1. A firm hires two risk-neutral workers to assemble bicycles and pays $24 for each assembly. Charlie's total cost of allocating effort to the production process is C = 2N2, where N is the number of bicycles assembled per day. Donna's cost is C = N2/2.
(a) What will be each worker's daily earnings?
(b) Suppose the firm pays a flat wage of $160 per day and fires any worker who does not assemble at least 9 bicycles per day. A dismissed worker remains unemployed and has zero income. How many bicycles will each worker assemble per day?
2. Dan and Ann are chemical engineers working for a biotech company. Both are risk-neutral and have disutility of effort given by C(e) = 2e2. Their supervisors have indicated that the one who produces more publications in scientific journals over the next 3 years will be promoted to a managerial position. Each published article increases the firm's revenue by $100,000.
The number of articles each can produce depends on how hard they work. If y is the number of published articles at the end of the third year, then yA = 0.5eA + εA and yD = 0.5eD + εD, where e represents effort and ε is a luck factor over which the researchers have no control. εA and εD are distributed such that (εA - εD) is uniform on [-1/2, 1/2].
Let w0 = 0 be the wage each of the two employees gets during the 3 years before the promotion decision, W+ the lifetime income of a manager, and W- the lifetime income of the unpromoted employee. The firm wants to set wages so as to maximize profit. Dan and Ann are willing to engage in the promotion contest if their expected lifetime utility is at least zero.
Calculate the optimal lifetime incomes W+ and W- the firm will promise the two employees.
3. John, Bengt, and Carla, all three of them risk-neutral, own an online herbal tea store. The company's profit per year is given by y = $600(eJ + eB + eC ), where eJ , eB , and eJ are the effort levels provided by John, Bengt, and Carla respectively. Each person's utility is equal to his/her earnings minus the disutility from effort, given by e2. Individual efforts are not observable.
(a) How much will each person earn per year if they share profits equally?
(b) What will be each person's total utility if they share profits equally?
(c) Now suppose Carla suggests reorganizing the company as follows: Carla becomes the company's president, receives a fixed salary of $52,000 per year, and is no longer expected to provide any effort. John and Bengt provide effort and split the profit that is left after paying Carla's salary. However, if the firm's profit (before subtracting Carla's salary) falls below $360,000, Carla gets all of the profit, while John and Bengt receive nothing.
Would John and Bengt agree to rearrange the company according to Carla's suggestion? Show why yes or why not.
PART II Multiple Choice
1. Most elementary school teachers are paid a flat salary that is not directly related to how well their students do in performance tests. Which of the following can best explain this observation?
A. Teachers do not need incentives.
B. There are important aspects of a teacher's job that are hard to measure.
C. School principals do not know how to design incentive contracts.
D. Teachers are risk averse.
E. Teachers are not able to influence how well their students do in performance tests.
2. Which of the following is a problem with output contingent performance pay?
A. There is no empirical evidence that it would lead to increased productivity.
B. Workers always prefer working for a fixed wage.
C. It provides workers with an incentive to neglect aspects of their jobs that are hard to measure.
D. It provides workers with an incentive to neglect aspects of their jobs that are easy to measure.
E. All of the above.
3. Consider a worker on a piece rate incentive scheme installing car windshields. Suppose the market price of windshields increases while at the same time the firm improves the installation technology so that the worker's per hour productivity (in terms of the number of windshields
installed) becomes less variable. From this, we can conclude that
A. the optimal piece rate should increase.
B. the optimal piece rate should decrease.
C. the optimal piece rate should increase if the effect of the price increase is stronger than the effect of the smaller variation in productivity.
D. the optimal piece rate should increase if the effect of the price increase is weaker than the effect of the smaller variation in productivity.
E. the worker should be shifted to a fixed salary.
4. Donald, who is risk-averse, works in an ice-cream shop. The owner of the shop, who is risk-neutral, cannot observe how hard Donald works. She pays Donald a fixed monthly salary plus a share of the revenues from the ice-cream sales. Assume that the contract is chosen optimally so as to maximize the owner's profit and that there are several similar ice-cream shops in the town that would like to hire Donald (i.e., the shops compete for his services).
Now suppose the owner installs a camera in the shop, which allows her to monitor precisely the effort Donald provides every day and to base Donald's pay on the supplied level of effort. Which of the following is not true under this new pay scheme?
A. Donald works harder than under the old pay scheme.
B. Donald's income is higher than under the old pay scheme.
C. Donald is exposed to less variation in his income than under the old pay scheme.
D. Donald's expected utility is lower than under the old contract.
E. Total surplus from the employment relationship is higher than under the old pay scheme.
5. Eric produces hand carved wooden toys that he can sell for $X per toy. If Eric produces q toys on a given day, his total cost of effort for that day is given by C(q) = 5q2. Eric finds it optimal to produce 4 toys per day. What is the price at which Eric sells the toys?
A. X = $25
B. X = $30
C. X = $35
D. X = $40
E. X = $45
6. Suppose a risk-averse worker is employed by a risk-neutral firm. The worker's output is given by y = e + ε, where e is the worker's effort and ε is a noise term that represents random variation in output that is beyond the worker's control. If the worker's effort is observable and contractible, which of the following is true?
A. The optimal contract is such that if the worker chooses the effort that maximizes her expected utility, her pay is a fixed wage that does not depend on output.
B. The optimal contract requires the firm to sell the firm to the worker.
C. The optimal contract is a piece-rate between zero and one.
D. No optimal contract exists.
E. None of the above.
7. Consider two firms offering piece rate incentive contracts to their workers. If firm A offers a piece rate bA = 0.6 and firm B a piece rate bB = 0.5, which of the following statements is not consistent with the basic principal-agent model of incentive contracting?
A. Firm A employs workers with a higher marginal productivity of effort than firm B.
B. The production process is more noisy (variable) in firm B than in firm A.
C. The workers in firm A will work harder than the workers in firm B.
D. The workers in firm A are less risk-averse than the workers in firm B.
E. The workers in both firms are risk-neutral.
8. The principal-agent problem arises primarily because:
A. firms create internal labour markets in which principals and agents compete.
B. principals and agents have common interests.
C. principals want to hire agents as cheaply as possible.
D. agents pursue some of their own objectives that may conflict with the objectives of the principals.
E. agents would like to become principals.
9. Which of the following is a disadvantage of using promotion tournaments to provide incentives?
A. Common luck factors cancel out from the workers' performance measures.
B. Promotion tournaments preserve specific human capital, which decreases the firm's profitability.
C. Tournaments may discourage workers from cooperating with each other.
D. The outcome of a tournament only depends on the workers' relative performance, which is harder to measure than their absolute performance.
E. None of the above.
10. The advantage of a relative performance pay scheme is that
A. it allows the firm to increase the marginal productivity of each worker.
B. it allows the firm to filter out common noise from the workers' performance measures.
C. it allows the firm to filter out idiosyncratic noise from the workers' performance measures.
D. it allows the firm to focus the workers' attention on quantity, not just quality.
E. it allows the workers to produce more while working at a more leisurely pace.
11. Which of the following would increase the spread between the prizes to the winner and to the losers in an optimal promotion tournament?
A. An increase in the number of workers that participate in the tournament.
B. An increase in the wages the workers' could get in their alternative jobs.
C. A decrease in the value of each worker's marginal product.
D. A decrease in the wages the workers' could get in their alternative jobs.
E. A decrease in the number of workers that participate in the tournament.
12. If all firms in the market try to offer efficiency wages, then
A. efficiency wages cannot provide incentives because all firms pay the same wage.
B. there is excess demand for workers.
C. in equilibrium there is unemployment.
D. demand for workers decreases because each worker works less hard.
E. competition pushes the wage back down to the market-clearing level.
The next two questions refer to the following problem. A risk-neutral worker can provide high effort (at personal cost $7) or low effort (at zero cost). A high effort worker contributes $X to the company's revenues, a low effort worker contributes $25. If the worker chooses low effort, then with probability 0.7 he is detected by his supervisor and fired. If fired, the worker can earn $10 without providing high effort.
13. What is the lowest efficiency wage, weff, that can induce the worker to provide high effort?
A. weff = $40
B. weff = $30
C. weff = $20
D. weff = $15
E. weff = $10
14. What is the lowest value of X for which the firm is willing to pay the above efficiency wage?
A. X = $50
B. X = $45
C. X = $40
D. X = $35
E. X = $30