1. [Spring 2013 final, Problem A2 and Fall 2013 final, Problem B5] Consider a market for used cars. There are two types of cars: "good" and "bad". Good cars are worth $10,000 to buyers and $5,000 to sellers, while bad cars are worth $6,000 to buyers and $4,000 to sellers. Fraction p of all cars are good. Assume that each seller knows the type of their own car, but that the buyers cannot observe the type of any car. All agents are risk-neutral and have quasilinear utility. a) Describe the Pareto efficient allocation of cars. Is it achievable? If so, state the range(s) of the relevant price(s). If not, justify your answer. Now suppose additionally that sellers have the entire bargaining power, so they can charge the buyers their entire willingness to pay. Buyers still cannot observe the type of any car. However, each seller can get a "good car certificate" (GCC) from a mechanic. Buyers can see whether a car has a GCC, so their willingness to pay can depend on it. A GCC costs: $500 to sellers of good cars, $(X 500) to sellers of bad cars (think of X as a bribe). b) Answer each