rk Ch 20 Average 13 Suppose there are two types of individua

rk (Ch 20) Average: 13 Suppose there are two types of individuals: those with $112,000.00 in the bank and those with $2,800.00 in the bank. Assume that individuals with $2,800.00 in the bank declare bankruptcy If they get in an accident. In bankruptcy, creditors receive only what individuals have in the bank. Assume that both types of individuals are only slightly risk averse. nsurance. (Hint: For each type of driver, compare the price of insurance to the expected cost without insurance.)

Solution

From the given information, probability of accident (loss)= 1% = 0.01 and the size of loss = $14,000.

Actuarially fair insurance price = Probability of loss * Size of loss

Or actuarially fair insurance price = 0.01* $14000 = $140.

Thus, the actuarially fair insurance price is $140 for each driver.

For the driver with $2800, the loss will be the amount he has in the bank which is $2800. Thus, the expected cost to this driver is : Probability of accident * cost due to accident = 0.01*$2800 = $28.

Similarly, for the driver with $112,000 the cost of accident will be $14000. Therefore the expected cost to this driver will be $14000*0.01 = $140.

If the price is set at actuarially fair price = $140, the second driver will buy the insurance but the first driver will not because his expected loss or expected cost that he has to bear for the accident is less than the amount that the premium requires to be paid.

At this price, drivers with $2800 in the bank likely will not buy insurance, and those with $112,000 in the bank likely will buy insurance.

If a state law is passed which forces all individuals to purchase the insurance at actuarially fair premium, then the drivers with $2800 end up paying more for the insurance than they would have to pay in case of an accident. Thus, these drivers are at a disadvantage and the other drivers with $112,000 are at an advantage. At the actuarially fair price, the drivers with $112000 were already buying insurance therefore their behaviour will not be affected. However the behaviour of drivers with $2800 will be affected because they are being forced to buy the insurance against their will.

Thus, the statement that the law will affect the behaviour of both types of drivers is false.