An agent can work for a principal. The agent's effort, a affects current profits, q₁ = a +₁, and future profits, 92= a + Eq₂, where q, are random shocks, and they are i.i.d with normal distribution N(0,2). The agent retires at the end of the first period, and his compensation cannot be based on 92. However, his compensation can depend on the stock price P = 2a+Ep, where ep~ N(0,0). The agent's utility function is exponential and equal to where it is the agent's income, while his reservation utility is . The principal chooses the agent's compen- sation contract t = w+fq₁ +sP to maximize her expected profit, while accounting for the agent's IR and IC constraints. 1. Derive the optimal compensation contract i = w+fq₁ + sp. 2. Discuss how it depends on and on its relation with o. Offer some intuition?

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
icon
Related questions
icon
Concept explainers
Topic Video
Question
hand write
Problem 4.
An agent can work for a principal. The agent's effort, a affects current profits, q1 = a +Eg, and future
profits, 92 = a + Eqp, where ég, are random shocks, and they are i.i.d with normal distribution N(0, 0).
The agent retires at the end of the first period, and his compensation cannot be based on q2. However, his
compensation can depend on the stock price P = 2a + Ep, where ep - N(0,07). The agent's utility function
is exponential and equal to
where t is the agent's income, while his reservation utility is I.' The principal chooses the agent's compen-
sation contract t = w+ fq1 +sP to maximize her expected profit, while accounting for the agent's IR and
IC constraints.
1. Derive the optimal compensation contract t = w + fq1 +sP.
2. Discuss how it depends on of and on its relation with of. Offer some intuition?
Transcribed Image Text:Problem 4. An agent can work for a principal. The agent's effort, a affects current profits, q1 = a +Eg, and future profits, 92 = a + Eqp, where ég, are random shocks, and they are i.i.d with normal distribution N(0, 0). The agent retires at the end of the first period, and his compensation cannot be based on q2. However, his compensation can depend on the stock price P = 2a + Ep, where ep - N(0,07). The agent's utility function is exponential and equal to where t is the agent's income, while his reservation utility is I.' The principal chooses the agent's compen- sation contract t = w+ fq1 +sP to maximize her expected profit, while accounting for the agent's IR and IC constraints. 1. Derive the optimal compensation contract t = w + fq1 +sP. 2. Discuss how it depends on of and on its relation with of. Offer some intuition?
Expert Solution
steps

Step by step

Solved in 4 steps with 27 images

Blurred answer
Knowledge Booster
Stock Valuation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, finance and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Essentials Of Investments
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
FUNDAMENTALS OF CORPORATE FINANCE
FUNDAMENTALS OF CORPORATE FINANCE
Finance
ISBN:
9781260013962
Author:
BREALEY
Publisher:
RENT MCG
Financial Management: Theory & Practice
Financial Management: Theory & Practice
Finance
ISBN:
9781337909730
Author:
Brigham
Publisher:
Cengage
Foundations Of Finance
Foundations Of Finance
Finance
ISBN:
9780134897264
Author:
KEOWN, Arthur J., Martin, John D., PETTY, J. William
Publisher:
Pearson,
Fundamentals of Financial Management (MindTap Cou…
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…
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