Question

Suppose people cannot tell for sure whether they will fall ill in any given year. High-risk people correctly perceive their chance of falling ill in a year is 30 percent, and low-risk people correctly perceive that their chance of falling ill is 10 percent. Both high-risk and low-risk people have to pay $10,000 in medical expenses if they fall ill, and nothing if they remain healthy.a. What are the expected annual medical expenses of a high-risk person?$ per yearb. What are the expected annual medical expenses of a low-risk person?$ per yearc. Suppose insurance companies cannot tell whether someone is high-risk or low-risk. They only know that half of all people are high-risk, and half of all people are low-risk. So, they offer a health insurance policy that costs $2,000 per year in exchange for covering all of a person's medical expenses should they fall ill. If high-risk people, and low-risk people are risk-neutral, then who will purchase this insurance policy? Will the insurance company be able to stay in business if it continues to charge $2,000 per year? Briefly explain.(Click to select) Only low-risk people or Neither high-risk nor low-risk people or Only high-risk people or Both high-risk and low-risk people will want to purchase the insurance policy.The insurance company (Click to select) will not or will be able to stay in business because on average the company will (Click to select) break even or pay less to each customer than the revenue it receives from each customer or pay more to each customer than the revenue it receives from each customer .

Answer 1

The expected annual medical expenses of a high-risk person is $3000 per year while that of a low-risk person is $1000 per year.

The expected annual medical expenses of a high-risk person will be calculated as:

= Probability of falling ill × Expenses in case of illness

= 30% × $10000

= 0.3 × $10000

= $3000

The expected annual medical expenses of a low-risk person will be calculated as:

= Probability of falling ill × Expenses in case of illness

= 10% × $10000

= 0.1 × $10000

= $1000

It should be noted that in a situation where the individuals are risk neutral, the low-risk persons will not buy insurance as only the high-risk individuals will be expected to buy insurance.

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