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...

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 high effort?

(e) Which level of effort does the company want to induce from its manager? Why?