1. This question concerns the second welfare theorem. [20 points total] (a) Explain the economic intuition for why the second welfare theorem requires convexity of preferences. [10 points] (b) Briey indicate how convexity of preferences is used in the proof of the second welfare theorem. To answer this, you may just name or state the theorem from mathematics that is used in the proof and requires convexity. DO NOT attempt to write a proof for the second welfare theorem. [10 points]