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The used cars vary in their quality. There are 101 sellers each with a car that they value at $1,000, $1,010, $1,020, … $2,000. Sellers know the quality exactly, but buyers only know the distribution. If buyers did know the quality, they would value each car by $300 more than sellers value the car.
At a price of, say, $1,400, how much would buyers value the average car offered for sale? Would buyers be willing to pay $1,400?
At a price of, say, $1,800, how much would buyers value the average car offered for sale? Would buyers be willing to pay $1,800?
At what price is the buyer’s expected value just equal to the price?
What fraction of the available gains from trade are realized?
Suppose a used car dealer can perfectly determine a car’s value and offers a money back guarantee to buyers. However, this used car dealer intermediation costs $100 per car. Now would a car worth $2,000 to the seller get sold?
Would the seller who values her car at, say, $1,400 prefer to sell to the buyer directly or through the used car dealer?