Question: Joe is currently unemployed and without health insurance coverage. He derives utility (U) from his interest income on his savings (Y) according to the following function:
U = 5(Y1/2)
Joe presently makes about $40,000 of interest income per year. He realizes that there is about a 5 percent probability that he may suffer a heart attack. The cost of treatment will be about $20,000 if a heart attack occurs.
a. Calculate Joe's expected utility level without any health insurance coverage.
b. Calculate Joe's expected income without any insurance coverage.
c. Suppose Joe must pay a premium of $1,500 for health insurance coverage with ACME insurance. Would he buy the health insurance? Why or why not?
d. Suppose now that the government passes a law that allows all people "not just the self-employed or employed" to have their entire insurance premium exempted from taxes. Joe is in the 33 percent tax bracket. Would he buy the health insurance at a premium cost of $1,500? Why or why not? What implications can be drawn from the analysis?