I. Cau university is located on the steep hillside, thus during the winter snow season the students are at risk of slipping related injuries. The total number of the students is 200, of which 100 are careless and the other 100 are careful. The careless students do not pay attention when stepping down the stairs, and their annual average chance of slipping related injuries is 10%. The careful students are cautious when walking on the campus, having only 0.1% of the annual average chance of slipping related injuries. An injury will result in the medical cost of 5 million won. Now Doo Corporation considers selling full- coverage insurance to the students against the injuries. 1. Suppose Doo Corporation has full information, thus charging different premiums to the careless and careful students. How much are the actuarially fair premiums for each type? 2. Due to asymmetric information, Doo Corporation decided to sell the insurance plan at the premium of 252,500 won. How much would be the net profits of the Corporation? 3. Suppose the careful students are risk averse, and their risk premium is as much as all the careful students purchase the insurance and the Corporation's expected net benefit is zero at the premium of 252,500 won. How much is a careful student's risk premium? 4. Now consider the Corporation sells the following two policies. One policy offers full coverage for the 5 million won of medical costs at 500,000 won. The other policy covers up to 1 million won at 1,000 won. Assume each individual student has an identical utility function of VC, where C is the initial income of 6 million won subtracted by any payment for the insurance premium and medical costs. Calculate the expected utility of a student of each type, and explain how the market has a separating equilibrium. a 1 I. Cau university is located on the steep hillside, thus during the winter snow season the students are at risk of slipping related injuries. The total number of the students is 200, of which 100 are careless and the other 100 are careful. The careless students do not pay attention when stepping down the stairs, and their annual average chance of slipping related injuries is 10%. The careful students are cautious when walking on the campus, having only 0.1% of the annual average chance of slipping related injuries. An injury will result in the medical cost of 5 million won. Now Doo Corporation considers selling full- coverage insurance to the students against the injuries. 1. Suppose Doo Corporation has full information, thus charging different premiums to the careless and careful students. How much are the actuarially fair premiums for each type? 2. Due to asymmetric information, Doo Corporation decided to sell the insurance plan at the premium of 252,500 won. How much would be the net profits of the Corporation? 3. Suppose the careful students are risk averse, and their risk premium is as much as all the careful students purchase the insurance and the Corporation's expected net benefit is zero at the premium of 252,500 won. How much is a careful student's risk premium? 4. Now consider the Corporation sells the following two policies. One policy offers full coverage for the 5 million won of medical costs at 500,000 won. The other policy covers up to 1 million won at 1,000 won. Assume each individual student has an identical utility function of VC, where C is the initial income of 6 million won subtracted by any payment for the insurance premium and medical costs. Calculate the expected utility of a student of each type, and explain how the market has a separating equilibrium. a 1