Problem:
A firm hires a worker, and the worker chooses between two levels of effort (e), e=1 and e=4. Hiring the worker provides profits (s), and there are two possible levels of profits, s=40 and s=280. If e=1, the probabilities are 0.8 of s=40, and 0.2 of s=280. If e=4, the probabilities are 0.5of s=40 and 0.5 of s=280. The worker's utility function is:
U=w1/2 - e
Where w is the wage. The reservation level of utility is 6 ( the minimum level at which he or she will accept a contract from the firm).
While effort is not observable, profits are. The firm is risk neutral and so maximizes expected profits net of wages.
(a) Find the firm's optimal wage schedule.
(b) What would happen if there were full information?