1. Suppose that Sam's income, which he fully consumes, is $30,000 per year. There is a 1% chance that Sam gets hit by a car, resulting in $30,000 in medical expenses. Sam has a choice of insuring some, none, or all of these potential medical expenses. To analyze Sam's choice, assume, and premiums are actuarially fair. (a) What would be the actuarially fair premium if the insurance company in addition to SAM insures 4 more people who has similar chance of getting hit by a car? (b) What would be the actuarially fair premium if in addition to insuring the above 5 people, the insurance company want to insure another group of 5 more people with 5% chance of getting hit by a car? For, simplicity assume that Insurance company do not know exactly know who is more high-risk or low-risk individual, but they know the composition of the total population that is being insured (c) Is there a group of people who might overpay if the insurance company charge actuarially fair premium in the above scenario? If so, which group? (d) What type of market failure issue might arise in such case? Explain in terms of the above scenario Hint: The group that overpays (pays even more than the maximum insurance they are willing to pay) will leave. So Compare what they need to pay in the current scenario with what is their maximum willingness to pay to make a decision