An insurance market may fail to exist due to asymmetric information and adverse selection that results from it (buyers dont know the repair risks associated with the sellers car, just like insurers may not know the repair risks associated with the person who is requesting insurance from them).

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).

1. 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. i.e. 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 navethey 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)? Why or why not? Please explain your answer fully.
2. Suppose the price changes to $21. At this price, would any transactions take place?
3. 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 occurinstead, 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?