Exercise 5: Insurance Consider two individuals, Dave and Eva. Both Dave and Eva have initial wealth...

Transcribed Image Text:

Exercise 5: Insurance Consider two individuals, Dave and Eva. Both Dave and Eva have initial wealth 810, 000 and face a 40% chance of losing L= 450,000. Dave has von Neumann-Morgenstern utility function up(x) = x and Eva has von Neumann-Morgenstern utility function u(x) = √x. 1. What do you know about Dave's and Eva's risk preferences? 2. What is the most Dave would be willing to pay for complete insurance against the loss? 3. What is the most Eva would be willing to pay for complete insurance against the loss? Suppose they are each able to choose insurance with any coverage z € [0,1] (i.e. 0 ≤ z ≤ 1). If an individual buys insurance coverage at level z, they will get reimbursed z 450, 000 if the loss occurs. Insurance coverage at level z costs z - 200,000. 4. What coverage level z would Dave choose? Explain. 5. Based on your result for 25, try to explain that Eva chooses strictly positive coverage level z > 0. 6. Could Eva's optimal choice be z = 1? Exercise 5: Insurance Consider two individuals, Dave and Eva. Both Dave and Eva have initial wealth 810, 000 and face a 40% chance of losing L= 450,000. Dave has von Neumann-Morgenstern utility function up(x) = x and Eva has von Neumann-Morgenstern utility function u(x) = √x. 1. What do you know about Dave's and Eva's risk preferences? 2. What is the most Dave would be willing to pay for complete insurance against the loss? 3. What is the most Eva would be willing to pay for complete insurance against the loss? Suppose they are each able to choose insurance with any coverage z € [0,1] (i.e. 0 ≤ z ≤ 1). If an individual buys insurance coverage at level z, they will get reimbursed z 450, 000 if the loss occurs. Insurance coverage at level z costs z - 200,000. 4. What coverage level z would Dave choose? Explain. 5. Based on your result for 25, try to explain that Eva chooses strictly positive coverage level z > 0. 6. Could Eva's optimal choice be z = 1?

Answer rating: 100% (QA)

1 Daves utility function is ux I which represents that he has no risk preference meaning that he is ... View the full answer