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2 Nov 2020

3. All insurance involves imperfect information in both an obvious way and in a deeper way. 

a. At an obvious level, future events cannot be predicted with certainty.

b. At the deeper level, it is difficult for an insurance company to estimate the risk attached to an event.

c. both a and b

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Raushan Raj
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2 Nov 2020

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(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 group’s 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.

Suppose there are two types of people who need health insurance; high-risk and low-risk consumers. High-risk consumers have a relatively high probability of needing expensive medical care and on average incur $2,000 of medical expenses per year. The high-risk consumers would be willing to pay up to $2,500 for insurance that covers all their medical bills. Low-risk consumers would be willing to pay up to $1,400 for full-coverage insurance and on average would incur on average $1,200 in medical bills. Assume 1/3 of all consumers are high-risk and the remaining 2/3 of consumers are low-risk. Consumers know whether they are high-risk or low-risk. The insurance company knows 2/3 of all consumers are low-risk but cannot identify which consumers are low-risk.

If all consumers bought insurance, what price must the insurance company charge to break even in expectation? That is, what price must the insurance company charge so that the expected payments equals the premium?

Which consumers would purchase insurance at that price?

Are there wealth-creating transactions that are not consummated because of the information asymmetry?

If the low-risk consumers were willing to pay $1,500 for the insurance, how would your answers to questions 2 and 3 change?

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