micro exam

BEE2022

UNIVERSITY OF EXETER

BUSINESS SCHOOL

April 2013

Intermediate MicroeconomicsMOCK EXAM

(Module convenor: Dieter Balkenborg, Todd Kaplan)

Duration : THREE HOURS

Please fill in your student ID number:

and your candidate number:

Use a single answer book for working out your detailed answers before giving your sum-

mary answers in this handout.

Materials to be collected after this exam: This question handout, answer book.

Do not forget to return this handout. Otherwise your exam will be invalid!Approved calculators are permitted.

This is a closed note examination.

Full work must be shown on your script. Please write legibly.

1

Question 1 : (4+3 marks) (i) George has a utility function of x1+3x2. The price of

good 1 is 1 and the price of good 2 is 2. If George consumes 2 of good 2 how much does he

consume of good 1? If there isn’t enough information to answer, then write N.E.I. (Not

Enough Information) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) Marc consumes 2 pizzas and 4 beers. He wins 20 pounds in the lottery and now

consumes 3 pizzas and 6 beers. Which type of preferences April he have?

a Cobb-Douglas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

b Perfect Complements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

c Quasilinear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

d More than one of the above. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

e None of the above. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Question 2 : (2+2+2+2 marks) Which of the following preferences can be repre-

sented by a utility function? Check which ones.

(i) Comparing jobs based upon which is better in the majority of 3 criteria.. . . . . . . . .

(ii) Dieter compares two DVDs based upon the alphabetical order of their titles. He likesthe one that alphabetically comes earlier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(iii) Bradley who likes water and hates work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(iv) Tim likes fruit, but does not care about which type of fruit he consumes.. . . . . . .

Question 3 : (2+2 marks) True or False?

(i) All Necessities are Normal goods.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TRUE/FALSE

(ii) All Luxury goods are inferior.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TRUE/FALSE

Do not forget to return this handout. Otherwise your exam will be invalid!(BEE2022 April 2012) (Please turn over.)

2

Question 4 : (3 marks) Preferences with utility represented by x3axb2 can also be

represented by a utility function x1−γ1 xγ2 where γ equals

a b/(a+ b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

b a/(a+ b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

c a/(3a+ b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

d b/(3a+ b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

e 3b/(a+ 3b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Question 5 : (2+2 marks) Sam has utility u(x) =√x. There is a gamble of 50%

chance of receiving 0 and 50% chance of receiving 4.

(i) What is the certainty equivalence of this gamble? . . . . . . . . . . . . . . . .

(ii) What is the risk premium?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Question 6 : (4 marks) Chris that “falls” for the Alais paradox when given the

following options: w is 80% chance of $4000, x is $3000 for sure, y is 20% chance of $4000

and z is 25% chance of $3000.

a Chris would choose x over w and y over z. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

b Chris would choose x over w and z over y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

c. Chris would choose w over x and y over z. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

d. Chris would choose w over x and z over y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

e. None of the Above. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


3

Question 7 : (1+4 marks) There is a production function of√` · k

(i) What is the returns to scale?

a Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

b Decreasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

c. Increasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

d. It changes from one to another. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) What is `(w, r, x)? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


4

Question 8 (3 marks) : (Mark your answer with “√”.)

A two-part tariff April be used by a company to:

a. Capture all the surplus of homogeneous consumers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

b. Discriminate between high demand consumers and low demand consumers. . . . . . .

c. Capture rents from a franchise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

d. All of the above. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

e. None of the above. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Question 9 (2 + 2 marks) : The university has decided that only special calculators

can be used during the exam. The Student Guild has a monopoly on the calculators

that are sold before and not during the exam. Ari and Jodi are both students taking the

microeconomics exam. Ari feels that he can get by with only one calculator. Jodi feels

that a second calculator would be helpful in case the first calculator breaks down. The

following table shows their valuations (note the number under the heading “2 calculators”

means the valuation for two calculators rather than for the 2nd calculator). Assume it

costs them 5 pounds per calculator. (Assume if indifferent in valuation terms to buying

or not, Jodi and Ari buy.)1 calculator 2 calculators

Ari £ 10 £ 10

Jodi £ 30 £ 40(i) (Fill in the numbers.) If the Guild could not tell who is who, but can charge

different prices for different quantities what would they charge?

Price for 1: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Price for 2: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) (Mark your answer with “√”.) If the Guild could tell who is who, but must charge

a constant price per calculator, what would the profits be?

a. £ 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

b. £ 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

c. £ 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

d. £ 40. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

e. £ 50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


5

Question 10 (3 + 3 +3 marks) : Everstrong has developed a pill that tricks the body

into thinking it has spent two hours weight-training. It has no unintended side effects.

Only the US and UK have permitted its sale. Demand in the US is q = 500 − p and inthe UK is q = 200 − p. Note that q is in thousands and p is in pounds and answer is inthousands of pounds. The marginal cost of the pill is zero.

(i) What would Everstrong’s profits be assuming that the Americans will only buy pills

sold in America and English will only buy the English pills?

a. 61250 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

b. 62500. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

c. 71250 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

d. 72500. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

e. 85000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) What would Everstrong’s profits be assuming that it only decides to sell to Americans

and ignore the UK market?

a. 61250 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

b. 62500. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

c. 71250 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

d. 72500. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

e. 85000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(iii) What would Everstrong’s profits be assuming that the Americans can buy pills sold in

the UK and vice-versa and Everstrong considers selling to both the British and Americans

(at a price less than 200) or just sticking with Americans?

a. 61250 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

b. 62500. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

c. 71250 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

d. 72500. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

e. 85000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


6

Question 11 (7 marks) True or false? (Please encircle your answer.)

• If bidders are fully rational, then in a common-value, second-price auction, thewinner will never lose money.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TRUE/FALSE

• In a private-value auction, a bidder will always submit a higher bid under secondprice than under all pay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TRUE/FALSE

• In a first-price auction, it can be advantageous to submit multiple bids.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TRUE/FALSE

• The possibility of a winner’s curse helps seller revenue, even if buyers know this. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TRUE/FALSE

• In a private-value auction with two bidders, one should always bid half their value.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TRUE/FALSE

• Even under asymmetry, auctions always yield effi cient outcomes (the bidder withthe highest value wins). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TRUE/FALSE

• Because of revenue equivalence, having a minimum bid will not affect revenue in anauction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TRUE/FALSE


7

Question 12 : (3+3 marks) (Mark your answer with “√”.)

If the probability of winning in a first-price, private-value auction is Probwin(b) = 3b and

your value is 1/2, what should you bid?

a. 1/4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

b. 1/3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

c. 1/2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

d. 2/3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

e. 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

If the probability of winning in a second-price private-value auction is Probwin(b) = b/2

and your value is 1, what should you bid?

a. 1/4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

b. 1/3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

c. 1/2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

d. 2/3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

e. 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


8

Question 13 : (8 marks) Consider the following 2× 2game.

L R

3 0

T 9 0

0 6

B 0 6

Let (1− p)T + pB denote the strategy where player 1 plays B with probability p. Let

(1− q)T + qB denote the strategy where player 2 plays R with probability q. Which

of the following statements is correct? Write TRUE after the statements you considercorrect, FALSE after the staments you consider false.

a. (B,R) is the only Nash equilibrium of the game. . . . . . . . . . . . . . . . . . . .

b.(23T + 1

3B, 1

4L+ 3

4R)is a Nash equilibrium. . . . . . . . . . . . . . . . . . . . . . . . .

c. (T, L) and (B,R) are Nash equilibria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

d. The game has at most four Nash equilibria. . . . . . . . . . . . . . . . . . . . . . . . .


9

Question 14 : (1+2+5 marks) Consider the following game.

First, player 1 can decide between “F”, and “U”.

Then player 2 gets the move after observing the choice of player 1. She can decide between

playing “A”or “R”. If she chooses “R”both players get zero. Otherwise, both players

get 5 after “F”while player 1 gets 10 and player 2 gets zero after “U”.

(i) (2 marks) Draw the extensive form for this game on the graph paper provided.

(i) (3 marks) Draw the normal form.

(iii) (6 marks) Which of the following statements are correct? Write TRUE after the

statements you consider correct, FALSE after the staments you consider false.

a. (AF , RU) is a weakly dominated strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . .

b. (RF , AU) is a weakly dominated strategy . . . . . . . . . . . . . . . . . . . . . . . . . . .

c. (F, (AF , RU)) is a subgame perfect equilibrium . . . . . . . . . . . . . . . . . . . . .

d. (U, (AF , RU)) is a subgame perfect Nash equilibrium . . . . . . . . . . . . . . .

e.(12K + 1

2U,AF ,

12AU +

12RU

)is a subgame perfect Nash equilibrium .


10

Question 15 : (14 marks) Suppose that Tom and Jerry are the only sellers of designer

umbrellas, which consumers view as differentiated products. For simplicity, assume each

seller has constant marginal costs equal to zero. When Tom charges a price of pT and

Jerry charges a prices of pJ , consumers would buy a total of

qJ = 100− pJ + pT

umbrellas from Jerry and

qT = 100− pT + pJ

umbrellas from Tom.

To answer this question you need to calculate: i) the reaction curve, ii) the Nash

equilibrium of the simultanoeus price setting game, when both firms set their prices

simultaneously and independently, and iii) the Nash equilibrium of the Stackelberg-type

leadership gamel, where Tom can set his price first and then Jerry, having observed Tom’s

price, decides on his price.

Which of the following statements are correct? Write TRUE after the statements

you consider correct, FALSE after the staments you consider false.

a. Suppose Jerry knew that Tom is setting a price of 200. Then it is a profit maximizingbest reply of Jerry to set a price of 150. . . . . . . . . . . . . . . . . . . . . . . . . . .

b. The reaction curve is upward sloping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

c. Tom sets a price of 20 in the Nash equilibrium of the simultaneous price setting

game. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

d. Tom and Jerry set the same price in the Nash equilibrium of the simultaneous price

setting game. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

e. In the Nash equilibrium of Stackelberg-type leadership game, Tom makes a profit of

1200.98. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

f. In the Nash equilibrium of Stackelberg-type leadership game, Tom makes a higher

profit than Jerry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

g. In the Nash equilibrium of Stackelberg-type leadership game Tommakes a higher profitthan he would make in the simultaneous price setting game. . . . . .


11

Question 16 : (5 marks) Astrid’s utility function is UA(HA, CA) = HACA, Birgers

utility function is UB(HB, CB) = min [HB, CB] , where H denotes the amount of herring

and C the amount of cheese consumed. If Astrid’s initial endowment is no cheese and 20

units of herring and if Birger’s intial endowment is 9 units of chees and no herring, then,

where p is the competitive price for herring when the equilibrium price for cheese is nor-

malized to 1, demand equals supply in both markets. Which of the following statements

are correct?

a. 9/p+ 20/2p = 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

b. 9/20 = p. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

c. 4/20 = p.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

d. 9/ (p+ 1) + 10 = 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

e. min [20, 9] = p. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Do not forget to return this handout. Otherwise your exam will be invalid!(BEE2022 April 2012) (End of the exam paper.)

12

micro exam

Documents

weakly dominated strategy

buy pills sold

type leadership game

3a

utility function

nash equilibrium

nash equilibria

reaction curve