Suppose Michael has a rental income of $20,000 per year and has a job that pays...

Suppose Michael has a rental income of $20,000 per year and has a job that pays $50,000. Michael has no other income sources. With a 20% probability, Michael would lose his job and has an income of 0. Suppose an unemployment insurance policy is available. With the unemployment insurance, the insurer pays $10,000 in the case of unemployment. The premium of the unemployment insurance is $2,500. Michael has a utility function that exhibits diminishing marginal return of consumption. Which is the following statements is correct?

The insurance is actuarially fair.

Michale will purchase the insurance for sure.

Michale will not purchase the insurance for sure.

It is unclear whether Michael would purchase the insurance.

Solutions

Expert Solution

There is a 20% probability that Michael will lose all his income and an 80% probability that he won't lose any of his income. The expected value of the loss in income is

(70,000 * 0.20 + 0 * 0.80) = 14,000

The insurance is said to be actuarially fair when the expected value of the loss is equal to the cost of the insurance ( i.e. the premium). But in this case, the premium is $2,500 and the expected loss is $14,000, so we can say that the insurance is actuarially not fair.

Given that the utility function of Michael exhibits diminishing marginal return of consumption, through which we can conclude that Michael is risk-averse and can consider buying the unemployment insurance policy.

Because the premium for the insurance is less than the expected loss which Michael would incur, he would definitely buy the insurance.

The second statement is correct, Michael will purchase the insurance for sure.

Rahul Sunny answered 1 year ago

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