It has been observed that investment bankers in New York who ride bicycles for recreation or exercise face a greater risk of having their bike stolen than professional bicycle messengers. Specifically, there is an 80% chance that a banker will lose a $1,000 bicycle during a given year but only a 20% chance that a messenger will lose a bicycle. An equal number of bankers and messengers own bicycles in New York. The bankers and messengers both have the logarithmic utility functions u(C) = log C, and they both earn $10,000 a year. a. Suppose that the insurance company can observe the "type" of the customer. What will be the actuarially-fair insurance premium(s) charged by the insurance company? Will both types of customers be served by the insurance company? Explain. It has been observed that investment bankers in New York who ride bicycles for recreation or exercise face a greater risk of having their bike stolen than professional bicycle messengers. Specifically, there is an 80% chance that a banker will lose a $1,000 bicycle during a given year but only a 20% chance that a messenger will lose a bicycle. An equal number of bankers and messengers own bicycles in New York. The bankers and messengers both have the logarithmic utility functions u(C) = log C, and they both earn $10,000 a year. a. Suppose that the insurance company can observe the "type" of the customer. What will be the actuarially-fair insurance premium(s) charged by the insurance company? Will both types of customers be served by the insurance company? Explain