# Utility from Income & Insurance

A person derives utility from income, and assume that the utility function is U=Y0.5. Assume a person has annual income of $40,000 but in any given year there is a 10% chance the person's car will be damaged requiring a repair of $17,500.

a. Provide an equation that describes expected utility in this instance and provide a numeric value for expected utility.

b. Suppose this person could purchase insurance that would pay for all losses if the car accident occurs. What is the most this person is willing to pay for this type of car insurance? Please show all your work.

c. Suppose the utility function is not the square root of income but instead, utility is linear in income, where U=Y. How does your answer to parts a) and b) change when utility is linear?

d. Provide an intuitive explanation for why the person in part a) is willing to pay more for insurance than the person in part c)?

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#### Solution Preview

A person derives utility from income, and assume that the utility function is U=Y0.5. Assume a person has annual income of $40,000 but in any given year there is a 10% chance the person's car will be damaged requiring a repair of $17,500.

a. Provide an equation that describes expected utility in this instance and provide a numeric value for expected utility.

So, simply work this guy out by specifying his utility in each situation.

EU=0.9*(40,000)1/2+0.1*(22500)1/2

Make sure you take the root of 40,000 before you multiply it by "0.9"

b. Suppose ...

#### Solution Summary

The utility from income and insurance is examined. Purchase insurance that would pay is determined.

Health insurance

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?