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1. There are 2 future states and 02. The probability of O and 02 eventuating are 71 and T2 respectively. Endowments differ by state. There are two agents with utility function U(c) = Co + In(ci) + T2 In(c2) There are 2 zero net supply AD securities (i.e. (1,0) and (0,1)). Denote demand for these securities as where k is agent 1 or 2 and i is state 1 or 2. Assume the following: ee2 Agent 1 Agent 2 eo 3 3 egi 1 5 7 2 0.4 0.6 71 Answer the following: (a) Set up the maximization problem for both agents. (b) Take the FOCs with respect to z, z, zi, and zz. (c) Solve for optimal z], zz, z1, and zz. (d) Solve for q1 and 42: (e) What are the post trade allocations? (f) What is the expected utility of both agents post and pre-trade. (g) Are the post trade allocations Pareto Optimal? Why? 1. There are 2 future states and 02. The probability of O and 02 eventuating are 71 and T2 respectively. Endowments differ by state. There are two agents with utility function U(c) = Co + In(ci) + T2 In(c2) There are 2 zero net supply AD securities (i.e. (1,0) and (0,1)). Denote demand for these securities as where k is agent 1 or 2 and i is state 1 or 2. Assume the following: ee2 Agent 1 Agent 2 eo 3 3 egi 1 5 7 2 0.4 0.6 71 Answer the following: (a) Set up the maximization problem for both agents. (b) Take the FOCs with respect to z, z, zi, and zz. (c) Solve for optimal z], zz, z1, and zz. (d) Solve for q1 and 42: (e) What are the post trade allocations? (f) What is the expected utility of both agents post and pre-trade. (g) Are the post trade allocations Pareto Optimal? Why

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