3. In a used car market, there is a total mass of M potential sellers and M potential buyers. Suppose that each seller knows the quality of the car he is selling, but buyers cannot observe a car's quality before making the purchase. Moreover, for a car of quality q, the value of this car to the seller is q, and the value of this car to any buyer is aq for some a > 1. We assume that, from each buyer's perspective, the quality of cars is uniformly distributed on [0, 10]. Suppose first that o = 1.5. (a) If the price is p, which sellers will put their cars on the market? How many cars are supplied in total? (b) If the price is p, then from each consumer's perspective, what is the average quality of the cars on the market? How much is he willing to pay for a car on the market without knowing its quality? Will any buyer purchase a car at this price? (c) What is the competitive equilibrium of this market? Suppose now that a = 3. (d) If the price is p, How much is he willing to pay for a car on the market without knowing its quality? What is the market demand at this price? (e) What is the competitive equilibrium of this market