Advanced Microeconomics Question

3. Consider the lemons' market environment. With probability (1 6 (0,1), the car is good and worth in; = 100 to a buyer and '01-; = 90 to the seller. With probability 1 q, the car is bad and worth m; = 10 to a buyer and "UL = 0 to a seller. A seller's payoff is equal to the car's worth to him (11,-, i = H, L) if he keeps the car or the money he gets if he sells the car. A buyer's payoff is equal to the car's worth to her (ui, i = H, L) minus the price she pays for the car. Assume that there are many more buyers than sellers, so the equilibrium price(s) is equal to the expected valuation of the buyer, which always leaves her with a zero expected surplus conditional on the price charged. Assume when a buyer is indifferent between buying the car and not buying it, she always chooses to buy it. (a) Assume first that the quality of a car is common knowledge between sellers and buyers. What are the equilibrium prices of good cars (pH) and bad cars (191,)? (b) Assume neither buyers nor sellers know the quality of a car. What are the equilibrium prices? (c) Assume now a seller knows the quality of his car, but buyers do not. What are the equilibrium prices? Under which values of q does market failure occur