Assume that one-third of all used cars are lemons. If the supply of good used cars is upward sloping, then it may be the case that the blended price is lower than the reservation price for some good used car owners. Such owners would not sell. Let G represent the fraction of good used car owners who actually sell their good used car, 0 ≤ G ≤ 1. Parts a to d of this problem examine the implications of selling only some good used cars on the portion of lemons sold.
a. If all good cars are sold (G = 1.0), what fraction ol all used cars are sold? What is the fraction of sold cars that are lemons?
b. If half the good cars are sold, G = 0.5, what fraction of all used cars are sold? What is the fraction of sold cars that are lemons?
c. If one-quarter of the good cars are sold, G - 0.25, what fraction of all used cars are sold? What is the fraction of sold cars that are lemons?
d. If a general portion G is sold, what fraction of all used cars is sold? What are the fractions of sold cars that are lemons? Make sure that your algebraic answers are consistent with your specific answers in parts a to c.
Suppose the perfect information prices for lemons and cherries are PL = $5,000 and PH = $10,000. Consider how good used car owners view their cars. Suppose no owner would be willing to sell at a price of $6,000, and all good used car owners would be willing to sell at a price of $9,000. (This contrasts with Problem 6, where we assumed that all would sell at a price of $8,000.) If we assume that good used car owners are uniformly distributed between these upper and lower bounds, then we can describe the supply curve as being linear between these two endpoints. We can then write the inverse supply of good used cars as a function of G, the fraction of good used cars sold, as: PS(G) = 6,000 + 3,000G. In this context, PB denotes the price at which good used car sellers are willing to sell their car.
e. Given that one-third of used cars are lemons and the full information prices of Pf = $5,000 and P" = $10,000, will all used cars be sold in this situation?
f. If the fraction G of good used cars is sold, then what price will clear the market? Write this as PB(G). In this context, PB denotes the price that buyers are willing to pay.
g. Use the equation from part f and the equation for inverse supply to determine the market-clearing price in this market. What portion of good used cars is sold? What portion of the cars sold are lemons?