3. (10 points) Consider a state contingent claims economy. Let L = 1, S = 2, and I = 2. There are two consumers in the economy: Alice (A) and Bob (B). Alice's endowment is e = (0, 1, 2), and Bob's endowment is eB = (0,3, 1). Both consumers have expected utility V(x) = lx1 + 72 In12, where {1, 2} = {} is the probability distribution over the future states. You can view {1, 2} as the common beliefs Alice and Bob share about probabilities of the future states. Let (1, 2) be the (t = 0) prices of one unit of state contingent consumption in states 1 and 2, respectively. (a) Write down Alice's constrained optimization problem and solve it. (b) Write down Bob's constrained optimization problem and solve it. (c) Find the equilibrium price ratio 21. Do Alice and/or Bob bear risk in equilibrium? Discuss. (d) Draw the Edgeworth box diagram for this equilibrium model. Plot the indifference curves of both agents through the endowment point. Plot the interstate budget line. Plot the indifference curves of both agents through the equilibrium allocation. Looking at your diagram, can you say the the equilibrium allocation is Pareto optimal? If yes, explain why. If no, explain why