Imagine a society of 1,000 people divided into five groups based on their likelihood of illness....

Imagine a society of 1,000 people divided into five groups based on their likelihood of illness. The groups, respectively, have 10%, 30%, 40%, 70%, and 90% probabilities of getting sick. Getting sick costs $10,000. Agents are risk averse so, if given a choice, are willing to pay up to 1.5x their expected expenses for insurance. (a) Initially, everyone is required to purchase insurance and insurers are not allowed to discriminate based on one’s likelihood of illness. How much would an actuarily fair policy cost?

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Expert Solution

The fair premium is the premium at which insurance company breaks even i.e. make zero profits (premium=expected cost)
Expected cost = 10000*10% + 10000*30% + 10000*40% + 10000*70% + 10000*90% = 24000
Fair premium = 24000

Rahul Sunny answered 1 year ago

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