Covid Insurance Problem (only the first 2 parts)

Problem V. COVID Insurance (35 points) People with preexisting conditions like asthma, diabetes, etc. are more severely all'ectml by COV'ID-IQ infection. Suppose both types of people, normal (N) and the ones with preexisting conditions (0), might be infected at the probabilities 1r\" = 5% and arc = 10%_ Additionally, suppose that unlike normal people, the ones with preexisting conditions will require hospitalization il' infected. Therefore, normal people incur a mist of $1500 in the case of infection while people with preexisting conditions incur a mat of $5000. Each person has an income of $10,000. Health insurance companies provide two plans: low-deductible plan (L) which covers all cost above $100 and the high-deductible plan (H) which covers all costs above $1000. Individuals obtain utility from consumption uc) = 1. What is the actuarially l'air premium [or each type and policy? fpbmpuy, pHN,pH-C) [Ill pts) 2. Compute the utility of both types in either policy plan assuming that the insurance com- panies charge the actuarially l'air premium of normal people. [ohmuuhumncq [Ill pts) 3. What is the favorite plan of each type? Explain the intuition. (5 pts) 4. Suppose the insurance company does not observe the types. Therefore, insurance com- pany sets only one premium [or H policy and one for L policy, either N or C premium. Determine the two premiums, (gammy). Is there a market failure? Why? (10 pts)