Reference no: EM13218682
A principal hires an agent to run a business for one year. The agent can exert high eff ort or low eff ort. High ef fort lowers the agent's utility by 10,000. Low e ffort is costless. If the agent exerts high e ffort, the business makes a pro t of $150,000 with probability .5 and breaks even with probability .5. If the agent exerts low e ort, the business makes a $150,000 pro fit with probability .25, and breaks even with probability .75. The principal cannot tell what eff ort level is exerted, although he is of course aware of the business's profi t. The agent's utility function is his annual salary minus the cost of eff ort, and he can be guaranteed a utility of $50,000 if he quits and works for his borther's landscaping business (his outside option).
a. If the principal pays the agent a fixed salary S, what e ort level does the agent choose?
b. Now suppose that the principal pays the agent a xed salary S and a bonus B, to incentivize the agent to exert high e ffort. Write down the participation constraint and the incentive constraint, and clearly label each.
c. Solve for the choices of S and B that maximize the owner's profi t. Be sure to show that o ering a contract with a bonus is more profi table to the owner than o ering a contract with no bonus, and only a fi xed salary.