代做ECON30019 Assignment 3代写留学生Matlab语言程序

ECON30019 Assignment 3

Due at 11:59 pm on Sep 10, 2024

Question 1. (35 points)

Suppose Ann has the following value function

and the probability-weighting function π (p) = p for any p ∈ [0, 1]. Ann’s car broke down so she just spent $100 at the auto repair shop. Afterwards, she picked up a $10 bill on the sidewalk on her way home.

1. (5 points) If Ann integrates the loss and the gain, calculate the change in her utility.

2. (5 points) If Ann segregates the loss and the gain, calculate the change in her utility.

3. (3 points) From your answers to Questions (1.1) and (1.2), which way of thinking about this (integration or segregation) makes Ann feel better? Explain using the effects or biases we discussed in class.

4. (9 points) Try to reach the same conclusion using the graphical analysis we conducted in class for bundling.

Now suppose Rob has the same value function and probability-weighting function as Ann. Rob won a $10,000 lottery but had to pay a $900 tax on his winnings.

5. (5 points) If Rob integrates the loss and the gain, calculate the change in his utility.

6. (5 points) If Rob segregates the loss and the gain, calculate the change in his utility.

7. (3 points) According to your calculation, which way of thinking about this (integration or segregation) makes Rob feel better? Explain using the effects or biases we discussed in class.

Question 2. (30 points)

Ann is a participant of an experiment. Her value function is

and her probability-weighting function is π (p) = p for any p ∈ [0, 1]. In the experiment, Ann is asked to choose between

Option 1: receiving a sure $10, and

Option 2: a lottery that pays $20 and $0 with equal probability.

1. (12 points) If Ann takes her endowment before participating in the experiment as her reference point, which option would she choose according to the prospect theory?

2. (12 points) Suppose Ann has participated in a different experiment before, and from that experiment she earned $25. If Ann takes her earning from the previous experiment as her reference point, which option would she choose according to the prospect theory?

3. (6 points) From your answers to Questions (2.1) and (2.2), what can you say about Ann’s risk preference? Explain.

Question 3. (35 points)

Maurice faces the following options. He must first choose between (1a) and (1b), and then choose between (2a) and (2b).

(1a) $25 for sure

(1b) $36 with probability 20%,

        $25 with probability 79%,

        $0 with probability 1%

(2a) $36 with probability 20%,

        $0 with probability 80%

(2b) $25 with probability 21%,

        $0 with probability 79%

Suppose Maurice chooses (1a) and (2a).

1. (15 points) Show that Maurice’s choices are inconsistent with the Expected Utility Theory. Assume Maurice’s initial wealth is 0.

2. (20 points) Consider the Prospect Theory. Assume Maurice takes his endowment before choosing as his reference point. His value function is

His probability-weighting function is given by

Show that the above v(·) and π (·) functions can explain Maurice’s choices.