It is totally forbidden to talk at any stage during the...
Transcript of It is totally forbidden to talk at any stage during the...
DO NOT LOOK AT THE EXAMINATION PAPER
UNTIL YOU ARE TOLD TO DO SO
READ CAREFULLY THE RULES OF THIS EXAM
The first thing that you should do is fill in the oval corresponding to
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.
2. Any student discovered using forbidden material (books, notes etc.) will be immediately
expelled from the examination session.
3. Students who wish to talk to one of the academic staff should raise their hand.
4. The academic staff will not discuss any points concerning the answers to the examination.
5. Answers to the questions on the examination paper should be indicated on the answer sheet
by filling in the appropriate circle, as indicated below.
6. Your matriculation number should be indicated on the answer sheet by filling in the
appropriate circles.
8. Students cannot leave the examination room in the final ten minutes of the examination.
9. When the academic staff announce the end of the examination, students should stop writing
immediately. Those who continue to write after this point will have their answer sheets
destroyed. 10. When the academic staff announce the end of the examination period, all the answer sheets
should be passed along the row to the student at the end of the row. Students should not talk
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?
� There is no equilibrium inside the box
� 6.00
� 0.00
� 3.33
Question 7: What is the quantity exchanged of good 2 to reach the competitive equilibrium?
� There is no equilibrium inside the box
� 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.
DO NOT LOOK AT THE EXAMINATION PAPER
UNTIL YOU ARE TOLD TO DO SO
READ CAREFULLY THE RULES OF THIS EXAM
The first thing that you should do is fill in the oval corresponding to
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.
2. Any student discovered using forbidden material (books, notes etc.) will be immediately
expelled from the examination session.
3. Students who wish to talk to one of the academic staff should raise their hand.
4. The academic staff will not discuss any points concerning the answers to the examination.
5. Answers to the questions on the examination paper should be indicated on the answer sheet
by filling in the appropriate circle, as indicated below.
6. Your matriculation number should be indicated on the answer sheet by filling in the
appropriate circles.
8. Students cannot leave the examination room in the final ten minutes of the examination.
9. When the academic staff announce the end of the examination, students should stop writing
immediately. Those who continue to write after this point will have their answer sheets
destroyed. 10. When the academic staff announce the end of the examination period, all the answer sheets
should be passed along the row to the student at the end of the row. Students should not talk
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. 2
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: 4, 8, 5, 7, 6. Sellers: 7, 1, 3, 4, 6, 3.
Question 1: What is the competitive equilibrium price (specify a range if more than one equilibrium price)?
� 3
� 6
� 4
� Any price between 4 and 5
Question 2: What is the quantity exchanged in the competitive equilibrium?
� 5
� 6
� 7
� 4
Question 3: What price would the buyers choose if they could?
� 6
� 4
� 2
� 3
Question 4: What price would the sellers choose if they could?
� 6
� 4
� 3
� 5
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 = 1. Total endowment of good 1 is 10 and that of good 2 is 8.
Individual A's endowment of good 1 is 5 and that of good 2 is 3.
Question 5: What is the competitive equilibrium price ratio?
� 0.50
� 1.00
� 2.00
� There is no equilibrium inside the box
Question 6: What is the quantity exchanged of good 1 to reach the competitive equilibrium?
� 4.00
� 5.00
� There is no equilibrium inside the box
� 2.00
Question 7: What is the quantity exchanged of good 2 to reach the competitive equilibrium?
� 1.00
� 2.00
� There is no equilibrium inside the box
� 3.00
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 20.00 and at prices 1.00 and 1.00 the demands were 10.00 and 10.00. With income 30.00 and
at prices 2.00 and 0.50 the demands were 7.50 and 30.00. With income 20.00 and at prices 0.50 and 0.50
the demands were 20.00 and 20.00.
Question 8: What are the individual's preferences?
� There is not enough information
� Cobb-Douglas
� Perfect complements
� Perfect Substitutes
Question 9: What is the value of the parameter a?
� 0.25
� 0.50
� 1.25
� 1.00
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 = 0.0, c = 3.0. Suppose that the price of the firm's output is 20.
Question 10: Determine the optimal output of the firm.
� 20.00
� 0.00
� 7.55
� 3.33
Question 11: What is the firm's profit?
� 66.67
� 13.33
� 0.00
� 150.99
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 = 1. Total endowment of factor 1 is 8 and that of factor 2 is 8.
Question 12: Find the maximum output for firm 2 if firm 1 has an output of 2
� 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:
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 = (9,1;0.25,0.75) Q = (25,9;0.75,0.25)
Question 14: Does the individual prefer P or Q?
� P
� We cannot tell from the information given
� The individual is indifferent
� Q
Question 15: What is the individual's certainty equivalent for P?
� 9.00
� 2.25
� 3.00
� 1.00
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, 10, 9, 1. Player 2: 5, 9, 3, 6.
Question 16: Specify ALL the Nash Equilibria in pure strategies.
� BA
� There are none
� AB
� AA
Question 17: Specify ALL other outcomes (not a Nash Equilibrium) that Pareto dominate any of these.
� BA and BB dominate AA
� BA dominates BB
� There are none
� BB dominates BA
For every correct answer you get 2 marks. For every wrong answer 1 mark will be deducted.
DO NOT LOOK AT THE EXAMINATION PAPER
UNTIL YOU ARE TOLD TO DO SO
READ CAREFULLY THE RULES OF THIS EXAM
The first thing that you should do is fill in the oval corresponding to
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.
2. Any student discovered using forbidden material (books, notes etc.) will be immediately
expelled from the examination session.
3. Students who wish to talk to one of the academic staff should raise their hand.
4. The academic staff will not discuss any points concerning the answers to the examination.
5. Answers to the questions on the examination paper should be indicated on the answer sheet
by filling in the appropriate circle, as indicated below.
6. Your matriculation number should be indicated on the answer sheet by filling in the
appropriate circles.
8. Students cannot leave the examination room in the final ten minutes of the examination.
9. When the academic staff announce the end of the examination, students should stop writing
immediately. Those who continue to write after this point will have their answer sheets
destroyed. 10. When the academic staff announce the end of the examination period, all the answer sheets
should be passed along the row to the student at the end of the row. Students should not talk
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. 3
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: 4, 7, 7, 8, 5. Sellers: 4, 2, 1, 4.
Question 1: What is the competitive equilibrium price (specify a range if more than one equilibrium price)?
� 3
� 5
� 6
� Any price between 4 and 5
Question 2: What is the quantity exchanged in the competitive equilibrium?
� 4
� 5
� 3
� 1
Question 3: What price would the buyers choose if they could?
� 2
� 4
� 3
� 7
Question 4: What price would the sellers choose if they could?
� 5
� 7
� 8
� 6
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 = 1. Total endowment of good 1 is 8 and that of good 2 is 10.
Individual A's endowment of good 1 is 1 and that of good 2 is 6.
Question 5: What is the competitive equilibrium price ratio?
� 1.25
� 0.50
� 2.00
� 1.00
Question 6: What is the quantity exchanged of good 1 to reach the competitive equilibrium?
� 7.00
� 1.00
� 4.00
� 2.00
Question 7: What is the quantity exchanged of good 2 to reach the competitive equilibrium?
� 1.00
� 4.00
� 5.00
� 2.00
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 0.50 the demands were 15.00 and 30.00. With income 30.00 and
at prices 1.00 and 1.00 the demands were 15.00 and 15.00. With income 20.00 and at prices 1.00 and 2.00
the demands were 10.00 and 5.00.
Question 8: What are the individual's preferences?
� There is not enough information
� Perfect complements
� Cobb-Douglas
� Perfect Substitutes
Question 9: What is the value of the parameter a?
� 1.50
� 1.00
� 0.50
� 2.00
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 = 0.0, c = 3.0. Suppose that the price of the firm's output is 40.
Question 10: Determine the optimal output of the firm.
� 40.00
� 6.67
� 13.82
� 0.00
Question 11: What is the firm's profit?
� 552.63
� 113.33
� 0.00
� 266.67
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 = 0.5. Total endowment of factor 1 is 6 and that of factor 2 is 6.
Question 12: Find the maximum output for firm 2 if firm 1 has an output of 4
� 9.00
� 2.50
� 0.00
� 10.00
Question 13: Find the maximum output of firm 1 if firm 2 has an output of 14
� 2.00
� 0.50
� 3.00
� 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 = (16,1;0.25,0.75) Q = (4,1;0.75,0.25)
Question 14: Does the individual prefer P or Q?
� We cannot tell from the information given
� Q
� The individual is indifferent
� P
Question 15: What is the individual's certainty equivalent for P?
� 3.0625
� 4.75
� 3.25
� 8.50
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, 10, 4, 4. Player 2: 5, 7, 9, 8.
Question 16: Specify ALL the Nash Equilibria in pure strategies.
� AB BA
� AB
� BA
� There are none
Question 17: Specify ALL other outcomes (not a Nash Equilibrium) that Pareto dominate any of these.
� There are none
� BB and AB dominate AA
� BB dominates AB
� AB dominates BB
For every correct answer you get 2 marks. For every wrong answer 1 mark will be deducted.
DO NOT LOOK AT THE EXAMINATION PAPER
UNTIL YOU ARE TOLD TO DO SO
READ CAREFULLY THE RULES OF THIS EXAM
The first thing that you should do is fill in the oval corresponding to
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.
2. Any student discovered using forbidden material (books, notes etc.) will be immediately
expelled from the examination session.
3. Students who wish to talk to one of the academic staff should raise their hand.
4. The academic staff will not discuss any points concerning the answers to the examination.
5. Answers to the questions on the examination paper should be indicated on the answer sheet
by filling in the appropriate circle, as indicated below.
6. Your matriculation number should be indicated on the answer sheet by filling in the
appropriate circles.
8. Students cannot leave the examination room in the final ten minutes of the examination.
9. When the academic staff announce the end of the examination, students should stop writing
immediately. Those who continue to write after this point will have their answer sheets
destroyed. 10. When the academic staff announce the end of the examination period, all the answer sheets
should be passed along the row to the student at the end of the row. Students should not talk
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. 4
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: 4, 6, 10, 8, 4. Sellers: 2, 3, 6, 4, 5.
Question 1: What is the competitive equilibrium price (specify a range if more than one equilibrium price)?
� 3
� 6
� Any price between 4 and 5
� 5
Question 2: What is the quantity exchanged in the competitive equilibrium?
� 1
� 4
� 2
� 3
Question 3: What price would the buyers choose if they could?
� 5
� 2
� 8
� 4
Question 4: What price would the sellers choose if they could?
� 6
� 4
� 5
� 8
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 = 1. Individual B has Perfect
Complement preferences with parameter a = 2. Total endowment of good 1 is 10 and that of good 2 is 10.
Individual A's endowment of good 1 is 4 and that of good 2 is 10.
Question 5: What is the competitive equilibrium price ratio?
� 2.50
� 0.50
� 1.00
� 0.00
Question 6: What is the quantity exchanged of good 1 to reach the competitive equilibrium?
� 0.00
� 6.00
� 1.00
� 6.50
Question 7: What is the quantity exchanged of good 2 to reach the competitive equilibrium?
� 0.00
� 6.00
� 1.00
� 0.50
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 20.00 and at prices 1.00 and 2.00 the demands were 10.00 and 5.00. With income 20.00 and
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.
Question 8: What are the individual's preferences?
� Perfect Substitutes
� There is not enough information
� Cobb-Douglas
� Perfect complements
Question 9: What is the value of the parameter a?
� 2.00
� 4.00
� 1.00
� 0.50
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 = 0.0, c = 3.0. Suppose that the price of the firm's output is 30.
Question 10: Determine the optimal output of the firm.
� 30.00
� 0.00
� 5.00
� 10.63
Question 11: What is the firm's profit?
� 150.00
� 0.00
� 318.82
� 55.00
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 8 and that of factor 2 is 8.
Question 12: Find the maximum output for firm 2 if firm 1 has an output of 4
� 12.00
� 4.00
� 0.00
� 7.00
Question 13: Find the maximum output of firm 1 if firm 2 has an output of 8
� 8.00
� 3.20
� 0.00
� 1.00
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 = (4,36;0.25,0.75) Q = (9,16;0.25,0.75)
Question 14: Does the individual prefer P or Q?
� P
� We cannot tell from the information given
� The individual is indifferent
� Q
Question 15: What is the individual's certainty equivalent for P?
� 14.25
� 14.0625
� 28
� 25
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: 10, 9, 9, 5. Player 2: 6, 2, 2, 3.
Question 16: Specify ALL the Nash Equilibria in pure strategies.
� BB
� BA
� There are none
� AA
Question 17: Specify ALL other outcomes (not a Nash Equilibrium) that Pareto dominate any of these.
� AA dominates BB
� BB dominates AA
� AA and BB dominate AB
� There are none
For every correct answer you get 2 marks. For every wrong answer 1 mark will be deducted.
DO NOT LOOK AT THE EXAMINATION PAPER
UNTIL YOU ARE TOLD TO DO SO
READ CAREFULLY THE RULES OF THIS EXAM
The first thing that you should do is fill in the oval corresponding to
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.
2. Any student discovered using forbidden material (books, notes etc.) will be immediately
expelled from the examination session.
3. Students who wish to talk to one of the academic staff should raise their hand.
4. The academic staff will not discuss any points concerning the answers to the examination.
5. Answers to the questions on the examination paper should be indicated on the answer sheet
by filling in the appropriate circle, as indicated below.
6. Your matriculation number should be indicated on the answer sheet by filling in the
appropriate circles.
8. Students cannot leave the examination room in the final ten minutes of the examination.
9. When the academic staff announce the end of the examination, students should stop writing
immediately. Those who continue to write after this point will have their answer sheets
destroyed. 10. When the academic staff announce the end of the examination period, all the answer sheets
should be passed along the row to the student at the end of the row. Students should not talk
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. 5
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: 4, 5, 5, 8, 10. Sellers: 6, 3, 3, 5, 5, 7, 2.
Question 1: What is the competitive equilibrium price (specify a range if more than one equilibrium price)?
� 6
� 5
� 4
� There is no competitive equilibrium
Question 2: What is the quantity exchanged in the competitive equilibrium?
� 3
� 6
� 4
� 5
Question 3: What price would the buyers choose if they could?
� 5
� 4
� 8
� 3
Question 4: What price would the sellers choose if they could?
� 7
� 5
� 8
� 3
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 = 0.5. Individual B has Perfect
Complement preferences with parameter a = 1. Total endowment of good 1 is 8 and that of good 2 is 6.
Individual A's endowment of good 1 is 6 and that of good 2 is 4.
Question 5: What is the competitive equilibrium price ratio?
� There is no equilibrium inside the box
� 0.67
� 0.75
� 1.00
Question 6: What is the quantity exchanged of good 1 to reach the competitive equilibrium?
� 3.00
� 2.00
� 3.50
� There is no equilibrium inside the box
Question 7: What is the quantity exchanged of good 2 to reach the competitive equilibrium?
� 3.00
� 2.00
� There is no equilibrium inside the box
� 2.50
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 1.00 the demands were 15.00 and 15.00. With income 20.00 and
at prices 1.00 and 0.50 the demands were 10.00 and 20.00. With income 20.00 and at prices 1.00 and 1.00
the demands were 10.00 and 10.00.
Question 8: What are the individual's preferences?
� Perfect complements
� Cobb-Douglas
� There is not enough information
� Perfect Substitutes
Question 9: What is the value of the parameter a?
� 0.50
� 1.25
� 1.00
� 0.75
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 = 10.0, b = 0.0, 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
� 0.00
� 30.33
� 15.00
Question 11: What is the firm's profit?
� 450.00
� 0.00
� 215.00
� 909.89
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 = 1. Total endowment of factor 1 is 6 and that of factor 2 is 6.
Question 12: Find the maximum output for firm 2 if firm 1 has an output of 0
� 9.00
� 7.50
� 0.00
� 12.00
Question 13: Find the maximum output of firm 1 if firm 2 has an output of 3
� 0.00
� 7.00
� 3.00
� 6.00
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 = (16,36;0.25,0.75) Q = (25,25;0.25,0.75)
Question 14: Does the individual prefer P or Q?
� We cannot tell from the information given
� Q
� The individual is indifferent
� P
Question 15: What is the individual's certainty equivalent for P?
� 25
� 27
� 31
� 30.25
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, 9, 4, 8. Player 2: 6, 10, 7, 5.
Question 16: Specify ALL the Nash Equilibria in pure strategies.
� AA
� There are none
� BB
� AB BA
Question 17: Specify ALL other outcomes (not a Nash Equilibrium) that Pareto dominate any of these.
� There are none
� BB and AB dominate AA
� AB dominates BB
� BB dominates AB
For every correct answer you get 2 marks. For every wrong answer 1 mark will be deducted.