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Examiners’ commentaries 2015

Examiners’ commentaries 2015 MN3028 Managerial economics

Important note

This commentary reflects the examination and assessment arrangements for this course in the academic year 2014–15. 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 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 completed the Essential reading and 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 applies, of course, if you find negative prices or quantities, or probabilities greater than one or less than zero. 1

MN3028 Managerial economics

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 that 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 2015

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. The Examiners’ commentaries suggest ways of addressing common problems and improving your performance. 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 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 each course. 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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MN3028 Managerial economics

Examiners’ commentaries 2015 MN3028 Managerial economics – Zone A

Important note

This commentary reflects the examination and assessment arrangements for this course in the academic year 2014–15. 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 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 SIX of the following TEN questions: all FOUR from Section A (12.5 marks each) and TWO from Section B (25 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.

Section A Answer all four questions from this section.

Question 1 A manufacturer grows oranges which are used to produce orange juice and orange marmalade. One orange gives 1 unit of orange juice AND 2 units of marmalade. Assume that the cost function of growing oranges is given by 2

C(q)=0.05 q

(and assume that there are no further costs of production).

Demand for orange juice is given by q = 25 – 50 p and demand for marmalade J

is given by q

M

= 100 – 50 p

M

J

where p and p J

M

denote the prices for orange juice

and marmalade respectively. How many oranges should the manufacturer grow and what prices should she set for marmalade and juice? Assume that disposal is free.

Reading for this question See subject guide, Chapter 10.

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Examiners’ commentaries 2015

Approaching the question Let’s start by calculating the marginal cost of an orange MC(q) = 0.1q We want to equate total marginal revenue (from juice and marmalade) to this marginal cost. Marginal revenue for juice equals MR(q) = ½ – q/25 which is positive for q < 25/2. Marginal revenue for marmalade (taking into account that each orange gives 2 units of marmalade) equals MR(2q) = 2 – 2q/25 which is positive for q < 25. So, as long as q < 25/2, total marginal revenue equals 2.5 – 3q/25. Setting this equal to marginal cost gives q = 125/11 which is less than 25/2 so that the total marginal revenue function above does apply. The manufacturer should produce 125/11 oranges. This will give 125/11 units of juice so that the price for juice is 0.27. The quantity of marmalade produced is 250/11 so that the price for marmalade is 0.045.

Question 2 For utility function U = x x 1

2

show that the consumer spends half his income on x

1

and half on x . 2

Reading for this question See subject guide, Chapter 6.

Approaching the question At the consumer optimum the ratio of marginal utilities equals the price ratio, i.e. x /x 2

1

= p /p 1

2

Hence p x 1

1

= p x , or, in words, the amount spent on each of the two 2

2

goods is identical and therefore has to be half of income.

Question 3 For production function f(x,y)=x+min(x,y), draw isoquants and calculate marginal products of inputs.

Reading for this question See subject guide, Chapter 7.

Approaching the question The production function is f(x,y) = 2x if x < y f(x,y) = x + y if x > y On an isoquant, production is constant, let’s say at level K. So, for x < y, we have x = K/2 and for x>y we have y = K-x. The isoquants therefore look like the bold line below.

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MN3028 Managerial economics

y

y =x

k

K/2

MP

x

K

x

= 2 if x < y and 1 if x > y

MP = 0 if x < y and 1 if x > y. y

Question 4 Consider the following game with 10 players. Each player is given $1. Each player then privately decides whether to keep the $1 or give it back. If at least 8 players give back their $1, all players are given an additional $2. Find a Nash equilibrium and explain your answer.

Reading for this question See subject guide, Chapter 2.

Approaching the question Eight players giving $1 back is a Nash equilibrium. Why? Consider a player who is one of the 8 giving $1 back. If he changes his strategy and keeps his $1 then, assuming no other player changes his strategy, he will be worse off as he would have $1 rather than $2. Now consider a player who is one of the 2 keeping their $1. Clearly this player would be worse off if he changed his strategy and gave back his $1 as he would then have $2 rather than $3. There is another Nash equilibrium where everyone keeps their $1. If everyone else keeps their $1 then you would be worse off giving yours back (you would have zero rather than $1).

Section B Answer two questions from this section.

Question 5 There are two firms producing the same product and sharing the same market. Market demand is given by Q(p)=1000–1000p. Each firm has constant marginal costs of 0.28. Firms are not constrained in the amount they can produce.

Reading for this question See subject guide, Chapter 11.

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Examiners’ commentaries 2015

Approaching the question a.

Find the Cournot output levels, price and profits.

The profit function for Firm1 is

∏

1

= [1–(

q

1

+

q

2

)/1000 – 0.28]

Set the derivative wrt q

1

1–(

q

1

/500 –

q

2

q

…

1

equal to zero:

/1000 – 0.28]

q

1

… (1)

We can now use symmetry and set q = q = q and solve for q. This gives q 1

2

= 240. At the Cournot equilibrium, both firms produce 240 units and the price is 1 – 480/1000 = 0.52. Profits are (0.52 – 0.28)240 = 57.6. b.

Find the Stackelberg output levels, price and profits.

Assuming Firm 2 is the leader, then we know from (1) that Firm 1 will set the following output level: q

1

= 360 – q /2 2

Taking this into account, Firm 2’s profit function is

∏

2

= (1 – 0.360 +

q

2

/2000 –

q

2

/1000 – 0.28)

q

2

Firm 2’s optimal output level is therefore q =360. Firm 1 produces 180 2

units. Price is 1 – (360 + 180)/1000 = 0.46. Profits are 180(0.46 – 0.28) = 32.4 and 64.8 for Firm 1 and Firm 2 respectively. c.

If the firms form a cartel, what is the cartel’s output level, price and profit? How is production shared between the firms?

A cartel would set output so that marginal revenue equals marginal cost: 1 – Q/500 = 0.28 or Q = 360. This makes the price 1 – 0.360 = 0.72 and total profit (0.72 – 0.28)360 = 158.4. Production can be divided in any way between the two firms as there are no fixed costs and the firms have identical marginal costs. d.

Find the Bertrand output levels, price and profits.

At the Bertrand equilibrium, price equals marginal cost (0.28). At this price demand is 720. Each firm produces 360 units and neither makes any profit.

Question 6 The manager of a book store must decide on the number of copies of a new best-seller to order. Suppose the best-seller’s estimated demand is P=24-Q, where P is the price in dollars and Q is quantity in hundreds of copies sold per month. The book store buys directly from the publisher who charges $12 per copy.

Reading for this question See subject guide, Chapter 9.

Approaching the question a.

How many copies should the manager order and what price should she charge?

Setting marginal revenue equal to marginal cost (i.e. 24 – 2Q = 12) gives Q = 6. The manager should order 600 copies and charge 24 – 6 = 18.

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MN3028 Managerial economics

b.

Now suppose shelf space is severely limited and stocking the best-seller will take shelf space away from other books. The manager estimates there is a $4 profit on the sale of a book stocked. (The best-seller takes up the same amount of shelf space as the typical book.) Now what are the optimal price and order quantity?

We have to add the $4 opportunity cost to the wholesale price to get the total cost per unit. Setting marginal revenue equal to the new marginal cost (i.e. 24 – 2Q = 16) gives Q = 4. Hence the manager should order 400 copies and charge 24 – 4 = 20. c.

After receiving the order of best-sellers in part b) the manager is disappointed to find that sales of the best-seller are considerably lower than predicted. Actual demand is P=18-2Q. The manager is now considering returning some or all of the best-sellers to the publisher who is obligated to refund $6 for every copy returned. How many (if any) copies should be returned and how many should be sold and at what price?

The manager now has a stock of 400 (Q = 4). Suppose she keeps x (hundred) copies and returns 4 – x. Her profit would then be (we ignore the sunk cost of buying the stock) (18 – 2x)x + (6 + 4)(4 – x). The first term is the revenue from sales and the second term is the refund plus profit from other books which is now made due to the freed up space. Optimising this gives x = 2. The manager should keep 200 copies and return the other 200 copies.

Question 7 Consider a standard private cost first price sealed bid procurement auction with n bidders whose costs are independently and uniformly distributed on [0,30].

Reading for this question See subject guide, Chapter 5.

Approaching the question a.

Find a Nash equilibrium. (Hint: Start by assuming that all bidders but one use a linear bidding strategy.)

Assume bidder i (i = 2,…,n) uses a linear bidding strategy, i.e. b = x + yc . i

Consider bidder 1’s response. Bidder 1 gets b he loses. He wins if b

1

The probability that b

1

1

– c

1

if he wins and nothing if

is the lowest bid. is the lowest bid is

Prob (b < x + yc )*Prob(b < x + yc )*…= 1

2

Prob(c >(b 2

3



1

n–1





3

– x)/y)* Prob(c > (b – x)/y)*…=

1

30 – b1 – x y

30





1

Maximising expected profit, i.e. the above expression multiplied by – c ) gives 1

b1 =

8

 

n–1 n







1



(b

c1 +

30y + x n

i

Examiners’ commentaries 2015

This represents the same linear bidding strategy as for the other bidders if x=(30y + x)/n and y = (n – 1)/n or when x = 30/n and y = (n – 1)/n. There is therefore a Nash equilibrium with bidding strategies b = 30/n+c i

i

(n – 1)/n. b.

Now suppose there are 2 bidders and c =10 and c =20 and these costs 1

2

are common knowledge. To encourage participation by both bidders, the government will give a payoff of 1 to the firm which loses the bid. Find a Nash equilibrium.

Suppose bidder 1 bids 20 – Against b

1

= 20 –

ε and bidder 2 bids 20.

ε, bidder 2 cannot do better than bidding 20.

Against b = 20, bidder 1 cannot do better than bidding 20 – 2

ε.

Hence we have a Nash equilibrium. c.

For the setup in b) suppose the government announces that it will award the contract to Firm 2 if its bid is not more than 10 higher than Firm 1’s bid. Find a Nash equilibrium.

If bidder 1 bids 10 then the optimal response for bidder 2 is to bid 20. If bidder 2 bids 20 then the best response for bidder 1 is to bid at least 10. Hence b = 10 and b = 20 is a Nash equilibrium. 1

2

Question 8 a.

Explain how adverse selection and moral hazard can affect the insurance market.

b.

Now assume that due to regulation only a sin...