A principal hires an agent to run a business for one year. The agent can exert high effort or low effort. High effort lowers the agent’s utility by 10,000. Low effort is costless. If the agent exerts high effort, the business makes profit 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 utility of $50,000 if he quits and works for his brother’s landscaping business (his outside option).

a. If the principal pays the agent a fixed salary of $75,000 which is the expected profit when the agent exerts high effort, what effort level does the agent choose?

b. Now suppose that the principal pays the agent a salary when the business makes profit of $150,000 while pays when it makes zero profit. Write down the participation constraint and the incentive constraint, and clearly label each.

c. Solve for the choices of and .