Fiona has von Neumann-Morgenstern utility function u(x) = VT and initial wealth 640, 000. She faces a 25% chance of losing L = 280, 000. 1. Is Fiona risk averse? 2. What is Fiona's utility if no loss occurs, what is her utility if the loss occurs? What is Fiona's expected utility? 3. What is the cost of fair insurance against the possible loss?
Fiona has von Neumann-Morgenstern utility function u(x) = VT and initial wealth 640, 000. She faces a 25% chance of losing L = 280, 000. 1. Is Fiona risk averse? 2. What is Fiona's utility if no loss occurs, what is her utility if the loss occurs? What is Fiona's expected utility? 3. What is the cost of fair insurance against the possible loss?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![Exercise 4: Insurance
Fiona has von Neumann-Morgenstern utility function u(x) =
VT and initial wealth 640, 000. She faces a
25% chance of losing L = 280, 000.
1. Is Fiona risk averse?
2. What is Fiona's utility if no loss occurs, what is her utility if the loss occurs? What is Fiona's expected
utility?
3. What is the cost of fair insurance against the possible loss?
Suppose Fiona is able to choose insurance with any coverage z E [0, 1] (i.e. 0 < z < 1). If she buys insurance
coverage at level z, she will get reimbursed z · 280, 000 if the loss occurs. Insurance coverage at level z costs
co + z· C1
if
z > 0
C(z) =
0 if
z = 0
4. Suppose co = 0 and c1 = 70, 000. Is insurance at coverage level z > 0 fair insurance? What coverage
level z* would Fiona choose? Explain.
5. Suppose co = 100 and ci = 70, 000. Is insurance at coverage level z > 0 fair insurance? What coverage
level z** would Fiona choose? Explain. (Note that co = 100 is an "avoidable fixed cost" which is only
paid if she chooses strictly positive insurance coverage. However, the "marginal cost" of additional
insurance, c1 = 70, 000, is the same as in the previous part.)
6. Suppose co = 100 and c1 = 72,000. Is full insurance, that is, coverage level z = 1 optimal? Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F984ca259-54f9-4683-afd9-6096ed5265a3%2Fd4757ed3-d294-4430-8483-c84057015dfb%2Fxzq5zvd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise 4: Insurance
Fiona has von Neumann-Morgenstern utility function u(x) =
VT and initial wealth 640, 000. She faces a
25% chance of losing L = 280, 000.
1. Is Fiona risk averse?
2. What is Fiona's utility if no loss occurs, what is her utility if the loss occurs? What is Fiona's expected
utility?
3. What is the cost of fair insurance against the possible loss?
Suppose Fiona is able to choose insurance with any coverage z E [0, 1] (i.e. 0 < z < 1). If she buys insurance
coverage at level z, she will get reimbursed z · 280, 000 if the loss occurs. Insurance coverage at level z costs
co + z· C1
if
z > 0
C(z) =
0 if
z = 0
4. Suppose co = 0 and c1 = 70, 000. Is insurance at coverage level z > 0 fair insurance? What coverage
level z* would Fiona choose? Explain.
5. Suppose co = 100 and ci = 70, 000. Is insurance at coverage level z > 0 fair insurance? What coverage
level z** would Fiona choose? Explain. (Note that co = 100 is an "avoidable fixed cost" which is only
paid if she chooses strictly positive insurance coverage. However, the "marginal cost" of additional
insurance, c1 = 70, 000, is the same as in the previous part.)
6. Suppose co = 100 and c1 = 72,000. Is full insurance, that is, coverage level z = 1 optimal? Explain.
Expert Solution
Step 1
Risk-averse people will not be willing to take risks.
Given:
u(x)=x1/2
Initial Worth = 640,000
Loosing probability = 0.25
Loosing amount = 280,000
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