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?

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

ogorwyne ogorwyne · Answer 2 · 2021-11-25T19:11:45+01:00

At 800 dollars people would want to buy the insurance given that this value is lower than the valuation.

At the price of 800 to 2000 the unhealthy would be the only ones buying the insurance. When it is higher than 2000, there would be no buyers.

When every one takes up insurance we would have

[tex]0.75*600 + 0.25*1600 = $850[/tex]

The company is not going to charge for lower than this amount. If it does it would be at loss. But at this price the healthy people wont buy. There valuation is at $800.

At 850 the unhealthy would buy but the payout per customer is 1600 dollars. So the customer would still be at loss except they charge more than $1600

Therefore at equilibrium the price of the insurance should be at $1600.

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