Section 5.A of this chapter discusses the principal–agent
problem in the context of a company deciding whether and how to induce a
manager to put in high effort to increase the chances that the project
succeeds. The value of a successful project is $1 million; the probability of
success given high effort is 0.5; the probability of success given low effort
is 0.25. The manager’s utility is the square root of compensation (measured in
millions of dollars), and his disutility from exerting high effort is 0.1.
However, the reservation wage of the manager is now $160,000.
(a) What contract does the company offer if it wants only
low effort from the manager?
(b) What is the expected profit to the company when it
induces low managerial effort?
(c) What contract pair (y, x)—where y is the salary given
for a successful project and x is the salary given for a failed project—should
the company offer the manager to induce high effort?
(d) What is the company’s expected profit when it induces
(e) Which level of effort does the company want to induce
from its manager? Why?