1. Consider a two person exchange economy with preferences for person i={1,2} given by a utility function u'(c) and endowments being w; where ci = (C) and w; = (wi, wi) >> 0. Assume both consumers have Cobb-Douglas Utility functions (not identical). a. Construct the Edgeworth box carefully for this economy. b. Define mathematically the set of socially feasible allocations. c. Define mathematically the Contract Curve, and show it in the Edgeworth box. d. Define mathematically the Pareto Improvement set from any initial allo- cation w = (w1, W2) e. Depict a competitive equilibrium in this economy. f. Explain why the first welfare theorem holds. g. Define the Second Welfare theorem. Explain also why it holds in this economy. 2. In question 1, assume person 1 has preferences that are perfect substitutes, and person 2 has Cobb-Douglas preferences. Redo parts (a)-(g) for this economy. 3. In question 2, assume person 1 has preferences that are perfect complete- ments, and person 2 has preferences that are perfect substitutes. Redo parts (a)-(g) for this economy