(a) Set up the maximization problem for both agents. (b) Take the FOCs with respect to z, z, z₁, and zz. (c) Solve for optimal z, z, z, and z. (d) Solve for qi and 92. (e) What are the post trade allocations? (f) Are the post trade allocations Pareto Optimal? 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) + 2 In(c2) There are 2 zero net supply AD securities. Denote demand for these securities as where k is agent 1 or 2 and i is state 1 or 2. Assume the following: eo €82 Agent 1 4 4 8 Agent 2 4 10 5 П 0.40 0.60
(a) Set up the maximization problem for both agents. (b) Take the FOCs with respect to z, z, z₁, and zz. (c) Solve for optimal z, z, z, and z. (d) Solve for qi and 92. (e) What are the post trade allocations? (f) Are the post trade allocations Pareto Optimal? 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) + 2 In(c2) There are 2 zero net supply AD securities. Denote demand for these securities as where k is agent 1 or 2 and i is state 1 or 2. Assume the following: eo €82 Agent 1 4 4 8 Agent 2 4 10 5 П 0.40 0.60
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Question
just e and f
Transcribed Image Text:(a) Set up the maximization problem for both agents.
(b) Take the FOCs with respect to z, z, z₁, and zz.
(c) Solve for optimal z, z, z, and z.
(d) Solve for qi and 92.
(e) What are the post trade allocations?
(f) Are the post trade allocations Pareto Optimal?
Transcribed Image Text: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) + 2 In(c2) There are 2 zero net supply AD securities. Denote demand for these
securities as where k is agent 1 or 2 and i is state 1 or 2. Assume the following:
eo
€82
Agent 1
4
4
8
Agent 2 4
10
5
П
0.40
0.60
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