18ECC001 Developments in Microeconomics Coursework Test – ANSWERS
AND FEEDBACK
Overall Feedback:
I was relatively pleased with the cohort’s performance on a hard test – with an
overall of around 58%. With a good performance in the group presentations,
many students will have excellent coursework marks going into the final exam.
The average score on the multiple-choice section was 56% and the average
score on the written section was 61%. Specific feedback on the written section is
given below. For more information, see your individual emailed feedback and the
lecture capture recording of the session immediately after the test.
Test Answers:
The test will last for 45 minutes. Answer all questions in Sections A and B.
Section A contains 9 multiple-choice questions. Each question is worth 2 marks.
Section B contains 1 written question worth a total of 12 marks.
University approved calculators are allowed.
Answer Section A on the Multiple Choice Answer Sheet.
Answer Section B on the lined paper provided.
Make sure you add your registration number to all answer sheets.
Section A
1. Davina is thinking about selling her old car. If she decided to keep the car
she would receive an expected utility of 60. In contrast, if she decided to sell the
car, she believes that is a 50% chance of selling it for £2000, a 30% chance of
selling it for £5000, and 20% chance of selling it for £𝑍 (where 𝑍 is a parameter).
Over any monetary income, Davina has a utility function 𝑢(𝑥) = √𝑥. At what level
of 𝑍 would Davina be indifferent between keeping and selling her car (to zero
decimal places)?
A. 82
B. 56
C. 3100
D. 6745
E. 3152
1
, Answer: The expected utility of selling her car equals
0.5√2000+𝟎.𝟑√5000+𝟎.2√Z. Davina would be indifferent if this equalled the utility
of keeping her car, 60. Therefore, we require 0.5√2000+𝟎.𝟑√5000+𝟎.2√Z=60.
This simplifies to 43.574+ 𝟎.2√Z=60 and so √Z=(60-43.574)/0.2=82.131 and
therefore Z=6745.
2. A terrorist has taken a hostage and is demanding a ransom to release them.
If the police pay the ransom, the police receive a payoff of -1000 and the terrorist
receives a payoff of 1000. Alternatively, the police could make an attack. In response
to an attack, the terrorist may kill the hostage, injure the hostage, or let the hostage
escape unharmed. If the terrorist kills the hostage, the police lose 5000 and the
terrorist loses 5000. If the terrorist injures the hostage, the police lose 2000 and the
terrorist loses 2000. If the terrorist lets the hostage escape, the terrorist loses 1000
and the police gain 1000. Under all the necessary standard assumptions, which one
of the following statements is correct?
A. The unique SPNE is where the police attack and the hostage escapes.
B. The unique SPNE is where the police pay the ransom.
C. The unique SPNE is where the police attack and the hostage is injured.
D. The unique SPNE is where the police attack and the hostage is killed.
E. There are multiple SPNE.
Answer: The unique SPNE involves an attack and the terrorist releasing the hostage.
After an attack, the terrorist will optimally release the hostage as -1000>-2000>-
5000. Knowing this, the police will strictly prefer to attack to receive 1000 rather than
paying the ransom which will lose 1000.
3. Consider the following normal form game between Player 1 (P1) and
player 2 (P2). Suppose each player independently selects action m with
probability p and action n with probability (1-p). Which one of the statements is
correct?
P2
m n
P1 m 1,3 3,1
n 3,1 1,3
A. The game has two pure strategy Nash equilibria, and one mixed strategy
Nash equilibrium with p=0.5.
B. The game has two pure strategy Nash equilibria, and one mixed strategy
Nash equilibrium with p=0.25.
C. The game has no pure strategy Nash equilibria, but it has one mixed
strategy Nash equilibrium with p=0.5.
D. The game has no pure strategy Nash equilibria, but it has one mixed strategy
Nash equilibrium with p=0.25.
E. The game has one pure strategy Nash equilibrium, and one mixed strategy
Nash equilibrium with p=0.25.
2
AND FEEDBACK
Overall Feedback:
I was relatively pleased with the cohort’s performance on a hard test – with an
overall of around 58%. With a good performance in the group presentations,
many students will have excellent coursework marks going into the final exam.
The average score on the multiple-choice section was 56% and the average
score on the written section was 61%. Specific feedback on the written section is
given below. For more information, see your individual emailed feedback and the
lecture capture recording of the session immediately after the test.
Test Answers:
The test will last for 45 minutes. Answer all questions in Sections A and B.
Section A contains 9 multiple-choice questions. Each question is worth 2 marks.
Section B contains 1 written question worth a total of 12 marks.
University approved calculators are allowed.
Answer Section A on the Multiple Choice Answer Sheet.
Answer Section B on the lined paper provided.
Make sure you add your registration number to all answer sheets.
Section A
1. Davina is thinking about selling her old car. If she decided to keep the car
she would receive an expected utility of 60. In contrast, if she decided to sell the
car, she believes that is a 50% chance of selling it for £2000, a 30% chance of
selling it for £5000, and 20% chance of selling it for £𝑍 (where 𝑍 is a parameter).
Over any monetary income, Davina has a utility function 𝑢(𝑥) = √𝑥. At what level
of 𝑍 would Davina be indifferent between keeping and selling her car (to zero
decimal places)?
A. 82
B. 56
C. 3100
D. 6745
E. 3152
1
, Answer: The expected utility of selling her car equals
0.5√2000+𝟎.𝟑√5000+𝟎.2√Z. Davina would be indifferent if this equalled the utility
of keeping her car, 60. Therefore, we require 0.5√2000+𝟎.𝟑√5000+𝟎.2√Z=60.
This simplifies to 43.574+ 𝟎.2√Z=60 and so √Z=(60-43.574)/0.2=82.131 and
therefore Z=6745.
2. A terrorist has taken a hostage and is demanding a ransom to release them.
If the police pay the ransom, the police receive a payoff of -1000 and the terrorist
receives a payoff of 1000. Alternatively, the police could make an attack. In response
to an attack, the terrorist may kill the hostage, injure the hostage, or let the hostage
escape unharmed. If the terrorist kills the hostage, the police lose 5000 and the
terrorist loses 5000. If the terrorist injures the hostage, the police lose 2000 and the
terrorist loses 2000. If the terrorist lets the hostage escape, the terrorist loses 1000
and the police gain 1000. Under all the necessary standard assumptions, which one
of the following statements is correct?
A. The unique SPNE is where the police attack and the hostage escapes.
B. The unique SPNE is where the police pay the ransom.
C. The unique SPNE is where the police attack and the hostage is injured.
D. The unique SPNE is where the police attack and the hostage is killed.
E. There are multiple SPNE.
Answer: The unique SPNE involves an attack and the terrorist releasing the hostage.
After an attack, the terrorist will optimally release the hostage as -1000>-2000>-
5000. Knowing this, the police will strictly prefer to attack to receive 1000 rather than
paying the ransom which will lose 1000.
3. Consider the following normal form game between Player 1 (P1) and
player 2 (P2). Suppose each player independently selects action m with
probability p and action n with probability (1-p). Which one of the statements is
correct?
P2
m n
P1 m 1,3 3,1
n 3,1 1,3
A. The game has two pure strategy Nash equilibria, and one mixed strategy
Nash equilibrium with p=0.5.
B. The game has two pure strategy Nash equilibria, and one mixed strategy
Nash equilibrium with p=0.25.
C. The game has no pure strategy Nash equilibria, but it has one mixed
strategy Nash equilibrium with p=0.5.
D. The game has no pure strategy Nash equilibria, but it has one mixed strategy
Nash equilibrium with p=0.25.
E. The game has one pure strategy Nash equilibrium, and one mixed strategy
Nash equilibrium with p=0.25.
2
