A seller sells a good of quality q at a price t. The cost of producing at quality level q is given by q2/2. There is a buyer who receives a utility of Xq − t by consuming the unit of quality q at price t. If he decides not to buy, he gets a utility of zero. X can take two values X1 = 1 and X2 = 4.   (a) Suppose the seller can observe X. Derive the profit maximizing price-quality pairs offered when the type is X1 = 1 and when the type is X2 = 4.   (b) Show that the full information price-quality pairs are not incentive compatible if the seller cannot observe X.

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