Question

Gamma’s utility function over wealth levels w is given by u(w) = √ w. His initial wealth is $400. With probability π, Gamma will get into an accident that will result in a loss of $300. With probability (1 − π), Gamma does not have an accident, and hence suffers no loss.

1. Argue (mathematically) that Gamma is risk averse.

2. What is the expected value of Gamma’s loss?

3. ABC Inc. sells auto insurance. It charges a premium of $ d 10 for the insurance plan that reimburses $d ≤ 300 in case of an accident.

(a) Suppose π > 0.06. Does Gamma buy any insurance plan from ABC Inc.? If yes, which one?

(b) Suppose π ≤ 0.05. Does Gamma buy any insurance plan from ABC Inc.? If yes, which one?

(c) For which value of π does Gamma buy full insurance (i.e., d = 300)?

4. You do not have to answer this question but you can earn bonus points if you do. Suppose Gamma’s utility function over wealth levels w is given by u(w) = w. Find Gamma’s optimal insurance choice as a function of π.

Answer 1

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