A firm writes a contract for an employee to work on a specific project. If the project is successful, then it yields $40000 to the firm. If the project is unsuccessful, then the firm receives $0. If the employee puts in a high level of effort, then the project is successful with probability 80%. If the employee puts in a low amount of effort, then the project is successful with probability 55%. The employee's cost of high effort is 100. The employee's cost of low effort is 0. The employee's outside option is 1000. The employee is risk-neutral. (a) Suppose that the principal offers a bonus of $1000. Would the employee put in a high level of effort, or a low level of effort? (4 Marks) (b) Is this an incentive constraint or a participation constraint? (2 Marks) (c) What is the minimum bonus that the firm must offer the employee for her to put in a high level of effort? (4 Marks) (d) Assume that the firm offers the bonus that you found in part (c). What is the minimum fixed wage that the firm can offer so that the employee will work for the firm? (6 Marks) (e) Is this an incentive constraint or a participation constraint? (2 Marks) (f) Suppose that the firm offers the bonus and fixed wages that you found in parts (c) and (d). What are the firm's expected profits? What is the employee's utility? (6 Marks)