Consider an exchange economy consisting of two consumers and two goods. Let two consumers h = 1 and 2 have preferences described by the utility function Uh(xh,xh) = logx +logxh. Consumer 1's endowment is w = (4,2) and Consumer 2's endowment is w = (0,2) (a) Write down each player's utility maximization problem. (b) Find the first-order conditions of the two maximization problems. (Don't worry about the second-order conditions.) (c) Fix p2 = 1, and draw consumer 2's demand function for good 1: (d) Suppose that p = 2 and p2 = 1. Can this price vector p = (2,1) be a competitive equilibrium price vector? Why? Or Why not? (e) Find all competitive equilibria.