Car buyers value a high-quality used car at $16,000 and a low-quality used car at $8,000. The supply of high-quality cars is given by Q_H = -200 + 0.05P_H; the supply of low-quality cars is given by Q_L = -200 + 0.1P_L. Potential buyers cannot tell the difference between high-quality and low-quality cars when purchasing one.

a. Assume that buyers believe there is a 75% chance that a used car will be of high quality. What would be the price buyers are willing to pay for a used car of unknown quality?

b. If the price you found in (a) is offered in the market for used cars, how many high-quality cars will be offered for sale? How many low-quality cars? What will be the overall proportion of high-quality cars offered for sale? Does it match buyers’ expectations?

c. What is likely to happen when the true proportion of high-quality cars becomes known? Describe the impact on the price of a used car and the quantity of high-quality used cars offered for sale. What is the logical conclusion of this process?