Suppose there are two types of people in an insurance market: high and low risks.The high-risk person is sick 10% of the time and the low-risk person is sick 5% of the time.The probability that any individual is high risk is 40%.Upon getting sick,an individual loses $10,000 in medical expenses.What are the actuarially fair premiums for the types?

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The Answer is The actuarially fair premiums are equivalent to each individual's expected loss.For a high premium,(high)= $10,000(Pr[ sick | high ])= $10,000(.10)= $1,000.For a low premium (low)= $10,000*(Pr[ sick | low ])= $10,000(.05)= $500.

Suppose There Are Two Types of People in an Insurance