Help with microeconomics question

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 $1,500, melons at $2,400, and peaches at $3,600. The sellers value lemons at $900, melons at $1,800 and peaches at $2,700. Everybody knows that 1f3 of the cars are lemons, the fraction 2/3 A are melons, and the remaining fraction A are peaches. Buyers and sellers are risk neutral. Price p is given exogenously. a. Which cars should be traded from an efficiency perspective? Briefly explain why. (5 Marks) b. Suppose that neither buyers nor sellers observe the quality of the car. Determine the range of prices at which all cars will be traded. (6 Marks) 0. Now suppose that sellers observe the quality perfectly, but buyers have no informa- tion at all. i. Will it be possible to trade different cars at different prices? (4 Marks) ii. For what range of values of A will there exist a price at which all types of cars are traded? (8 Marks) d. Finally, suppose sellers can perfectly observe their cars' types, while buyers can identify lemons, but cannot tell peaches apart from melons. i. Will it now be possible to trade different cars at different prices? (3 Marks) ii. For what range of values of A will there exist a price at which both peaches and melons are traded? (8 Marks)