Exercise 4: InsuranceFiona has von Neumann-Morgenstern utility function u(x) =VT and initial wealth 640, 000. She faces a25% 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 expectedutility?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 insurancecoverage at level z, she will get reimbursed z · 280, 000 if the loss occurs. Insurance coverage at level z costsco + z. c1 ifz >0C(z) =ifz = 04. Suppose co = 0 and c1 = 70,000. Is insurance at coverage level z > 0 fair insurance? What coveragelevel z* would Fiona choose? Explain.5. Suppose co = 100 and c1 = 70,000. Is insurance at coverage level z > 0 fair insurance? What coveragelevel z** would Fiona choose? Explain. (Note that co = 100 is an "avoidable fixed cost" which is onlypaid if she chooses strictly positive insurance coverage. However, the "marginal cost" of additionalinsurance, 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.

Answered: Exercise 4: Insurance Fiona has von…

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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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) =
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 c1 = 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

Since we answer only the first 3 subparts questions 1-3 will be answered here. Please reupload the question mentioning the subparts you would like answered.

1. By looking at the utility function we see it is concave. Hence Fiona is risk averse.

More formally we can calculate the degree of absolute risk aversion given by

$\begin{array}{rcl} A (x) & = & - \frac{u'' (x)}{u' (x)} \\ = & \frac{2 \sqrt{x}}{4 x^{\frac{3}{2}}} \\ = & \frac{1}{2 x} > 0 \end{array}$

A positive degree of absolute risk aversion shows that Fiona is risk averse.

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