Chapter 7
1. Suppose than an individual has a 30% probability of getting sick this year. If they get sick their income will be $20,000. If they do not get sick their income will be $75,000. This individual only derives utility from income, and his utility function is $U = I^{0.75}$.
a. What is the individual's expected income this year? (2 pts)
b. What is the individual's expected utility this year? (2 pts)
c. What is the individual's utility from their expected income this year? (2pts)
d. Is the individual risk averse? How do you know? (2pts)
2. Using the same individual from question 1, assume he is offered a health insurance plan with a $6,000 premium that will pay out $15,000 if the individual falls ill.
a. Is this insurance plan actuarially fair? Why or why not? (2pts)
b. If the plan is not actuarially fair, what would the insurance payout need to be for a $6,000 premium? (2 pts)
c. Now assume the insurance policy is actuarially fair. What would the insurance payout need to be for the insurance to be full? (3 pts)
3. Draw the utility curve and expected utility line segment (Be sure to label all relevant points) for the individual if they purchase:
a. no insurance (3 pts)
b. the insurance policy in question 2 (3 pts)
c. the full insurance from question 2c (3 pts)