I really need help on this problem. So if you could help it would be greatly appreciated.
Adverse Selection, Unraveling and Mandate in Insurance.Consider an economy with three types of drivers: safe (s), inexperienced (i), and crazy (2). Each type makes up1/ 3 of the population. Everyone earns the same income of $289. The probability of having an accident is 40%for type S, 50% for type i and 60% for type 2. An accident leads to repair expenses of $64. Everyone has the sameutility function U(0) : \/(—7where C is consumption and is given by C : Income — Expenses. An insurance company offers full-coverage insurance to these drivers, i.e. it will cover the $64 of expenses incase of an accident. Each individual driver chooses whether to buy the full insurance or not. (Partial insuranceis not an option – they either buy full-coverage insurance or don’t buy insurance at all.) (a) Suppose the insurance company can tell what type of driver a person is and charges each personan actuarially fair premium What types of drivers will buy the policy? Why? [Hint you do not need tocalculate the premium for each type of driver to answer this question] (b) Now suppose that the insurance company cannot distinguish the three types of drivers. Instead,it has to charge everyone the same premium. Assuming everyone buys the insurance, what will the premiumbe? What is the consumption level of the drivers in case of an accident? What is the consumption level ofthe drivers in case of no accident? (c) Prove that the safe drivers (type S) would not be willing to buy insurance given the premiumyou found in part (b). (d) (5 points) Since safe drivers do not buy the insurance, the insurance company cannot offer the policy at theprice you found in part (b). Assuming that only inexperienced and crazy types uy the insurance, what would be the premium? (e) Prove that the inexperienced drivers (type i) would not be willing to buy insurance given thepremiLun you found in part (d). (f) What you have demonstrated is an example of market failure due to adverse selection. Discusshow the exercise above tells you about the role of individual mandate in the Affordable Care Act?
