Consider a market for used cars under adverse selection (i.e., sellers know the quality of the cars they own but buyers do not). There are more buyers than sellers in the market. For any given car quality, the value to the buyer of that quality is V T B = 1.2 V T O + B where V T O is the value that the seller (owner) places on that quality, and B is a number specified below. The value to the seller (owner) is uniformly distributed between $A and $10,000, where A is a number specified below.

(i) Suppose that A = $5, 000 and B = $400. Can trade take place at P = $9, 000? Explain.

(ii) Find the equilibrium price in this market when A = $5, 000 and B = $400. Are all the gains from trade realized at this price? Explain.

(iii) Draw a picture (demand and supply) of the equilibrium found in part (ii). How would the picture change if there were fewer buyers than sellers? (No need to solve here; just try to explain with a picture.)

(iii) What would be the equilibrium price in this market if A = 0 and B = 0? Explain.