Suppose that the market is comprised of 2 groups of people of differing risk cat
ID: 3179381 • Letter: S
Question
Suppose that the market is comprised of 2 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
The insurance company has no loading costs (t=0) The proportion of people on each group and their probability of requiring medical treatment is as follows:
Group
Low Risk
High Risk
Proportion of People
80%
20%
Probability of Medical Treatment
0.20
0.80
a. What is the most money an individual on each group will be willing to pay (WTP) for an insurance policy that fully insures them in the event they require medical treatment?
b. What is the expected loss for an individual on each group?
c. What is the risk premium an individual on each group would be willing to pay to fully insure against the cost of medical treatment?
d.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 actuarially fair premium be? Which group(s) would buy insurance at this price? Why?
e. 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 actuarially fair premium that the insurance company would charge all its clients to fully insure against the cost of medical treatment? Which group(s) would buy insurance at this price? Why?
f. What fraction of the population is insured? What fraction of the population is uninsured? Is this an efficient outcome? Explain.
g. Describe at least three different options the health insurance company has to address the problem you found on part (f).
Group
Low Risk
High Risk
Proportion of People
80%
20%
Probability of Medical Treatment
0.20
0.80
Explanation / Answer
4th group of people would be willing to pay the maximum premium as they are most likely to get ill
b) Each group has different risk potential here, If their premium is same they would not pay the premium
Group 1 has lowest risk so must be charged lowest premium, Group 2 has little higher risk so little higher premium, 3 and 4 has higher risk so more premium]
d) There is nothing like average risk, Each group has different risk
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