The manager is hired to run a project for a firm. The probability of the project being successful and profits being high depends on the effort of the manager. If manager band exerts a high level of effort (eh), the probability of success is φ1. If the manager shirks and exerts a low level of effort (el), the probability of acceptance is reduced to φ2. The reservation utility of the manager has been normalized to 0. The utility function of the manager is
𝑈(𝑦,𝑒)=2 𝑦 − 𝑒.
Where y is the money that manager earns. Suppose that eh =2, el =1, φ1 =.75, and φ2 =.25. If the project is successful, gross profits for the firm will be 10. If it fails, gross profits will fall to 5. Gross profits are the profits the firm will earn before payments to the manager.
a. What is the full-information contract?
b. Suppose that the firm owner cannot observe the effort level of the manager.
Explain why the full information contract is not incentive compatible.
c. Find the optimal incentive-compatible contract.
d. What is the expected income of the firm owner under full and asymmetric
information? Why is the firm worse off under asymmetric information?
- The Manager Is Hired To Run A Project For A Firm The Probability Of The Project Being Successful And Profits Being High 1 (56.81 KiB) Viewed 32 times
1. The manager is hired to run a project for a firm. The probability of the project being successful and profits being high depends on the effort of the manager. If manager band exerts a high level of effort (4), the probability of success is 4. If the manager shirks and exerts a low level of effort (e), the probability of acceptance is reduced to 2. The reservation utility of the manager has been normalized to 0. The utility function of the manager is U(y, e) = 2Vy - e. Where y is the money that manager earns. Suppose that e =2, 4 =1, 4. =.75, and 42 = 25. If the project is successful, gross profits for the firm will be 10. If it fails, gross profits will fall to 5. Gross profits are the profits the firm will earn before payments to the manager. a. What is the full-information contract? b. Suppose that the firm owner cannot observe the effort level of the manager. Explain why the full information contract is not incentive compatible. c. Find the optimal incentive-compatible contract. d. What is the expected income of the firm owner under full and asymmetric information? Why is the firm worse off under asymmetric information?