# 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)?

#### 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.