Problem Set 1
Answer Key
Labour Economics
ECC3710
1-Read the article attached and list the main concepts expressed by the author. For each
one of these concepts, choose whether it is the outcome of a positive or normative
economic analysis, being careful to explain the reasoning behind your choice.
Concept 1: American labour markets are over-regulated: 22% of the American
workers must hold a license to do their job.
Concept 2: This regulation decreases competition in the labour market and therefore
protects the earnings of incumbent workers from downwards competitive pressures.
Concept 3: Most of the benefits of this regulation occur to high-income workers (high
skilled).
Concept 4: US states should allow both licensed and not licensed workers to operate
and let consumers choose what they prefer.
Concept 5: US states should inspect workers rather than imposing licensing because
this would reduce the regulation and increase competition.
Concepts 1 to 3 are examples of positive economic analysis because they address the
question “what is” the effect of labour market regulation on income inequality using
empirical evidence. This analysis does not require to take a particular positions or
make any judgment.
Concepts 4 and 5 are examples of normative economic analysis because they address
the issue of “what should be done ” to increase competition in some segments of the
labour markets. These suggestions however involve some judgment. In this particular
case, the author assumes that lowering income inequality would be beneficial for the
US society and that consumers protection wouldn’t be at great risk from taking away
some of the licenses.
2-Suppose that you work as an intern for the Australian Department of Education and
Training. Due to an increase in the population, the head of the department is worried that
the average class size in Australian primary schools will increase and this will hurt
students’ performances. They ask you to test this prediction using data on average test
scores and average class size from a sample of 420 schools in Australia. Since you took
the labour class at Monash the first thing you do is to estimate a linear regression. You
obtain the following results:
Test Score = 55.12 – 2.51*(Class size)
(15.4) (1.6)
R-squared=0.88
where the standard errors are in parenthesis.
In what follow we will refer to the first coefficient as alpha=55.12 and the second
coefficient as beta=- 2.51.
a. Based only on the coefficient beta, do the results of this regression support
the prediction of the head of the department?
b. What is the interpretation of the coefficient beta? What is the
interpretation of the coefficient alpha?
c. Based only on the coefficient beta, can we conclude that class size causally
affect the test scores of students in Australian primary schools? Explain.
d. Compute the 95% confidence interval around the coefficient beta
e. Compute the t-statistic relative to the coefficient beta
f. Based on the t-statistic derived in e, is the coefficient beta statistically
significant at 5% level?
g. Based on your answer to point f, do the results of this regression support
the prediction of the head of the department?
a. Yes, average class size is negatively correlated with test scores
b. beta= an increase by one individual in average class size is associated to a
decrease by 2.51 in average test scores;
alpha= if average class size is zero, then the average test score is 55.12
c. No we can’t. In fact, there may be omitted variables that might explain, at
least part of, the negative correlation between test scores and class size.
For instance, if schools that cannot afford to pay many teachers or to have
many classrooms also happen to be located in neighborhoods where students
are less motivated then the location of the school might explain part of the
negative correlation between school size and test scores. Therefore absent a
control for the location of the school, beta would capture this effect as well.
d. [-2.51-(1.96*1.6) , -2.51+(1.96*1.6)] = [-5.646, 0.626]
e. t-statistic=absolute value of beta/standard error = 2.51/1.6=1.568
f. No, t-statistic is smaller than 1.96 so this coefficient cannot be considered
statistically different from zero at 5% level
g. No, the results of this regression show that there is no statistically significant
relation between class size and test scores.
3-How many hours will a person allocate to leisure activities if her indifference curves
between consumption and goods are concave to the origin?
A worker will either work all available time or will not work at all. As drawn in
Figure 1, point B is preferred to points A and C. Thus, the worker chooses not to enter
the labor market. As drawn in Figure 2, point C is preferred to both points A and B.
Thus, the worker chooses not to consume any leisure and to work all available time.
Figure 1
Figure 2
Goods
Goods
C
C
U1
A
U0
U0
B
Hours of Leisure
U1
A
B
Hours of Leisure
4- Shelly’s preferences for consumption and leisure can be expressed as
U(C, L) = (C – 100)  (L – 40).
This utility function implies that Shelly’s marginal utility of leisure is C – 100 and her marginal
utility of consumption is L – 40. There are 110 (non-sleeping) hours in the week available to split
between work and leisure. Shelly earns $10 per hour after taxes. She also receives $320 worth of
welfare benefits each week regardless of how much she works.
(a) Graph Shelly’s budget line.
If Shelly does not work, she leisures for 110 hours and consumes $320. If she does
not leisure at all, she consumes $320 + $10(110) = $1,420. Shelly’s weekly budget
line, therefore, is:
Dollars of
Consumption
$1,420
$320
110 Hours of Leisure
(b) What is Shelly’s marginal rate of substitution when L = 100 and she is on her budget line?
If Shelly leisures for 100 hours, she works for 10 hours and consumes $320 + $10(10) =
$420. Thus, her MRS when doing this is:
MRS 
MU L C  100 420  100 320



 $5.33 .
MUc
L  40
100  40
60
(c) Find Shelly’s optimal amount of consumption and leisure.
Her optimal mix of consumption and leisure is found by setting her MRS equal to her wage
and solving for hours of leisure given the budget line: C = 320 + 10(110 – L).
w  MRS
10 
10 
C  100
L  40
320  10(110  L)  100
L  40
10L  400  1320  10L
L  186.
Thus, Shelly will choose to leisure 86 hours, work 24 hours, and consume $320 + $10(24) =
$560 each week.