Employees (Agents) in many occupations face compensation packages from the Employers (Principles) that have two components: a fixed salary: , and a commission rate: for each unit of output produced, which depends on the effort level the employee put forth. Assume that the employee's effort is unobservable to the employer. Total income of the employee is: = + $200 , where is the effort level. The employee has a cost of effort function: () = 1 4 2 The employee's net payoff function is thus: = () The employee's reservation net payoff is zero, which means that the employee will not exert any effort if the net payoff she receives is smaller than 0. The employer's sales function: () = 200 The employer's profit function is thus: = () Suppose the employer is setting the optimal and to maximize her profit and the employee is setting her optimal choice of effort level to maximize her net payoff.

What is the employee's optimal choice of effort level (as a function of )?

b) (5 Points) Write down the employer's profit function as a function of and (plug in your answer from part a), should not show in the employer's profit function anymore).

c) (5 Points) Suppose the employer set a fixed salary = ( $200)2, use your answers from part a) and b) to show that the employer's optimal choice of is 100% (Hint: Plug the function into the employer's profit function, take derivatives with respect to and set it equal to 0: () = 0).

d) (5 Points) Under the employer's choice of and from part c), what are the employee's net payoff and the employer's profit