Ali's wage W is his only source of income. He is considering buying health insurance for...

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Ali's wage W is his only source of income. He is considering buying health insurance for the year. Ali can be in 3 different health states (denoted by j = 1,2,3) at the end of the period. The probability of each state, p; and the total medical expenditures for each state, c;, are shown in the Table below. Assume Ali's utility function over income is a concave utility function U(I). j Pj 0.6 Cj 0 1 (Healthy) 2 (Mildly unhealthy) 0.3 2000 3 (Unhealthy) 0.1 20000 (a) Provide an expression that implicitly solves for the certainty equivalent income ICE of the lottery. (b) Calculate the premium r of a full and actuarially fair contract (contract "A") (c) Calculate the premium r of contract "B"; a partial, actuarially fair contract, with a deductible of 1000 and 10% coinsurance rate (so that the insurance company covers 90% of the medical bills in excess of 1000). A numerical expression is sufficient to get full credit. (d) Give an expression (do not solve explicitly) for the premium r such that the indi- vidual is indifferent between a full contract with premium r and contract B (with premium r). Is r'a > b, r'a = B or r < B? Explain (e) Consider now contract "C"; a partial contract with a deductible of 1000 and 0% coinsurance rate (so that the insurance company covers (100)% of the medical bills in excess of 1000). Calculate the premium rc such that the individual is indifferent contract "B" and contract "C". Is rc an actuarially fair premium? Explain why, or why not. Ali's wage W is his only source of income. He is considering buying health insurance for the year. Ali can be in 3 different health states (denoted by j = 1,2,3) at the end of the period. The probability of each state, p; and the total medical expenditures for each state, c;, are shown in the Table below. Assume Ali's utility function over income is a concave utility function U(I). j Pj 0.6 Cj 0 1 (Healthy) 2 (Mildly unhealthy) 0.3 2000 3 (Unhealthy) 0.1 20000 (a) Provide an expression that implicitly solves for the certainty equivalent income ICE of the lottery. (b) Calculate the premium r of a full and actuarially fair contract (contract "A") (c) Calculate the premium r of contract "B"; a partial, actuarially fair contract, with a deductible of 1000 and 10% coinsurance rate (so that the insurance company covers 90% of the medical bills in excess of 1000). A numerical expression is sufficient to get full credit. (d) Give an expression (do not solve explicitly) for the premium r such that the indi- vidual is indifferent between a full contract with premium r and contract B (with premium r). Is r'a > b, r'a = B or r < B? Explain (e) Consider now contract "C"; a partial contract with a deductible of 1000 and 0% coinsurance rate (so that the insurance company covers (100)% of the medical bills in excess of 1000). Calculate the premium rc such that the individual is indifferent contract "B" and contract "C". Is rc an actuarially fair premium? Explain why, or why not.