Consider a society with three kinds of drivers: safe, careless, and crazy. There is an equal...

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Consider a society with three kinds of drivers: safe, careless, and crazy. There is an equal number of each of these drivers, and each driver has initial wealth of $150 and utility U(W) = W. In any given year, a safe driver gets into an accident with probability P = 0.1; a careless driver gets into an accident with probability Pa = 0.2, and a crazy driver gets into an accident with probability P = 0.3. An accident leads to repair costs of $50, and has no other consequences. Suppose that an insurance company offers full coverage insurance policies to these drivers; i.e., when accidents occur, claim payments of $50 are made which fully cover repair costs. The drivers decide whether to purchase these full coverage policies. A. (8 points) Suppose the insurance company can distinguish between the three types of drivers, and offers each driver an actuarially fair full coverage insurance policy based on his or her accident probability. Which of the drivers will buy such a policy? B. (8 points) Now suppose that although the insurance company cannot distinguish between the three types of drivers, it decides to offer to offer a full coverage insurance policy to all drivers for a price of $10. Show that safe drivers are not willing to purchase such a policy, whereas careless and crazy drivers will purchase such a policy. C. (8 points) Since safe drivers are not willing to purchase the policy described in part B, the insurance company decides to increase the price of the policy, hoping to not lose money. This time, it offers a full coverage insurance policy for a price of $15. Show that safe and careless drivers are not willing to purchase such a policy, whereas crazy drivers will purchase such a policy. D. (8 points) This problem illustrates how adverse selection can limit insurability; here, even though safe and careless drivers are risk averse and would certainly be interested in purchasing coverage, the presence of the crazy drivers makes this challenging. Explain how offering partial coverage to the safe and careless drivers can solve this problem. Consider a society with three kinds of drivers: safe, careless, and crazy. There is an equal number of each of these drivers, and each driver has initial wealth of $150 and utility U(W) = W. In any given year, a safe driver gets into an accident with probability P = 0.1; a careless driver gets into an accident with probability Pa = 0.2, and a crazy driver gets into an accident with probability P = 0.3. An accident leads to repair costs of $50, and has no other consequences. Suppose that an insurance company offers full coverage insurance policies to these drivers; i.e., when accidents occur, claim payments of $50 are made which fully cover repair costs. The drivers decide whether to purchase these full coverage policies. A. (8 points) Suppose the insurance company can distinguish between the three types of drivers, and offers each driver an actuarially fair full coverage insurance policy based on his or her accident probability. Which of the drivers will buy such a policy? B. (8 points) Now suppose that although the insurance company cannot distinguish between the three types of drivers, it decides to offer to offer a full coverage insurance policy to all drivers for a price of $10. Show that safe drivers are not willing to purchase such a policy, whereas careless and crazy drivers will purchase such a policy. C. (8 points) Since safe drivers are not willing to purchase the policy described in part B, the insurance company decides to increase the price of the policy, hoping to not lose money. This time, it offers a full coverage insurance policy for a price of $15. Show that safe and careless drivers are not willing to purchase such a policy, whereas crazy drivers will purchase such a policy. D. (8 points) This problem illustrates how adverse selection can limit insurability; here, even though safe and careless drivers are risk averse and would certainly be interested in purchasing coverage, the presence of the crazy drivers makes this challenging. Explain how offering partial coverage to the safe and careless drivers can solve this problem.