(25 pts) Suppose that the market is comprised of 4 groups of people of differing risk categories. Individuals know their own risk, but insurers cannot tell which group a person belongs to. Each individuals has a current income equal to $40,000 and faces a risk of requiring medical treatment costing $7,600. Each individual has an utility function given by U = X1/2 Each groupâs probability of requiring medical treatment is as follows:
Group 1 2 3 4 # of People 1,000 1,000 1,000 1,000 Probability of Medical Treatment 0.20 0.40 0.60 0.80 a. (
5 pts) What is the most money each group will be willing to pay for an insurance policy that fully insures them in the event they require medical treatment (premium)?
b. (4 pts) What is the expected loss for each group? How does it compare to their maximum willingness to pay for insurance? Why are these different? c. (4 pts) What is the average riskiness of a person seeking insurance? If an insurance company were to charge all its clients the same premium to fully insure them, what would the fair premium be? Which group(s) would buy insurance at this price? Why?
c. (4 pts) What is the average riskiness of a person seeking insurance? If an insurance company were to charge all its clients the same premium to fully insure them, what would the fair premium be? Which group(s) would buy insurance at this price? Why?
d. (4 pts) What is the average riskiness of the persons now seeking insurance? (the group(s) identified in the last part of question (c) above). What would be the new fair premium that the insurance company would charge all its clients? Which group(s) would buy insurance at this price? Why? e. (4 pts) What is the average riskiness of the persons now seeking insurance? (the group(s) identified in the last part of question
(d) above). What would be the new fair premium that the insurance company would charge all its clients? Which group(s) would buy insurance at this price? Why? f. (4 pts) Is this an efficient outcome? Explain. Describe the different options the firm has to address this problem.
(25 pts) Suppose that the market is comprised of 4 groups of people of differing risk categories. Individuals know their own risk, but insurers cannot tell which group a person belongs to. Each individuals has a current income equal to $40,000 and faces a risk of requiring medical treatment costing $7,600. Each individual has an utility function given by U = X1/2 Each groupâs probability of requiring medical treatment is as follows:
Group 1 2 3 4 # of People 1,000 1,000 1,000 1,000 Probability of Medical Treatment 0.20 0.40 0.60 0.80 a. (
5 pts) What is the most money each group will be willing to pay for an insurance policy that fully insures them in the event they require medical treatment (premium)?
b. (4 pts) What is the expected loss for each group? How does it compare to their maximum willingness to pay for insurance? Why are these different? c. (4 pts) What is the average riskiness of a person seeking insurance? If an insurance company were to charge all its clients the same premium to fully insure them, what would the fair premium be? Which group(s) would buy insurance at this price? Why?
c. (4 pts) What is the average riskiness of a person seeking insurance? If an insurance company were to charge all its clients the same premium to fully insure them, what would the fair premium be? Which group(s) would buy insurance at this price? Why?
d. (4 pts) What is the average riskiness of the persons now seeking insurance? (the group(s) identified in the last part of question (c) above). What would be the new fair premium that the insurance company would charge all its clients? Which group(s) would buy insurance at this price? Why? e. (4 pts) What is the average riskiness of the persons now seeking insurance? (the group(s) identified in the last part of question
(d) above). What would be the new fair premium that the insurance company would charge all its clients? Which group(s) would buy insurance at this price? Why? f. (4 pts) Is this an efficient outcome? Explain. Describe the different options the firm has to address this problem.
