A firm is contemplating whether to invest in a new project. The project requires an investment of 1 unit and can be “good” or “bad.” If the project is good, it pays off 1.5 units. If it is bad, it pays of 0.5 units. The manager and the shareholders have symmetric prior beliefs about the quality of the project and believe that it is good with probability 0.4. The investment in the project is borne entirely by shareholders. The manager obtains a wage of 0.1 units (paid from the project's payoff) if the project is undertaken, but no wage otherwise. The manager and shareholders are risk-neutral.
(i) Are shareholders willing to finance the project?
(ii) Characterize the set of beliefs under which shareholders would be willing to finance the project.
(iii) Suppose that the manager can choose a monitoring/screening technology that generates an informative signal about the project's quality. The realization of the signal can be “good” or “bad”, but the signal could be noisy in that its realization could be ”good” even though the project is “bad” and vice versa. What is the optimal technology that the manager should choose? Characterize the technology in terms of the distribution of the signal's realizations conditional on the project being good or bad.