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Used car dealers are faced with the following problem. There are two types of used cars: gems and lemons. Buyers are willing to pay \$8,000 for gems and \$5,000 for lemons. Sellers of lemons want \$3,000, while the sellers of gems want a minimum price of \$6,000. Half of the cars offered for sale are gems and half are lemons. The sellers know which cars are gems and which are lemons, but the buyers and the dealer do not.

a) Assuming that neither the dealer nor the buyers of used cars can tell a gem or lemon apart, what will gems sell for in the used car market? What will lemons sell for? (You may ignore any costs of operating the used car business beside the costs of cars offered for resale).

b) A test is developed that flawlessly tells a gem from a lemon. The test, which costs nothing, is widely known. Any owner can run the test (though buyers cannot). An owner can easily offer to sell his car enclosing a certified copy of the test. The certification is an infallible sign of whether the car is a gem or a lemon. Assuming that every auto seller provides the test, what would then be the price for gems and lemons?

c) Assume now that the test costs \$50. What will happen to the price of gems and lemons?

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