Exercises 153 monopoly reserves where, intuitively, we run the surplus maximiza- tion mechanism SM and then reject any winner i whose value is below her monopoly price o: (a) (a',p') + SM(v), Sz if v, 2 10 otherwise, and (c) P = max(6;, p). (b) z, = Prove that the revenue of this mechanism is an e approximation to the optimal social surplus in any downward-closed, monotone- hazard-rate environment. Conclude Theorem 4.37 as a corollary.