition is given by 3 − q1 = 0 implying that q1 = 3. It follows that
q2 = 3/2. The market price is 10 − 3 − 3/2 = 11/2 = 5.5.
(d) The private marginal cost is 4, and the marginal externality cost is 2Q. Therefore the
socially optimal quantity is given by
4 + 2Q = P
which implies
4 + 2Q = 10 − Q
which implies that the socially optimal quantity is Q0 = 2 and the associated price is P0 = 8.
At the total Cournot quantity 4, the social marginal cost is 4 + 2 × 4 = 12, and the social
marginal benefit is simply the height of the demand curve given by 10 − 2 × 4 = 6.
Therefore the deadweight loss is given by
1
1
(4 − Q0 )(12 − 6) = (4 − 2)(12 − 6) = 6
2
2
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Examiners’ commentaries 2013
Price,
Cost
MC = 4 + 2Q
12
10
Deadweight Loss
8
6
P = 10 - Q
4
2
4
Quantity
Calculating the deadweight loss from Cournot equilibrium with private
marginal cost of 4 and an additional social marginal cost of 2Q.
Question 12
Consider a market for used cars. There are some low quality cars and some high quality cars.
Potential sellers have a car each, and there are many more buyers than possible sellers in the
market. A high quality car never breaks down. A low quality car provides a poorer ride
quality over longer journeys and also breaks down with positive probability.
A seller values a high quality car at 9000 and a low quality car at 4000. A buyer values a high
quality car at 10,000 and a low quality car at 5000. All agents are risk-neutral.
In answering the following questions, assume that the sellers get the entire surplus from
trade.
(a) Suppose quality is observable to sellers but not to buyers. Buyers only know that a
fraction 3/5 of the cars in the market are high quality and the rest are low quality. Would
cars of both low and high qualities be traded in equilibrium? Derive the equilibrium
price(s) at which such trade takes place.
[5 marks]
(b) Is the market outcome in part (a) efficient? Explain your answer.
[5 marks]
(c) Now suppose low quality cars break down with probability 0.7. Recall that high quality
cars never break down. Suppose the sellers of high quality cars announce a guarantee
that promises a full refund if the car breaks down. Show that with this guarantee, high
quality cars sell for 10000 and low quality cars sell for 5000.
[5 marks]
(d) Suppose, as in part (c), that low quality cars break down with probability 0.7. Suppose
the government decides to force each seller to offer a full refund if the car sold by the
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EC2066 Microeconomics
seller breaks down. How does this change the market outcome? Is the market outcome
efficient? Explain your answer.
[5 marks]
Reading for this question
MKR Chapter 17; Subject guide Chapter 12 (Asymmetric information).
Approaching the question
(a) If all cars are offered for sale, the average value of buyers is
3
2
10000 + 5000 = 8000.
5
5
Since buyers would not pay more than 8,000 for a car, high quality sellers would not sell.
Anticipating this, a buyer would know that any car being offered for sale must be a low
quality car and therefore buyers would be willing to pay at most 5,000 for a car. Since
sellers get the entire surplus, the equilibrium market price would be 5,000 and only low
quality cars would be traded in equilibrium.
(b) The market outcome is inefficient as there are gains from trade in high quality cars, but this
gain is left unexploited.
(c) The key idea you should understand is that to establish a separating equilibrium as
described in the question, we must show that the low quality sellers would not want to
mimic the behaviour of the high quality sellers.
The high quality sellers have no cost of offering a guarantee. So the crucial question is
whether low quality car sellers would also offer a guarantee. By offering a guarantee they
could mimic the high quality sellers and sell at 10,000. But the cars would break down with
probability 0.7, so that they would have to pay back 10,000 with probability 0.7. Thus the
payoff of low quality sellers from offering a guarantee is 0.3 × 10000 = 3000. But if a seller
sells without a guarantee, he reveals himself as a low quality seller and his car sells at 5,000
in equilibrium. Since 5000 > 3000, a low quality seller has no incentive to imitate a high
quality seller by offering a guarantee.
It follows that there is a separating equilibrium: high quality cars sell with a guarantee at
the buyers’ valuation of 10,000 and low quality cars sell at the buyers’ valuation of 5,000.
(d) If low quality sellers are forced to give a guarantee, the best they can hope for is to sell at
10,000 with a guarantee. But as calculated above, they get a payoff of 3,000 even if they
could sell at the maximum price of 10,000. But 3000 < 4000, which is their reservation value
for their cars. So low quality sellers would quit the market, and only high quality sellers
would sell their cars with a guarantee at 10,000.
This outcome is inefficient since there are gains from trade in low quality cars, and this gain
is left unexploited.
Question 13
(a) Find the pure and mixed strategy Nash equilibria of the following game.
Player 1
A1
B1
Player 2
A2 B2
2,7 3,2
0,0 4,1
[8 marks]
(b) Consider the following extensive-form game with two players. Player 2 moves after
player 1. Each player can produce a high output or a low output. Player 1’s payoff is
additionally influenced by an exogenous event which occurs with probability p ∈ [0, 1].
The payoffs are written as ((Payoff to 1), Payoff to 2).
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Examiners’ commentaries 2013
i. Suppose p > 1/3. Find the subgame perfect Nash equilibrium of the game above.
[6 marks]
ii. Suppose, before the start of the game, player 2 has the option of committing to
produce a high output (H2 ). Making such a commitment requires player 2 to incur a
cost of 1. Find the range of values of p for which it is optimal to make such a costly
commitment.
[6 marks]
Reading for this question
The coverage of game theory in MKR (Chapter 16) is not ideal. See Chapter 9 (Game theory: an
introduction) of the subject guide for a detailed discussion.
Approaching the question
(a) The pure NE are ( A1 , A2 ) and ( B1 , B2 ). The mixed NE is as follows.
Suppose 1 plays A1 with probability p and B1 with probability (1 − p). Then p must be
such that 2 is indifferent between A2 and B2 . This gives us
7p = 2p + (1 − p).
Solving, p = 1/6. Now suppose 2 plays A2 with probability q and B2 with probability
(1 − q). Then q must be such that 1 is indifferent between A1 and B1 . This gives us
2q + 3(1 − q) = 4(1 − q).
Solving, q = 1/3. Therefore the mixed NE is given by 1 playing A1 with probability 1/6 and
B1 with probability 5/6 and 2 playing A2 with probability 1/3 and B2 with probability 2/3.
Many candidates derive the mixed strategies correctly using the method above. Some use a
slightly different method: first write down the expected payoff of each player given that
each plays a mixed strategy. Let Eπ1 denote the expected payoff of player 1. Now
differentiate this with respect to p and set this equal to zero. What does this do? Well, this
should give us the value of q for which Eπ1 does not depend on p (i.e. the derivative of Eπ1
with respect to p is zero, so that the expected payoff of 1 does not change when p changes).
This is precisely the value of q for which 1 would be indifferent between A1 and B1 . For all
other values of q, the derivative is either positive or negative, so that the optimal choice of p
is either 1 (when the derivative is positive) or 0 (when the derivative is negative). Similarly
we can find the p for which 2 is indifferent.
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EC2066 Microeconomics
1
However, it is very important to note that when you set dEπ
dp = 0, this is not a maximisation
exercise (i.e. this is not a first order condition). If you say you are maximising with respect
to p, this tells the Examiners that you have not understood the exercise you are carrying
out, and you are unlikely to get any credit for your answer. In general, we would encourage
you to adopt the first method discussed above for deriving mixed strategy Nash equilibria.
That method is the simplest, makes the underlying intuition clear and minimises the chance
of making a mistake.
(b) i. A subgame perfect Nash equilibrium (which is a formalisation of the notion of
credibility) is a Nash equilibrium of the whole game that also induces Nash equilibrium
play in every subgame. For games of perfect information, we can obtain subgame
perfect Nash equilibria using backward induction. (In more complicated games where a
player does not have perfect information about moves of previous players, backward
induction may not work, but such games are outside the scope of this course.)
Solving backwards, we see that if 1 plays L1 , 2’s optimal action is H2 (the payoff from H2
is 4, while that from L2 is 1), and if 1 plays H1 , 2’s optimal action is L2 . Therefore in any
subgame-perfect equilibrium, 2’s strategy must be (H2 if L1 and L2 if H1 ). Given this, 1
compares between L1 which yields a payoff of 3 − 2p and H1 which yields a payoff of
2 + p.
Now,
2 + p > 3 − 2p
implies
p>
1
.
3
Since this is the case given by the question, 1’s optimal choice is H1 .
Therefore the subgame perfect Nash equilibrium is given by the strategy combination
(H1 , (H2 if L1 and L2 if H1 )).
Many candidates answer this question by saying that the subgame perfect Nash
equilibrium is ( H1 , L2 ). It is very important for you to understand that this is not fully
correct. You should carefully study the notion of a strategy in a dynamic game and the
concept of subgame perfect Nash equilibrium from the subject guide. A strategy in a
dynamic game with sequential moves (also called an extensive-form game) is a
complete plan of actions, and therefore you need to specify an action for the second
mover after every action of the first mover. An incomplete specification would earn you
very little credit.
ii. There are two crucial points to understand. First, if p < 1/3, 1 would optimally play L1
so that 2 would get 4 simply by playing the subgame-perfect equilibrium strategy as
above. In this case commitment is not useful, so the first condition is that p > 1/3.
The second point to understand is that if 1 plays H1 optimally, commitment would have
no value for 2 (indeed, he would get 1 minus the cost of commitment, giving 2 a payoff
of 0 – but he could get 2 as above by not getting into any such commitment). Thus for
commitment to have any value, it must be that without the commitment 1 would play
H1 , but the commitment makes it optimal for 1 to play L1 , so that player 2 can get 4
minus the cost of commitment, giving 2 a payoff of 3. If 2 commits to playing H2 after
both L1 and H1 , 1 plays L1 optimally if
3 − 2p > 1 + p
which implies p < 23 . Thus it is optimal to make a commitment to high output if
2
1
<p< .
3
3
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Examiners’ commentaries 2013
Question 14
Consider a competitive industry with several identical firms. You are given the following
information about this industry
QD
= 320 − 2P
C (q) = 50 + 10q + 50q2
(Market demand)
(Total cost function of a firm)
Here P is the market price and q denotes the output of the representative firm.
(a) Derive the supply function of the representative firm, paying proper attention to the
shut-down point.
[5 marks]
(b) Suppose there are 100 firms in the industry. Derive the market supply function and
equilibrium market price and quantity.
[5 marks]
(c) Suppose a tax of 30 per unit of output is imposed on sellers. Calculate the deadweight
loss from the tax.
[5 marks]
(d) Calculate the burden of the tax on consumers, and the burden of the tax on sellers.
[5 marks]
Reading for this question
MKR Chapters 10.1, 11; Subject guide Chapter 8 (Competition and monopoly). For a better
discussion of this issue, see Chapter 8.3 of Perloff.
Approaching the question
(a) The supply function is the part of the marginal cost curve that is above the average variable
cost curve. The marginal cost is 10 + 100q which always exceeds the average variable cost
10 + 50q. Therefore the supply curve of a firm is simply P = MC for all q > 0. The supply
curve is therefore given by
P = 10 + 100q,
or
q=
P − 10
.
100
(b) Market quantity is Q = 100q. Therefore market supply is given by Q = P − 10. Equilibrium
market price is given by equating demand and supply:
P − 10 = 320 − 2P
which implies 3P = 330, i.e. P = 110. The equilibrium market quantity is therefore Q = 100.
(c) The inverse market supply is P = 10 + Q. With a tax of 30 per unit, this becomes
P = 40 + Q or Q = P − 40. Equating with demand,
P − 40 = 320 − 2P
which implies P = 120 and Q = 80. Therefore the deadweight loss is
1
(100 − 80)30 = 300
2
(d) Note that the total tax revenue is 80 × 30 = 2400. The burden on consumers is
(120 − 110)80 = 800. The sellers get a net price per unit of 120 − 30 = 90. Therefore the
burden on sellers is given by (110 − 90)80 = 1600.
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EC2066 Microeconomics
Price
P = 40+Q
160
30
D
120 A
110 F
E
G
90 B
P = 10+Q
P = 160 - Q/2
C
40
10
80
100
Quantity
Calculating the tax revenue and deadweight loss from tax.
The rectangular area ABCD is the tax revenue, and the shaded
triangle CDE is the deadweight loss from the tax. The rectangle AFGD
is the burden of the tax on consumers and the rectangle FBCG is the
burden on sellers.
Question 15
(a) Explain the social cost arising from monopoly using a diagram. Suppose a lump-sum tax
is imposed on a monopolist and the revenue is redistributed among consumers. Would
such a measure reduce the social cost of monopoly?
[5 marks]
(b) Write the monopolist’s profit maximization condition in terms of the price-elasticity of
demand.
[5 marks]
(c) Assuming marginal cost is positive, show that demand must be elastic (i.e. the absolute
value of elasticity must be greater than 1) at the equilibrium output level under
monopoly.
[5 marks]
(d) Explain, using a diagram, why attaining the socially optimal level of output under a
natural monopoly requires a government subsidy.
[5 marks]
Reading for this question
MKR Chapter 13; Subject guide Chapter 8 (Competition and monopoly). See also Perloff,
Chapters 11.4–11.5.
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Examiners’ commentaries 2013
Approaching the question
(a) A deadweight loss arises because the monopolist, to maximise profit, produces a lower
quantity compared to the competitive level of output. A lump-sum tax does not change the
monopolist’s profit maximising quantity (such a tax does not have any effect on the
monopolist’s marginal cost) and therefore the measure would have no impact on
deadweight loss.
Price
Deadweight Loss
PM
MC
P
C
D = AR
MR
QM
QC
Q
Deadweight loss under monopoly.
(b) Marginal revenue (MR) is the derivative of total revenue (price (P) times quantity (Q). This
can be written as
d
dP
Q dP
1
P.Q = P + Q
= P 1+
= P 1−
.
dQ
dQ
P dQ
ε
where price-elasticity of demand is given by
ε=−
dQ P
.
dP Q
The monopolist’s profit maximisation condition is MR=MC where MC denotes marginal
cost. Using the expression for MR from above, this can be written as
1
MC = P 1 −
.
ε
(c) Since MC is positive, the right hand side of the equation above must also be positive, which
implies ε > 1 at the equilibrium output.
(d) Since the average cost (AC) is falling, MC<AC. The socially optimal level of output is
obtained from the demand curve by setting P = MC. But at this price, the firm makes a loss
(AC exceeds P). Thus a subsidy is required.
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EC2066 Microeconomics
Price,
Cost
Demand
B
A
AC
C
D
MC
Q Eff
Q
The need for a subsidy at the efficient output under natural monopoly.
Since AC is falling, MC is below AC. Setting P=MC we get the efficient
quantity Q Eff . At this quantity the fim makes a loss given by the rectangle
ABCD. A subsidy is therefore required for the firm to break even.
Question 16
(a) Explain how private individuals can avoid inefficiencies arising from the presence of
externalities through (i) mergers and (ii) bargaining.
[7 marks]
(b) Identify examples in which the problem of externalities cannot be solved well by the
methods discussed in part (a).
[6 marks]
(c) Briefly discuss how the government can address some types of externalities by creating a
market for trading of permits in the externality-generating activity.
[7 marks]
Reading for this question
MKR Chapter 18; Subject guide Chapter 13 (Externalities and public goods). See also Perloff,
Chapter 17.5.
Approaching the question
(a) You should consider two parties one of whom takes some action that generates a negative
externality for the other party. Now discuss how a merger would align incentives of the two
parties such that the externalities would be internalised. Next, discuss how, in the absence
of transaction costs, bargaining can solve the problem of externalities. Good answers
would, in addition, identify some real-life situations to illustrate the answer in each case.
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Examiners’ commentaries 2013
(b) You should identify some factors that limit the effectiveness of the solutions discussed in
the previous part. Mergers, for example, are possible only in a narrow range of cases (an
upstream chemicals factory is not going to merge with downstream fishermen). When two
firms merge, that can create its own distortions by concentrating market power. Similarly,
effective Coasian bargaining is possible only in a limited set of circumstances. If there are
several parties who generate and suffer from externalities, bargaining is difficult. Coasian
solutions are also subject to inefficiencies when bargaining takes place under asymmetric
information.
(c) You must discuss pollution-permit markets such as the market for carbon-emission permits
or sulfur dioxide emission permits. The critical point that you must make is as follows.
Firms differ in their ability to reduce pollution. Some firms can switch to a cleaner
production process at a lower cost than others. The role of pollution-permit markets is to
set an overall quota, and then implement this quota at the minimum possible cost. Trading
implements the quota at the lowest cost as there are gains from trade between parties who
have lower costs of reducing pollution and parties with higher costs of reducing pollution.
The former can sell permits to the latter, and such trade reduces the total cost of
implementing the overall quota.
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