Suppose that there are two types of people in a country: The careful (C) and careless (L) people. There are 500 of each type of people. Both types of people have $50.000 of annual income and they consume all their income. Both types have the utility function U = 2vI where I is consumption (= income). Careful people take extra precautions to avoid injuries of all types and only have a 12% chance of getting injured in a year. The careless people, on the other hand, aremore likely to get injured and have 30% chance of getting injured. If injured. people pay healthcare costs of $45,000. The government is planning to implement public health insurance, and is consid ering two plans. The first plan, the high-coverage plan. pays an injured person $30,000. The second plan, the low-coverage plan, pays an injured person $10,000. The government plans to finance both plans with a lump-sum tax implemented on each person. (a) (1 point) For the high-coverage plan, what is the amount of tax the govern- ment must set in order to maintain a balanced budget? (b) (1 point) For the low-coverage plan, what is the amount of tax the govern- ment must set in order to maintain a balanced budget? (c) (2 points) Consider three cases: i) The government implements the high- coverage plan and sets the tax rate equal to what you found in (a), ii) the government implements the low-coverage plan and sets the tax rate equal to what you found in (b), and iii) the government does not implement any plan (i.e., maintains the status quo). How do the careful and careless people rank the three cases? (d) (2 points) Interpret the findings from (c) in terms of risk-aversion and re- distribution with 2-3 sentences