Reference no: EM13999079

PART I: Short questions

Write your answers in the assignment, on the page on which the question is given. Always provide an explanation for your final answer, or indicate how you got it.

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 w^m = 1,800 + 90s and w^f = 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 ½. 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 overweight 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. The National Basketball League teams draft new basketball players based (partly) on a vertical jump test. Suppose there are two types of basketball players, Good (G) and Awesome (A). The share of the A-types in the population of basketball players is 20%. Team owners believe that in the jump test an A-type jumps at least 30 inches with probability 50% and less than 30 inches with probability 50%. For a G-type player, the probabilities are 10% of jumping at least 30 inches and 90% of jumping less than 30 inches.

(a) Let P denote a team owner's posterior probability belief that a player who in the test jumped more than 30 inches is an A-type and Q her probability belief that a player who jumped less than 30 inches is an A-type. Calculate P and Q.

(b) Suppose an A-type player would contribute $5 million per year to the team's revenue whereas a G-type would contribute $0.5 million. What is the maximum a team owner would be willing to pay to a player who in the test jumped more than 30 inches? Denote the salary as smax.

PART II Multiple Choice. Please indicate your answers on the Scantron cards distributed in class. Answers not indicated on the Scantron card will be ignored. Please do not staple the Scantron to the rest of your answers.

1. Suppose there are two types of persons: high-ability and low-ability. The cost of one year of education is $10,000 to a high-ability person and $15,000 to a low-ability person. Regardless of their level of education, the lifetime productivity of a high ability worker is $800,000 and the lifetime productivity of a low ability worker is $650,000. Suppose high ability individuals choose SH years of schooling and low ability individuals choose SL years of schooling. If labour markets are competitive, education will be an effective signaling device if
A. S_H = 16 years and S_L = 0 years.
B. S_H = 12 years and S_L = 0 years.
C. S_H = 8 years and S_L = 0 years.
D. S_H = 0 years and S_L = 8 years.
E. In this example, there are no values for SH and SL that would make education an effective signaling device.

Questions 2 and 3 refer to the following setup: Suppose 30% of people are high-ability individuals and 70% are low-ability. The cost of one year of postgraduate education is $10,000 to a low-ability person and $15,000 to a high-ability person. Regardless of their level of education, the lifetime VMPL of a worker is $848,000 if she is of high ability and $800,000 if she is of low ability. A person's ability level is her private information. Apart from this informational asymmetry, labour markets are competitive.

2. Denote as SH the number of years of postgraduate schooling chosen by the high ability individuals. In this setting,
A. a separating signaling equilibrium is feasible if S_H = 5 years.
B. a separating signaling equilibrium is feasible if S_H = 4 years.
C. a separating signaling equilibrium is feasible if S_H = 3 years.
D. a separating signaling equilibrium is feasible if S_H = 2 years.
E. there is no value of SH such that a separating signaling equilibrium is feasible.

3. Let wH and wL denote the respective equilibrium lifetime earnings of a high ability and a low ability individual. Which of the following is true about a pooling equilibrium?
A. w_H > w_L = $800,000 B. w_H = w_L = $814,400 C. w_H = w_L = $824,000
D. a pooling equilibrium is feasible only if SH = 3 years.
E. a pooling equilibrium does not exist in this setting.

4. Which of the following is not 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 w1 but accepts his 2nd period offer w2, then w2 > w1.
E. Unemployment can be voluntary.

The next two questions refer to the following 2-period search model: The wage offers in a given period are distributed uniformly on [$1000,$2000], the unemployment benefit is $1100 per period, and the search cost is $85 per period. Each worker has lifetime utility given by U = m₁ + m₂, where mt is the worker's income in period t (net of the search costs). There is no discounting.

5. The workers' reservation wage in the first period is

A. $1,100 B. $1,185

C. $1,260 D. $1,300

E. $1,340

6. The probability a given worker will remain unemployed in period 1 is

A. 0.16
B. 0.26

C. 0.36
D. 0.22

E. 0.38

7. 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 firm-specific on-the-job training.

8. 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.

9. Which of the following is the best measure of gender discrimination in the labour market?
A. The difference between average wages for men and women.
B. The difference between average wages for men and women who are in the same occupation and have the same levels of education and experience.
C. The difference between average wages for men and women of the same age.
D. The difference between average wages for men and women of the same race.
E. The difference between average wages for twins who choose different occupations and different levels of education.

10. Which of the following would not 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.

11. Both men and women have abilities uniformly distributed on [0,100]. Person i's marginal product per hour is equal to his or her ability ai : VMPi = ai. Employers use an application test that perfectly reveals the abilities of female applicants, but provides no information about the abilities of male applicants. How will the distribution of competitive wages for women compare with the distribution of wages for men?
A. The wage distribution for women will be more compressed than that for men.
B. The wage distribution for women will coincide with the true distribution of their abilities but nothing can be said about the wage distribution for men.
C. The wage distribution for women will coincide with the true distribution of their abilities while all men will earn the exact same wage.
D. The wage distribution for men will coincide with the true distribution of their abilities while all women will earn the exact same wage.
E. Women will on average earn higher wages than men.

12. Consider two sales workers, Smith and Ricardo. Each worker is 35 years old and has 30 years of working life ahead of them. 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 their 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 wage offers?
A. W_S < W_R
B. W_S > W_R
C. W_S = W_R
D. Each of W_S = W_R and W_S > W_R is possible.
E. WR = $40,000 but W_S cannot be determined from the information given.

13. 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 B. $100,000 C. $185,300

D. $165,000 E. $124,000

14. A firm uses a probationary period to separate high from low ability workers. There are two periods and the probationary period lasts the whole 1st period. At the end of the 1st 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, an H-type can earn $100,000 per period, while an L-type can earn $80,000 per period. Detection is not perfect: H-types are always revealed as such, but an L-type is mistaken for an H-type with probability 0.5. If the wage during probation is w1 = $0, which of the following 2nd period wages would attract the H-types but not the L-types? Ignore discounting.

A. w₂ = $180,000 B. w₂ = $220,000 C. w₂ = $260,000

D. w₂ = $280,000 E. w₂ = $320,000

15. A firm uses a probationary period before offering workers permanent employment. Each individual's working life has 11 periods and the probationary period lasts the entire 1st 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. Detection is not perfect: H-types are always revealed as such, but an L-type is mistaken for an H-type with probability 0.2. Which of the following 1st period wages would attract the H-types but not the L-types? Ignore discounting.

A. w₁ = $17,000 B. w₁ = $24,000 C. w₁ = $39,000

D. w₁ = $41,000 E. w₁ = $48,000

16. 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?

A. b = 0.15 B. b = 0.25 C. b = 0.3

D. b = 0.38
E. There is no value for b such that only the H-types are attracted.

The next two questions refer to the following setup: Workers can work for one of two farms, picking strawberries. The number of trays, y, that a worker of ability a picks per day is y = 2a. Assume that a is uniform between 0 and 20. Farmer Jones pays $3 per tray and subtracts $10 a day from each worker's pay to cover the cost of measuring the output. Farmer Smith pays a straight salary of $38 per day.

17. Which workers will choose to work for farmer Smith?
A. All of the workers with abilities greater than 8.
B. All of the workers with abilities less than 8.
C. All of the workers with abilities between 12 and 14.
D. All of the workers with abilities greater than 14.
E. All of the workers with abilities less than 14.

18. Suppose each tray of strawberries sells for $5. Farmer Jones' cost of monitoring each worker is $10 per day, while farmer Smith incurs no monitoring costs. Apart from wage costs there are no other costs. In equilibrium, the two farmers' respective profits are
A. π^Jones = $24 per worker and π^Smith= $18 per worker
B. π^Jones = $18 per worker and π^Smith = $24 per worker
C. π^Jones = $2 per worker and π^Smith = $56 per worker
D. π^Jones = $56 per worker and π^Smith = $2 per worker
E. π^Jones = $16 per worker and π^Smith = $16 per worker