1. In trying to understand the important role played by convexity in the second welfare theorem, you are asked to construct two counterexamples. (a) Think of an exchange economy in which one of the consumers does not have convex indifference curves and where the conclusion of the second welfare theorem is violated. (b) Can you think of a counterexample to the theorem in a general equilibrium economy with pro- duction? Hint: a leading violation of convexity in technology is increasing returns. Construct an example with increasing returns where the conclusion of the second welfare theorem fails