A decision-maker faces the following decision under conditions of uncertainty. This decision-maker has $1 million in assets. Most of those assets, $750,000, are the individualâ€™s equity in his house. The remaining $250,000 are absolutely secure. Unhappily, there is a risk that the individualâ€™s house will burn down in a fire, which would be a total loss of the $750,000. The individual can insure his house against the loss from this fire. The premium for the insurance is $40,000, and it will insure the individual completely; that is, if the individual chooses to purchase this insurance policy, his assets will be $960,000, whether or not there is a fire. (There is no mortgage on the house, so $750,000 is the full amount paid by the insurance company.) The probability of a fire is 0.05.

Required:
a. What is the expected net earnings, the premium less the expected amount paid out to the client, to the insurance company from this policy?
b. If the individual in question were risk neutral, would he buy this insurance policy?
c. If the individual in question is an expected utility maximizer, with the utility function u(a) = where a is the individuala's total assets, would this individual buy the insurance?

A- The net earnings of the individual in question will be $710000 after the individual's claim for loss by fire is settled by the insurance company. B- Yes, he would buy the insurance if he were risk neutral.

C- Yes, the individual will buy the insurance policy if he were a expected utility maximizer as he would want to claim complete settlement of this amount to be claimed in case of fire loss.

The expected net earnings from the insurance after deducting the amount from the premium paid and total claim endorsed by the insurance company will be $710000 which can be shown as below

[tex]\rm Net\ earnings= claim\ received - premium\ of\ policy[/tex]

[tex]\rm Net\ earnings= 750000-40000[/tex]

We get,

[tex]\rm Net\ earnings= 710000[/tex]

If the individual were risk neutral he would like to take the insurance as the risk of fire in the example given above is 0.5 which is greater than zero and this ultimately implies that risk cannot be taken.

In the case if the individual is expected utility maximizer he would take the insurance as it would not only give him the claims from losses due to fire but also help him secure his house against beta of fire.

Hence, the correct answers will be A- $710000; B- Yes.; C- Yes. and imply that taking insurance will be a wise decision by the individual.

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