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Question

Suppose an individual makes $50,000 of income per year. Her utility function is given by , where x is her income

minus expenses. She realizes that there is about a 5% probability that she may suffer a heart attach in any given year. The cost of treatment will be $20,000 if a heart attack occurs.

She has the option of buying health insurance for $1,000 per year, which will cover all expenses in case of a heart attack. Should she buy this health insurance?(Note:  is a different way of writing the square root of x)


a.Yes, she is risk averse and wants to avoid losses at all costs.

b.She is indifferent between buying insurance and not buying insurance, as her expected income is 49,000 for either option.

c.No, her expected utility without insurance is 985.36, which is higher than her expected utility with insurance.

d.Yes, her expected utility with insurance is higher by 2.73 than without insurance.

e.None of these options.


Part Two

Suppose an individual makes $50,000 of income per year. Her utility function is given by , where x is her income minus expenses. She realizes that there is about a 5% probability that she may suffer a heart attach in any given year. The cost of treatment will be $20,000 if a heart attack occurs.

She has the option of buying health insurance for $1,000 per year, which will cover all expenses in case of a heart attack. What is the maximal amount she is willing to pay for health insurance?

(Note:  is a different way of writing the square root of x)


Round all answers (also intermediate answers to 2 decimals).

a.1162.63

b.981.07

c.1120.54

d.2213.59

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