The Supply of Used High-Quality Motorcycles Is Q_H = 0

Essay

The supply of used high-quality motorcycles is Q_H = 0.2P_H - 1,000, and the supply of used low-quality motorcycles is Q_L = 0.5P_L - 1,000. In the used-motorcycle market, potential buyers cannot tell them apart.
a. Consumers value high-quality motorcycles at $10,000 and low-quality motorcycles at $6,000. If consumers believe there is a 50% probability that a used motorcycle is high quality, what price are consumers willing to pay for any used motorcycle?
b. At the price determined in part a, how many high-quality and low-quality motorcycles will be offered for sale? What will happen over time to the consumers' willingness to pay for used motorcycles?