QUESTION 1 Use the following scenario to answer the questions below. 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 S40,000. 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. Supoose an insurance comoany has two plans. The first olan is a high deductible olan, 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 h h 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). 30 93 300 930 QUESTION 2 Calculate the actuarially fair premium in the high deductible plan for the careless 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). 30 93 300 930 QUESTION 3 Calculate the actuarially fair premium in the low 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) 100 1000 93 O 930 QUESTION 4 Calculate the actuarialyfair premium in the low deductible plan for the careless 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) 100 1000 93 930 QUESTION 5 Calculate the expected utility for the careful driver if he chose the high deductible plan. (Hint: Think of what the driver has to pay in terms of repairs and insurance and how it affects his consumption and utility. Drivers pay insurance premiums whether they have an accident or not.) O 10.5697 10.5939 O 10.5941 O 10.5713 QUESTION 6 Calculate the expected utility for the careless driver if he chose the high deductible plan. (Hint: Think of what the driver has to pay in terms of repairs and insurance and how it affects his consumption and utility. Drivers pay insurance premiums whether they have an accident or not.) 10.5697 O 10.5939 10.5941 10.5713 QUESTION 7 Calculate the expected utility for the careful driver if he chose the low deductible plan. (Hint: Think of what the driver has to pay in terms of repairs and insurance and how it affects his consumption and utility. Drivers pay insurance premiums whether they have an accident or not.) O 10.5697 O 10.5939 10.5941 10.5713 QUESTION 8 Calculate the expected utility for the careless driver if he chose the low deductible plan. (Hint: Think of what the driver has to pay in terms of repairs and insurance and how it affects his consumption and utility. Drivers pay insurance premiums whether they have an accident or not.) 10.5697 O 10.5939 10.5941 10.5713 QUESTION 9 Based on answers (5) to (8), the careful driver chooses the the careless driver chooses the, low deductible:high deductible Olow deductible; low deductible high deductible; low deductible high deductible: high deductible QUESTION 10 For questions (10) to (15), you willl suppose that the insurance company does not know who is a careful driver or a careless driver and decides to offer the same low deductible plan to all drivers, and the same high deductible plan to all drivers 550: 3850 3850: 511.5 0115: 511.5 511.5: 115 QUESTION 11 what is the expected utility for the careful driver with the high deductible plan? 10.57 10.58 10.59 10.61 QUESTION 12 What is the expected utility for the careless driver with the high deductible plan? O10.57 O 10.58 O 10.59 10.61 QUESTION 13 What is the expected utility for the careful driver with the low deductible plan? O 10.57 O 10.58 10.59 O 10.61 QUESTION 14 What is the expected utility for the careless driver with the low deductible plan? 10.57 10.58 10.59 O10.61 QUESTION 15 Based on your answers to questions (11) to (14), the careful driver chooses the deductible plan and the careless driver chooses the deductible plan O high; lovw O high: high low low low: high