ECO 499 S1 Problem Set 1

[I will collect all works and then discuss the solutions in class, so
you may wish to make a copy of your work before submitting it]
1. Answer the following questions AS BRIEFLY AS POSSIBLE:
(a) Do you expect that the share of stock and option grants in CEO
total pay should be increasing or decreasing with the volatility of the ?rm?s
stock returns. Explain.
(b) Which measure of executive compensation should we use
(i) when estimating the strength of managerial incentives
(ii) when estimating the company?s cost of hiring the executive.
(c) When may a principal want to sell a project to the agent?
(d) Which is greater: the mean or the median of CEO pay?
(e) Is the historical increase in CEO pay driven by cash pay or equity-
based pay?
(f) What are the implications of the theory of career concerns for the
pay-performance sensitivity of junior versus senior CEOs?
(g) Why may RPE fail for senior CEOs?
2. A principal (she) hires an agent (he) to run a project which has a payo¤
xS if successful and 0 if unsuccessful, where xS > 0 If the agent receives a wage
w and exerts e¤ort a, his utility is ln(w) ?? a. The agent can either shirk in
which case a = 0 or work hard in which case a = 1. If the agent works hard and
the state of the economy is good, then the project is successful with probability
0:9. If the agent shirks and the state of the economy is bad, then the project
is successful with probability 0:1. If the agent works hard, but the state of
the economy is bad, then the project is successful with probability 0:8. This
is also the case if the state of the economy is good, but the agent shirks. The
principal is risk-neutral and cares about the payo¤ of the project net of agent?s
compensation. The agent?s reservation utility is 0 and does not depend on the
state of the economy.
(a) Assume that the principal can observe both the state of the economy
and the e¤ort of the agent. Also assume xS = 20.
(i) Suppose that the state of the economy is GOOD. Find the level of
e¤ort that the principal would recommend to the agent, the wage received by
the agent if the project fails, and the wage received by the agent if the project
succeeds.
1
(ii) Would your answers change if the state of the economy is BAD? If
no, why? If yes, how?
(b) Now, assume that the principal can observe the state of the economy,
but not the e¤ort exerted by the agent. Also assume that xS is such that the
principal ?nds it optimal to recommend HIGH EFFORT no matter the state of
the economy.
(i) Suppose that the state of the economy is GOOD. Find the wage
received by the agent if the project fails and the wage received by the agent if
the project succeeds. Which of these wages is higher?
(ii) Suppose that the state of the economy is BAD. Find the wage re-
ceived by the agent if the project fails and the wage received by the agent if the
project succeeds. Which of these wages is higher?
(iii) Find whether the wage received by the agent if the project SUC-
CEEDS is higher when the state of the economy is good or when it is bad. So,
does it satisfy relative performance evaluation (RPE)?
(iv) Find whether the wage received by the agent if the project FAILS
is higher when the state of the economy is good or when it is bad. So, does it
satisfy RPE?
2

[I will collect all works and then discuss the solutions in class, so
you may wish to make a copy of your work before submitting it]
1. Answer the following questions AS BRIEFLY AS POSSIBLE:
(a) Do you expect that the share of stock and option grants in CEO
total pay should be increasing or decreasing with the volatility of the ?rm?s
stock returns. Explain.
(b) Which measure of executive compensation should we use
(i) when estimating the strength of managerial incentives
(ii) when estimating the company?s cost of hiring the executive.
(c) When may a principal want to sell a project to the agent?
(d) Which is greater: the mean or the median of CEO pay?
(e) Is the historical increase in CEO pay driven by cash pay or equity-
based pay?
(f) What are the implications of the theory of career concerns for the
pay-performance sensitivity of junior versus senior CEOs?
(g) Why may RPE fail for senior CEOs?
2. A principal (she) hires an agent (he) to run a project which has a payo¤
xS if successful and 0 if unsuccessful, where xS > 0 If the agent receives a wage
w and exerts e¤ort a, his utility is ln(w) ?? a. The agent can either shirk in
which case a = 0 or work hard in which case a = 1. If the agent works hard and
the state of the economy is good, then the project is successful with probability
0:9. If the agent shirks and the state of the economy is bad, then the project
is successful with probability 0:1. If the agent works hard, but the state of
the economy is bad, then the project is successful with probability 0:8. This
is also the case if the state of the economy is good, but the agent shirks. The
principal is risk-neutral and cares about the payo¤ of the project net of agent?s
compensation. The agent?s reservation utility is 0 and does not depend on the
state of the economy.
(a) Assume that the principal can observe both the state of the economy
and the e¤ort of the agent. Also assume xS = 20.
(i) Suppose that the state of the economy is GOOD. Find the level of
e¤ort that the principal would recommend to the agent, the wage received by
the agent if the project fails, and the wage received by the agent if the project
succeeds.
1
(ii) Would your answers change if the state of the economy is BAD? If
no, why? If yes, how?
(b) Now, assume that the principal can observe the state of the economy,
but not the e¤ort exerted by the agent. Also assume that xS is such that the
principal ?nds it optimal to recommend HIGH EFFORT no matter the state of
the economy.
(i) Suppose that the state of the economy is GOOD. Find the wage
received by the agent if the project fails and the wage received by the agent if
the project succeeds. Which of these wages is higher?
(ii) Suppose that the state of the economy is BAD. Find the wage re-
ceived by the agent if the project fails and the wage received by the agent if the
project succeeds. Which of these wages is higher?
(iii) Find whether the wage received by the agent if the project SUC-
CEEDS is higher when the state of the economy is good or when it is bad. So,
does it satisfy relative performance evaluation (RPE)?
(iv) Find whether the wage received by the agent if the project FAILS
is higher when the state of the economy is good or when it is bad. So, does it
satisfy RPE?
2

[I will collect all works and then discuss the solutions in class, so
you may wish to make a copy of your work before submitting it]
1. Answer the following questions AS BRIEFLY AS POSSIBLE:
(a) Do you expect that the share of stock and option grants in CEO
total pay should be increasing or decreasing with the volatility of the ?rm?s
stock returns. Explain.
(b) Which measure of executive compensation should we use
(i) when estimating the strength of managerial incentives
(ii) when estimating the company?s cost of hiring the executive.
(c) When may a principal want to sell a project to the agent?
(d) Which is greater: the mean or the median of CEO pay?
(e) Is the historical increase in CEO pay driven by cash pay or equity-
based pay?
(f) What are the implications of the theory of career concerns for the
pay-performance sensitivity of junior versus senior CEOs?
(g) Why may RPE fail for senior CEOs?
2. A principal (she) hires an agent (he) to run a project which has a payo¤
xS if successful and 0 if unsuccessful, where xS > 0 If the agent receives a wage
w and exerts e¤ort a, his utility is ln(w) ?? a. The agent can either shirk in
which case a = 0 or work hard in which case a = 1. If the agent works hard and
the state of the economy is good, then the project is successful with probability
0:9. If the agent shirks and the state of the economy is bad, then the project
is successful with probability 0:1. If the agent works hard, but the state of
the economy is bad, then the project is successful with probability 0:8. This
is also the case if the state of the economy is good, but the agent shirks. The
principal is risk-neutral and cares about the payo¤ of the project net of agent?s
compensation. The agent?s reservation utility is 0 and does not depend on the
state of the economy.
(a) Assume that the principal can observe both the state of the economy
and the e¤ort of the agent. Also assume xS = 20.
(i) Suppose that the state of the economy is GOOD. Find the level of
e¤ort that the principal would recommend to the agent, the wage received by
the agent if the project fails, and the wage received by the agent if the project
succeeds.
1
(ii) Would your answers change if the state of the economy is BAD? If
no, why? If yes, how?
(b) Now, assume that the principal can observe the state of the economy,
but not the e¤ort exerted by the agent. Also assume that xS is such that the
principal ?nds it optimal to recommend HIGH EFFORT no matter the state of
the economy.
(i) Suppose that the state of the economy is GOOD. Find the wage
received by the agent if the project fails and the wage received by the agent if
the project succeeds. Which of these wages is higher?
(ii) Suppose that the state of the economy is BAD. Find the wage re-
ceived by the agent if the project fails and the wage received by the agent if the
project succeeds. Which of these wages is higher?
(iii) Find whether the wage received by the agent if the project SUC-
CEEDS is higher when the state of the economy is good or when it is bad. So,
does it satisfy relative performance evaluation (RPE)?
(iv) Find whether the wage received by the agent if the project FAILS
is higher when the state of the economy is good or when it is bad. So, does it
satisfy RPE?
2