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7 June, 18:14

There is a town with exactly 1,000 residents. In the town, 75% of the residents make healthy choices and 25% of the residents consistently make unhealthy choices, but the health insurance company in town cannot tell who is healthy and who is unhealthy. A healthy person has an average of $600 in medical expenses each year and is willing to pay $800 for insurance. An unhealthy person has an average of $1,600 in medical expenses each year and is willing to pay $2,000 for insurance. The health insurance provider can offer insurance at only one price. In equilibrium, the price of insurance will be at least what?

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  1. 7 June, 20:18
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    The price of insurance will be at least = $1,600

    Explanation:

    As per the data given in the question,

    If the price is equal to or below $800, everyone would like to buy the insurance, if price is between $800 and $2,000, only unhealthy people will purchase the insurance. and if price is above $2,000, no one would buy the insurance.

    If everyone purchase the insurance then expected payout of company = 0.75 * $600 + 0.25 * $1,600 = $850

    Therefore, Insurance company can not charge more than $850 because if it charge less than $850, there would be loss to company. But if it charge $850 even no one is going to purchase it. The expected payout per consumer would be $1,600.

    Therefore, in equilibrium, the price of insurance will be at least $1,600
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