Suppose there are two kinds of people in society who are equally represented those with 15% chance of developing diabetes next year, and those with...
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Suppose there are two kinds of people in society who are equally represented — those with 15% chance of

developing diabetes next year, and those with 3% chance of developing diabetes next year. Individuals know their own risks but the insurers cannot discern this information (so they can't charge different prices to different people). Purchasing health insurance is voluntary in this society. Diabetes costs $8,000 to treat. If you are an insurer who will offer a full coverage policy (i.e. you will pay $8,000 on behalf of your customer if diabetes happens), what should you set as your premium, and why?

What are insurer practices that attempt to solve problems caused by the traditional, full-coverage, fee-for-service type insurance contracts? [3 points]


Suppose there are four cars for sale in a used car market. They have quality 0.25, 1, 1.5, and 2.

The car seller values the car at $10Q (i.e. car of quality 0.25, 1, 1.5 and 2 are valued at $2.50, $10, $15 and $20). The car buyer values the car at $15Q (i.e. values the car of quality 0.25, 1, 1.5 and 2 at $3.75, $15, $22.50 and $30).

a) Suppose that state law prevents car buyers from taking the offered car for independent quality verification for fear of discrimination towards "sicker" cars, but you do know that there are 4 possible quality cars out there (the buyer and seller both know all the information given above).

A car exchange opens up to facilitate possible sales. A price of $12 is first posted. That means, the exchange asks any car seller who is willing to accept $12 as the price to come list their cars, and buyers are invited to come and decide whether at $12 they would want to buy a car. Remember the cars on the exchange will look identical to the buyers since they cant tell car quality apart, but they are not naïve—they can figure out at a price of $12 which car sellers are going to show up on the exchange

Question: at this price of $12, will a car buyer want to buy a car (and thus would any transactions take place)?

b) Suppose the price changes to $21. At this price, would any transactions take place?

c) Now the state law changes and you are allowed to take the car for quality inspection from the exchange, and there is not just one unique price now at which transactions have to occur—instead, any car buyer and seller who meet at the exchange can negotiate a price after the independent mechanic verifies quality. What transactions are likely to occur now, and at what price ranges for each car?


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