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Suppose there are 100 sellers, each offering one used car, and 200 buyers, each wanting one...

Suppose there are 100 sellers, each offering one used car, and 200 buyers, each wanting one used car. A used car could be of high or low quality. There are 50 high-quality cars and 50 low-quality cars. A high-quality used car is worth $10,000 to the buyer whereas a low-quality used car is worth $2,0000 to the buyer. A seller knows the car’s quality.

(a) Suppose a buyer can observe the car’s quality. What is the buyer’s maximum willingness to pay for a high-quality car? What is the buyer’s maximum willingness to pay for a low-quality car?

(b) Now suppose a buyer cannot observe the car’s quality. What is the buyer’s maximum willingness to pay for a used car if the buyer believes that all sellers (high or low quality) are selling their used cars in the market? What is the buyer’s maximum willingness to pay for a used car if the buyer believes that only the low-quality sellers are selling their used cars in the market?

(c) Suppose a seller values a high-quality used car at $8000 and a low-quality car at $1000. What is the equilibrium price in the market if the buyers cannot observe the car’s quality? How does your answer change if a seller values a high-quality used car at $5000?

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