A worker can choose high (H) or low (L) effort. If the worker chooses high effort, she incurs a personal cost of 2. In this case, output is high with probability one. If the worker chooses low effort, she incurs a personal cost of 0. In this case, output is high with probability 1 and low with probability 1 .

When output is high, the firm receives revenue of θ and zero otherwise.
a. Under complete information, what is the lowest bonus for high effort that the firm can pay to induce the worker to exert high effort?
b. When there is complete information, under what condition on θ would the firm find it worthwhile to pay this bonus?
c. When output is observable, but effort is NOT, what is the lowest bonus for high output that the firm can pay to induce the worker to exert high effort?
d. Under what condition on θ would the firm find it worthwhile to pay this bonus under asymmetric information?
e. Briefly, and in words, explain why a higher bonus has to be paid to induce high effort under asymmetric information.