Barney has $50,000 in income per year and faces a 30% chance of having $20,000 i

Question

Barney has $50,000 in income per year and faces a 30% chance of having $20,000 in unexpected medical bills. Suppose Barney’s utility function over income is

U = I1/2

a. What is Barney's expected loss?

b. What is Barney's utility under insurance, if the price of insurance is equal to his expected loss (actuarially fair)?

c. Show mathematically that Barney would be better off with an actuarially fair insurance policy, as opposed to having no insurance.

d. What is the most Barney would be willing to pay for insurance?

Explanation / Answer

Barney's expected loss = 0.3 x 20000 = $6000

Barney's utility under insurance = 1/2 of 50000 same as previous as the expected loss and the actual loss if may be are covered by the insurance.

Barney's utility under insurance = 1/2 of 50000 = $25000 > Barney's utility with no insurance = 1/2 of 44000 = $22000. Hence he is better off with an insurance.

The most that Barney would be willing to pay for insurance = his expected loss of $6000.

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