Questions about labor supply: unemployment
1. How is the “unemployment rate” calculated?
2. There are two reasons why the measured unemployment rate might not
accurately represent the fraction of workers who want jobs but cannot find them.
Name and explain these problems.
3. Suppose the country has 200 million people age 16 or older. Of these, 120
million are currently working; 30 million are looking for work; and 50 million are
neither working nor looking for work. What is the unemployment rate?
4. Why are university students usually not considered unemployed, even though
most do not have jobs?
5. Suppose there are 90 million people in the population. Of these, 54 million are
currently employed and 18 million are unemployed. Calculate the labor force
participation rate and the unemployment rate.
6. There are 200 million inhabitants of Fantasia. Some have jobs, and others don’t;
some are searching for jobs, and others aren’t.
Have jobs and are not searching for different jobs: 90 million
Have jobs but are searching for different jobs: 35 million
Do not have jobs and are not searching for jobs: 50 million
Do not have jobs but are searching for jobs: 25 million
Calculate the unemployment rate and the labor force participation rate in
Fantasia.
7. In order to calculate the unemployment rate, the Bureau of Labor Statistics
divides all people over the age of 16 into three categories based on their work
status. Name these categories.
8. What two criteria must a person meet in order to be classified as
“unemployed”?
9. Suppose there are 100 million people age 16 or older. Of these, 60 million are
currently working; 15 million are looking for work; and 25 million are neither
working nor looking for work. What is the unemployment rate?
10. One of the indicators frequently used to gauge the health of the economy is
the Bureau of Labor Statistics’ measurement of the unemployment rate.
However, there are several reasons why this number may not accurately reflect
the number of workers who have lost their jobs. Name two of these problems,
explain what they are, and tell how they affect the measurement of the
unemployment rate.
Questions about labor supply: general model
1. A policy shifts a worker’s budget constraint upwards and, at the same time,
makes the budget constraint flatter. What effect will this have on his labor
supply?
2. (Long) Each week, Otto has 100 waking hours that he can either work or play.
For each hour he works, he is paid $10.00. In addition, he receives an $50.00 per
week in unearned income (renting out a spare room in his house). Then the
government mandates overtime pay. Up until 40 hours, Otto is still paid
$10.00/hour; for each hour over 40, he must be paid $15.00/hour. Explain how
this changes his labor supply behavior (keeping in mind that the effects might be
different depending on his initial hours).
3. When wages increase, workers tend to experience both an income effect and a
substitution effect. When is the substitution effect likely to dominate?
4. A proposed policy gives a tax credit of $2,000 to each family, regardless of how
much they earn. To fund this, the average income tax on labor earnings would
be increased from 18% to 23%. How would this policy affect labor supply?
5. Some policy changes a worker’s budget constraint. Explain, in general, how
you would analyze the effect of this change on his labor supply.
6. A person chooses not to work in the labor market if what is true?
7. When wages increase, workers tend to experience both an income effect and a
substitution effect. When is the substitution effect likely to dominate?
8a. Name the two types of fixed costs of working, and explain how each affects
labor supply.
8b. Some costs of working are variable: they depend on the number of hours that
a person works. How do these affect labor supply?
9. Explain why a worker’s reservation wage rises with his unearned income.
10. How does having a high value of leisure affect the shape of a worker’s
indifference curves? (In other words, in what ways would the indifferences
curves of high-value-of-leisure and low-value-of-leisure look different?)
11. Describe the shape of an individual’s labor supply curve, and explain why it
gets this shape.
12. What is “full income”?
13. (Long) Explain why a lump-sum government transfer can entice some
workers to stop working (and entices no one to start working), while the earned
income tax credit can entire some people who otherwise would not work to start
working (and entices no one to stop working).
14. In words, describe the marginal rate of substitution between consumption
and leisure. Then give the mathematical expression for the relationship between
it and the utility function.
15. Mr. Pig’s utility function is U (C, L) = lnC + ln L , where C is his weekly
consumption and L his hours of leisure. (This utility function implies that the
marginal utility of consumption is 1 C and the marginal utility of leisure is 1 L .)
There are 100 hours in the week, and he has $250 in unearned income. Calculate
his reservation wage.
16. (Long) As a worker in a small firm, Mr. Frog is paid $15.00/hour. He has no
other income. Assume that there are 100 waking hours in the week. His
preferences are given by the utility function U (C, L) = C 3 L . (The partial
derivatives of this function are ∂U ∂C = 3C 2 L and ∂U ∂L = C 3 .)
a. Draw his budget constraint, and carefully label important points. Show
his optimal choice of consumption and leisure.
b. Now his office must move to a different part of the city. If he continues
to work (which he does), he must travel 20 hours per week to and from
work. At the same time, his boss increases his wage by 25%. Show how
this changes Mr. Frog’s budget constraint, and also his choice of
consumption and leisure. After the change, does he work more or less?
17. Alec earns $10 for every hour that he works and also has lottery earnings of
$50 that he receives every week regardless of how much he works. His
reservation wage is $8. If he works 60 of the 168 hours in the week, what would
be his full income?
18. Liz’s utility function is U=C x L. Her rich uncle Jack gives her $200 every
week and there are 40 hours in one week. What is the lowest wage for which Liz
would work?
19. Tracy faces a fixed cost of $15 for working. Assuming that Tracy has been
working and will continue to work, what effect will this have on his labor
supply?
20. Suppose the government gives $500 to anyone who is out of work. For each
$1 earned, the benefit is reduced by 50 cents. If John is offered a job paying $12
an hour, what is his effective wage rate while he is a part of the government
program?
21. (Long) In general, supply curves always slope upward. Is this true of an
individual’s labor supply curve? (Explain your answer.)
22. (Long) Mr. Browning’s adult life spans sixty years, from age twenty to age
eighty. He cares about two things in life: his total lifetime consumption and the
number of years that he is retired. During each year that he works, he is paid
$50,000; in retirement, he initially receives nothing. (Disregard discounting for
this problem.)
a. Draw his budget constraint in this case.
b. Now the government introduces a policy to provide retirees with some
income. Mr. Browning receives a fixed payment of $300,000 at the time he
retires (spread out over the remainder of his lifetime, but that’s irrelevant);
he can retire at any age that he chooses. This program is financed with a
10% tax on workers’ earnings (including Mr. Browning’s).
c. How does this policy affect Mr. Browning’s retirement decision?
23. Mr. Pig’s utility function is U (C, L) = C ⋅ L , where C is his weekly
consumption and L his hours of leisure. There are 100 hours in the week, and he
has $250 in unearned income. Calculate his reservation wage.
24. What is the optimality condition for an individual worker’s choice of leisure
and consumption (i.e., “where BLANK equals BLANK”) for an interior solution?
25. Each week, Otto works 45 hours out of a maximum of 110 waking hours, and
receives $10 for each hour that he works. He also receives $50 weekly from a
family trust. What is his full income?
26. Why are individual labor-supply curves “backwards bending?”
27. The Michigan Family Independence Program (a social welfare program)
offers cash transfers to low-income families. Suppose that the maximum transfer
is $3,000 for households without no income; for each dollar earned, the transfer is
reduced by $0.20. Comment on how this program changes the recipient’s hours
worked: the income effect (assuming that leisure is normal), the substitution
effect, and the overall effect.
28. Describe what happens to a worker’s reservation wage as unearned income
increases, and why.
29. (Long) There are 5000 total hours in each year. Gary spends 2000 of these
working, for which he earns $10/hr. He receives a payment of $10,000 each year
(for having been a contestant on a reality game show).
a. Draw Gary’s initial budget constraint, and show his equilibrium choice
of leisure and consumption.
b. Assuming that Gary’s utility function is given by U (C, L) = C ⋅ L ,
calculate the amount that his consumption would have to increase for him
to give up another hour of leisure. (Showing work is important.)
30. Define the reservation wage of a worker.
31. Due to increasing gasoline prices, Professor Woodchuck must now spend
$100 each week driving to work, rather than $20. Assuming that she keeps
working, how does this change the number of hours that she works? What effect
causes this?
32. A particular welfare program (a wage rate subsidy) offers no guaranteed
income. Instead, it pays any low-wage worker an additional $1.00 for each hour
that she or he works. Comment on how this program changes an individual’s
hours worked: the income effect (assuming that leisure is normal), the
substitution effect, and the overall effect.
33. (Long) In a given week, Mr. Mustard receives $400 (as part of a settlement for
having cut himself with a razor while shaving in the dark). Initially, he faces a
wage rate of $10 for each hour that he works, and he chooses to work 55 hours
(out of 100 total hours in the week). After receiving a promotion to $15/hour, he
works 45 hours.
a. Draw Mr. Mustard’s initial budget constraint, and show his equilibrium
choice of leisure and consumption.
b. In the same picture, draw the budget constraint after the wage change,
and show the new equilibrium.
c. Graphically, decompose the change in hours worked into an income
effect and a substitution effect.
34. (Long) Prior to 2000, Social Security had an “earnings test”. Retirees could
earn up to $17,000 a year without any reduction in benefits. For every dollar they
earned above this threshold, the pension was reduced by a third of a dollar. This
earnings test was eliminated in 2000.
35. Suppose that an older worker is eligible for up to $12,000 in benefits (which
might be reduced if he earns more than the limit), and he has no other income.
He has 4000 hours in the year, and he could earn $20/hour working in the
market. Illustrate his budget constraint with and without the “earnings test”, and
explain how eliminating the earnings test affects his labor supply.
36. Name the four components of labor supply.
37. Give the mathematical expression that determines a worker’s optimal labor
supply (when he is not at a corner solution).
38. (Long) Explain how the Earned Income Tax Credit policy affects hours
worked and labor supply participation.
Questions about labor supply: efficiency wages
1. Explain how efficiency wages can lead to a greater supply of effort.
2. A worker’s “no-shirk wage” depends on what three factors?
3. What three variables determine the “no-shirk wage”, the lowest wage at which
a worker is willing to supply effort?
4. Dr. Leach earns $X for teaching an economics course. When grading exams, he
must make a decision. To grade all exams carefully causes disutility of $1000.
The alternative choice is to give everyone a 10, but then there’s about a 5%
chance that the head of the department will hear about this, and Dr. Leach will
lose his job (and receive no payment for the class). Find the wage that would
cause Dr. Leach to do his job carefully.
5. Dr. Tim gets paid $X for performing a surgery. He can either do a careful
operation, or do a quick operation. If he does it carefully, he has to miss his golf
game (worth $30 to him). If he does it quickly, he has a 1/100 chance of making
a mistake. If he makes a mistake, he receives no fee for the surgery, and he must
pay a $1,000 settlement. How much must $X be in order to induce Tim to
perform a careful operation?
Questions about labor supply: elasticities
1. This problem is about elasticities.
a. When her wage rate was $6/hour, Margaret used to work 40 hours out
of a maximal possible 100 hours in each week. She had no other sources
of income. When her wage increased to $8/hour, she decided that she
wanted to work 50 hours each week. Find her uncompensated wage
elasticity.
b. Pauline earns $10/hour, and she has a total of 100 hours in each week.
When she had no unearned income, she would work 40 hours each week.
After a rich uncle established a trust for her that would pay $200/week,
she chose to work only 35 hours each week. Find her income elasticity.
c. Find Margaret’s compensated wage elasticity, when she earned
$6/hour, had no other income, and worked 40 of 100 hours in the week.
(Use the information from Pauline where you need it; we’ll assume that
their preferences are the same.)
2. (Long) During a normal year (like 2001 or 2003), Ms. Apple works 2000 hours
(out of a possible 5000) for a wage of $15.00 per hour; she has $5,000 in additional
income. Unusual events eliminated this income in 2002. She returned to normal
in 2003. In 2004, a 33 13 % income tax rate reduced her effective wage rate. This
table shows the hours she worked in each year.
Annual hours of work
2001
2002
2003
2004
2,000
2,100
2,000
1,800
Hourly earnings (after tax) $15.00 $15.00 $15.00 $10.00
Additional income
$5,000 $0
$5,000 $5,000
a. Calculate her uncompensated wage elasticity and her income elasticity
of labor supply. (Suggestion: for each, use either 2001 or 2003 as the
“initial period.”)
b. Give the mathematical expression for the relationship between these
and the compensated wage elasticity.
c. Calculate how much the 2004 income tax changed her labor supply
through the substitution effect. (Give your answer in terms of hours.)
3. (Long) Veronica usually has a weekly unearned income of $100. During a
typical week, she works 50 hours a week (out of a maximal 90 hours in the week)
at a wage rate of $10. One week when her wage was decreased to $6/hour, you
observed her working only 45 hours. During a different week, when she had no
unearned income, she worked 52 hours.
a. Calculate the uncompensated elasticity of labor supply.
b. Calculate the income elasticity of labor supply.
c. Write down the formula to calculate the compensated elasticity from the
uncompensated elasticity of labor supply and the income elasticity of
labor supply.
d. Calculate the compensated elasticity of labor supply.
4. List the three types of elasticity associated with labor supply, and name the
effect (or effects) each one measures.
5. Both Paul and John have $100 in unearned income each week, and both have
168 hours in the week. Paul earns $10/hour and works 40 hours, while John
earns $15/hour and works 45 hours. This information allows you to calculate
which type of elasticity?
6. (Long) Pam has a weekly unearned income of $200 (which comes from
winning a beauty contest). She works 30 hours a week (out of a maximal 100
hours in the week) at a wage rate of $10. Her wage increases to $14/hour. Pam
has a compensated wage elasticity of 0.4 and an income elasticity of –0.5 for labor
supply.
a. Find the percentage increase in Pam’s wage rate and in her wealth due
to this wage change.
b. Find the percentage change in hours worked due to the substitution
effect and the income effect of the wage increase.
c. Write down the formula for calculating an uncompensated wage
elasticity from the compensated wage elasticity and the income elasticity.
d. Calculate Pam’s uncompensated wage elasticity. Is it positive or
negative? What does this say about the relative sizes of the income and
substitution effects?
Questions about household production
1. The Swedish government previously allowed husbands and wives to take a
combined paternity and maternity leave of two years to take care of children.
Because wives often took the full two years from work and husbands took no
time off from work, this government changes the policy so that spouses must
take off equal time for childcare. From the perspective of household production,
does this policy make sense? Why or why not?
2. My buddy, Doc Tim, lives in Ontario but is invited to a wedding in Texas. He
decides to drive instead of fly, since it is cheaper: the price of four airline tickets
for his family would be $1, 000 ; driving (plus meals and motels) would cost only
$300 . Comment on his behavior.
3. How do labor economists explain the drop in fertility as incomes rise?
4. This is a one-person household production problem about heating my house.
Suppose that there are two uses of my time: I can work in the marketplace to
purchase things that help heat my home (propane for the furnace, or gasoline for
the chainsaw), or I can work at home to cut down trees. Explain what happens to
my time use as the cost of the market inputs rises.
5. Mr. and Mrs. Johnson have 100 hours apiece each week, which they can spend
either working in the marketplace or working at home. For working in the
market, Mr. Johnson receives $8/hour; at home, he can cut 1 2 cord of firewood.
Mrs. Johnson receives $6/hour in the market, or she could produce 1 4 cord of
firewood each hour that she works at home. We observe that Mr. Johnson works
60 hours in the market and 40 hours at home; Mrs. Johnson works 20 hours in the
market and 80 at home. Is this behavior consistent with the household
production model?
6. Before she goes to medical school, Mrs. Snake works part-time for $7.00/hour,
and she spends the rest of her time at home with the children. Her husband
works full-time for $18.00/hour. After medical school, she earns $50.oo/hour,
but she still chooses to stay at home part of the day. In a model of household
production, is this behavior optimal? Why or why not?
7. Near my house, there is a fast-food restaurant that sells egg muffins for $1.69
apiece. At home, I have a fancy toaster-and-egg-steamer that can produce a
virtually identical product. You slice and butter an English muffin, stick it into
the toaster slots; scramble an egg, pour it into the egg steamer, and add water to
the steamer. Altogether, it takes about ten minutes of preparation and cleaning.
Producing an egg muffin at home costs only around $0.50. Nonetheless, I often
find myself stopping by McDonald’s instead. Is it irrational to buy the same
product for more money at McDonald’s?
8. (Long) During her life, Mrs. Horse has 20 years to work or to raise children.
For each child that she has, she must spend two years out of the labor force. She
is able to earn $40,000 for each year that she works. These labor earnings go
toward the quality of her children. Her utility depends on the quality and
quantity of her children, which are both normal goods.
a. Draw her budget constraint.
b. Now the government gives her a $2,000 credit for each child. To finance
this, they impose a 10% tax on labor earnings. Show how this changes the
budget constraint. In terms of income and substitution effects, explain
how this changes the quality/quantity decision.
9. Batman can earn $20 an hour picking up shifts at the county sheriff’s office.
Instead, he decides to buy a $50 ticket to see the Redskins football game, which
will last 3 hours. What is the full price of going to the game for Batman?
10. Over the past century, real household income has increased substantially in
the United States. At the same time, the average number of children born to a
woman during her lifetime has fallen from about three children per woman to
two children. Does this suggest that children are inferior goods?
11. What is the “full price” of a good?
12. (Long) Think of this as a household production model, where “quality of
children” and “quantity of children” are both goods. In your lifetime, you have
25 years during which you can either work or bear children. For each child you
have, you must take five years off from work. Each year that you work, you are
paid $20,000, which goes toward the quality of your children.
a. Draw your budget constraint, carefully labeling axes, where the budget
constraint intersects these axes, and the slope of the budget constraint.
b. The government offers you a tax credit of $10,000 per child. In the same
picture, show how this changes the budget constraint. Discuss how it
affects the quality and quantity of children (assuming that both are
normal goods).
13. In a two-person model of household production, what determines who works
in the market and who works at home?
14. According to the two-person model of household production, what will you
never find both household members doing?
15. In each hour, Count Dracula can earn $18 in the market, or he can produce 9
units of household production (new vampires). His wife (Countess Dracula) can
earn $15 or generate 5 units of household production. If one specializes in the
market, which will it be? If one specialized in household production, which will
it be?
16. (Long) Think of this as a household production problem, where a married
couple (“Frankenstein” and “Bride of Frankenstein”) face a quantity/quality
tradeoff in children. Each has a lifetime consisting of ten years. He earns $30,000
for each year that he works; she earns $40,000. For each child they have, she has
to take four years off from work (he cannot take time off to have children). You
may assume that both “quality” and “quantity” are normal goods.
a. Draw the household’s budget constraint.
b. Suppose that her yearly earnings increase to $50,000. In terms of
income and substitution effects, explain how this alters the household’s
fertility decision.
c. Suppose that his yearly earnings increase to $50,000. In terms of income
and substitution effects, explain how this alters the household’s fertility
decision.
17. Mr. And Mrs. Ghoul live together, and both enjoy market goods and
household services. Each has 10 hours in the day. For each hour that he works
in the labor force, Mr. Ghoul can earn $25 to buy market goods; for each hour
that he works at home, he produces household services worth $10. Mrs. Ghoul
can purchase $30 worth of market goods for each hour that she works in the
labor force, or she can produce $25 worth of household services for each hour
that she works at home. According to household production theory: if one
person specializes in working in the labor force, who should it be? If one person
specializes in working at home, who should that be? Briefly explain.
18. (Long) Think of this as a household production model, where “time spent
driving a car” is a non-market good, and “quality of car” is a market good.
Batman has 5000 total hours in a year. He can spend this time either driving his
car (let D be the number of hours that he drives his car) or fighting crime (H is
the number of hours that he works). The money that he gets from working ($W
per hour) is spent on improving the Batmobile, so that the quality of the car
(measured in dollars) is B = W ⋅ H . Batman’s indifference curves over the nonmarket good and the market good have the usual shape.
a. Draw Batman’s budget constraint, carefully labeling axes and where the
budget constraint intersects these axes.
b. The mayor of Gotham City has decided to subsidize crime-fighting,
paying an additional $Z per hour. Illustrate what this does to Batman’s
optimal combination of (D, B). (Assume that non-market goods are
inferior.) In which direction does this shift the intensity of his choice
(toward a mixture that is more intensive in market goods, or toward a
bundle that is more intensive in non-market)? Also, does he work more?
19. (Long) Initially, a worker earns an hourly wage of $W , and she no unearned
income. The total amount of time in the period is T . Then the government
introduces a social welfare program that works like a negative income tax: it
offers a transfer of $G to people with zero income; for each dollar of income you
have, the transfer is reduced by m (where 0 < m < 1 ), until the transfer equals
zero.
a. In the standard leisure/consumption model, show how this changes the
worker’s budget constraint, and explain how it affects her labor supply.
b. In the quality/quantity household production model of fertility, show
how this changes the worker’s budget constraint, and explain how it
affects the quality and quantity of children that she has.
Questions over matching and joint decision-making
1. In which model or models of joint household decisions do “outside options”
play a significant role? What effect do they have?
2. Explain the meaning of positive assortative matching and negative assortative
matching. What is the condition for each to be optimal in the marriage market?
3. (Long) Finances are important in making a marriage work. The marriage
market consists of four men and four women, all with different incomes.
Bachelor Earnings ( Yi ) Bachelorette Earnings ( Y j )
Albert
$20,000
Anne
$10,000
Bill
$45,000
Betty
$55,000
Charles
$55,000
Claire
$75,000
Donald
$80,000
Dana
$90,000
a. Suppose that the gains from marriage are determined by the function
Zij = Yi + Y j . Determine the outcome of the marriage market. (Show or
explain your work.)
b. Discuss why you think that this particular pattern arose. (I would like
your own interpretation, based on what we’ve discussed in class.)
4. In the Nash bargaining model of joint decision-making, what influences the
amount of weight that gets put on each person’s preferences?
5. (Long) This is a question about matching. There are four universities, and each
one can accept one new freshman. There are also four freshmen looking for
universities. The “surplus” (increased earnings) generated by matching student
s with college c is determined by the function:
Z sc = 1000 − (IQ c + IQ s )2
where IQs is the intelligence of the student, and IQc is the average intelligence
of the faculty at the college. These are given in the following table:
University
IQ
Student
IQ
U. of Michigan
122
Iggy
126
U. of North Carolina
146
Jacky
104
Ohio State U.
132
Kathy
112
Penn State U.
118
Larry
153
Determine the equilibrium assignment of students to universities, assuming that
universities can provide individual transfers to students.
6. (Long) In the marriage market, there are two eligible bachelors (Andy and
Bob) and two eligible bachelorettes (Claire and Dana). Here are the (gross)
utilities that each person gets from the prospective partners:
U A (Claire) = 9
U A (Dana) = 10
U B (Claire) = 10
U B (Dana) = 15
U C (Andy) = 8
U C (Bob) = 5
U D (Andy) = 7
U D (Bob) = 6
The value of remaining single is zero. (5 points each)
a. Find the stable equilibrium if there is transferable utility in the marriage
market. (Explain how you get your answer.)
b. Find the stable equilibrium in a marriage market where utility transfers
are not possible. (Explain how you get your answer.)
7. What does it mean for a match to be “stable”?
8. Suppose that the (monetary) value of the education that a student receives
depends on his own intelligence ( IQstud ) and the average intelligence of the
faculty at a particular university ( IQuniv ). This surplus can be calculated as
Z stud,univ = IQstud + IQuniv . Both students and universities vary in intelligence, and
universities can use scholarships to provide a specific price to each student.
What association would we expect to see between the intelligence of students
and faculty?
19. Which of the three models of joint decision-making predict income-pooling?
Which does not?
20. Explain positive assortative matching and negative assortative matching.
Under what circumstances is each optimal?
21. (Long) There are four universities, and each one can accept one new
freshman. There are also four freshmen looking for universities. The “surplus”
(increased earnings) generated by matching student s with college c is
determined by the function:
Zsc = 1000− (IQc − IQs )2
where IQs is the intelligence of the student, and IQc is the average intelligence
of the faculty at the college. These are given in the following table:
University
IQ
Student
IQ
U. of Michigan
146
Iggy
126
U. of Nebraska
122
Jacky
114
Ohio State U.
132
Kathy
102
Penn State U.
118
Larry
133
Determine the optimal way to assign students to universities.
22. There are two men and two women in a marriage market (with transferable
utility). The surplus generated from Ann marrying Carl is 10; from Ann
marrying Dan is 8. The surplus generated from Beth marrying Carl is 4; from
Beth marrying Dan is 7. What is the optimal way to match them?
23. According to the Nash-bargaining model, what mathematical expression does
the household maximize? Define all the variables used.
24. (Long) In 1963, Jimmy Soul’s remake of an old calypso song became a
number-one hit. This song advises a young man:
If you want to be happy for the rest of your life
Never make a pretty woman you wife.
So for my personal point of view
Get another girl to marry you.
Pretty woman with the pretty face
Attracts attention in every place.
Given what you know about household bargaining, comment on whether you
think this is good advice.
25. Explain the basic prediction of “bargaining models” of joint decision-making.
26a. Explain how to find a stable match in a (marriage) market with transferable
utility, where the surplus from the match can be written as a function of some
attribute of the husband and wife (that is, Zij = F(Si , S j ) ).
26b. Explain the procedure for finding a stable match in a (marriage) market
without transferable utility.
27. (Long) There are three job openings (1, 2, and 3) and three workers (A, B, and
C). Here are the workers’ rankings of firms, and the firms’ rankings of
applicants:
First choice
Second choice
Third choice
Worker A
Job 2
Job 1
Job 3
Worker B
Job 1
Job 2
Job 3
Worker C
Job 3
Job 2
Job 1
First choice
Second choice
Third choice
Job 1
Worker B
Worker A
Worker C
Job 2
Worker C
Worker A
Worker B
Job 3
Worker B
Worker A
Worker C
Find a stable match.
Questions over labor demand: general
1. Who benefits or loses from a low elasticity of demand for labor, and under
what circumstances?
2. When the price of an input rises, a firm experiences which two effects?
3. The labor demand elasticity is higher in the long run than in the short run.
Using one of Marshall’s laws of derived demand, explain why this is true.
4. In the short run, a firm determines its labor supply by the VMPL curve, except
in what case?
5. Suppose that competitive firms employ two types of labor, “skilled” and
“unskilled”. Explain how an increase in the interest rate affects demand for each.
6. A firm produces widgets using capital and labor. Initially, labor costs
W1 = $10 per hour, and the rental rate on capital is R1 = $15 per hour. Then the
price of labor drops to W2 = $8 , and the rental rate on capital falls to R2 = $10 .
Explain how this affects the firm’s demand for capital and labor in the long run.
7. Describe four things that would suggest a high elasticity of demand for labor.
(In other words, give me Marshall’s laws.)
8. A firm produces widgets using capital and labor. Explain how the firm
decides how much of each input to use in the short-run and long-run.
9. What is the optimal hiring rule for firms in the short run (provided that the
firm doesn’t shut down)?
10. Tarheel Town employed 20,000 workers and pays $20 an hour last year. This
year Tarheel town must pay workers $25 an hour and as a result hires only
18,000 workers. What is the elasticity of labor demand?
11. Suppose that Martians move to Earth and become workers. If Martians are
complements to human labor, what would be the effect of an increase in the
wage rate paid to Martians?
12. A firm has to make two choices regarding labor demand: how many
employees to hire, and how many hours each employee should work. Suppose
that the government imposes a per-worker cost on the firm—for example, it has
to pay a fixed amount for each worker’s health insurance, regardless of how
many hours he works. How would this affect each aspect of labor demand (the
number of workers and the hours per worker)?
13. What determines the short-run labor demand of a perfectly competitive firm?
14. According to the capital-skill complementarity hypothesis, what effect would
technological process have on income inequality?
15. In the long run, an increase in the wage paid to workers has two effects on the
labor demand of a competitive firm. Name and describe these.
16. Advances that make technology more affordable will benefit which type of
workers and hurt which other type?
17. What determines whether, and how much, workers will benefit from wages
artificially set above the market equilibrium?
18. Acme Widget Co. hires labor in a perfectly competitive market. Using a
graph, explain what happens to its labor demand (in the short run) when there is
an increase in the price of its output.
19. The labor demand elasticity is higher in the long run than in the short run.
Using one of Marshall’s laws of derived demand, explain why this is true.
20. What does the “capital-skill complementarity hypothesis” state?
21. What is the primary difference between labor demand in the short-run and in
the long-run? Which is more elastic?
22. Define the marginal rate of technical substitution between labor and capital
(in words) and also state the mathematical expression for it.
23. How does an increase in the interest rate affect demand for labor?
24. How does a competitive firm decide its use of capital and labor in the short
run?
25. When the economy is sluggish, the Federal Reserve often reduces interest
rates. What effect might this have on employment?
Questions over market equilibrium: competitive
1. Show how a minimum wage, set above the market equilibrium wage, affects
employment in the labor market.
2. The labor market has two sectors, which we will call “north” and “south”
regions. Workers are perfectly homogeneous, and free to migrate between the
two sectors. Argue that the competitive equilibrium allocates workers optimally
between the two sectors.
3. Suppose that the economy has only two industries, the agricultural industry
and the manufacturing industry, and that workers are free to move between the
two. The government imposes a per-worker tax on manufacturing firms (paid
by the firms, directly to the government). Show how this affects employment
and wages in each of the two industries.
4. Which affects employment and workers’ net wages (wages minus taxes) more:
a payroll tax imposed on the worker, a payroll tax imposed on the firm, or one
shared by both? Explain.
5. Show that a per-worker tax on labor paid by workers is equivalent to a perworker tax on labor paid by employers (equivalent in terms of surplus, earnings,
and employment).
6. The labor market has two sectors, which we will call “north” and “south”
regions. Workers are perfectly homogeneous, and free to migrate between the
two sectors. Argue that the competitive equilibrium allocates workers optimally
between the two sectors.
7. Suppose that a firm produces widgets using two different types of labor (and
capital, but that’s irrelevant for this question): skilled workers and unskilled
workers. What effect would an increase in the supply of unskilled workers have
on the wages and employment of skilled labor?
8. What does the “law of one wage” state?
9. (Long) At a wage of W , workers are willing to supply 2 ⋅W − 6 units of labor.
Labor is used to produce bread; if E units of labor are used, then 20 ⋅ E − 1 2 E 2
units of output are created. The firm’s output sells for $0.50 each. (5 points each)
a. If this labor market is perfectly competitive, find the equilibrium
employment and the equilibrium wages paid.
b. Suppose that the government imposes a (binding) minimum wage of
$7.00 per unit of labor. Find the level of employment in the competitive
market.
c. If a non-discriminating monopsonist controls this labor market, find the
amount of labor employed and the wages paid.
10. (Long) In this labor market, there is one worker (Bob) and one firm (Acme
Pest Control). (Assume, nonetheless, that it is a competitive market.) Bob gets
utility from consumption (C) and leisure (L), according to the function
U (C, L) = ln C + ln L . His budget constraint is C = Y + WH , where H is the
number of hours that he works in the week and W is his hourly wage rate. There
are a total of 100 hours in the week, which Bob can spend working or in leisure.
His unearned income is Y=$50. Note that the partial derivatives of this utility
function are ∂U / ∂C = 1/ C and ∂U / ∂L = 1/ L .
a. State the optimality condition for a worker’s utility maximization (just
the formula) for an interior solution.
b. Using Bob’s utility function, solve for his choice of optimal labor
supply, H * .
Acme Pest Control produces dead mice. If they hire someone to work for E
hours and they use K mousetraps, then the number of mice that they exterminate
is Q = F(E, K ) = 150⋅ ln E + 10⋅ ln K . They pay the employee a wage rate of W for
each hour that he works, and they rent the mousetraps for R=$2 apiece. They
receive a payment of P for each mouse they kill. The partial derivatives of this
production function are ∂F / ∂E = 150/ E and ∂F / ∂K = 10/ K .
c. State the optimality condition(s) for a firm’s profit-maximization (just
the formula, again) in the short run.
d. Using the firm’s production function, solve for their choice of optimal
labor demand, E * .
e. If the payment received for a dead mouse is P = $4 , find the wage rate
W * such that the market is in equilibrium.
11. (Long) At a wage of W, workers are willing to supply labor of H = 2 ⋅ W − 6 .
The marginal product of labor to a firm is MPL = 20 − E , where E is the amount
of labor employed. The firm’s output sells for $0.50 apiece.
a. If this labor market is perfectly competitive, find the equilibrium
employment and the equilibrium wages paid.
b. Suppose that the government imposes a (binding) minimum wage of
$7 per unit of labor. Find the level of employment in the competitive
market.
c. If this labor market is controlled by a non-discriminating monopsonist,
find the amount of labor employed and the wages paid.
d. Suppose that the government imposes a (binding) minimum wage of
$7 per unit of labor. Find the amount of labor that the non-discriminating
monopsonist employs.
Questions about non-competitive markets
1. What do we call a firm that can set wages and employment in the labor
market? What are the two different types of this firm?
2. Contrast the employment decisions and the wages paid by a discriminating
monopsonist with those of a non-discriminating monopsonist.
3. Why is the marginal cost of labor greater than the wage rate for a nondiscriminating monopsonist?
4. In some situations, professional workers (like athletes) sign contracts that give
a single employer exclusive rights to their services. However, this might not
result in an inefficient outcome, like other monopsony situations. Explain why
not.
5. At a wage of W , workers are willing to supply 20 ⋅W − 10 units of labor.
Labor is used to produce bread; if E units of labor are used, then 30 ⋅ E − E 2
units of output are created. The firm’s output sells for $3.00 each. If a nondiscriminating monopsonist controls this labor market, find the amount of labor.
6. How much does a discriminating monopsonist pay to its workers?
7. A firm may still behave like a monopsonist, even if it is not literally the sole
employer of labor in some market. In what circumstances might a firm exhibit
some monopsony power?
8. If the Acme Widget Company is the only producer of widgets (it is a
monopolist in this market) but hires labor competitively, how would its labor
demand and wages differ from a perfectly competitive firm?
9. Describe how a discriminating monopsonist determines wages and
employment.
10. Describe how a minimum wage would affect the wages offered and
employment decision of a monopsonist. (Assume that the minimum wage is
binding, but—for simplicity—that it is perhaps not as high as the competitive
equilibrium wage would have been.)
11. Explain why a monopolist in output employs less labor than a competitive
firm would have used, in the same situation.
12. How are the employment and wages of a monopolist (in output) different
from a competitive firm?
13. Professional associations, like the American Medical Association, frequently
maintain licensing standard that effectively restrict the supply of labor to the
market. Explain how this behavior could be purely self-interested (and not in the
best interest of the consumer).
14. Some athletes have the “rights” to their own labor (they are free agents, who
can work for any team they want), while others do not have the rights to their
own labor (these rights are owned by a team, which decides who he works for).
According to the Coase Theorem, [BLANK] will not be affected by whether the
worker owns the rights to his own labor, but who has the rights to his labor will
affect [BLANK]. (Fill in the blanks.)
Questions about minimum wages
1. How would an increase in the minimum wage affect demand for different
types of labor, like skilled workers? (Note: this is not a two-sector model.)
2. Under what circumstances can an increase in the minimum wage result in an
increase in employment?
3. Presidential candidate John Kerry proposes increasing the federal minimum
wage. Assuming that U.S. and Canadian workers are perfect substitutes for each
other and that they are free to move between the two countries, analyze how this
policy would affect immigration between the U.S. and Canada and the wages in
each.
4. Texas governor Rick Perry proposes increasing the state minimum wage.
Assuming that Texan and Mexican workers are perfect substitutes for each other
and that they are free to move between the two countries, analyze how this
policy would affect immigration between Texas and Mexico and the wages in
each.
5. Suppose that workers (but not firms) are free to move between two labor
markets, Ann Arbor and Ypsilanti. Ann Arbor passes a $12/hour “living wage”
that is above the going wage rate of $6.50. Discuss how this affects employment
and wages in both Ann Arbor and Ypsilanti.
6. Why can a minimum wage cause a monopsonist’s employment to increase?
7. Suppose that there are two industries, manufacturing and agriculture, and that
workers are perfectly mobile between these two industries. The legislature
introduces a minimum wage that covers only the manufacturing industry.
Explain how this affects wages and employment in each of the two industries.
8. Show how a minimum wage, set above the market equilibrium wage, affects
employment in the labor market.
9. How does a minimum wage for unskilled labor affect demand for other types
of workers?
10. Explain why we would use a “difference-in-differences” estimation technique
to find the effects of a minimum wage on employment.
11. (Long) This question is about minimum wages.
a. Explain how a minimum wage could increase employment in the sector
in which it is imposed.
b. Suppose that there are two perfectly competitive sectors in the labor
market: the manufacturing sector and the agricultural sector. Workers are
completely mobile between these two sectors. Explain what happens to
employment and wages in both sectors when the government imposes a
minimum wage (above
manufacturing sector.
the
market
equilibrium
wage)
in
the
12. Explain the theoretical effects of a minimum wage on employment and wages
of workers in the sector of the economy covered by the wage.
13. Explain the difference between the unemployment and the disemployment
caused by a minimum wage in a competitive market.
14. How does a minimum wage affect wellbeing of workers (in the sector of the
economy covered by the minimum wage)?
15. How does a minimum wage for unskilled labor affect demand for other types
of workers?
16. Suppose that workers are completely mobile between two sectors of the
economy. A minimum wage imposed on one sector will cause wages to change
in the other sector. Wages settle down when what condition is met?
17. Show graphically how workers might benefit from an increase in the
minimum wage, even in a competitive market.
Questions about immigration
1. Analyze how an influx of new immigrants affects the employment and wages
of native workers and the employment and wages of immigrants already in the
country.
2. Explain what it means for immigrants to be “positively selected” from another
country, and explain the condition that causes this.
3. How does the interest rate (or a worker’s “internal rate of return”) affect
migration decisions?
4. Suppose that immigrant labor is a perfect substitute for native workers.
Illustrate (using a graph) how an influx of immigrants affects employment and
wages of native workers.
5. Describe the effects of an influx of immigrants on the wages and employment
of each of the following groups: native workers, and immigrants already in the
country.
6. A study by David Card shows that after the Mariel Boatlift, the unemployment
rate for native workers in Miami remained the same, relative to a group of
comparable cities that did not experience immigration. However, this does not
necessarily mean that the immigration had no effect on wages of natives.
Explain why not.
7. What four factors affect whether a worker migrates?
8. In theory, what is the effect of an increase in immigration on the employment
and wages of native workers?
9. Empirical evidence shows that workers do not earn significantly more or less
in cities with large immigrant populations, than they do in cities with small
immigrant populations. Does this mean that immigration has no effect on labor
markets? Explain your answer.
10. (Long) Suppose that a worker’s productivity depends on his level of skill, s.
The distribution of units of skill is this: worker 1 has 1 unit of skill, worker 2 has
2 units of skill, worker 3 has 3 units of skill, etc. There are 100 workers in the
population. In deciding whether to move to Mexico, these workers compare
their earnings at home ( WTX ) to their earnings in Mexico ( WMX ). The relationship
between wages and skill in each country is determined by the functions:
WTX = 700 + 0.5s and WMX = 670 + s .
a. Assume there are no costs of moving. What is the average skill level of
people who choose to move? Are immigrants selected positively or
negatively?
b. Suppose that there is some positive cost, $C, to move to Mexico. What
effect does this have on the average skill level of people who choose to
move?
c. Now introduce a spouse into the problem. Suppose that partners’ skill
levels are positively correlated. What pattern of migration would we
expect to see?
11. What are “positive selection” and “negative selection”?
12. “A-list” celebrities earn much more than “B-list” celebrities, and major league
players earn much more than minor league players. What are the two conditions
under which “superstars” earn so much more than the second-best star?
13. Explain how an influx of immigrants affects the employment and wages of
native workers. Be as complete as possible.
14. The “Roy Model” attempts to explain two facts about the distribution of
earnings. Tell me what these are, and give me Roy’s explanation of each.
15. (Long) This question is about the effects of immigration.
a. Theoretically, the effects of an influx of immigrants on labor market
conditions for native workers depends on what?
b. When measuring the effects of immigrants on labor market conditions
for native workers, researchers often compare the wages of natives in
cities with large immigrant populations to those with small immigrant
populations. Borjas argues that finding “no difference” is not confirmation
of “no effect”. Explain why not.
16. What are “tied movers” and “tied stayers”?
Questions about human capital
1. Marvin’s annual earnings are determined by the function
$W = $30,000 + $6,000 ⋅ S , where S is the number of years of education he acquires
after high school. At an interest rate of 10%, how much education should he get?
2. Explain why a worker’s wages grow over time, but they grow quickly when
young and slowly when old.
3. When a worker can choose any level of education, what condition determines
the optimal number of years? (If you use variables, define them.)
4. In a simple (discrete) model of whether or not to invest in human capital, it is
apparent that the investment decision depends on what four factors?
5. Suppose that a worker can choose exactly how many years of education to get.
State the rule for the optimal investment, and show how we derive this result.
6. Explain verbally and show graphically how “ability bias” affects estimates of
the returns to education.
7. How does the “ability bias” affect estimates, and of what?
8. What is “specific human capital”, and who pays for and who benefits from it
(the firm or the worker)?
9. Explain how people’s patience, or “internal rates of return”, affect how much
education they obtain. (It would be helpful to reference a model when doing
this.)
10. (Long) Suppose that workers have either high-productivity, π H , or lowproductivity, π L . The fraction of workers that are high-productivity is α , so
1 − α are low-productivity. There is some action that workers could take—
obtaining s years of education past high school—that has different costs for the
different workers: each year of schooling costs cH for the high-productivity types
and cL for the low-productivity ones.
a. In a competitive market, what wages would be paid to the workers if
employers could not distinguish between the types, and what wages
would be paid if employers could identify each type?
b. Find a signal s* that would separate the two types of workers. (You
will probably find a range of values.)
c. Comment on the efficiency or inefficiency of the separating equilibrium.
11. If education is used only as a signal of a worker’s quality, the market
equilibrium might be inefficient. Explain why.
12. Economists have observed that women tend to have lower “internal rates of
return” than men (that is, women tend to be more patient than men). How
would we expect this to affect their educational attainment?
13. When firms must reduce the size of their labor force, they often take tenure
(duration of employment) into account: the longer a worker has been with the
firm, the less likely he is to be laid off. What might justify this behavior? Explain
your answer briefly.
14. (Long) Explain how the ability bias affects estimates of the returns to
education (using a graph, if possible), and explain some techniques that
researchers use in order to correct this problem.
15. Why can we not make accurate inferences about the returns to education by
simply comparing the salaries of college graduates to those of high school
graduates?
16. What is the distinction between specific and general training, and who
receives the benefits of each?
17. A firm cannot distinguish between two types of workers, “high-skill” ones
who produce $50,000 annually and “low-skill” ones who produce $40,000. They
know one difference: each hour of overtime causes disutility worth $10 to the
high-skill workers and worth $20 to the low-skill workers. How many hours of
(unpaid, unproductive) overtime could they require as a “signal” of the worker’s
quality?
18. Explain why a firm should never pay for a worker’s general training.
19. Why does on-the-job-training decline with age? What does this imply for
earnings growth over a worker’s lifetime?
20. (Long) Your employer has discovered a new seminar, which costs $3,000 per
worker. You know that this will increase the productivity of some workers, but
not others. Ideally, you would like to send only those workers whose
productivity would increase more than $3,000 to the seminar. However, you
can’t tell how much any particular worker will benefit from it. Workers
themselves are more likely to know this, but they might not have incentive to tell
you truthfully (after all, who wouldn’t like to spend a week at a seminar in
Hawaii?). Your boss suggests two policies: having the workers themselves pay if
they attend the seminar, or having the firm pay for it. What are the pros and
cons of each? In each case, how should you decide who attends? (Your answer
is likely to incorporate ideas relating to general and specific human capital, as
well as to self-selection.)
21. What must be true in order for employers to use schooling as a signal of a
worker’s quality?
22. Name the two types of training that a worker can receive after school, and
explain the difference between them.
23. Mr. Goblin is debating whether to become a plumber. Assume that he lives
for only two years, and that without training, he would receive $20,000 in each
year. If he goes to vocational school, he spends a year in training and pays
$10,000 in tuition; in the following year, he would earn $60,000. At what interest
rates would he be willing to undertake the training?
24. Explain the requirement for educational “signaling” to be able to distinguish
between high-skill and low-skill workers.
25. How do models of on-the-job training explain the fact that workers’ wages
typically increase rapidly early in life, slow down in middle age, and remain
almost constant closer to retirement?
26. (Long) A consulting firm has discovered that some of its employees opted to
take an economics class while in college, while others never did. They also notice
that the workers with an economics background are roughly 10% more
productive (their average annual product is worth $55,000) than those without
(who produce, on average, $50,000). A local college offers an economics course
for $3,000. [To simplify your analysis, ignore returns in future years: the firm
could make workers take the class in January 2003, and all the firm cares about
are the costs and benefits in the 2003 calendar year.]
a. The firm is considering making all its employees take this class, if they
have no economics background. Since you are their wisest worker, the
firm asks your opinion: given what you know about the returns to
education, do you think that the increase in productivity will be greater
than the cost? Explain your reasoning.
b. The firm has a second question. If they were to make this class a
requirement, who should pay for the cost of the class—the firm or the
worker (or should they split it somehow)? Explain why.
27. Whenever I hire a new babysitter, I have to explain my kids’ schedules,
preferences, eccentricities, as well as where we hide their supplies (food, sippy
cups, diapers, medicines, and so on). This is an example of what type of training?
Explain.
28. When a firm has to terminate workers, it usually begins with the ones with
the least seniority—a “last-hired, first-fired” policy. What economic concept
might explain this behavior?
29. Name two ways that a worker and a firm become “married” to each other (in
the sense that both prefer the relationship to being with anyone else).
Questions about compensating wage differentials
1. How do labor economists approximate the value of a person’s life to other
people (excluding himself)?
2. How do we interpret the slope of the “hedonic wage function”?
3. Explain the advantages and disadvantages of employer-purchased fringe
benefits.
4. (Long) This question is about compensating wage differentials.
a. Using a graph, explain how workers are overcompensated for the risk
they undertake in their jobs.
b. Give some reasons why workers might not be compensated adequately
for the riskiness of their jobs.
5. Suppose that econometricians were to estimate the “hedonic wage function”
for some job characteristic, like the risk of dying on the job. How do we then find
the implicit price (or “shadow price”) of this characteristic?
6. Explain why workers are likely to be overcompensated for any unpleasant job
characteristic (like risk).
7. (Long) Suppose that a firm decides to provide a fringe benefit (like an
employee discount on purchases at the firm) to its workers. Discuss the
advantages and disadvantages of this policy.
8. The hedonic wage function is determined by the tangency between workers’
indifferences curves and what else? (Be as specific as possible.)
9. What is the term for the additional pay that a worker receives in order to
accept a job with some undesirable characteristic?
10. (Long) This question is about the value of life.
a. How would you estimate the value of a worker’s life to society (to
people other than himself?)
b. What data would you need, and how would you calculate, the
statistical value of life (the value of a worker’s life to himself)?
11. Suppose that, in equilibrium, a worker chooses a job that offers risk level ρ *
and a wage of w* . A government agency, interested in ensuring worker safety,
regulates that firms in the industry must keep the risk level below ρ . Illustrate,
graphically, how this would affect the worker’s wage and utility in two different
cases: when he perceives risk accurately, and when he estimates risk incorrectly.
12. Work is dangerous at the Acme Mining Company, but it is even more
dangerous at Picacho Mining Company. On average, 1.8% of workers are killed
on the job each year at Acme, while 1.9% are killed at Picacho. A miner is paid
$45,000 at Acme, and $51,000 at Picacho. What does this tell us about the
statistical value of life?
13. Suppose that most firms offer a wage of W , and at this wage, a worker’s
optimal hours worked are H . However, the Acme Manufacturing Company
cannot let workers choose their hours as they wish; it is necessary that they work
H . (For simplicity, you might assume that this is more than workers would
choose on their own.) Graphically, show how we would calculate the
compensating wage differential necessary to entice a worker to pick this job.
14. (Long) We might worry whether soldiers are adequately compensated for the
risks they encounter during war. Give arguments on both sides of this case:
arguments that they receive enough compensation for the risks they take on, and
arguments that they are not paid sufficiently.
15. Suppose that, as countries develop, there is a bigger compensating wage
differential paid to workers in dangerous jobs. There are two explanations of
this phenomenon. The first is that firms start to use different technology, and it
is more expensive to supply safety. The second is that richer workers place more
value on their lives, and they demand a larger compensating wage differential.
How could you distinguish between these theories?
16. Suppose that there are two types of factories: “safe” factories and “risky”
factories. Workers in safe factories are paid $12,500 per month, while workers in
risky factories are paid $15,000 per month. The government passes a law
requiring that all factories become safe (and all workers who had been in a risky
factory must accept a $2,500 pay decrease). Are these workers helped by the
legislation, hurt by it, or indifferent to it?
17. Even though there is no explicit market for risk (you cannot pay to reduce
your chance of dying on the job), economists often say that there is an implicit
“hedonic” market. Using words and graphics, explain how the market for risky
labor clears, and show what is the implicit price of risk.
18. Explain how the “winner’s curse” applies to compensating wage differentials.
19. (Long) There are two reasons why free markets for insurance (like health
insurance) are likely to fail. Name these two problems, and explain what they
are. Provide an example of each.
20. The cook of the Maersk Alabama is suing his employer for sending him
through waters that everyone knew to be pirate-infested, without any protection.
Do you feel that he is entitled to compensation for his negative experience?
21. Employers often decide to provide workers with benefits (like health
insurance) that the workers could have purchased themselves. What effect do
these employer-provided benefits have on the consumption choices and the
wellbeing of workers?
22. (Long) You are working as a policy analyst in a legislator’s office. One
morning your boss comes in and announces, “I believe that local governments do
not adequately compensate police officers for the risk they encounter in their
jobs.” She asks for your input.
a. Argue against her position.
b. Argue in support of her position.
c. Your boss now proposes that it might be appropriate for the federal
government to give each police offer an extra $5,000 per year to
compensate for the risk encountered. Who would benefit from this
policy?
23. The theory of compensating wage differentials predicts that workers in
“dangerous jobs” should be paid more than workers in “safe jobs,” everything
else equal. However, if we actually look at data, we find that workers in risky
jobs (farm workers, construction workers, etc.) actually earn less than workers in
safe jobs (professionals, service providers, etc.). Explain why this might occur,
and how it is consistent with economic behavior.
24. Suppose that you observe two firms, one “risky” and the other “safe” (but
identical in all other regards). The risky firm pays workers $X more per year. At
the same time, workers are Z% more likely to die on the job each year at this
firm. Use this to calculate the statistical value of life.
25. If firms and workers pay the same price for health insurance, what effect do
employer-provided benefits have on workers’ wellbeing?
Questions about discrimination
1. What is “statistical discrimination”?
2. Why do some forms of labor market discrimination disappear in the long run,
according to economic theory?
3. Explain the various models of discrimination, and tell their implications for
wages and employment in both the short-run and long-run.
4. (Long) This question is about labor market discrimination.
a. Explain, in words, why economists believe that labor market
discrimination cannot affect wages or employment in the long-run in most
situations.
b. In what situations can discrimination survive in the long-run?
c. Explain, in words, how statistical discrimination can be a “self-fulfilling
prophecy”.
5. What effects can employer tastes for discrimination have on employment,
wages, and profits in the long-run?
6. Discrimination can have an effect on workers’ earnings in the long run if it
depends on whose tastes?
7. Discuss how discrimination may occur even in the absence of taste-based
prejudice. In particular, name this type of discrimination, and mention how it
affects employment, wages, and profits.
Questions about personnel economics
1. If a firm can pay a worker with a combination of a piece-rate and a base salary,
what is the profit-maximizing pay schedule that it would offer?
2. When a supervisor evaluates his workers, he tends to misstate their quality.
What are the supervisor’s two competing objectives?
3. (Long) Explain the advantages and disadvantages of offering “incentive pay”
to workers.
4. The state of Texas instituted a policy that linked teachers’ pay to the fraction of
students that passed a standardized test. A team of economists observed that
pass rates did increase, but they noticed two negative side effects of the policy.
What were these?
5. (Long) Acme Manufacturing Company produces gadgets, which sell for $20
each. The materials used to produce a gadget cost $6. The firm considers hiring
a worker named Jim, whose disutility from producing Q gadgets is C(Q) = Q 2 .
If Jim chooses not to work for the company, his next best option is watching
television at home, which has a value of $15 to him.
a. What is the Pareto optimal level of output in this situation?
b. If the firm wishes to maximize its profits, what pay schedule would it
offer to Jim?
6. What does it mean for a worker’s output to be “Pareto optimal”?
7. What does the “Peter Principle” state?
8. An economist studied the Safelite Glass company, as it switch from paying its
workers a fixed salary to paying them according to a piece-rate (with a
guaranteed minimum income). He found that productivity was higher under the
piece-rate, for two reasons. What were these?
9. (Long) You are in the human resources department of a large firm, and you
must design a worker-evaluation system. Supervisors will be asked to rate their
employees as “excellent”, “good”, “average”, “bad”, or “terrible”, and this
information will determine the worker’s salary for the next year. Predict what
would happen with this system. (A model is not necessary; a verbal explanation
is sufficient.) If the supervisor does not have the incentive to answer honestly,
can you suggest a system that would correct this problem?
10. This question is about efficiency wages. A firm has the option to pay a
worker a low wage of $W or a high wage of $(W + H ) . A worker has the choice
to work hard, causing disutility of C , or to shirk, causing no disutility. When he
works hard, he produces P for the firm (which is much more than C). If this
relationship lasts only a single period, what would we predict as the outcome of
the “game”?
11. When trying to motivate multiple types of workers, a firm might design two
wage contracts: one that should appeal to high-skill workers, and another that
should appeal to the low-skill workers. How do the base salaries and piece-rate
pay of these two schemes compare (when the firm cannot identify workers’
types)?
12. What is necessary to sustain an efficiency wage equilibrium?
13. Two workers, i and j, are competing in a tournament for a promotion. The
winner of the promotion receives $X as a prize. The cost of providing effort is
c(e) = ae + be2 , and i wins the tournament if ei − e j + ε > 0 . Describe the
equilibrium effort levels of the workers.
14. (Long) Describe the most profitable piece rate contract in each of the
following circumstances.
a. When effort is perfectly observable.
b. When effort is not perfectly observable. (Compare this to the answer
from part a.)
c. With multiple types of workers, which the firm cannot distinguish.
(Compare this to the answer from part a, also.)