Question

Sarah is currently unemployed and without health insurance coverage. She derives utility (U) from her interest income on her savings (Y = $6) according to the following function:

U = (Y+10), Y = $6 => U= 16

She realizes that there is about a 20% probability that she may suffer a heart attack with the cost of treatment of about $2.

A. Calculate Sarah expected utility level without any health insurance coverage.

B. Suppose Sarah must pay an annual premium of $2 for health insurance coverage with ACME insurance. Would she buy the health insurance? Why or why not?

C. Suppose Sarah must pay an annual premium of $1 for health insurance coverage with ACME insurance. Would she buy the health insurance? Why or why not?

Answer 1

Answer.

A. For Expected Utility in absence of insurance,  

E = p(Utility with no heart attack) +(1-p) (Utility with heart attack)

Here,

Probability of heart attack=p=0.20

Probability of no heart attack=1-p=1-0.20=0.80

So, E = 0.20 (14) + 0.80 (16) = 15.6

B. In case of insurace,

Expected Utility = 0.20 (14) + .80 (14) = 14. (As, she has to pay the insurance premium in either case)

Her expected utility with insurance is lower, so she will not buy theinsurance.

C. Smiliarly, in case of $1 premium,

Her expected utility = 0.20 (15) + .80 ( 15) = 15

It is still lower than with no insurance, so she will not buy the insurance.