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
Related questions
Question
c,d,e and f with explanation (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?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
Foundations Of Finance
Finance
ISBN:
9780134897264
Author:
KEOWN, Arthur J., Martin, John D., PETTY, J. William
Publisher:
Pearson,
Fundamentals of Financial Management (MindTap Cou…
Finance
ISBN:
9781337395250
Author:
Eugene F. Brigham, Joel F. Houston
Publisher:
Cengage Learning
Corporate Finance (The Mcgraw-hill/Irwin Series i…
Finance
ISBN:
9780077861759
Author:
Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor
Publisher:
McGraw-Hill Education