Examiners’ commentaries 2014
Examiners’ commentaries 2014
MN3028 Managerial economics
Important note
This commentary reflects the examination and assessment arrangements
for this course in the academic year 2013–14. 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 (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
At the end of this course and having completed the Essential reading and
Learning activities, you should be able to:
• prepare for Marketing and Strategy courses by being able to analyse
and discuss consumer behaviour and markets in general
• analyse business practices with respect to pricing and competition
• define and apply key concepts in decision analysis and game theory.
Format of the examination
The examination is three hours long and comprises two sections. You
have to answer all four questions in Section A (12.5 marks each) and two
questions in Section B (25 marks each).
Planning your time in the examination
The marks for each question correspond roughly to the proportion of time
you are expected to spend on it. Try not to spend too much time on any
one question. You can always go back to it later if you have time left.
When you select which questions to answer in Section B, take time to read
all the questions (and all parts of each question). Often candidates select a
question on the basis of the ‘topic’ of the question only to realise that they
are able to answer at most the first part of the question.
If you end up doing terribly complicated calculations taking up several
pages it is highly likely that you have misinterpreted the question or made
a mistake – go back and check the question and your answer. The same
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MN3028 Managerial economics
applies, of course, if you find negative prices or quantities, or probabilities
greater than one or less than zero.
Write down clearly what you are doing as the Examiners award marks for
correct logic and development even if there are numerical mistakes.
What are the Examiners looking for?
We are looking for evidence that you have truly understood the material
and can apply this knowledge. Memorising answers to past questions
will not get you very far. You should have the confidence to tackle
the questions from first principles. Of course, you will only have this
confidence if you have worked consistently throughout the year to
familiarise yourself with the way of thinking that this subject requires.
How to do well in the examination
A key success factor is obviously the time spent preparing and, as
mentioned before, an early start is definitely required. It is impossible
to acquire the thinking skills you need in the last few weeks before the
examination.
It is not good enough to simply repeat the material from the subject
guide. You must understand it! A good way to check whether you really
understand the material is to try to explain it to a friend.
You also have to spend a lot of time thinking about questions/problems/
exercises. Never look at answers or solutions until you have spent at least
an hour or two trying to figure out the solution yourself. Obviously during
the examination you will not have that much time, but the more time you
spend thinking about how to solve problems during the year, the easier
your revision and the examination will be.
Especially for the essay questions, do not write down everything you
know about a topic which is vaguely related to the question. Answer
the question! We do not expect polished essays with nicely constructed
sentences, and the use of bulleted lists is acceptable where appropriate.
The main thing is to show that you have understood the material. You can
give evidence of your understanding through clear exposition, including
models and numerical and verbal examples (preferably your own).
Diagrams should be clear. It is not important that the axes are drawn as
straight lines, etc. but diagrams have to be neat enough to illustrate the
point you are making.
Amazingly, we often find that candidates have not read the subject guide
properly. You do not need to read anything else to do well in this course,
so make sure you read and understand the subject guide.
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Examiners’ commentaries 2014
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.
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MN3028 Managerial economics
Examiners’ commentaries 2014
MN3028 Managerial economics – Zone A
Important note
This commentary reflects the examination and assessment arrangements
for this course in the academic year 2013–14. 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 (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
Candidates should answer SIX of the following TEN questions: FOUR
from Section A (12.5 marks each) and TWO from Section B (25 marks
each). Candidates are strongly advised to divide their time
appropriately.
Section A
Answer all four questions from this section (12.5 marks each).
Question 1
Consider a monopolist who can make a take-it-or-leave-it offer to a single
consumer. The monopolist’s cost function is given by C(q) = 4q. The consumer has
a budget of m = 100. The consumer’s utility function is given by U(y,q) = y1/2 +
2q where q is the quantity of the monopolist’s product and y denotes remaining
money. What is the optimal offer to the consumer?
Reading for this question
The reading for this question is in Chapter 10 of the subject guide.
Approaching the question
The monopolist maximises profit which equals the payment (R) he gets
from the consumer minus his costs:
Max R – 4q
(1)
The constraint is that the consumer must not prefer going without the
monopolist’s products to paying R for q units:
s.t. U(y – R,q) ≥ U(m,0)
At the optimum the consumer will be indifferent i.e. U(y – R,q) =
U(m,0), or (100 – R)1/2 + 2q = (100)1/2. Solving for q gives
q = 5 – 1/2(100 – R)1/2.
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Examiners’ commentaries 2014
Substituting this into (1) and maximising w.r.t. R gives R = 99 and
therefore q = 4.5.
We can then check that the consumer is indeed indifferent between taking
and leaving the offer: U(100 – 99,4.5) = U(100) = 10.
We also need to check that the monopolist is making positive profits: 99 –
4(4.5) > 0.
Very few candidates answered this question correctly in 2014. The
vast majority of candidates failed to utilise the consumer’s indifference
constraint to solve the problem. A few tried to use the marginal cost equal
to marginal revenue approach but this is clearly inappropriate here and
indicates an attempt to blindly apply rules rather than to think through the
problem.
Question 2
Show that, for linear demand (p = a – bq), per unit consumer surplus (consumer
surplus divided by quantity sold) equals 0.5p/η where η is price elasticity.
Reading for this question
The reading for this question is in Chapter 9 of the subject guide.
Approaching the question
Consumer surplus is given by triangle A, (a – p)2/(2b). Hence, per unit
consumer surplus equals (a – p)/2.
Most candidates were not able to identify consumer surplus as the triangle
A under the demand curve. Neither were they able to define consumer
surplus analytically or derive its formula for linear demand.
Question 3
Consider a market with two firms, A and B. Market demand equals Q = 20 – p.
The firms have identical and constant marginal costs c and zero fixed costs.
Reading for this question
The reading for this question is in Chapter 11 of the subject guide.
Approaching the question
a. Suppose firms set prices simultaneously. What are the equilibrium prices and
profits?
Both firms set price equal to marginal cost and profits are zero.
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MN3028 Managerial economics
b. Suppose firm B is able to delay its pricing decision until after it has observed
the price set by firm A. Find the subgame perfect equilibria.
Firm A will not set a price below c. If firm A sets any price above c, firm
B would undercut. In this setup firm A can never make a profit. At a
subgame perfect equilibrium, A sets any price ≥ c and B slightly undercuts
any price > c and matches a price = c.
Very few candidates answered this question correctly in 2014. Most
candidates tried to find a Cournot equilibrium which is not at all what the
question is asking you to do. You must read the question carefully. You get
no marks for answering a different question.
Question 4
Consider the following version of the finite alternating offer bargaining game.
Players divide a cake of size 1 and discount their payoffs after each rejection
with discount factor δ (0 < δ <1). In this version, player 1 gets to make the first
three offers. If player 2 rejects all 3 offers, he gets to make the final offer. If
player 1 rejects this final offer, both players get zero. What is the subgame
perfect equilibrium in this game?
Reading for this question
The reading for this question is in Chapter 3 of the subject guide.
Approaching the question
(x, 1 – x)
Offer to keep x
1
Accept
2
δy, δ(1–y))
Reject
Accept
Offer to keep y
1
2
Reject
1
Offer to keep z
2
Accept
δ2z, δ2(1–z))
1
Reject
Offer to keep α
Accept
Reject
(0, 0)
6
(δ3(1– α), δ3α)
Examiners’ commentaries 2014
At the final decision node, player 1 will accept any  and therefore player
2 will set α =1.
At player 2’s last decision node, he has a choice now of 3 or 2(1 – z).
Player 1 sets z such as to make player 2 indifferent, i.e. z = 1 – .
At player 2’s second decision node, he has a choice now of 2(1 – (1 – ))
or (1 – y). Player 1 sets y such as to make player 2 indifferent, i.e.
y = 1 – 2.
At player 2’s first decision node, he has a choice now of (1 – (1 – 2)) or
1 – x. Player 1 sets x such as to make player 2 indifferent, i.e. x = 1 – 3.
Candidates answered this question reasonably well in 2014 and it was
clear that they had prepared the topic. A common mistake was not
realising that the ordering of offers is non-standard and that therefore
the model from the subject guide should not be reproduced exactly. Some
candidates attempted to reproduce a solution from similar questions in
previous examination papers, which was also wrong. The lesson is not to
memorise but think for yourself! Surprisingly many candidates made small
(but significant) calculation mistakes so they came up with a similar, but
still incorrect solution.
Section B
Answer two questions from this section (25 marks each).
Question 5
Joanna’s utility of money function is given by U(x) = (x/10)2. She has to make a
choice between two lotteries, A and B, with outcomes and probabilities given in
the table below.
Lottery A
Lottery B
Outcome
Probability
Outcome
Probability
110
1/2
90
p
130
1/2
150
1–p
Reading for this question
The reading for this question is in Chapter 1 of the subject guide.
Approaching the question
a. Find the probability p for which Joanna is indifferent between the two
lotteries.
We need to find the probability p such that U(A) = U(B).
U(A) = 0.5U(110) + 0.5U(130) = 0.5(11)2 + 0.5(13)2
(1)
U(B) = pU(110) + (1 – p)U(130) = p(9) + (1 – p)(15)
2
2
(2)
Equating (1) and (2) and solving for p gives p = 160/288 = 0.56.
b. Is Joanna risk averse, risk neutral or risk loving?
Risk loving. The utility of money function is convex.
c. Calculate the certainty equivalent of lottery A and compare it to its expected
value.
The certainty equivalent is the sum of money which gives the same utility
as the lottery, so
U(CE) = U(A) = 145
As U(CE) = (CE/10)2, CE = 10(145)1/2 = 120.4.
The expected value of lottery A equals 120 which is less than the CE as
Joanna is risk loving.
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MN3028 Managerial economics
d. Set p = 0.6. For what percentage increase in outcomes in lottery B is Joanna
indifferent between the two lotteries?
Suppose we increase the outcomes in lottery B by x%, then the expected
utility equals
(0.6)81(1 + x)2 + (0.4)225(1 + x)2
Setting this equal to U(A) = 145 gives x = 0.023. Increasing the payoffs in
B by 2.3% makes Joanna indifferent between the two lotteries.
Candidates in 2014 expected a decision theory question and many chose
it. The question was effective in discriminating between good and bad
scripts. Many candidates, though obviously planning to answer a decision
analysis question, do not understand the difference between expected
utility and expected value.
Question 6
Seller A has a potential buyer with a valuation v drawn from a uniform
distribution on [0,1]. The buyer’s valuation is private information to the buyer. A’s
valuation is zero. Both parties are risk neutral.
Reading for this question
The reading for this question is in Chapter 4 of the subject guide.
Approaching the question
a. What is the best take-it-or-leave-it price offer A could make? What is the
resulting expected profit?
If A charges x, he receives x if v > x and nothing otherwise. Hence
expected profit equals x(1 – x) which is maximised at x = 1/2 and the
resulting expected profit is ¼.
b. Seller B also has a single item, which she values at zero, but she differs from
A in two respects. Firstly, she has two bidders, each with private valuations
drawn independently from a uniform distribution on [0,1]. Secondly, she
may only hold an English auction with no reserve price. What is her expected
profit?
In an English auction the expected profit equals the expected value of the
second highest valuation, i.e. 1/3.
c. Suppose seller B held an English auction with n+1 bidders, each with private
valuation drawn independently from a uniform distribution on [0,1]. What
would be her expected profit?
In an English auction with n + 1 bidders, the expected profit equals the
expected value of the second highest valuation, i.e. n/(n + 2).
d. Suppose A has n potential buyers each with private valuation drawn
independently from a uniform distribution on [0,1]. Determine the optimal
take-it-or-leave-it offer and the resulting expected profit.
Suppose A charges x. His profit will be x if at least one of the potential
buyers has v > x and zero otherwise. Hence, expected profit equals
x Prob(at least one buyer has v >x ) = x (1-Prob(all buyers have v < x))
= x(1 – xn)
Maximising this w.r.t. x yields x = 1/(n + 1)1/n.
Hence, expected profit is n/(n + 1)1/n+1.
Many candidates who attempted this question in 2014 appear to have
memorised the material without understanding it, which results in poor
performance.
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Examiners’ commentaries 2014
Question 7
Consider a contest with n risk neutral players who spend ei (i = 1,…,n) in an
attempt to win a single prize of value M. The probability of player i winning the
contest equals the ratio of ei to the total amount spent (i.e. sum of ei s).
Reading for this question
The reading for this question is in Chapter 2 of the subject guide.
Approaching the question
a. Find the equilibrium expenditure levels ei.
Player i maximises M Prob(i wins) – ei.
Substituting and differentiating the expected payoff w.r.t. ei gives the
following first order condition:
M  e j  ei 
 e 
2
1  0
j
We can now use symmetry and set all ei equal to e which yields
So that the equilibrium effort level equals e = M(n – 1)/n2 and total
expenditure equals M(n – 1)/n.
b. Assume n is even and divide the n players into two equal size groups. The
contest now consists of two stages. In the first stage, players within each
group compete for a chance to participate in the second round. The winners
from each group then enter a second round in which they compete for the
prize of value M as before. In each round the probability of player i winning
equals the ratio of ei to the total amount spent (i.e. sum of ei s). Find the
equilibrium expenditure levels in both rounds and compare total expenditure
to your answer in a).
In the second round there are two contestants and we know from a) that
each will set e = M/4 and the expected payoff for each is M/4.
In the first round the expected payoff for player i is then M/4 Prob(i wins
out of n/2 contestants) – ei.
Proceeding as in a) we find that the first stage equilibrium effort level
equals M(n – 2)/(2n2) and total expenditure over the two rounds equals
 M n  2    M  M (n  1)
n
  2  
2
n
  4 
 2n
The total effort level is the same as in a).
Although this question is not that difficult IF you understand what a Nash
equilibrium is, almost nobody attempted it.
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MN3028 Managerial economics
Question 8
Show, using graphs,
a. if firms are price takers in the labour market, a minimum wage imposition
creates unemployment, and
b. for a monopsony in the labour market, a minimum way imposition may
increase employment. In addition to graphs, provide the intuition for your
answers.
Reading for this question
The reading for this question is in Chapter 7 of the subject guide.
Approaching the question
The answers given here varied considerably in quality. It was clear
that several candidates had tried to memorise the analysis, including
the graphs, without understanding it and it showed. Others gave good
explanations in their answers.
Question 9
Explain what is meant by moral hazard and adverse selection. What problems do
moral hazard and adverse selection create?
Reading for this question
The reading for this question is in Chapter 4.
Approaching the question
This question was very popular. Many candidates in 2014 appear to have
understood the concept of adverse selection but only a few understood
moral hazard and were able to distinguish it from adverse selection.
Question 10
a. Explain the efficiency wage model including the minimum cost
implementation problem.
b. Give an efficiency wage based explanation for rising wage profiles.
Reading for this question
The reading for this question is in Chapter 8 of the subject guide.
Approaching the question
Very few candidates chose this question in 2014. Those who did answered
the question by attempting to reproduce the analysis in the subject guide.
The minimum cost implementation problem was not understood by many
of the candidates as was clear from the imprecise wording. A good answer
would have explained the parameters of the model in some detail and
would have given some plausible examples. Applying the efficiency wage
model to rising wage profiles was done well by and large.
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Examiners’ commentaries 2014
Examiners’ commentaries 2014
MN3028 Managerial economics
Important note
This commentary reflects the examination and assessment arrangements
for this course in the academic year 2013–14. 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 (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
Candidates should answer SIX of the following TEN questions: FOUR
from Section A (12.5 marks each) and TWO from Section B (25 marks
each). Candidates are strongly advised to divide their time
appropriately.
Section A
Answer all four questions from this section (12.5 marks each).
Question 1
In the last stage of the Golden Balls TV show, two contestants independently and
simultaneously choose ‘Steal’ or ‘Split’. If both choose Steal, both get nothing.
If both choose Split, each gets half of the jackpot. If one chooses Steal and the
other Split, the one that chooses Steal gets the entire jackpot and the one that
chooses Split gets nothing. Write down the normal form for this game and find
the Nash equilibria in pure strategies.
Reading for this question
The reading for this question is in Chapter 2 of the subject guide.
Approaching the question
Steal
Split
Steal
0,0
1,0
Split
0,1
0.5,0.5
All strategy combinations apart from (Split, Split) are Nash equilibria.
A simple question but amazingly effective in discriminating between
scripts. Most candidates in 2014 got the normal form right though some
insisted on displaying the extensive form. You must answer the question!
Very few candidates were able to identify all Nash equilibria.
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MN3028 Managerial economics
Question 2
Firm D is a dominant price-setting firm. It has zero fixed costs and marginal
costs of 1. There are also a number of price taking fringe firms supplying the
same market. The total quantity supplied by these fringe firms is given by q = 3p
where p is the unit price. Total demand is given by Q = 100-p. How much should
firm D produce to maximise its profit? How much will the fringe firms produce?
What is the resulting price?
Reading for this question
The reading for this question is in Chapter 11 of the subject guide.
Approaching the question
The demand faced by firm D equals QD=100 – p – 3p = 100 – 4p. Inverse
demand is p = (100 – QD)/4 and hence MRD = 25 – QD/2. Equating firm
D’s marginal revenue and marginal cost yields QD = 48 and p = 13. The
fringe firms produce 39 units. To check our calculations we can substitute
total output in market demand and find 48 + 39 = 100 – 13.
Most candidates in 2014 knew that profit optimisation requires marginal
revenue to be equal to marginal cost and the majority of candidates
could more or less carry out the calculations. However, some candidates
couldn’t correctly calculate marginal revenue. It is very important that
you understand the concept of marginal revenue i.e. it is the derivative of
revenue with respect to quantity.
Question 3
A firm has production function q = K1/2L1/2 where q is output, K is capital and L is
labour. The firm faces input prices r and w for capital and labour respectively.
Reading for this question
The reading for this question is in Chapter 7 of the subject guide.
Approaching the question
a. Carefully state the firm’s cost minimisation problem for a given quantity q
and find the marginal products of capital and labour.
The firm wants to minimise expenditure on inputs, i.e. rK + wL, subject
to producing output q= K1/2L1/2.
MPK = 1/2K-1/2L1/2
MPL = 1/2K1/2L-1/2
b. Derive the conditional input demand for capital.
At the cost minimum in (a), the ratio of marginal products equals the
input price ratio, i.e.
L/K = r/w or L = rK/w. Substituting this in the production function
gives
q = K1/2(rK/w)1/2 = K(r/w)1/2 so that the conditional demand for
capital equals K(q) = q(w/r)1/2.
Most candidates in 2014 could correctly calculate the marginal
products and many of them could then derive the conditional input
demand for capital. A small number of candidates didn’t calculate
correctly but their general approach was correct. However, many
candidates didn’t state the cost minimisation problem at all, although
they had no problem doing the calculations.
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Examiners’ commentaries 2014
Question 4
Consider the following bargaining game. Player 1 offers the division of a cake of
size 1 to player 2. Player 2 can either accept or reject. If he accepts, the proposed
division is realised. If player 2 rejects, then player 1 can once more propose a
division which player 2 can accept or reject. If player 2 rejects this second offer,
he can propose a division to player 1 and player 1 can accept or reject. If player
1 rejects, player 2 can make another offer. If player 1 rejects this second offer,
the game ends and both players get nothing. Both players discount their payoffs
after each rejection with discount factor δ (0 < δ < 1). What is the subgame
perfect equilibrium of this game?
Reading for this question
The reading for this question is in Chapter 3 of the subject guide.
Approaching the question
See game tree below.
At the final decision node, player 1 will accept any  and therefore player
2 will set  = 1.
At player 1’s next to last decision node, he has a choice now of 0 or
2(1 – z). Player 1 sets z such as to make player 2 indifferent, i.e. z = 1.
At player 2’s second decision node, he has a choice now of 2 or (1 – y).
Player 1 sets y such as to make player 2 indifferent, i.e. y = 1 – .
At player 2’s first decision node, he has a choice now of (1 – (1 – )) or
1 – x. Player 1 sets x such as to make player 2 indifferent, i.e. x = 1 – 2.
Candidates answered this question reasonably well in 2014 and it was
clear that they had prepared the topic. A common mistake by candidates
was that they did not realise that each player could offer twice instead of
only once as in the standard model. You must read the question carefully!
Surprisingly many candidates made small (but significant) calculation
mistakes so they came up with a similar but still incorrect solution.
13
MN3028 Managerial economics
(x, 1 – x)
Offer to keep x
Accept
1
2
δy, δ(1–y))
Accept
Reject
Offer to keep y
1
2
Offer to keep z
1
Accept
Reject
δ2(1–z)δ2z)
2
Offer to keep α
1
Accept
Reject
(0, 0)
(δ3(1– α), δ3α)
Section B
Answer two questions from this section (25 marks each).
Question 5
The LSE Senior Common Room holds an annual auction for the sale of periodicals
and newspapers. The auction has an unusual format in that bidders can either
submit a sealed bid or show up at an English auction at a specified time when
all sealed bids have been received. The English auction starts at the highest
submitted bid. Clearly, given the auction format, it is not rational for a bidder
who plans to be present at the English auction to submit a sealed bid (the
only effect this could have would be to potentially raise the starting bid in the
English auction). Assume there are n bidders and n1 of these submit a sealed bid,
the others show up at the auction. Bidders have independently drawn valuations
from a uniform distribution on [0,1].
Reading for this question
The reading for this question is in Chapter 5 of the subject guide.
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Examiners’ commentaries 2014
Approaching the question
a. Assume the highest sealed bid is b. What are the posssible outcomes at the
end of the English auction?
If there are no further bids in the English auction, the periodical is sold
at b. If there is one bid in the English auction, it is sold at b+. If there is
more than 1 bid in the English auction, the periodical is sold at the second
highest valuation of bidders in the English auction.
b. Show that all participants in the sealed bid auction bidding a fraction (n-1)/n
of their valuation is a Nash equilibrium. (Note: do not give the analysis for
standard first price sealed bid auctions or you will get zero marks for this
part of the question).
Let’s consider the bidding strategy of bidder 1 in the sealed bid auction.
Assume all other sealed bid auction bidders bid a fraction of their
valuation, i.e. bi = fvi where 0<f<1. In order for bidder 1 to win, he has to
beat all the other sealed bids and all participants in the English auction
should have valuations below bi. Hence, the probability that bidder 1 wins
is given by
b 
  1 
 f 
n1 1
b1n  n1
The expected gain to bidder 1 is (v1 – b1) multiplied by the above
probability. Optimising expected gain yields b1= v(n – 1)/n.
c. In this auction format, does the bidder with the highest valuation always
win? Explain your answer.
No. It is possible for a bidder in the English auction to win although his
valuation is lower than that of the bidder with the highest sealed bid, i.e.
when (n – 1)vs /n < vw< vs, where vs is the highest valuation among sealed
bid bidders and vw is the highest valuation among English auction bidders.
d. What is the probability that a participant in the sealed bid auction with
valuation v wins?
The probability of winning for a sealed bid participant with valuation v
equals
v
n1 1
 (n  1)v 
 n 
n  n1
 n 1


 n 
n  n1
v n 1
This probability increases in v and increases in n1 (given n).
e. What is the expected gain for a sealed bid participant with valuation v?
The expected gain for a sealed bid bidder equals v – b = v – (n – 1)
v/n = v/n multiplied by the above probability:
vn  n 1


n  n 
n  n1
The expected gain is increasing in v and increasing in n1 (given n).
f. What is the probability that an English auction participant with valuation v
wins? Compare this result to your answer to (d).
The probability of winning for an English auction participant with
valuation v is the probability that all sealed bids are below v and all other
valuations in the English auction are below v:
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MN3028 Managerial economics
 n  1 

 iinsealedbid P 
vi  v   jinEnglishauction P(v j  v)
 n 

Case 1: nv/(n – 1) < 1
In this case the above expression equals
This probability is increasing in v and increasing in n1 (given n).
Case 2: nv/(n – 1)>1
In this case the probability of winning equals
v n n1 1
This probability is increasing in v and increasing in n1 (given n).
In both cases the probability of winning given a valuation v is higher in the
English auction than in the sealed bid auction.
Question 6
The London School of Management wants to devise a scheme which allocates
a given number of lectures and classes fairly to its faculty. Teachers have
utility functions of the following form: U(L,C) = K – L – wC, where K and w are
constants, L is the number of lecture hours per week and C is the number of
class hours per week. The teaching point scheme assigns points to lectures and
classes, a class gets 1 point and a lecture gets z points, and each teacher has a
target of P points.
Reading for this question
The reading for this question is in Chapter 6 of the subject guide.
Approaching the question
a. Show that teachers will want to do only classes (and no lectures) or only
lectures (and no classes) unless wz = 1.
Teachers maximise U(L,C) subject to zL + C = P. The indifference curves
and the budget constraint are linear. The only possible optima are
corner solutions unless the budget constraint has the same slope as the
indifference curves, i.e. 1/w = z.
b. Assume z = 1/w. To find w, we ask the following question: ‘Teaching load A
consists of 3 lecture hours per week (and no classes) and teaching load B
consists of x class hours per week (and no lectures). What is the maximum x
for which you would prefer B to A? ‘ Show how the answer to this question
can be used to determine w. What is w? What is z? (Note that we are assuming
that people answer truthfully which in practice could be assured by making the
answers binding e.g. if someone says they would prefer to teach 30 class hours
rather than 3 lecture hours they could be told to teach 30 class hours.)
If a teacher answers x then he is indifferent between (L,C) = (3,0) and
(L,C) = (0,x).
Hence, U(3,0) = K – 3 = U(0,x)=K – wx so that w=3/x and thus z = x/3.
Very few candidates realised that the indifference curves are linear.
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Examiners’ commentaries 2014
Question 7
The manager of a large pharmaceutical company has to decide whether to invest
in the development of a new drug. The first stage of the drug development costs
$2 million and will result in a drug prototype with 10% probability (with 90%
probability the first stage will be unsuccessful and the investment is lost). If the
first stage is successful the manager can either sell the prototype to another
company or enter into clinical trials and if they are successful bring the final
drug to market. If the manager decides to sell to another company he knows
that he will receive either a price of $32 million or a price of $12 million, with
both prices equally likely. If the manager decides to enter clinical trials this will
cost another $2 million. The trials will be successful with probability 50%. In
that case the drug can be brought to the market where it generates a profit of
$44 million. If the clinical trials are unsuccessful the prototype is worthless to
everybody.
Reading for this question
The reading for this question is in Chapter 1 of the subject guide.
Approaching the question
a. Draw the decision tree. What should the (risk-neutral) manager do?
Invest 1st stage
prototype
0.2
0.2
No prototype
20
sell
0.1
0.9
-2
Clinical trials
Don’t
invest
18
0
0.5
-4
20
1/2
1/2
0.5
10
30
40
The payoffs in the decision tree above are in $m. The manager should
invest in the first stage and sell if there is a prototype.
b. Assume that if there is a prototype a market expert can predict with certainty
the price another company is willing to pay for the drug prototype (prior to
clinical trials and before the decision whether to sell the prototype is made).
How much would the manager be willing to pay for that advice?
At the point where there is a prototype, if the manager knows the price
is 32 he would sell and end up with 30; if the manager knows the price
is 12 he would not sell and end up (in EV) with 18. Hence, with perfect
information the manager would have 30(1/2) + 18(1/2) = 24. Without
perfect information he gets 20. Therefore he should be willing to pay up to
4 for the advice.
c. Ignore part (b) for this question. Assume that another expert can predict
whether the first stage of the drug development will be successful or not.
What should the expert charge for her advice?
If success is predicted, investment should go ahead and the expected
payoff is 20. If failure is predicted, investment should not go ahead and
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MN3028 Managerial economics
the payoff is zero. Hence, with perfect information the expected payoff is
20(0.1) + 0(0.9) = 2. Without perfect information the expected payoff is
0.2. Hence the expert can charge up to 1.8 for her advice.
A huge proportion of candidates chose this question in 2014, presumably
because decision analysis is a topic they have all studied and the question
did not look especially complicated. Many candidates did fairly well in
part (a). Some puzzlingly got the decision tree right but not the correct
decisions, and others only specified what to do at the first decision but not
at the second. Parts (b) and (c) were answered very poorly. Candidates
obviously had little idea of the problem they were required to solve and
calculated differences between two outcomes that were not clearly related
to the question. Consequently, very few candidates got full marks for this
question, and it seemed that few actually spent the allotted 45 minutes on
it. Many candidates failed to check their answers to make sure they made
sense.
Question 8
A monopolist book seller sells in two markets. Resale is impossible. Assume
constant marginal costs and linear demand in both markets.
a. Show, using graphs, how the monopolist determines prices in both markets.
b. Now assume resale is possible, i.e. it is possible to buy in the cheaper market
and resell, at a unit cost c, in the more expensive market. Explain how the
monopolist will adjust to this new scenario.
Reading for this question
The reading for this question is in Chapter 10 of the subject guide.
Approaching the question
Candidates vaguely remembered the graphs in the subject guide but most
made mistakes which showed they had not understood the material.
For (a), the graphs need to indicate that in each market marginal revenue
equals marginal cost.
For (b), candidates have to realise that if the seller is going to operate in
both markets then the price difference cannot exceed c.
Question 9
a. Explain the concepts of moral hazard and adverse selection.
b. Discuss how moral hazard can create a problem in the insurance market.
c. Discuss how adverse selection can be a problem when a firm introduces a
voluntary redundancy scheme.
Reading for this question
The reading for this question is in Chapter 4 of the subject guide.
Approaching the question
This question was very popular in 2014. The vast majority of candidates
appear to understand the concept of adverse selection. However, only
a small number of candidates understand moral hazard and many
candidates confused the concept with adverse selection. Very few
candidates could apply their knowledge to the context of a voluntary
redundancy scheme. In such a scheme, the most productive workers (those
who can find new jobs easily) are more likely to take advantage of the
offer of voluntary redundancy.
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Examiners’ commentaries 2014
Question 10
Suppose that a firm is a monopoly in the output market and a monopsony in the
input market. There is only one input. Explain, using graphs and equations, how
the firm determines its input demand and its output level.
Reading for this question
The reading for this question is in Chapter 7 of the subject guide.
Approaching the question
Very few candidates in 2014 gave an answer which analysed a firm which
is both a monopoly and a monopsony although this is clearly what is
required. The best answers demonstrated understanding of the concepts
involved and gave clear and thorough explanations and graphs. A good
starting point for this question is to write out the firm’s profit function and
then find the optimal input level.
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