Problem Set 1: Labor Supply / Labor Demand
Due February 3, BEGINNING OF CLASS
Please show your work, writing key equations in letters before solving them. Please clearly
label axes, slopes, and kink points on all graphs.
1. (All numbers in thousands) In January 2013, the civilian non--institutional population
was 244,663. The number of employed workers was 143,322. The number of
unemployed workers was 12,332. The number not in the labor force is 89,008.
a. What was the unemployment rate? The labor force participation rate? The
employment rate? Think about the appropriate denominator for each.
b. What are two reasons why the unemployment rate might underestimate the
severity of an economic downturn?
2. (Borjas 2--3) Tom earns $15 per hour for up to 40 hours of work each week. He is
paid $30 per hour for every hour in excess of 40. Tom faces a 20 percent tax rate
and pays $4 per hour in child--care expenses for each hour he works. Tom receives
$80 in child support payments (non--labor income) each week. There are 168 hours
in the week. Graph Tom’s weekly budget line, labeling axes, intercepts and slopes.
3. Consider an individual with the following utility function: U(C,L) = C1/2L1/2, where C
is quantity of consumption and L is hours of leisure in a week. Total time available
to allocate between leisure and consumption is 112 hours per week. The individual
has non--labor income of $100 per week and an hourly wage of $20.
a. What is the marginal rate of substitution of leisure for consumption?
b. Write down the equation for this individual’s budget constraint. Graph it.
c. Solve for this individual’s optimal level of consumption, leisure, and hours of
work
d. What is her reservation wage?
4. Let’s compare the incentives generated by two different types of public programs.
The Aid to Families with Dependent Children (AFDC -- welfare before reform)
provides an income subsidy, G, at 0 hours of work, that is taxed away at a rate t
when an individual chooses to work. The Earned Income Tax Credit (EITC), on the
other hand, consists of a subsidy (at rate s) for individuals working low hours, up to
a max credit (C) at a certain level of income, and then is phased out (at a rate t)
above a certain income cutoff.
a. Draw what an AFDC budget constraint looks like, including a standard
budget constraint for comparison. Why does the AFDC discourage work?
(Explain, using the concept of income and substitution effects in your
answer)
b. Draw what an EITC budget constraint looks like, including a standard budget
constraint for comparison. How does the EITC solve the work disincentive
problem created by the AFDC? (Again, refer to income and substitution
effects in your answer)
c. The effects of the EITC on labor supply are not positive for all individuals. On
a graph, illustrate a case in which the EITC reduces the number of hours
worked by an individual. Explain using income and substitution effects.
5. (Borjas 2--8) In 1999 TANF (welfare) recipients were asked how many hour they
worked in the previous week. In 2000, 4,392 of these recipients were again subject
to the same TANF rules and were again asked their hours of work during the
previous week. The remaining 468 individuals were randomly assigned to a
“Negative Income Tax” (NIT) experiment that gave out financial incentives for
welfare recipients to work and subjected them to its rules. Like the other group,
they were asked about their hours of work during the previous week. The data from
the experiment are contained in the table below. What effect did the NIT experiment
have on the employment rate of public assistance recipients? Develop a standard
difference--in--differences table to support your answer.
Number of
Recipients Who
Worked At Some
Time in the Survey
Week
Total Hours Of
Work By All
Recipients in the
Survey Week
Total
Number Of
Recipients
1999
2000
1999
2000
TANF
NIT
Total
4,392
468
4,860
1,217
131
1,348
1,568
213
1,781
15,578
1,638
17,216
20,698
2,535
23,233
6. Suppose you want to estimate the following labor supply equation:
Annual Work Hours = a + ß*(Average Hourly Wage) + e
You gather data on US workers aged 22 to 55 from the Current Population Survey.
You define the Average Hourly Wage as self--reported total annual labor income
divided by self--reported total annual work hours.
a. Describe in words how to interpret the coefficient ß (ignore any concerns
about causality for now)
b. Give two separate reasons why you might be concerned that ß is not a good
estimate of the causal effect of a change in the hourly wage a worker faces on
the number of hours that they work
