Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit 

Semester 2 Examination, 2022

ECON30019 Behavioural Economics

Question 1. (15 Points)

(5 Points) What is the decoy effect? Explain your answer with the help of an example. You can use an example we discussed in the lecture, or any other suitable example of your choosing, including an invented one.

(5 Points) Why is the decoy effect surprising from the point of view of neoclassical economic theory? Explain what assumption(s) in neoclassical theory preclude(s) the decoy effect, using your example from Question (1.1) as part of your argument.

(5 Points) Why do you think many people are subject to the decoy effect? Use your example from Question (1.1) to explain why the psychological feature of decision making that you refer to when answering this question can result in the decoy effect.

Question 2. (15 Points)

Polymerase chain reaction (PCR) is a method widely used to diagnose COVID-19 infections. Suppose that if a person does not have COVID-19, the test will be negative 84% of the time, and be positive 16% of the time; if the person does have COVID-19, the test will be positive 88% of the time, and be negative 12% of the time. Melbourne has a population of 5 million.

1. (6 Points) Suppose that on the 15^th of January 2021, there were 50 actual COVID-19 infections in Melbourne. A randomly selected person who lives in Melbourne is given a PCR test.  This PCR test is positive. Without any other information about this person, what is the probability that this person has COVID-19?

2. (6 Points) Suppose that on the 15^th of January 2022, there were 300,000 actual COVID-19 infections in Melbourne. A randomly selected person who lives in Melbourne is given a PCR test.  This PCR test is positive. Without any other information about this person, what is the probability that this person has COVID-19?

3. (3 Points) Based on your answers to Questions (2.1) and (2.2), explain why it is important to take the base rate into account when drawing conclusions from the test?

Question 3. (17 Points)

Sam evaluates prospects according to prospect theory with probability-weighing function  and value function

He is considering a gamble. If he plays the gamble, he can win $900 or lose $400 with equal probability. Take Sam’s endowment before the gamble as his reference point.

1. (7 Points) Which of the following options will Sam choose if given the choice between them?

(a) not playing the gamble;

(b) playing the gamble one time;

(c) playing the gamble two times and receiving a single payment at the end by adding up the two results (that is, integrating the two results).

2. (5 Points) Suppose now Sam has an additional option:

(d) playing the gamble two times and receiving a payment after each time (that is, segregating the two results).

Among (a), (b), (c), and (d), which option will Sam choose?

3. (5 Points) Use the concepts we learned in class to explain Sam's choice between (c) and (d).

Question 4. (18 Points)

Suppose that you run an experiment in which you elicit the certainty equivalent for the following four lotteries:

· Lottery , offering $1 with 99% chance (and nothing otherwise)

· Lottery , offering $1 with 94% chance (and nothing otherwise)

· Lottery , offering $1 with 39% chance (and nothing otherwise)

· Lottery , offering $1 with 34% chance (and nothing otherwise)

In your experiment, there is a subject named Bobby. Let  denote Bobby's certainty equivalent for a lottery . Let  denote the difference between the certainty equivalents of lottery  and lottery . Similarly, let  denote the difference between the certainty equivalents of lottery  and lottery .

(4 Points) Suppose Bobby's preference is consistent with the Expected Utility Theory and he is risk neutral. Solve for and  and compare them.

(5 Points) Suppose Bobby's preference is instead consistent with the Prospect Theory with a value function  and a probability-weighting function . Take Bobby's endowment before the experiment as his reference point. Solve for and  and compare them.

(4 Points) How would your answers to Question (4.1) change if instead of being risk neutral, Bobby is risk averse with a utility function ?

(5 Points) How would your answers to Question (4.2) change if Bobby instead has a value function

and a probability-weighting function ?

Question 5. (15 Points)

Consider the following game. There are two players, Red and Blue. Both players must choose between low effort (0) and high effort (1). The cost of exerting low effort is zero. The cost of exerting high effort is $10, and the benefits to each person depend on the total effort of the two individuals combined. Since each person can choose an effort of 0 or 1, the total effort must be 0, 1, or 2, and the benefit per person is given in the table below.

1. (2 Points) Write down the payoff matrix of the game.

2. (3 Points) Assume that both players only care about their own material payoffs. Suppose these preferences are commonly known to both players. Derive the Nash equilibrium/equilibria of the game. Does a player’s best choice depend on the strategy chosen by the other player?

3. (5 Points) Assume that both players exhibit inequity aversion as specified in the model of Fehr and Schmidt (1999). The parameters for player Red are  and . The parameters for player Blue are  and . Suppose these preferences are commonly known to both players. Derive the Nash equilibrium/equilibria of the game.

4. (5 Points) Assume that player Red has inequity aversion as specified in question 6.3 (with  and ), but that player Blue cares only about his/her own material payoff. Suppose these preferences are commonly known to both players. Derive the Nash equilibrium/equilibria of the game.

Question 6. (20 Points)

On Monday Bob discovers mould growing in the bathroom of his apartment. The mould initially covers 2 square meters. If Bob does not clean the mould on Monday, it would grow to 3 square meters on Tuesday, 5 square meters on Wednesday, 8 square meters on Thursday, and 13 square meters on Friday. Bob's choice is whether to clean the mould on Monday, Tuesday, Wednesday, Thursday, Friday, or never. Cleaning the mould on a day in which it covers  square meters has a utility cost of . Bob will host an important brunch on Saturday. If Bob fails to clean the mould before Saturday, he would not have enough time to clean it before his guests arrive on Saturday. Then his guests would be extremely disappointed, causing him a utility loss of 50 on Saturday. Bob is a hyperbolic discounter with   and .

1. (5 Points) When (if at all) would Bob clean the mould if he is naïve? Explain carefully.

2. (7 Points) When (if at all) would Bob clean the mould if he is sophisticated? Explain carefully.

3. (8 Points) Suppose that Bob has a further option: rescheduling by asking his guests to come earlier in the week. Doing this comes at a utility cost of 1.5 that is incurred on the day of the rescheduled brunch.

For example, on Tuesday Bob can either keep the brunch on Saturday, or reschedule it to one of the three remaining days (Wednesday, Thursday, or Friday, depending on his preference). Suppose on Tuesday Bob decides to reschedule the brunch to Thursday, he incurs a cost of 1.5 on Thursday.

The consequence of disappointing his guests is as before: if the mould hasn't been cleaned before the day of the rescheduled brunch, he would incur a utility loss of 50 on the day of the rescheduled brunch. Would Bob choose to reschedule? On which day would Bob end up cleaning the mould? Does it matter if he is naive or sophisticated? Explain carefully.