Examiners’ commentaries 2020
Examiners’ commentaries 2020
EC2066 Microeconomics
Important note
This commentary reflects the examination and assessment arrangements for this course in the
academic year 2019–20. The format and structure of the examination may change in future years,
and any such changes will be publicised on the virtual learning environment (VLE).
Information about the subject guide and the Essential reading
references
Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2016).
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 refer 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
At the end of this course, and having read this guide, completed the Essential reading and activities,
you should:
be able to define and describe:
• the determinants of consumer choice, including inter-temporal choice and choice under
uncertainty
• the behaviour of firms under different market structures
• how firms and households determine factor prices
• behaviour of agents in static as well as dynamic strategic situations
• the nature of economic interaction under asymmetric information
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
• the effects of strategic behaviour and asymmetric information on efficiency
• the nature of policies and contracts aimed at improving welfare
be prepared for further courses which require a knowledge of microeconomics.
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EC2066 Microeconomics
Time management
Section A comprises eight questions, all of which must be answered (accounting for 40% of the total
marks). 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 Nicholson & Snyder as the principal text. There are also some references
to Perloff. In addition to this, you should practise questions from other texts. A few ‘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. For this topic, you should primarily rely
on the exposition in the subject guide. You should make sure that you understand the key ideas
covered in some detail in the subject guide.
Principal text
Nicholson, W. and C. Snyder, Intermediate Microeconomics and its Application (Cengage
Learning 2015) twelfth edition [ISBN 9781133189039].
Auxiliary texts
Perloff, J.M. Microeconomics with Calculus (Pearson Education, 2014) third edition [ISBN
9780273789987].
Besanko, D. and R. Braeutigam, Microeconomics (John Wiley & Sons, 2014) fifth edition,
international student version [ISBN 9781118716380].
Varian, H.R. Intermediate Microeconomics: A Modern Approach (W.W. Norton, 2014)
ninth edition [ISBN 9780393920772].
Pindyck, R.S. and D.L. Rubinfeld, Microeconomics (Prentice–Hall/Pearson, 2012) eighth
edition [ISBN 9780133041705].
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Examiners’ commentaries 2020
Examination revision strategy
Many candidates are disappointed to find that their examination performance is poorer than they
expected. This may be due to a number of reasons, but one particular failing is ‘question
spotting’, that is, confining your examination preparation to a few questions and/or topics which
have come up in past papers for the course. This can have serious consequences.
We recognise that candidates might 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 available on the VLE. You should read
the syllabus 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. Examination papers may legitimately include
questions on any topic in the syllabus. So, although past papers can be helpful during your 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. We strongly advise you not to adopt this strategy.
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EC2066 Microeconomics
Examiners’ commentaries 2020
EC2066 Microeconomics
Important note
This commentary reflects the examination and assessment arrangements for this course in the
academic year 2019–20. The format and structure of the examination may change in future years,
and any such changes will be publicised on the virtual learning environment (VLE).
Information about the subject guide and the Essential reading
references
Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2016).
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 refer 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
Candidates should answer ELEVEN of the following FOURTEEN questions: all EIGHT from
Section A (5 marks each) and THREE from Section B (20 marks each). Candidates are strongly
advised to divide their time accordingly. If more than ELEVEN questions are answered,
only the first answers attempted will be counted.
Section A
Answer all EIGHT questions from this section (5 marks each).
Question 1
Consider the strategic-form game below with two players, 1 and 2. Solve the game
by iteratively eliminating dominated strategies.
Player 1
Reading for this question
Subject guide, Chapter 4.
4
A1
B1
C1
A2
2, 2
4, 0
6, 4
Player 2
B2
C2
4, 2 0, 0
5, 3 2, 2
4, 0 0, 6
Examiners’ commentaries 2020
Approaching the question
B1 dominates A1 . Remove A1 . In the remaining game, C2 dominates A2 . Remove A2 . In the
remaining game, B1 dominates C1 . Remove C1 . In the remaining game, B2 dominates C2 .
Remove C2 . We then have the solution B1 , B2 .
Question 2
Consider an economy with two goods, x and y with prices px and py , respectively.
We observe the following choices made by Rob: if px > py he chooses to consume
only y, and if py > px he chooses to consume only x. Suggest a utility function for
Rob that represents preferences consistent with the given data.
Reading for this question
Subject guide, Chapter 2.
Approaching the question
Rob’s preferences can be represented most obviously by the following utility function (perfect
substitutes):
u(x, y) = x + y.
Other functions that work include max{x, y}, or any order-preserving transformations of these.
Question 3
Consider a market for used cars. There are many sellers and even more buyers. A
seller values a high quality car at 800 and a low quality car at 200. For any quality,
the value to buyers is m times the value to sellers, where m > 1. All agents are
risk-neutral. Sellers know the quality of their own car, but buyers only know that
2/3 of the cars are low quality and the remaining 1/3 of them are high quality. For
what values of m do all sellers sell their used cars?
Reading for this question
Subject guide, Chapter 10.
Approaching the question
The average value for a buyer is:
2
1
× 800m + × 200m = 400m.
3
3
All sellers can sell cars if the average value of buyers is at least as high as 800. So we need
400m ≥ 800, implying m ≥ 2.
Question 4
If the price elasticity of supply is zero, a tax on suppliers will raise the market price.
Is this true or false? Explain your answer.
Reading for this question
Subject guide, Chapter 6.
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EC2066 Microeconomics
Approaching the question
This is false. In this case the market price does not change after tax (neither does market
quantity) – the incidence is fully on suppliers who receive the same price as before but the net
price received goes down by the per unit tax. Candidates should draw a diagram showing a
vertical supply curve and a downward-sloping demand curve and note that the market outcome
is unaffected after the tax is imposed.
Question 5
Amal consumes pizzas and also consumes good O which is a composite of all other
goods. His income–consumption curve is a vertical line as shown in the picture
below. Pizza might be a Giffen good for Amal. Is this true or false? Explain your
answer.
Reading for this question
Subject guide, Chapter 2.
Approaching the question
This is true. ICC as drawn indicates pizza consumption is constant as income rises, implying
that the income effect on pizza is zero. So as price of pizza changes, only the substitution effect is
present. It follows that pizza consumption falls as price rises. Therefore, it is impossible for pizza
to be a Giffen good.
Question 6
An individual consumes two goods and her preferences satisfy non-satiation. It
follows that at least one of the two goods must be a normal good. Is this true or
false? Explain your answer.
Reading for this question
Subject guide, Chapter 2.
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Examiners’ commentaries 2020
Approaching the question
This is true. If both goods are inferior, the consumer would consume lower amounts of both at
higher incomes – so that the optimal point would be inside the budget set. This violates
non-satiation.
Question 7
Under first-degree price discrimination, a monopolist produces the efficient output.
Is this true or false? Explain using an appropriate diagram.
Reading for this question
Subject guide, Chapter 8.
Approaching the question
This is true. Since the monopolist can extract all surplus, the monopolist wants to maximise
surplus, implying that the optimal output coincides with competitive output and there is no
deadweight loss.
Question 8
Several generators pollute the environment by emitting carbon dioxide. Generators
have different costs of reducing carbon emissions. The government wants to put a
cap on total emissions. Putting a cap on each generator is more efficient compared
to issuing tradeable emissions permits to each generator. Is this true or false?
Explain your answer.
Reading for this question
Subject guide, Chapter 12.
Approaching the question
This is false. Tradeable permits allow generators with lower cost of abatement to sell permits to
those with higher costs, which implies that most of the reduction is done by those best placed to
reduce emissions, hence achieving the overall cap at lower cost than if each generator had to
reduce emissions by a certain amount.
Section B
Answer THREE questions from this section (20 marks each).
Question 9
(a) Consider the following simultaneous move game with two players.
2
1
A1
B1
A2
3, 1
1, 2
B2
1, 2
3, 1
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EC2066 Microeconomics
Consider the pure strategies of player 1. Note that A1 does not dominate B1 ,
and B1 does not dominate A1 . Is it possible for a mixed strategy of player 1 to
be a dominant strategy? Explain.
(Hint: For any mixed strategy of 1 to be a dominant strategy, it must dominate
both A1 and B1 . Is this possible?)
(5 marks)
(b) For the following extensive-form game:
i. Identify the pure and mixed strategy Nash equilibria.
(5 marks)
ii. Identify all Subgame Perfect Nash equilibria.
(5 marks)
(c) Suppose the following game is repeated infinitely. The players have a common
discount factor δ ∈ (0, 1). Show that for high enough values of δ, there is an
equilibrium of the infinitely repeated game in which (C, C) is played in every
period. Your answer must state the strategies of the players clearly.
2
1
C
D
C
4, 2
5, 0
D
0, 3
1, 1
(5 marks)
Reading for this question
Subject guide, Chapter 4.
Approaching the question
(a) For each choice of strategy for 2, the payoff from a mixed strategy of 1 is a mixture over the
pure strategy payoffs in the relevant column. Therefore, it is impossible for a mixed strategy
to have a payoff that is higher than all the pure strategies.
To see this another way, suppose a mixed strategy that chooses A1 with probability p and
B1 with probability (1 − p) is a dominant strategy. Then we must have:
3p + (1 − p) > 3
and p + 3(1 − p) > 3.
It is, of course, impossible to satisfy these with any p such that 0 < p < 1.
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Examiners’ commentaries 2020
(b) i. The normal form is:
Player 1
A
B
Player 2
C
D
3, 2
1, −1
−1, 0
2, 3
Pure strategy Nash equilibria: A, C and B, D. Mixed strategy Nash equilibrium: Player
1 plays A with probability 1/2 and B with probability 1/2. Player 2 plays C with
probability 1/5 and D with probability 4/5.
ii. There are no strict subgames. The only (trivial) subgame is the whole game. Therefore,
all Nash equilibria identified above are also subgame perfect Nash equilibria.
(c) The strategy profile is as follows. Start by playing (C, C) in period t = 0. In any period
t > 0, if (C, C) was played last period, play (C, C), otherwise switch to (D, D).
Under this strategy profile, player 1 will not deviate if:
4
δ
≥5+
1−δ
1−δ
which implies δ ≥ 1/4.
Player 2 will not deviate if:
2
δ
≥3+
1−δ
1−δ
which implies δ ≥ 1/2.
Therefore, cooperation can be sustained in the repeated game if δ ≥ 1/2.
Question 10
A seller sells a good of quality q at a price t. The cost of producing at quality level q
is given by q 2 /2. There is a buyer who receives a utility of θq − t by consuming the
unit of quality q at price t. If he decides not to buy, he gets a utility of zero. θ can
take two values θ1 = 1 and θ2 = 4.
(a) Suppose the seller can observe θ. Derive the profit maximising price–quality
pairs offered when the type is θ1 = 1 and when the type is θ2 = 4.
(6 marks)
(b) Prove that the full information price–quality pairs are not incentive compatible
if the seller cannot observe θ.
(7 marks)
(c) Suppose the seller cannot observe θ, and suppose he decides to set q1 = 1/4 and
q2 = 4. Calculate the optimal values of t1 and t2 such that both types
participate, type θ1 = 1 takes the contract (q1 , t1 ) and type θ2 = 4 takes the
contract (q2 , t2 ).
[Hint: write down the participation constraint of type θ1 and the incentive
constraint of type θ2 and solve for t1 and t2 .]
(7 marks)
Reading for this question
Subject guide, Chapter 10.
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EC2066 Microeconomics
Approaching the question
(a) The seller will just satisfy the participation constraint of a buyer, so that the seller
maximises t − q 2 /2 subject to θq = t. Substituting the value of t, the seller maximises
θq − q 2 /2, so that the optimal choice is given by q = θ. This implies t = θq = θ2 .
Here θ1 = 1 and θ2 = 4. Therefore, the optimal choice is q1 = θ1 = 1, and q2 = θ2 = 4.
Further, t1 = θ1 q1 = 1 and t2 = θ2 q2 = 16.
(b) The incentive constraint of type θ2 is:
θ2 q 2 − t2 ≥ θ2 q 1 − t1 .
Here, the left-hand side is 0 while the right-hand side is 4 − 1 = 3. Therefore, the incentive
constraint of type θ2 is violated.
(c) The participation constraint of type θ1 and the incentive constraint of type θ2 bind. So we
have:
θ1 q 1 − t1 = 0
(PC1 )
θ2 q2 − t2 = θ2 q1 − t1 .
From these:
t1 = θ1 q1 = 1 ×
(IC2 )
1
1
=
4
4
and:
1 1
3
61
+ = 16 − =
= 15.25.
4 4
4
4
This is not required for the answer, but if you want you can check that the other two
constraints do not bind.
t2 = θ2 q2 − θ2 q1 + t1 = 4 × 4 − 4 ×
First, the participation constraint of type θ2 requires:
θ2 q2 − t2 ≥ 0.
Here the left-hand side is 16 − 15.25 > 0. Therefore, this constraint does not bind.
Second, the incentive constraint of type θ1 requires:
θ1 q1 − t1 ≥ θ1 q2 − t2 .
Here, the left-hand side is 0 and the right-hand side is 4 − 15.25 < 0. Therefore, this does
not bind as well.
Question 11
Suppose two firms (1 and 2) sell differentiated products and compete by setting
prices. The demand functions are:
q 1 = 7 − P1 +
and:
q 2 = 7 − P2 +
P2
2
P1
2
.
Firms have a zero cost of production.
(a) Find the Nash equilibrium in the simultaneous-move game. Also find the
quantities sold by each firm.
(5 marks)
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Examiners’ commentaries 2020
(b) Find the subgame-perfect equilibrium if 1 moves before 2. Also find the
quantities sold by each firm.
(5 marks)
(c) Calculate the profits of the two firms for the case in part (b). Which firm gets a
higher profit, the first mover or the second mover?
(5 marks)
(d) Briefly explain the intuition for the result in part (c).
(5 marks)
Reading for this question
Subject guide, Chapter 9.
Approaching the question
(a) Firm 1 maximises profit:
π1 = q1 P1 = 7P1 − P12 +
The first-order condition is:
7 − 2P1 +
P1 P2
.
2
P2
=0
2
implying:
7 P2
+
.
2
4
Applying symmetry, we know P1 = P2 = P ∗ . So:
P1 =
P∗ =
7 P∗
+
=0
2
4
implies that the Nash equilibrium is P1 = P2 = P ∗ = 14/3.
At this price, q1 = q2 = 14/3.
(b) 1 now maximises:
max 7 − P1 +
P1
7 P1
+
4
8
P1
which simplifies to:
max
P1
35 7
− P1 P1 .
4
8
This solves to P1 = 5. Then P2 = 7/2 + 5/4 = 19/4. The associated quantities are:
q1 = 7 − 5 +
19
35
=
8
8
and q2 = 7 −
19 5
19
+ =
.
4
2
4
(c) The profits for the case in part (b) are:
π1 = q1 P1 =
35
× 5 = 21.88
8
and π2 = q2 P2 =
19
4
2
= 22.56.
The second-mover gets a higher profit.
(d) The first-mover sets a higher price (compared to the simultaneous-move game), which
creates a less competitive environment for the second-mover, who exploits it to set a slightly
lower price than the first-mover, which earns a profit greater than the first-mover.
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EC2066 Microeconomics
Question 12
A risk neutral principal hires a risk averse agent to work on a project. The agent’s
utility function is:
√
V (w, ei ) = w − g(ei )
where w is wage, g(ei ) is the disutility associated with the effort level ei exerted on
the project.
The agent can choose one of two possible effort levels, eH or eL , with associated
disutility levels g(eH ) = 2, and g(eL ) = 1. If the agent chooses effort level eH , the
project yields 20 with probability 3/4, and 0 with probability 1/4. If he chooses eL ,
the project yields 20 with probability 1/4 and 0 with probability 3/4.
The reservation utility of the agent is 0.
Let {wH , wL } be an output-contingent wage contract, where wH is the wage paid if
the project yields 20, and wL is the wage if the yield is 0. The agent receives a fixed
wage if wH = wL .
(a) If effort is observable, which effort level should the principal implement? What
is the best wage contract that implements this effort?
(8 marks)
(b) Suppose effort is not observable. What is the optimal contract that the principal
should offer the agent? What effort level does this contract implement?
(8 marks)
(c) Explain in words why the principal’s payoff differs across the cases considered in
parts (a) and (b) above.
(4 marks)
Reading for this question
Subject guide, Chapter 11.
Approaching the question
(a) When effort is observable, to implement any effort e at minimum cost, the principal simply
needs to pay a fixed wage w (i.e. a wage that does not depend on the firm’s profit level) to
satisfy the participation constraint for that effort level, given by:
√
w − g(e) = u0 = 0.
• To implement high effort eH , the principal pays the fixed wage w∗ such that:
√
w∗ − 2 = 0 (PC for eH )
which implies w∗ = 4. The principal’s profit is:
π(eH ) =
3
× 20 − 4 = 11.
4
• To implement low effort eL : pay fixed wage w∗∗ such that:
√
w∗∗ = 1 (PC for eL )
which implies w∗∗ = 1. The principal’s profit is:
π(eL ) =
12
1
× 20 − 1 = 4.
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Examiners’ commentaries 2020
Since π(eH ) > π(eL ), the principal will implement eH .
(b) Now consider the case in which effort is not observable.
1. Implementing high effort eH : Under asymmetric information, to implement eH , we
need a state dependent wage contract {wH , wL }. Implementing eH at minimum expected
wage cost requires minimising:
3
1
wH + wL
4
4
subject to the participation constraint as well as incentive constraint of the agent.
Solving the two constraints completely determines wH and wL , so that there is no
further minimisation to be done. Therefore, we can simply solve for the wage schedule
from the two constraints.
Further, since there are two constraints and two unknowns, the principal can find wage
values so that they both bind (both hold with equality). So we have the following two
equations:
1√
3√
wH +
wL − 2 = 0
4
4
3√
1√
1√
3√
wH +
wL − 2 =
wH +
wL − 1.
4
4
4
4
(PC)
(IC)
(IC) implies:
which simplifies to
√
wH
√
1 √
( wH − wL ) = 1
2
√
= 2 + wL . We can use this in (PC) and obtain:
√
1√
3
wL = 1
(2 + wL ) +
4
4
√
√
which implies wL = 1/2, which implies wL = 1/4. Then from above, wH = 5/2 and
hence wH = 25/4.
Therefore, when effort is not observable, the optimal wage schedule to implement eH is
(wL = 1/4, wH = 25/4).
The associated profit of the principal is:
3
1
164
25
1
1
165
π(eH ) =
−
=
= 10.25.
20 −
+
0−
=
4
4
4
4
16
16
16
2. Implementing low effort eL : To implement eL : Any flat wage that satisfies the
agent’s participation constraint implements eL . The cheapest way for the principal to do
this is to offer the full information flat wage. Therefore, as before, w∗∗ = 1 and
π(eL ) = 4.
Since π(eH ) > π(eL ) under asymmetric information as well, the principal’s optimal
choice under asymmetric information is eH .
(c) The principal’s profit is 11 under full information and 10.25 under asymmetric information.
In both cases, the agent’s PC binds, so the agent gets 0. However, in the case of asymmetric
information the principal pays the agent a risky wage. Putting risk on the agent is costly for
the principal: the expected wage that the principal pays is now higher by 0.75, hence the
profit is lower by that amount compared to the case when effort is observable.
Question 13
Pip consumes two goods, x and y. Pip’s utility function is given by:
u(x, y) = x1/2 y 1/2 .
The price of x is p and the price of y is 1. Pip has an income of M .
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EC2066 Microeconomics
(a) Derive Pip’s demand functions for x and y.
(5 marks)
(b) Suppose M = 72 and p falls from 9 to 4. Calculate the income and substitution
effects of the price change.
(5 marks)
(c) Calculate the compensating variation of the price change.
(5 marks)
(d) Calculate the price elasticity of demand for x.
(5 marks)
Reading for this question
Subject guide, Chapter 2.
Approaching the question
(a) Equating MRS to p, we get y/x = p or y = px. Using this in the budget constraint:
x=
M
2p
and y =
M
.
2
(b) At M = 72 and p = 9, x = 4 and at p = 4, x = 9. Therefore, the total price effect is 5.
The utility at optimal consumption is given by:
M M
M
u
,
= √ .
2p 2
2 p
To find out the substitution effect, note that at the initial bundle at price p0 = 9, utility is:
M
72
= 12.
√ =
2 p0
6
We need to find the bundle such that utility remains the same, but MRS (which is y/x) is
equal to the new price 4. So we have:
x1/2 y 1/2 = 12
and
y
= 4.
x
Using y = 4x, we get x1/2 (4x)1/2 = 2x. Since 2x = 12, x = 6. Then y = 4x = 24. Hence the
bundle consumed after compensating variation in income is x = 6, y = 24.
Therefore, the substitution effect is the movement from 4 to 6, i.e. the substitution effect is
2. The income effect is then 3 (movement from 6 to 9).
(c) The bundle (6, 24) calculated above is the bundle reached after income is taken away after
the price fall so that the consumer remains on the original indifference curve. The spending
at (6, 24) is 4 × 6 + 24 = 48. Therefore, the compensating variation is initial income minus
48, i.e. 72 − 48 = 24.
(d) It is fine to simply state that the price elasticity is obviously −1 (some candidates might
also state the absolute value, which is fine). This can be guessed easily by noting that
px = M/2. Given any income, px is fixed, which implies unit elasticity. However, this can
also be derived as follows:
εp =
14
M p
M1
x
dx p
=− 2 =−
= − = −1.
dp x
2p x
2p x
x
Examiners’ commentaries 2020
Question 14
Each firm belonging to a competitive industry has the following long-run cost
function:
C(q) = 10q − 2q 2 + q 3
where q denotes the output of a representative firm. Firms can enter and exit the
industry freely. The industry has constant costs: input prices do not change as
industry output changes. The market demand facing the industry is given by:
Q = 20 − P.
(a) Derive the long-run industry supply curve.
(5 marks)
(b) How many firms operate in the industry?
(5 marks)
(c) Suppose a regulator imposes a lump-sum tax of 8 on each firm. Does the output
produced by a firm rise or fall as a consequence of this policy? Explain.
(Hint: Consider the following equation:
−
8
q2
− 2 + 2q = 0.
The solution to this is q = 2.)
(5 marks)
(d) How much revenue does the tax policy in part (c) raise?
(5 marks)
Reading for this question
Subject guide, Chapter 7.
Approaching the question
(a) This is a constant cost industry, so the long-run supply curve is flat at the minimum LR
average cost. So the supply curve is given by P = LRAC min . Here:
LRAC = 10 − 2q + q 2 .
Minimising, we get the first-order condition −2 + 2q = 0, implying q = 1 (it is easy to see
that the second-order condition for a minimum holds). At q = 1, LRAC is 9. Therefore, the
LR supply curve is P = 9.
(b) Total quantity can be derived from the demand curve. At P = 9, Q = 11. Since each firm
produces 1 unit, there are 11 firms in the industry in the LR equilibrium.
(c) Total cost of each firm rises by 8. The new LRAC is:
8
+ 10 − 2q + q 2 .
q
Minimising, the first-order condition is:
−
8
− 2 + 2q = 0.
q2
We know from the hint given that the solution to this is q = 2. Hence output of each
operational firm goes up from 1 to 2.
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EC2066 Microeconomics
(d) At output q = 2, LRAC is:
8
+ 10 − 4 + 4 = 14.
2
Therefore, the new LR supply curve is P = 14. At this price, Q = 6. Hence 3 firms, each
producing 2 units, remain in the industry. The 3 firms that remain in the industry each pay
the lump sum tax of 8. Therefore, the revenue raised from the tax is 8 × 3 = 24.
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