Part A: Caleb has the expected utility maximizer U(wealth) = wealth^0.8 and starts with wealth = 1,000. He is offered the following gambling opportunities:

gamble_1: 25% chance of losing $50 & a 75% chance of winning $20

gamble_2: a 25% chance of losing 100 and a 75% chance of winning $45

1) Compute the expected change in wealth for gamble_1.

2) Compute the expected change in wealth for gamble_2.

3) Compute the final expected utility of wealth if Caleb chooses gamble_1.

4) Compute the final expected utility of wealth if Caleb chooses gamble_2.

5) Specify which gamble Caleb would choose based on results.

Part B: Megan has the following prospect theory preferences:

U(wealth) = wealth - reference_point if wealth ends up being greater than the reference point

U(wealth) = -1.75*(reference_point - wealth) when wealth ends up being less than the reference point.

Assume reference_point = initial wealth at $1000.

1) What is the expected utility for Megan if she chooses gamble_1?

2) What is the expected utility for Megan if she chooses gamble_2?

3) Which gamble would Megan prefer?

4) Explain what 1.75 in this exercise signifies.

Source: Course Practice Problems