10. 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 Oq t by consuming the unit of quality q at price t. If he decides not to buy, he gets a utility Of zero. O can take two values 01 I and 02 4. (a) Suppose the seller can observe O. Derive the profit maximizing price-quality pairs offered when the type is 01 = I and when the type is 02 = 4. [6 marks] (b) Prove that the full information price-quality pairs are not incentive com- patible if the seller cannot observe 0. [7 marks] (c) Suppose the seller cannot observe O, and suppose he decides to set ql 1/4 and = 4. Calculate the optimal values Of tl and [2 such that both types participate, type 01 = 1 takes the contract (n, h) and type 02 = 4 takes the contract (ft, t2) [7 marks] [Hint: write down the participation constraint of type 01 and the incentive constraint of type 02 and solve for tl and 12-1