5. Lola Lowrisk is a careful driver with a perfect driving record living in the suburbs of a major metropolitan area. Heidi Highrisk is an aggressive driver with several speeding tickets who lives in the metropolitan area near Lola. The metropolitan area is cursed with lots of traffic. Both drivers have an initial wealth level equal to $121 and measure the utility that they derive from wealth as utility = wealth0.5. The two drivers loss distributions are shown below. Based on this data, answer questions A through E.

Lola Lowrisk.: 1/3 probability of $40 loss and 2/3 probability of no loss Heidi Highrisk: 2/3 probability of $40 loss and 1/3 probability of no loss A. Determine each drivers expected utility if she is does not buy insurance protection, based on the drivers true probability of suffering a loss.

B. Determine the price that an insurer would charge each driver, assuming that the insurer knew the drivers true probability of suffering a loss. In your answer, you can assume that the insurer is basing the premium on the drivers expected loss without adding in a charge for insurance overhead and administrative expenses.

C. Calculate each drivers utility level after buying insurance at the prices calculated in part B above.

D. Assume that the insurer cannot differentiate between low- and high- risks in the immediate geographic area in which Lola and Heidi live. As a result, the insurer charges a pooled premium equal to the sum of the two premiums found in part B, divided by two. Calculate the pooled premium rate.

E. Calculate each drivers utility level after buying insurance at the price calculated in part D. Discuss whether either Lola or Heidi will buy insurance at the price calculated in part D.