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Question 1.
Sally recently finished her full-time training and received certification as a nurse’s aid at the end
of August. She sent out applications to prospective employers during the last three weeks of
August so that she would start work on September 1st. She followed up on her applications by
making phone calls starting the day after she submitted them. During the month of September
she continued to look for employment in the help-wanted ads of local newspapers and job
openings listed online while she waited for calls for interviews.
a) How would the Bureau of Labor Statistics count Sally for the month of July? For the
month of August?For the month of September? Explain your answers.
Towards the end of September, Sally’s savings dwindled to only afford her $600 per month on
consumption goods. She then decided to put an application in at her local grocery store for a
cashier position. The grocery store, D-Town, offers her at a wage of $8.00 an hour for 30 hrs a
week (five days of six hour shifts). Even though she gladly accepts the position (that starts
October 1st), she keeps hoping that someone will hire her as a full-time nurse’s assistant.
b) According to Bureau of Labor Statistics definitions, what kind of worker will Sally be for
the month of October? (Remember the BLS’s different types of underutilization of the
labor force.)
As mentioned in class, the labor supply model supposes that workers choose how many hours
they will work. Every week Sally asks her manager if she can have some additional hours (she
prefers 10 more), but her manager says, “Sorry, but we don’t need you more than 30 hours a
week right now.” Labor Economics Problem Set One Fall 2011
c) Graph Sally’s labor supply decision for the month of October. Assume that she maintains
her $600 savings over the month, which (because Sally needs to sleep 8 hours each day)
has a total of 496 hours available for working and/or leisure. For the moment, assume
that Sally has typical, smooth, convex shaped indifference curves. Be sure to depict her
dissatisfaction with her manager’s choice of hours.
In the last week of October Sally’s manager asks her to work for 5 additional hours twice a week
(for the Halloween-weekend rush), such that on two days she will work a total of 11 hours. The
labor laws of the state where this D-Town does business say that grocery store workers must be
paid overtime for the hours of labor in excess of eight hours per day even if the worker does not
work more than 40 hours a week. The overtime pay stipulated in the law is “time and a half,” or
w(1 + 0.5) per hour. Sally likes the higher pay so much that her optimal amount of hours of
work—with the overtime pay—turns out to be more than 40 hours per week.
d) Assuming the same, typical indifference curves used in the previous question, graph
Sally’s labor supply decision for the last week (124 hours) of October. Your graph should
include Sally’s preference of 40 hours per week over 30 hours at $8.00 an hour, her
indifference curve at 40 hours per week at the overtime wage, and her optimal hours at

2. the overtime wage. Also, be sure to include the amount of the overtime wage, her $600
savings adjusted to a weekly amount, the amount of hours for which the overtime wage
is paid, and her final consumption level under the ‘30 hrs at $8.00’ and ‘40hrs at
overtime’ schedules
Sally gets a call from Mount St. Barclays Hospital for an interview November 1st. In the interview
a hospital administrator states that the salary for the position will be determined later, only
after all the interviews of the job candidates have been completed. Minutes afterwards during
the interview they ask Sally if she is willing to work 60 hours a week if the hospital needs her to
(which could be a regularity). Given that Sally can only give honest responses to questions, she is
perplexed as to how to answer the question, since the range for a nurse’s assistant salary is
between $24,000/year and $33,000/year.
e) Provide a graph that explains why Sally has difficulty in answering the question on a
weekly basis (i.e., T = 124). Assume the following (1) there are 48 work weeks per year,
(2) that she’ll be paid a salary (not a wage), (3) that the 60 hours they are asking about
are mandatory for the job, and (4) that she is comparing these two extreme salaries to
each other and being Out-of-the-Labor Market (that is, she is not comparing them to her
current situation at D-Town). Assume also that she would maintain $600 savings per
month for consumption.
The day after the interview at Mount St. Barclays, Sally receives an offer from them: a salary of
$30,000 as a nurse’s assistant for five days a week at their outpatient site in the town of Boufou,
which is approximately a two hour drive from where she lives. (The mandatory hours are
40/week and will not regularly exceed amount.) She tells them that she needs a day to think it
over, in which time she determines that the commute each day will total four hrs. Moreover,
there is no public transportation Labor Economics Problem Set One Fall 2011

3. she can take for the commute, so she will need to buy a car (which she estimates will exhaust all
of her $600 set aside for monthly consumption).
f) Graph Sally’s offer. Assume T = 496. Be sure to show her effective reservation wage under
the combined commute and car purchase required for her to do this job. Draw the
graph such that she would readily accept the offer if there was no need for a car and
four hr commute per day, but that she will have to reject it as it is.
After Sally rejects the offer from Mount St. Barclays, she is called in for an interview at Regis
Medical Group, which goes extremely well: by the end of the week she is offered a position with
a salary of $30,000/year. The total hours per week requested from her can vary, but she is
required to supply at least 40 hours a week. (For the following questions, use a weekly amount
of hours, T = 124, assuming 48 work weeks in the year. She also maintains her $600/month
savings for consumption goods.)
g) Sally’s utility function over hours of consumption (C) and leisure (L) is U(C, L) = C0.7L0.3.
What is her level of utility at 40 hours of labor per week at this salary?
h) Even though she is required to work 40 hours per week, what are her optimal amount of
hours at Regis Medical Group? (Note, you will need to figure out the implicit wage of
this salary position.)
i) What is the amount of the change in Sally’s utility when she goes from D-Town to Regis
Medical Group? Do not use her optimal hours of work for each wage.
j) When Sally goes from D-Town to Regis Medical Group, the (implicit) wage she faces
changes. What are the substitution and income effects according to her optimal
amounts of labor supplied at these implicit wages? Express these effects in hours of
Leisure (L).
Come January, Sally realizes that she is eligible for an Earned Income Tax Credit. The brackets
that apply to her (as a single, childless woman) are as follows: for annual incomes above $1, the
worker receives a 40% credit that is maximized at $500. The full credit is limited to incomes
below $13,500, above which the worker’s credited-income is taxed at a flat rate of 20%. (The
level of income at which the credit is completely phased out is for you to determine.)
k) What is Sally’s after-tax income—that is, with the EITC? Assume that, because EITC is
based on earned income, her $600/month non-labor income does not factor into the
EITC brackets. Also, since we are using annual amounts, your value of T will be based on
496 hrs per 48 weeks of the year. Hint: you need to figure out level of income at which
the credit is completely phased out.
l) By how much does she change her hours of labor supplied in response (if at all) to the
EITC? Hint: you may have reasoned that, because of her preferences, the only likely shift

4. in her hours would be to that level which renders an income of $13,500. So, check her
utility at this level of income and see if this is greater than her utility at $30,000 and 40
hrs of labor.
Question 2.
Answer the following questions using the Bureau of Labor Statistic’s Employment Situation
Report of to be released Friday, October 7th, 2011.
(a) Ignoring the revisions of population estimates introduced by this Report, fill in the
table below using the Household Data (“Summary Table A” will be sufficient).
(b)
(c) (b) What happened to the Participation Rate since over the past year?
(d) (c) Why isn’t the absolute change in Employed the negative of the change in
Unemployed?
(e) (d) Did the amount of workers in the Labor Force increase or decrease over the past
year? By how much?
(f) (e) Did the amount of workers Not-In-The-Labor Force increase or decrease over the
past year? By how much?
(g) (f) Why isn’t the change in the Labor Force (LF) the negative of the change in the stock
of ~LF?
(h) (g) Is it possible that part of the increase in Population went into Unemployment? Why
or Why not?
(i) (h) How is it possible for the Population to increase less than the stock of people Not-in-
the-Labor Force? Does this mean all of the new people in the population went into ~LF?
(j) (i) What was the change in Employment between August 2011 and September 2011
according to the Household Data?
(k) (j) What was the change in employment between August 2011 and January 2011 as
measured by the over-the-month change in the Establishment Data (the total non-farm
employment of Summary Table B is sufficient)?
(l) (k) What would the Unemployment Rate be for September 2011 if the value of
Employed (E) was taken from the Establishment Data (seasonally adjusted total non-
farm employment on Table B-1), while the value of Unemployed (U) was taken from the
Household Data?
Labor Employed Unemploye Unemploy Not-in-the Population Participati Employme
Force (LF) (E) d (U) ment Rate Labor on Rate nt
Force Population
(~LF) Ratio
09/2010:
09/2011:
Changes:
Percent change: