11. Consider a market for used cars. There are some low quality cars and some high quality cars. Potential sellers have a car each, and there are many more buyers than possible sellers in the market. A high quality car never breaks down. A low quality car provides a poorer ride quality over longer journeys and also breaks down with positive probability.

A seller values a high quality car at 9000 and a low quality car at 4000. A buyer values a high quality car at 10,000 and a low quality car at 5000. All agents are risk-neutral. In answering the following questions, assume that the sellers get the entire surplus from trade.

(a) Suppose quality is observable to sellers but not to buyers. Buyers only know that a fraction 3/5 of the cars in the market are high quality and the rest are low quality. Would cars of both low and high qualities be traded in equilibrium? Derive the equilibrium price(s) at which such trade takes place.

(b) Is the market outcome in part (a) efficient? Explain your answer

(c) Now suppose low quality cars break down with probability 0.7. Recall that high quality cars never break down. Suppose the sellers of high quality cars announce a guarantee that promises a full refund if the car breaks down. Show that with this guarantee, high quality cars sell for 10000 and low quality cars sell for 5000.

(d) Suppose, as in part (c), that low quality cars break down with probability 0.7. Suppose the government decides to force each seller to offer a full refund if the car sold by the seller breaks down. How does this change the market outcome? Is the market outcome efficient? Explain your answer