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Attempts: Average: 13 4. Individual Problems 20-4 Suppose that every driver face

ID: 1162972 • Letter: A

Question

Attempts: Average: 13 4. Individual Problems 20-4 Suppose that every driver faces a 5% probability of an automobile accident every year. An accident wi , on average, cost each driver $12,000 Suppose there are two types of individuals: those with $60,000.00 in the bank and those with $6,000.00 in the bank. Assume that indn $6,000.00 in the bank declare bankruptcy if they get in an accident. In bankruptcy, creditors receive only what ind that both types of individuals are only slightly risk averse. ividuals have in the bank. Assume In this scenario, the actuarially fair price of ful nsurance, in which all damages are paid by the insurance company, is S Assume that the price of insurance is set at the actuarially fair price. At this price, drivers with $60,000.00 in the bank likely willbuy insurance, and those with $6,000.00 in the ba nk likely buy insurance. (Hint: For each type of driver, compare the price Suppose a state law has been passed forcing all individuals to purchase insurance at the actuarially fair price. True or False: The law will affect the behavior of both types of drivers. of insurance to the expected cost without insurance.)

Explanation / Answer

ANS:

1.actuarially fair premium = prob. of loss * loss amount = 0.05 * 12000 = $600

2. expected wealth of driver with$6000 in bank(when no insurance) = prob of loss * wealth after loss + prob. of no loss * wealth after no loss

= 0.05 * 0 + 0.95 * 6000 = $5700

expected wealth of driver with$6000 in bank(when insurance) = prob of loss * wealth after loss(i.e. wealth - loss +coverage - premium) + prob. of no loss * wealth after no loss(i.e. wealth-premium)

= 0.05 * (6000-12000+12000- 600) + 0.95 (6000-600)

=$ 5400

hence, his expected wealth is higher with no insurance(as 5700>5400) . hence, the driver with $6000 in bank will not buy insurance policy.