Question 3: [15 minutes] Suppose that there are three types of cars on the market: good cars, bad cars and lemons. Buyers value good cars, bad cars and lemons at 240, 120, 0 respectively. Sellers value the good cars, bad cars and lemons at 150, 70, 0 respectively. Also suppose that there are more buyers than sellers so that competition on the demand side pushes prices up to the maximum buyers are willing to pay (when trade happens). (i) Suppose the proportion of good cars, bad cars and lemons is (1/3,1/3, 1/3) respectively. Show that only lemons are traded at equilibrium. (ii) Suppose instead that the proportion of good cars, bad cars and lemons is (1/4,1/2,1/4) respectively. Show that there is an equilibrium price at which both bad cars and lemons are sold but no equilibrium price at which good cars are sold. Explain the difference between the answers of parts (i) and (ii)