It is totally forbidden to talk at any stage during the ...static.luiss.it/hey/microeconomia/esami/new/09/me109_all.pdf · Answers to the questions on the examination paper should

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READ CAREFULLY THE RULES OF THIS EXAM

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the number of your traccia. Otherwise we cannot mark your answers.

RULES

1. It is forbidden to communicate with the other candidates. If you do so you will be expelled

from the examination session and your compito destroyed.

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expelled from the examination session.

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during the collection of the answer sheets.

It is totally forbidden to talk at any

stage during the examination.

LUISS MICROECONOMICS Appello di 15-01-2010 Appello n.9 Traccia n. 1

YOU HAVE 2 HOURS

QUESTIONS 1-4: Consider a market for a hypothetical good in which there are a number of buyers and sellers, each of which

wants to buy or sell one unit of the good. Assume that a buyer who is indifferent about buying always buys

and a seller who is indifferent about selling always sells. The reservation prices are given below, first for the

buyers and then for the sellers.

Buyers: 10, 8, 10, 7, 7. Sellers: 2, 7, 6, 4.

Question 1: What is the competitive equilibrium price (specify a range if more than one equilibrium price)?

� 8

� 7

� 6

� There is no competitive equilibrium

Question 2: What is the quantity exchanged in the competitive equilibrium?

� 5

� 2

� 4

� 3

Question 3: What price would the buyers choose if they could?

� 10

� 6

� 5

� 4

Question 4: What price would the sellers choose if they could?

� 4

� 9

� 10

� 7

QUESTIONS 5-7:

Consider, in an Edgeworth Box, exchange between two individuals, Individual A and Individual B, with

preferences as specified below, endowed with two goods, Good 1 and Good 2. (Consider only competitive

equilibrium in which at least one individual is better off compared to the initial position.)

Individual A has Perfect Complement preferences with parameter a = 2. Individual B has Perfect

Complement preferences with parameter a = 0.5. Total endowment of good 1 is 8 and that of good 2 is 6.

Individual A's endowment of good 1 is 3 and that of good 2 is 6.

Question 5: What is the competitive equilibrium price ratio?

� 0.75

� 1.00

� There is no equilibrium inside the box

� 3.00

Question 6: What is the quantity exchanged of good 1 to reach the competitive equilibrium?


� 6.00

� 0.00

� 3.33



� 0.00

� 0.50

� 0.67

QUESTIONS 8-9: In the next two questions you will be asked to consider an individual who has the following demands. You

will be asked to infer his or her preferences, which will be either Perfect Substitutes with parameter a,

Perfect Complements with parameter a, or Cobb-Douglas with parameter a.

With income 30.00 and at prices 1.00 and 2.00 the demands were 15.00 and 7.50. With income 20.00 and

at prices 2.00 and 0.50 the demands were 5.00 and 20.00. With income 20.00 and at prices 1.00 and 0.50

the demands were 10.00 and 20.00.

Question 8: What are the individual's preferences?

� Cobb-Douglas

� Perfect complements

� Perfect Substitutes

� There is not enough information

Question 9: What is the value of the parameter a?

� 2.00

� 1.25

� 0.50

� 0.25

QUESTIONS 10-11: In the next two questions you will be asked to consider a competive firm which has a cost function C(q) = a

+ b*q + c*q^2 where a, b and c are given below.

a = 20.0, b = 20.0, c = 1.0. Suppose that the price of the firm's output is 30.

Question 10: Determine the optimal output of the firm.

� 30.00

� 5.00

� 0.00

� 11.71

Question 11: What is the firm's profit?

� 0.00

� 5.00

� 351.25

� 150.00

QUESTIONS 12-13:

In the next two questions you will be asked to identify two points on the production possibility frontier in an

economy with two firms and two factors of production, the quantities of which are fixed.

Firm 1 has Perfect Complements technology with parameter a = 0.5. Firm 2 has Perfect Substitutes

technology with parameter a = 2. Total endowment of factor 1 is 6 and that of factor 2 is 8.

Question 12: Find the maximum output for firm 2 if firm 1 has an output of 0

� 10.00

� 11.00

� 9.50

� 0.00

Question 13: Find the maximum output of firm 1 if firm 2 has an output of 0.5

� 6.00

� 8.00

� 9.00

� 0.00

QUESTIONS 14-15:

In the next two questions you will be asked to consider an individual, taking decisions under conditions of

risk, with Expected Utility preferences and utility function u(x) = x^0.5 (that is, the utility of x is the square

root of x). Suppose the individual is faced with two lotteries P and Q as specified below. A lottery is denoted

by (a,b;p,1-p) and means that the outcome is a with probability p and b with probability 1-p.

The lotteries are: P = (16,25;0.25,0.75) Q = (4,4;0.75,0.25)

Question 14: Does the individual prefer P or Q?

� Q

� We cannot tell from the information given

� P

� The individual is indifferent

Question 15: What is the individual's certainty equivalent for P?

� 4

� 20.50

� 22.5625

� 22.75

QUESTIONS 16-17: In the next two questions you will be asked to consider a game played simultaneously, and without

communication between two players, 1 and 2, each of whom can choose one of two options A and B. The

payoffs to the two players are given below, the first for Player 1 and then for Player 2. The order of the

payoffs is AA, AB, BA, BB where XY indicates the outcome when Player 1 plays X and Player 2 plays Y.

Player 1: 1, 1, 3, 9. Player 2: 5, 4, 10, 2.

Question 16: Specify ALL the Nash Equilibria in pure strategies.

� BA

� BB

� There are none

� AB

Question 17: Specify ALL other outcomes (not a Nash Equilibrium) that Pareto dominate any of these.

� BA dominates BB

� There are none

� BA and BB dominate AA

� BB dominates BA

For every correct answer you get 2 marks. For every wrong answer 1 mark will be deducted.






RULES




















YOU HAVE 2 HOURS





Buyers: 4, 8, 5, 7, 6. Sellers: 7, 1, 3, 4, 6, 3.


� 3

� 6

� 4

� Any price between 4 and 5


� 5

� 6

� 7

� 4


� 6

� 4

� 2

� 3


� 6

� 4

� 3

� 5

QUESTIONS 5-7:





Complement preferences with parameter a = 1. Total endowment of good 1 is 10 and that of good 2 is 8.



� 0.50

� 1.00

� 2.00



� 4.00

� 5.00


� 2.00


� 1.00

� 2.00


� 3.00









� Cobb-Douglas




� 0.25

� 0.50

� 1.25

� 1.00





� 20.00

� 0.00

� 7.55

� 3.33


� 66.67

� 13.33

� 0.00

� 150.99

QUESTIONS 12-13:






� 13.00

� 12.00

� 0.00

� 7.50

Question 13: Find the maximum output of firm 1 if firm 2 has an output of 7

� 0.00

� 3.00

� 6.00

� 8.00

QUESTIONS 14-15:







� P



� Q


� 9.00

� 2.25

� 3.00

� 1.00





Player 1: 1, 10, 9, 1. Player 2: 5, 9, 3, 6.


� BA

� There are none

� AB

� AA


� BA and BB dominate AA

� BA dominates BB

� There are none

� BB dominates BA







RULES




















YOU HAVE 2 HOURS





Buyers: 4, 7, 7, 8, 5. Sellers: 4, 2, 1, 4.


� 3

� 5

� 6



� 4

� 5

� 3

� 1


� 2

� 4

� 3

� 7


� 5

� 7

� 8

� 6

QUESTIONS 5-7:








� 1.25

� 0.50

� 2.00

� 1.00


� 7.00

� 1.00

� 4.00

� 2.00


� 1.00

� 4.00

� 5.00

� 2.00










� Cobb-Douglas



� 1.50

� 1.00

� 0.50

� 2.00





� 40.00

� 6.67

� 13.82

� 0.00


� 552.63

� 113.33

� 0.00

� 266.67

QUESTIONS 12-13:




technology with parameter a = 0.5. Total endowment of factor 1 is 6 and that of factor 2 is 6.


� 9.00

� 2.50

� 0.00

� 10.00


� 2.00

� 0.50

� 3.00

� 0.00

QUESTIONS 14-15:








� Q


� P


� 3.0625

� 4.75

� 3.25

� 8.50





Player 1: 1, 10, 4, 4. Player 2: 5, 7, 9, 8.


� AB BA

� AB

� BA

� There are none


� There are none

� BB and AB dominate AA

� BB dominates AB

� AB dominates BB







RULES




















YOU HAVE 2 HOURS





Buyers: 4, 6, 10, 8, 4. Sellers: 2, 3, 6, 4, 5.


� 3

� 6


� 5


� 1

� 4

� 2

� 3


� 5

� 2

� 8

� 4


� 6

� 4

� 5

� 8

QUESTIONS 5-7:








� 2.50

� 0.50

� 1.00

� 0.00


� 0.00

� 6.00

� 1.00

� 6.50


� 0.00

� 6.00

� 1.00

� 0.50





at prices 2.00 and 2.00 the demands were 5.00 and 5.00. With income 20.00 and at prices 0.50 and 2.00 the

demands were 20.00 and 5.00.




� Cobb-Douglas



� 2.00

� 4.00

� 1.00

� 0.50





� 30.00

� 0.00

� 5.00

� 10.63


� 150.00

� 0.00

� 318.82

� 55.00

QUESTIONS 12-13:






� 12.00

� 4.00

� 0.00

� 7.00


� 8.00

� 3.20

� 0.00

� 1.00

QUESTIONS 14-15:







� P



� Q


� 14.25

� 14.0625

� 28

� 25





Player 1: 10, 9, 9, 5. Player 2: 6, 2, 2, 3.


� BB

� BA

� There are none

� AA


� AA dominates BB

� BB dominates AA

� AA and BB dominate AB

� There are none







RULES




















YOU HAVE 2 HOURS





Buyers: 4, 5, 5, 8, 10. Sellers: 6, 3, 3, 5, 5, 7, 2.


� 6

� 5

� 4

� There is no competitive equilibrium


� 3

� 6

� 4

� 5


� 5

� 4

� 8

� 3


� 7

� 5

� 8

� 3

QUESTIONS 5-7:




Individual A has Perfect Complement preferences with parameter a = 0.5. Individual B has Perfect





� 0.67

� 0.75

� 1.00


� 3.00

� 2.00

� 3.50



� 3.00

� 2.00


� 2.50









� Cobb-Douglas




� 0.50

� 1.25

� 1.00

� 0.75





� 30.00

� 0.00

� 30.33

� 15.00


� 450.00

� 0.00

� 215.00

� 909.89

QUESTIONS 12-13:






� 9.00

� 7.50

� 0.00

� 12.00


� 0.00

� 7.00

� 3.00

� 6.00

QUESTIONS 14-15:








� Q


� P


� 25

� 27

� 31

� 30.25





Player 1: 1, 9, 4, 8. Player 2: 6, 10, 7, 5.


� AA

� There are none

� BB

� AB BA


� There are none

� BB and AB dominate AA

� AB dominates BB

� BB dominates AB


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It is totally forbidden to talk at any stage during the ...static.luiss.it/hey/microeconomia/esami/new/09/me109_all.pdf · Answers to the questions on the examination paper should