Consider a community of individuals that have different probabilities of falling ill. Individuals of type H have a probability of falling ill of pH=0.6. These individuals form 43 of the population. Individuals of type L, the remaining 41 of the population, have a probability of falling ill of pL=0.2. All individuals have the same income y and linear utility over their income: u=y. When individuals get sick, they suffer an income loss of 200. a. Assume there is perfect information. What is the actuarially fair premium for each group (pL,pH) to be fully insured against illness? What is their utility under the insurance and under no insurance? Why? b. Assume there is asymmetric information and insurance providers cannot distinguish between the two types. The same contract must be offered to everyone. What is the premium of this contract p ? Does everyone purchase insurance? If not, which group does and which group doesn't? You can assume individuals purchase insurance if they are indifferent. c. in b., does the insurance market unravel? If so, what is the outcome of market unraveling? d. Is it possible for insurance providers to offer two different contracts such that everyone purchase insurance and insurance providers know who belong to which group? What conditions must these contracts satisfy? Consider a community of individuals that have different probabilities of falling ill. Individuals of type H have a probability of falling ill of pH=0.6. These individuals form 43 of the population. Individuals of type L, the remaining 41 of the population, have a probability of falling ill of pL=0.2. All individuals have the same income y and linear utility over their income: u=y. When individuals get sick, they suffer an income loss of 200. a. Assume there is perfect information. What is the actuarially fair premium for each group (pL,pH) to be fully insured against illness? What is their utility under the insurance and under no insurance? Why? b. Assume there is asymmetric information and insurance providers cannot distinguish between the two types. The same contract must be offered to everyone. What is the premium of this contract p ? Does everyone purchase insurance? If not, which group does and which group doesn't? You can assume individuals purchase insurance if they are indifferent. c. in b., does the insurance market unravel? If so, what is the outcome of market unraveling? d. Is it possible for insurance providers to offer two different contracts such that everyone purchase insurance and insurance providers know who belong to which group? What conditions must these contracts satisfy