Business, 31.03.2020 00:35 bgf12032

Suppose there are two equal size groups of people, careless drivers and careful drivers. Careless drivers have a 10% chance to have an accident and careful drivers have a 1% chance to have an accident. Both types of people have utility U=Ln(C), where C is the amount of consumption that people have in any period. People spend their entire income of $40,000. In case there is an accident, the cost of car repairs is $10,000. However, insurance companies do not reimburse the full cost of car repairs. Even when individuals are fully insured, individuals have to pay an amount called the deductible. When insurance plans are generous, individuals pay low deductibles, and when insurance plans are not generous, individuals pay high deductibles. For questions (1) to (9), consider the following. Suppose an insurance company has two plans. The first plan is a high deductible plan, which covers car repairs above $7,000 (which is the amount of the deductible). The second plan is a low deductible plan, which covers car repairs above $700 (which is the amount of the deductible). Calculate the actuarially fair premium in the high deductible plan for the careful driver. (Hint: you have to think as if you were the insurance company and consider the expected amount of money that you would expect to reimburse in case of an accident)

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