2. Moral Hazard in Health Insurance. (35 points) Suppose that agents have a utility function that is given by U(c) = e. Agents have an income of $1,500. If they decide not to get a vaccine, the probability of getting the associated infectious disease is 20%. However, if they get a vaccine, the probability of getting the infectious disease is 2%. Contracting the infectious disease requires agents to pay $1,300 in medical expenditures. Assume, for simplicity, that getting the vaccine has a utility cost of 1 util (because of, say, time and side effects costs). Suppose that an insurance company offers an actuarially fair contract that covers all the costs above $200, i.e., there is a $200 deductible. (a) Compute the actuarially fair premiums for both vaccinated and unvaccinated agents. (5 points) (b) Suppose the insurance company charges the actuarially fair premium for a vaccinated indi- vidual, since it is not able to observe the vaccination status. Assuming that individuals get insurance, is it convenient for them to get vaccinated? (10 points) Now suppose the insurance company offers an actuarially fair contract with a $500 deductible. (c) Compute the actuarially fair premiums for both vaccinated and unvaccinated agents. (5 points) (d) Suppose the insurance company charges the actuarially fair premium for a vaccinated indi- vidual, since it is not able to observe the vaccination status. Assuming that individuals get insurance, is it convenient for them to get vaccinated? (10 points) nswer to part (d) differ from the answer to part (b)? Why? Briefly explain. (5 points) (e) Does the answe