Suppose both the principal and agent are risk neutral. The agent has two possible levels of effort, eH and eL. There is a probability that the project the agent is hired to carry out succeeds or fails where this probability depends on the agent’s effort. More specifically, if the agent chooses effort efl, the project succeeds with probability 1 . If he chooses eL, the project succeeds with probability pin(0.1) and fails otherwise. If the project succeeds, then profits are πS. If it fails, profits are πF where πSu003eπF≥0. The agent’s pay-off is w-c if he chooses eH, while his pay-off is w if he chooses eL and is paid w. The principal’s pay-off is π-w if profits are π and he pays the agent w. The agent’s outside option is 0 .Assume there is a limited liability constraint meaning that w must be non-negative.
When effort is observable, find the optimal contract for the principal.
Now suppose effort is not observable by the principal.
If the principal wants the agent to choose eL, what is the ptimal contract for the principal?
What is the optimal contract for eII ?
Under what conditions the principal wants to implement eH ?
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