Suppose a typical used car buyer is willing to pay $6000 dollars for a low-quali

Question

Suppose a typical used car buyer is willing to pay $6000 dollars for a low-quality used car (Lemon), and $16,000 for a high-quality car (Plum). Also, suppose the market supply of Plums is given by Q P = -30 +.005P and the market supply of Lemons is given by Q L = -40 +.01 P. Let the typical buyer’s belief that a car of unknown quality is a Plum = z, so (1-z) is the probability that a car of unknown quality is a Lemon. Assume that buyers are risk-neutral so that the price a buyer will offer for a car of unknown quality is given by:

P = z($16,000) + (1-z)($6000). Therefore P = $6000 + $10,000z.

A) State the equilibrium condition in this market.

B) Determine the two values of z that lead to a market equilibrium

Explanation / Answer

a) z = QP/(QP+ QL)

b) z = 0 and z = .20

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