In the used car market buyers are willing to pay $10,000 for a good car and $5,000 for a lemon. Sellers are willing to sell lemons (bad cars, which will have high repair costs) for $4,000 and they are willing to sell good cars for $9,000.

What is the Pareto efficient allocation of cars in this market?

Sellers know the quality of the car they are selling but buyers cannot determine the quality of the car. If good cars and lemons are equally common, what is the highest price that a (risk neutral) buyer would pay for a random car?

If a seller agreed to sell a car for the price you determined in the previous question, what quality could that car be? In the market equilibrium, which cars are sold in this market?

Explain the inefficiency of this market?