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# This post answers problem 7.4 Nicholson - actuarially cost

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This corresponds to problem 7.4 in Nicholson (notes are available online from the publisher, SW learning, but they are not necessary).

Suppose there is a 50-50 chance that a risk-averse individual with a current wealth of \$20,000 will contract a debilitating disease and suffer a loss of \$10,000.

A. Calculate the cost of actuarially fair insurance in this situation and use a utility-of-wealth graph to show that the individual will prefer fair insurance against this loss to accepting the gamble uninsured.

B. Suppose two types of insurance policies were available:

(1) a fair policy covering the complete loss; and
(2) a fair policy covering only half of any loss incurred

Calculate the cost of the second type of policy and show that the individual will generally regard it as inferior to the first.

#### Solution Preview

Solution plus attached image.

A. Calculate the cost of actuarially fair insurance in this situation and use a utility-of-wealth graph to show that the individual will prefer fair insurance against this loss to accepting the gamble uninsured.

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#### Solution Summary

The solution provides the complete solution and graph needed for problem 7.4 in Nicholson, calculating each part of the problem.

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