Claire’s future wealth is random. She has a probability of 0.2 percent

| August 30, 2017

Question
Claire’s future wealth is random. She has a probability of 0.2 percent of having an accident that will reduce her wealth to $2,000. If she makes it through the year without an accident her wealth will be $10,000. The utility she receives from different levels of wealth are given in the table below:

W

U(W)

$1,000

200

2,000

440

3,000

640

4,000

800

5,000

920

6,000

1,020

7,000

1,100

8,000

1,160

9,000

1,200

10,000

1,220

11,000

1,230

Being risk averse, Claire approaches an insurance company seeking to insure her against loss caused by this potential accident.

14. Without insurance against the potential loss, Claire’s expected utility of wealth equals:

a) 1,064.00 b) 1,192.24 c) 1,204.40 d) 1,218.44 e) 1,242.12

15. The maximum premium Claire will be willing to pay for this insurance equals ______ dollars.

a) 46.00 b) 62.00 c) 78.00 d) 94.00 e) 110.00

16. The maximum expected profit the insurance company can earn from insuring Claire equals ______ dollars.

a) 24.00 b) 30.00 c) 46.00 d) 62.00 e) 78.00

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