Suppose there are three types of cars, lemons (L), melons (M), and peaches (P). There is a continuum of buyers and sellers. Potential buyers value lemons at 1,200, melons at 1,800, and peaches at 2,100. The sellers value lemons at 900, melons at 1,470 and peaches at 1,860. Everybody knows that 1/3 of the cars are peaches, the fraction 2/3 - A are melons, and the remaining fraction are lemons. Buyers and sellers are risk neutral. Prices are given exogenously. (a) 5 marks Which cars should be traded from an efficiency perspective? (b) 15 marks Suppose that neither buyers nor sellers observe the quality of the car. Determine the range of prices at which all cars will be traded. Prove that this range of prices is nonempty for all valid values of X. (c) Now suppose that sellers observe the quality perfectly, but buyers have no informa- tion at all. i. [2 marks Will it be possible to trade different cars at different prices? ii. 5 marks What cars and at what prices can possibly be traded when = 1/3? iii. 5 marks For what range of values of A will there exist a price at which all types of cars are traded? (d) Finally, suppose sellers can perfectly observe their cars' types, while buyers can identify peaches, but cannot tell lemons apart from melons. i. 3 marks Will it now be possible to trade different cars at different prices? ii. 5 marks What cars and at what prices can possibly be traded when X = 1/3? iii. 5 marks For what range of values of A will there exist prices at which all cars are traded?