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 uE (x) = VT. 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?

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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 ug (x) = VT.
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
choose insurance with any coverage level z
[0, 1] (i.e. 0< z < 1). If an
individual buys insurance coverage at level z, they will get reimbursed 450, 000-z if the loss occurs. Insurance
coverage at level z costs c(z) = z · 200, 000.
4. What coverage level z, would Dave choose? Explain.
5. Based on your previous results, try to explain that Eva chooses a strictly positive coverage z > 0.
6. Is Eva's optimal choice full insurance, i.e. z = 1?
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 ug (x) = VT. 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 choose insurance with any coverage level z [0, 1] (i.e. 0< z < 1). If an individual buys insurance coverage at level z, they will get reimbursed 450, 000-z if the loss occurs. Insurance coverage at level z costs c(z) = z · 200, 000. 4. What coverage level z, would Dave choose? Explain. 5. Based on your previous results, try to explain that Eva chooses a strictly positive coverage z > 0. 6. Is Eva's optimal choice full insurance, i.e. z = 1?
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