Problem
Consider the case where Person A is an expected utility maximizer with U(wealth) = wealth^.8 (wealth to the .8 power) and initial wealth of $1000. She is offered a gamble (gamble a) with a 25% chance of losing $50 and 75% chance of winning $20 or a gamble (gamble b) with a 25% chance of losing 100 and a 75% chance of winning $45.
• What is the expected change in wealth for gamble a?
• What is the expected change in wealth for gamble b?
• What is the final expected utility of wealth if gamble a is chosen? What is the final expected utility of wealth if gamble b is chosen? Which gamble would Person A prefer?
Now consider Person B with prospect theory preferences. For this person,
U(wealth) = wealth - reference_point if wealth ends up being greater than the reference point and U(wealth) = -1.75*(reference_point - wealth) when wealth ends up being less than the reference point.
• Assume that the reference point in this case is the initial wealth level ($1,000). What is the expected utility for Person B if gamble a is chosen?
• What is the expected utility for Person B if gamble b is chosen?
• Which gamble would Person B prefer?
• In 2-3 sentences, explain the meaning of the number 1.75 in this problem.