Suppose there are two types of used cars; peaches and lemons. A peach, if it is known to be a peach, is worth 3,000 to buyers and 2,500 to seller. A lemon, if it is known to be a lemon, is worth 2,000 to a buyer and 1,000 to a seller. Let us assume that the total number of used cars is fixed to N in the economy and that the potential buyers is infinite. There are twice as many lemons and peaches and everybody knows this fact.

1) Suppose a used-car dealer purchases all cars in town and sells them to buyers. Let us assume that the dealer employs an excellent mechanic and can always identify the quality of a car. Construct a stage game played by the dealer and a buyer.

2) Find a Nash equilibrium in which the dealer does not sell a high quality car due to the adverse selection problem in the stage game found above.

3) Find a new equilibrium for the infinitely repeated game in which the dealer reveals the true quality of a car to buyers.