Two types of individuals are seeking health insurance: skydivers and groundhuggers. Skydivers have a 75% chance of suffering an injury in a given year; groundhuggers have a 25% chance of suffering an injury. All injuries require a $4,000 surgery to repair.

a. You run a health insurance company, and believe there are equal numbers of skydivers and groundhuggers in the population. Unfortunately, you can’t, at first glance, distinguish a skydiver from a groundhugger. How much of a premium would you have to collect from each individual if you were to just cover your expected payouts for surgeries?

b. At the premium you set in (a), who thinks insurance looks like a great deal? Who thinks it looks like a poor deal?

c. Describe the likely reaction of skydivers and groundhuggers when informed of your premiums. What are the implications for who decides to buy insurance? What are the implications for the premiums you must charge?

d. Smokers have a greater risk of illness than nonsmokers, in the same way skydivers have a higher risk of injury than groundhuggers. Explain why both smokers and nonsmokers remain in the pool of the insured in the real world, but only the skydivers in this problem obtained insurance.