Please solve (a) to (i) all problems observable effort and unobservable effort

6. Moral Hazard and Principal - Agent - 20 points The revenue generated by an employee in a firm is either $10,000 or zero. The probability of generating $10,000 of revenue depends on whether the employee exerts effort and works hard or whether he shirks and does not exert any effort. If the employee works hard, there is a - probability (or 25 percent) that the firm makes zero revenues. Whereas if he shirks, this probability increases to ~ (or 75 percent). The table below shows the probabilities in each case Revenue $10,000 High Effort, H Low Effort, L $0 $0.75 $0.25 $0.25 $0.75 Assume the following: The employee's cost of effort is $100. . The reservation wage is $150. (This is the wage the employee receives in a different offer if he does not accept the current employment offer.) Both employee and firm are risk-neutral. The market supply of labor is competitive, so that the employee is paid the lowest possible wage that will make him accept the employment. Compensation with Observable Effort First assume that the firm can observe and enforce the employee's effort and it offers an employment contract (w, $150), where the employee receives a wage of w if he exerts effort and a wage of $150 if he does not exert effort. a) What is the lowest w that will get the employee to accept the employment and exert high effort? Denote this wage by wo. (2 points) Consider the employment contract (w, $150). b) What are the expected profits to the firm? (2 points) c) What is the employee's surplus? (2 points) d) What is the total surplus? (1 point) Page 9 of 10 Compensation with Unobservable Effort Now suppose the firm cannot observe the effort exerted by the worker, but it does observe the revenues generated. Consider a wage contract where the employee gets a wage wh if the firm makes positive revenues and wl if the firm makes zero revenues e) Write down the incentive compatibility constraint (ICC) that wh and w must satisfy in order to ensure that the manager exerts high effort. (2 points) f) What is the participation constraint (PC) that wh and w must satisfy in order to get the worker to accept the employment contract and exert high effort? (2 points) g) Does the employment contract (w, $150) where wh = w and wL = $150, obtained in part a) satisfy the incentive constraint? (3 points) h) Does the employment contract (w, $150) where wh = w and wl = $150 meet the participation constraint? (3 points) i) Derive the profit-maximizing wage contract that satisfies both the incentive and participations constraints? Call this wage contract (wu, wu). (3 points)