10. A seller sells a good of quality q at a price t. The cost of producing at quality level q is given by q /2. There is a buyer who receives a utility of 0q - t by consuming the unit of quality q at price t. If he decides not to buy, he gets a utility of zero. 0 can take two values 01 = 1 and 02 = 4. (a) Suppose the seller can observe 0. Derive the profit maximizing price-quality pairs offered when the type is 61 = 1 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 0, and suppose he decides to set q1 = 1/4 and 92 = 4. Calculate the optimal values of t, and to such that both types participate, type 01 = 1 takes the contract (q1, t1) and type 02 = 4 takes the contract (92, t2). [7 marks] [Hint: write down the participation constraint of type 01 and the incentive constraint of type 62 and solve for t1 and t2.]