PART I
1. Suppose years of schooling, s, is the only variable that affects earnings. The equations for the weekly salaries of male and female workers are given by iv.= 1,800 + 90s and wt.= 1,700 + 65s. On average, men have 14 years of schooling and women have 12 years of schooling.
(a) What is the male-female wage differential in the labour market?
(b) Calculate how much of this wage differential is due to discrimination and how much is due to difference in skills.
2. A concessionaire at a hockey stadium hires hotdog sellers. Each hotdog sells for $2 and costs $1.70 to produce. There are two types of sellers: A high productivity seller can sell 40 hotdogs per hour; a low productivity one sells 10 hotdogs per hour. The share of each in the population is 4. A job applicant's true productivity is not observable, but there are 2 types of applicants: those with little body fat and T-shirts that advertise long-distance running, and overweight smokers. The owner believes that a high productivity type is more likely to become a runner (prob. 60%) than to become a smoker (prob. 40%). For a low productivity type, the respective probabilities are reversed: 40% and 60%.
a) Let P denote the owner's posterior probability belief that a runner is a high productivity worker and Q her probability belief that an ovenveight smoker is a high productivity worker. Calculate P and Q.
b) What is the maximum wage the owner would be willing to pay to a runner? To a smoker?
3. 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 = 2W, 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?
4. Dan and Ann are chemical engineers working, for a biotech company. Both are risk-neutral and have disutility of effort given by C(e) = . 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. Ify is the number of published articles at the end of the third year, then yA = 0.5e4 + cA and yo = 0.5ec + eh, where e represents effort and c is a luck factor over which the researchers have no control. cA and en are distributed such that (cA - co) is uniform on [-Yo,Let wo = 0 be the wage each of the two employees gets during the 3 years before the promotion decision, Ir the lifetime income of a manager, and W the lifetime income of the un-promoted 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 Hr and W the firm will promise the two employees. What are the firm's expected profits from hiring Dan and Ann?
PART II
1. Which of the following is tint a prediction of the job search theory?
A. Unemployment benefits increase the length of the average unemployment spell.
B. All else equal, a 30 year old worker will have a higher reservation wage than a 54 year old.
C. In a 2-period model, the 1st period reservation wage exceeds the 2nd period reservation wage.
D. In a 2-period model, if a worker rejects his 1st period wage offer (wi) but accepts his 2nd period offer (w2), then w2>
E. Unemployment can be voluntary.
2. Newly hired workers tend to leave their jobs within 24 months of hire, while workers with more seniority rarely leave their jobs. Which of the following could explain this?
A. The theory of equalizing wage differentials.
B. The signaling theory of education.
C. The human capital theory of education.
D. The theory of general on-the-job training.
E. The theory of fine-specific on-the-job training.
3. Most elementary school teachers are paid a flat salary, which 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 do not care about money.
4. According to the theory of statistical discrimination
A. firms use the average characteristics of demographic groups to estimate a worker's productivity.
B. a firm always makes the same profit, whether it discriminates or not.
C. firms discriminate against women because they are less productive.
D. discriminating firms earn lower profits.
E. firms discriminate against statisticians.
5. Suppose employers use job interviews to estimate the ability of job applicants. The distribution of ability is the same for men and women, but the interviewers are better able to identify high ability individuals among female applicants than among male applicants. The theory of statistical discrimination predicts that
A. the wage distribution for men will be more compressed than that for women.
B. the wage distribution for women will be more compressed than that for men.
C. men will on average earn higher wages than women.
D. women will on average earn higher wages than men.
E. low ability men will earn higher wages than high ability women.
6. Which of the following would 191 help a firm attract high ability job applicants while discouraging low ability applicants?
A. Offering a piece rate pay scheme.
B. Offering a probationary period with low wage, followed by dismissal of unsuccessful workers and permanent employment with a high wage for successful workers.
C. Offering higher salaries than other firms.
D. Requiring credentials such as a diploma.
E. None of the above can help in this respect.
7. A firm is deciding whether to hire Benson or Larson for a vacant sales position. Benson's productivity is known - she would generate $140,000 worth in revenues per year. Larson's productivity is not known precisely, but the firm could learn it within one year if Larson is hired. With probability 1/3, Larson is a high productivity worker who would generate $300,000 in revenues per year. With probability 2/3, he is a low productivity worker who would generate zero revenue. If Larson turns out to be a low productivity worker, the firm can lay him off Both Benson and Larson would be willing to stay in the firm for the next 22 years. Suppose Benson is asking for the salary of $100,000 dollars per year, while Larson is asking for the salary of wL dollars per year. Which of the following values for wL would make the firm indifferent between the two applicants? Ignore discounting.
A. $137,500 D. $165,000
B. $100,000 E. $124,000
C. $185,300
8. Consider two sales workers, Smith and Ricardo. Each worker is 35 years old and retires when 65. Smith's productivity is known - she is sure to generate $40,000 per year in sales. Ricardo's productivity is uncertain. With probability 1/4 he is a high productivity worker and will generate $400,000 per year in sales, but with probability 3/4 he is a disaster and generates (- $80,000) per year. It takes one year for Ricardo's employer to learn his type. Assume that many identical firms compete for the two workers at the beginning of the workers' careers and that the workers' respective annual wages, Ws and WR, remain unchanged until they retire or are laid off. Ignore discounting. Which of the following will be true for the workers' equilibrium wages?
A. Ws > WR
B. Ws < WR
C. Ws = WR
D. Each of Ws = WR and Ws > WR could be true.
Ii Wit = $40,000 but Ws cannot be determined from the information given.
9. 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
10. A firm uses a probationary period before offering workers permanent employment. Each individual's working life has II periods and the probationary period lasts the entire period. A successful worker is retained for the remaining 10 periods and paid wage w2 = $84,000 per period; an unsuccessful worker is fired and goes to her alternative job. In the alternative job, a high productivity worker (an H-type) can earn $80,000 per period; a low productivity worker (an L-type) can earn $70,000 per period. Ignore discounting.
Detection is not perfect: H-types are always revealed as such, but L-types are mistaken for H-types with probability 0.2. Which of the following 111 period wages would attract the H-types but not the L-types?
A. w, = $17,000 D. w, = $41,000
B. w, = $24,000 E. w, = $48,000
C. w, = $39,000
11. 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.
12. 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 focus the workers' attention on quality, not just quantity
C. it allows the workers to produce more while working at a more leisurely pace
D. it allows the firm to filter out common noise from the workers' performance measures
E. it allows the firm to filter out idiosyncratic noise from the workers' performance measures
13. 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.
14. 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 a X = $40
B. X=S30 E. X= $45
C. X = $35
15. 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 no 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.
16. Suppose a risk-averse worker is employed by a risk-neutral firm. The worker's output is given by y = e + c, where e is the worker's effort and a 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.
17. Dunder Mifflin Company is a paper and office-supply distributor. They recognize that there are two types of sales people: An H-type sells $10,000 worth of supplies per month; an L-type sells $6,000. The alternative wages of these two types are $3,200 per month for the L-types and $4,000 per month for the H-types. A minimum wage law requires that each employee must get a base salary of at least $1,200 per month. The company offers a monthly pay of w = $1,200 + by, where b is a piece-rate and y is the monthly sales made by the given employee. Which of the following values for b will attract the H-types but discourage the L-types from applying?
b = 0.15 D. b = 0.38
B. b= 0.25 E. There is no value for b such that only
C. b= 0.3 the H-types are attracted.
18. A firm uses a probationary period to separate high from low ability workers. Each individual's working life has two periods and the probationary period lasts the whole lg period At the end of the 1g period, a successful worker is retained for the 2nd period and paid wage w2; an unsuccessful worker is fired and goes to his alternative job. In the alternative job, a high productivity worker (an H-type) can earn $100,000 per period; a low productivity worker (an L-type) can earn $80,000 per period.
Detection is not perfect: H-types are always revealed as such, but L-types are mistaken for H-types with probability 0.5. If the wage the firm pays during probation is wl = $0, which of the following 2nd period wages would attract the H-types but not the L-types? Ignore discounting.
A. w2= $180,000 D. w2 = $280,000
B. w2= $220,000 E. w2 = $320,000
C. w2= $260,000