9) Consider 3,000 people who each have an 8% chance of getting seriously sick this year. If they get seriously sick, they will have a $13,500 hospital bill. If they do not get seriously sick, they will have minor medical expenses of $1,000. All 3,000 people are risk-averse, but they differ with respect to the degree of their risk-aversion. 1,000 of them are very risk-averse and willing to pay a risk premium equal to 50% of the actuarially fair premium. Another 1,000 are moderately risk-averse and willing to pay a risk premium equal to 30% of the actuarially fair premium. The final 1,000 are minimally risk-averse and are only willing to pay a risk premium equal to 10% of the actuarially fair premium.

a. What is the actuarially fair premium for a very risk-averse person? What is the actuarially fair premium for a moderately risk-averse person? What is the actuarially fair premium for a minimally risk-averse person?

b. What premium is a very risk-averse person willing to pay? What premium is a moderately risk-averse person willing to pay? What premium is a minimally risk-averse person willing to pay?

c. What does the demand curve for insurance look like? Plot it in a standard diagram with quantity of people who buy insurance on the horizontal axis and the price of insurance (i.e., premium) on the vertical axis. (Hint: Demand is not a smooth, straight line. The quantity demand abruptly jumps up when the insurance premium crosses certain thresholds.)

d. Suppose that the insurance market is competitive with free entry and exit. Competitive forces therefore lead insurers to sell insurance at the actuarially fair price. How many people buy insurance? What is the consumer surplus for the 1,000 people who are highly risk-averse? What is it for the 1,000 people who are moderately risk-averse? What is it for the 1,000 people who are minimally risk-averse? What are insurers' expected profits? (Note: It may help to identify the consumer surplus in your diagram from part c.)

e. Now suppose insurers are successful at lobbying legislators to disallow entry from new insurance companies. Without as much competition, insurers are now able to charge a premium that is 25% more than actuarially fair price. How many people buy insurance now? What is the consumer surplus for the 1,000 people who are very risk-averse? What is it for the 1,000 people who are moderately risk-averse? What is it for the 1,000 people who are minimally risk-averse? What are insurers' expected profits? (Note: It may help to identify the new consumer and producer surplus in your diagram from part c.)

f. What is the effect of part e's barrier to entry on consumer surplus? What is the effect on producer surplus (i.e., insurers expected profits)? What is the effect on social surplus (i.e., the sum of consumer and producer surplus)?