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
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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?
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