micro theory

4. (25 points) Car Insurance Assume that drivers can be divided into two groups based on their driving style: safe drivers and risky drivers. Safe drivers have a. probability of 0.05 of having an accident every year, while risky drivers have a probability of 0.25 each year. Assume that there are 1000 safe drivers and 1000 risky drivers. The cost of an accident is estimated to be $2,000. Consumers utility is simply u(Y) : Y where Y is their disposable income level. Consider the problem of a car insurance company in a perfectly competitive market: (a) (10 points) Find how much will the insurance company charge if it sets the price of the insurance to the actuarially fair premium. (b) (10 points) Using your solution for part (a), determine which consumers will end up buying insurance. Then, determine if the insurance company have an incentive to charge a. premium different than the actuarially fair premium. (Explain). (c) (5 points) Consider that the government introduces a law that mandates every individual, regardless of their driving skills to own a car insurance. Who benets and who suffers from this policy? (Explain)