Consider the following market for used cars. High-quality cars are known as plums and low-quality cars are known as lemons. Buyers are willing to pay $3,000 for a plum and $1,500 for a lemon. Sellers are willing to sell a plum for $vand a lemon for $1,000. The fraction of lemons in this market is 6: 0.25. This market is characterized by asymmetric information sellers know whether their car is a lemon or plum, but buyers only know what fraction of cars are lemons. All participants are risk neutral. (a) What is the expected value of a car with unknown quality for buyers? (b) Suppose that v: 2700. Can this market have a pooling equilibrium (i.e. we can find a price such that all cars will be sold)? Briefly explain in 30 words. (c) Suppose that v: 2500. Can this market have a pooling equilibrium? Briefly explain in 30 words. (d) What is the maximum value of Vsuch that a pooling equilibrium can exist? Briefly explain. (Answering only the maximum value of VWithout any reasoning is worth 0 point.)