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Medical evidence has strongly shown the correlation between smoking and heart disease. The insurance companies have noticed it too. In fact, suppose that they have compiled data that shows the likely claims to be filed by various classes of smokers. To make the analysis simpler, suppose that the typical client for insurance has 100,000 in wealth and that the disease caused by smoking (if it hits them) will cause damages of 50,000. The insurance company only offers full coverage policies, i.e., a policy which would pay the holder all damages incurred. The table below shows the results of the insurance companies study:
Potential Client Type Probability of filing claim Expected claim
Non smoker 0.1 5,000
Light smoker 0.2 10,000
Medium smoker 0.3 15,000
Heavy smoker 0.4 20,000
Continuous smoker 0.5 25,000
The insurance company is risk neutral but potential clients are risk averse with a utility function of
U = W0.5, where W is the client's net wealth after incurring illness (if any), paying for insurance (if any), and receiving a payment from the insurance company (if any).
The insurance commissioner of the state in which the insurance company does business requires that all clients must pay the same insurance premium and that the aggregate of all premium income to the company must equal the expected payout of claims by the insurance company.
What insurance rate would exist in the above market and which customer type(s) would buy insurance? Why?
The insurance rate would be ________ and customer type(s) ______________ would buy insurance.
because ___________________________________________________________________________
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Solution Summary
The solution answers the question(s) below. The insurance commissioners are examined.
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Medical evidence has strongly shown the correlation between smoking and heart disease. The insurance companies have noticed it too. In fact, suppose that they have compiled data that shows the likely claims to be filed by various classes of smokers. To make the analysis simpler, suppose that the typical client for insurance has 100,000 in wealth and that the disease caused by smoking (if it hits them) will cause damages of 50,000. The insurance company only offers full coverage policies, i.e., a policy which would pay the holder all damages incurred. The table below shows the results of the insurance companies study:
Potential Client Type Probability of filing claim Expected claim
Non smoker 0.1 5,000
Light smoker 0.2 10,000
Medium smoker ...
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