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Expected utility level

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1. 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 Joeâ??s expected utility level without any health insurance coverage.
b. Calculate Joeâ??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 peopleâ?"not just the self-employed or employedâ?"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?

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This posting offers help with calculating expected utility levels.

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Joe is making $40000 per year. It is given that there is a 5% chance of heart-attack that will cost him $20000. It is also given that his utility function is U = 5Y^(1/2).

The first thing to do is find the expected income. There is 5% chance that he will have a heart-attack that will cost $20000, thus bringing down his income to $20000 ($40000 income - $20000 cost of treatment = $20000 in remaining income). That means, there is a 95% chance that he will earn $40000. This mean his expected income is

(40000*95%) + (20000*5%) = (40000*0.95) + (20000*0.05) = 38000 + 1000 = 39000.

(a) Now Joe's expected utility is E(U) = 5E(Y)^(1/2) = 5*(39000)^(0.5) = 987.420.

(b) His expected income without any insurance coverage is ...

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