A principal hires an agent to run a business for one year. The agent can exert high effort or low effort. High e ffort lowers the agent's utility by 10,000. Low effort is costless. If the agent exerts high effort, the business makes a profi t of $150,000 with probability .5 and breaks even with probability .5. If the agent exerts low effort, the business makes a $150,000 profit with probability .25, and breaks even with probability .75. The principal cannot tell what effort level is exerted, although he is of course aware of the business's profit. The agent's utility function is his annual salary minus the cost of effort, 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 effort level does the agent choose?
b. Now suppose that the principal pays the agent a fixed salary S and a bonus B, to incentivize the agent to exert high effort. 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 profit. Be sure to show that o ering a contract with a bonus is more pro table to the owner than offering a contract with no bonus, and only a fixed salary.