Suppose that in a principal-agent relation there are two possible outcomes with values of 1,000 and 100. The agent can choose among two different effort levels, which cannot be observed by the principal. The probabilities of each outcome given the respective effort level are given in the table below:

The principal is risk-neutral and the agent is risk-averse. The two have the following utility functions:
B(x,w)=x - w U(w,e)=w 1/4 - e
Where x represents the outcome, w the salary paid to the agent, and e is effort. The reservation utility of the agent is 1.

Question

Suppose that in a principal-agent relation there are two possible outcomes with values of 1,000 and 100. The agent can choose among two different effort levels, which cannot be observed by the principal. The probabilities of each outcome given the respective effort level are given in the table below:
  
 The principal is risk-neutral and the agent is risk-averse. The two have the following utility functions: 
 B(x,w)=x - w    U(w,e)=w 1/4  - e 
 Where x represents the outcome, w the salary paid to the agent, and e is effort. The reservation utility of the agent is 1.

Accepted Answer

The principal would be willing to pay up to 111 to be able to monitor effort.

Accepted Answer

If effort is observable, the principal will choose the high effort level.

Answer

Under moral hazard, it would be possible for the principal to pay a fixed wage of 0 in order to obtain low effort.

Answer

Under moral hazard, the principal will choose the low effort level.

	1,000	100
e=0	¼	¾
e=2	3/4	1/4

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