Find quantity supplied and quantity demanded:

Suppose there are 300 used cars, with 3 quality levels: bad, medium, and good.  A seller knows the quality of his car but a buyer does not.  The only thing buyers know is that 100 of all used cars are bad, 100 medium, and 100 good.  The values of each type of car to a seller and a buyer are: 

a)  Let P denote the price of a used car.  Find quantity supplied (Q ) and quantity demanded (Q^d) of cars if P ≥ 3000. 
b)  Find Q^s and Q^d if 2000 ≤ P < 3000.
 
c)  With quantity (Q) on the horizontal axis and price (P) on the vertical, draw the supply curve for cars.  Then draw the demand curve assuming that there is an infinite number of buyers.  Label the curves and key points in your graph clearly.
 
d)  In equilibrium, what is the price and quantity of cars?  What kind(s) of cars are traded?