Suppose that there are 6 qualities of car, q, equal to 0, 1/4, 1/2, 3/4, 1, 5/4, 3/2, 7/4, and 2. one thousand people currently own each quality of car and there are as many people interested in buying them. the value of the cars to the people that currently own them is given by 2000*q. prospective buyers are willing to pay 3000*q.

i) suppose that buyers and sellers know the quality of each car. what is the competitive market price for each quality of car? do all cars get sold? price for each car? do all cars get sold? price for each car? do all cars get sold? carefully show your reasoning.
ii) suppose that neither buyer nor seller can observe the quality of the car. what is the competitive market
iii) suppose that the sellers know the quality of the car they have to sell. what is the competitive market
iv) the market described in part iii above is usually called adverse selection (also the market for lemons). describe some institutions that might evolve to fight the adverse selection problem for used cars.