There are 2 future states 01 and 02. The probability of 0 and 02 eventuating are...

 

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There are 2 future states 01 and 02. The probability of 0₁ and 02 eventuating are ₁ and 2 respectively. Endowments differ by state. There are two agents with utility function U(c) co + 1 ln(c₁) +72 ln(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: Agent 1 Agent 2 T eo 3 3 co₂ 5 eg₂ 1 7 0.4 0.6 2 Answer the following: (a) Set up the maximization problem for both agents. (b) Take the FOCs with respect to zi, z, z1, and 22. (c) Solve for optimal z1,z2, z², and z. (d) Solve for q₁ and 92. (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? There are 2 future states 01 and 02. The probability of 0₁ and 02 eventuating are ₁ and 2 respectively. Endowments differ by state. There are two agents with utility function U(c) co + 1 ln(c₁) +72 ln(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: Agent 1 Agent 2 T eo 3 3 co₂ 5 eg₂ 1 7 0.4 0.6 2 Answer the following: (a) Set up the maximization problem for both agents. (b) Take the FOCs with respect to zi, z, z1, and 22. (c) Solve for optimal z1,z2, z², and z. (d) Solve for q₁ and 92. (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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a For agent 1 we have max5c1m1lnc1m2lnc2 st c1c25 c10 c20 For agent 2 we have max5c1m1lnc1m2lnc2 st ... View the full answer