Expected Utility Health Insurance

1. Woody 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 = 6(Y1/2)
Woody 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 Woody’s expected utility level without any health insurance coverage.

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B. Calculate Woody’s expected income without any insurance coverage.

C. Suppose Woody 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. Woody is in the 40 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?

E. Suppose Woody purchases the health insurance coverage and represents the average subscriber, and his expectations are correct. Calculate the loading fee the insurance company will receive.