Consider an exchange economy with 2 agents and 2 goods. Suppose agent A has the utility function uA(x, y) = x + y and agent B has the utility function uB (x, y) = xy and the endowment of A is (1,0), one unit of good x and 0 units of good 2, and the endowment of B is (0,1), zero unit of good x and 0 unit of good y. a. In an Edgeworth-Bowley diagram, illustrate the endowment allocation, the competitive (Walrasian) equilibrium prices and the competitive (Walrasian) equilibrium allocations for A and B. Explain. b. In an Edgeworth-Bowley diagram, illustrate the contract curve (the set of Pareto optimal allocations). Is the endowment allocation Pareto optimal? Explain. c. Compute the competitive (Walrasian) equilibrium prices (px, py), the competitive (Walrasian) equilibrium allocations, and explain how much of good x and of good y is sold or bought by agent A and agent B in this equilibrium. Explain. d. Derive and compute the contract curve and illustrate. State the First Theorem of Welfare Economics.