Questions are attached. Please provide all possible working.

Assume that there are 2000 owners of lemons (bad used cars). They want to sell their lemons as long as a buyer offers $12, 000 or more. There is a very large number potential buyers who are willing to pay $16, 000 for a lemon or $32, 000 for a good used car. There are 6000 owners of good used cars. They want to sell their good used cars as long as a buyer offers $20, 000 or more. Assume that sellers know the quality of their cars. There are 8,000 used cars in the market. (i) If buyers know the quality of a. car as soon as they see it, what are the equilibrium price of a. lemon and that of a. good used car? (5 marks.) (ii) Now suppose that buyers cannot tell the quality of a car. Find the expected value of a used car to a buyer. (5 marks.) (iii) Use your answer to part (ii) to nd the market equilibrium if buyers cannot tell the quality of a car and they are riskneutral. (5 marks.) (iv) Now, let us change an assumption by supposing that owners of good used cars are willing to sell only if they get an offer exceeding (or equal to) v = $29, 000. What is the market equilibrium in this case? Is the equilibrium eicient'? (5 marks.)