There are 2 future states 01 and 02. The probability of 01 and 02 eventuating are #1 and T2 respectively. Endowments differ by state. There are two agents with utility function U(c) = co+1 ln(ci) + 2 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 4 Agent 2 4 C01 C02 1 5 7 2 0.4 0.6 Answer the following: (a) Set up the maximization problem for both agents. (b) Take the FOCs with respect to z, z, 2, and 3. (c) Solve for optimal zł, z, zỉ, and z. (d) Solve for qi and q2. (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 T2 respectively. Endowments differ by state. There are two agents with utility function U(c) = co+1 ln(ci) + 2 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 4 Agent 2 4 C01 C02 1 5 7 2 0.4 0.6 Answer the following: (a) Set up the maximization problem for both agents. (b) Take the FOCs with respect to z, z, 2, and 3. (c) Solve for optimal zł, z, zỉ, and z. (d) Solve for qi and q2. (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?
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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just a,b,c and d please (with working out)
Transcribed Image Text:There are 2 future states 01 and 02. The probability of 01 and 02 eventuating are #1 and
T2 respectively. Endowments differ by state. There are two agents with utility function
U(c) = co+1 ln(ci) + 2 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 4
Agent 2 4
C01 C02
1 5
7 2
0.4 0.6
Answer the following:
(a) Set up the maximization problem for both agents.
(b) Take the FOCs with respect to z, z, 2, and 3.
(c) Solve for optimal zł, z, zỉ, and z.
(d) Solve for qi and q2.
(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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