Labour Market Economics
9th Edition
Chapter No. 01: Introduction to Labour Market Economics (no solutions available)
Chapter No. 02: Labour Supply: Individual Attachment to the Labour Market
Answers to End-of-Chapter Problems
1. (LO 2, 3, 4) This is a neat and doable problem
a. The intercept for the lower, right-hand side of the budget constraint is $5,000. The
intercept for the upper left-hand side of the budget constraint is 5,000 + 15*4,160 =
$67,400. The slope of the budget line is -$15.00. The equilibrium occurs at the
tangency point with coordinates (4,160 – 2,000 = 2,160 hours, 5,000 + 15*2,000 =
$35,000).
b. The intercept for the lower right-hand side of the budget constraint is still $5,000.
The intercept for the upper left-hand side of the budget constraint is 5,000 +
18*4,160 = $74,880. The slope of the new budget line is -$18.00. The new
equilibrium occurs at the tangency point with coordinates (4,160 – 2,040 = 2,120
hours, 5,000 + 18*2,040 = $41,720). In order to obtain the income effect, draw
another budget line reflecting a wage of $18.00, which will be parallel to the new
budget line but below it, that is tangent to the old indifference curve at a point whose
abscissa is 4,160 – 2,200 = 1,960 hours. We do not need to know the income level;
we only need to know the values for the number of hours worked. The total effect is
2,040 – 2,000 = + 40 hours. The income effect is 2,040 – 2,200 = -160 hours. That is
the difference between the new choice and how many hours they would have worked
at the old indifference curve had the wage been $18.00. The substitution effect is
given as the residual: (2,040 – 2,000) – (2,040 – 2,200) = +200. The general
expression for the wage elasticity of supply is the % change in hours worked divided
by the % change in the wage. In both cases the % change in the wage is about 18 [(18
– 15)/16.50]. The raw, or the uncompensated wage elasticity of supply, is the total
observed % change in hours is: 40/2,020) = 1.8 divided by 18. This elasticity is about
0.1, which is positive but inelastic. The compensated wage elasticity of supply is the
change in hours attributed to the substitution effect = (200/2,020) = 10 divided by 18.
This elasticity is about 0.54, which is positive, inelastic, but much higher than the raw
elasticity. We have netted out the income effect.
,2. (LO3, 4, 5) This question pertains to the estimated linear equation of aggregate labour
force participation for women. You are asked to interpret the coefficients. It is important
to pay attention to the units that are given for each variable, which in turn is very
important for the interpretation of the coefficient.
a. Ceteris paribus, this effect is -7 percentage points. As the spouse’s expected earnings
increase, there is a fairly strong negative effect on the woman’s participation rate,
which is called a cross-income effect.
b. Ceteris paribus, this effect is +18 percentage points. As the spouse’s expected
earnings increase, there is a very strong positive effect on the woman's participation.
This is primarily attributable to a substitution effect.
c. We can interpret the effect of the spouse’s income as a pure effect stemming from
non-labour income. Assuming that this cross-income effect is the same as the
woman’s own-income effect stemming from her own earnings, the substitution effect
is +25 percentage points, which is partially offset by an income effect of -7
percentage points. This means that as the woman’s earnings increase, the opportunity
cost of them not working increases, which induces her to work longer. At the same
time, they become richer, and can maintain the living standard while purchasing
more leisure. That effect pushes her to work less. The net effect of +18 induces them
to work more.
d. According to this equation, it would lead to a net increase of 25 percentage points.
The pay cut for the spouse would increase the labour force participation of woman,
as they have to work more to maintain living standards.
e. We are given no information on the hourly wage, so technically we cannot answer
this question. The variables which appear in this equation for expected earnings
include both wages and hours worked. For the less precisely defined quantities of
uncompensated and the pure elasticities for expected income, the former is 18*(6/35),
and the latter is 25*(6/35). We use only the coefficient pertaining to the woman for
these 'own' elasticities.
f. Yes it does. The total effect of the expected earnings of women on their labour force
participation far outweighs the negative income effect of non-labour income earned
by their spouses. As the returns from working for women increased a lot in recent
decades, the labour force participation rate increased. The main reason is a
substitution effect that dominated the income effects from both earners on women's
labour force participation.
,3. (LO2, 3, 4) Consider the income-leisure trade-off diagram, as in Figure 2.6a. In this
case, the horizontal axis runs from 0 to 60 hours per week, which are to be allocated
between market and non-market activities. Leisure increases as we move from left to
right, while work increases as we move from right to left. The variable on the vertical
axis is income. The budget constraint consists only of 2 points for the time being; there is
no line segment.
a. Now you can draw a budget constraint whose slope is -7.5. Worker A voluntarily
chooses to work 40 hours per week. They reached their highest possible indifference
curve (call it Ua) at the point (20, $300), with 20 hours of leisure. Left to their own
devices, worker B would choose the point (40, $150), which is where the income
constraint is tangent to worker B’s highest possible indifference curve (call it Ub). If
they are forced to work 40 hours per week, they are at the same point as worker A
(20, $300), but worker B’s indifference curve is not tangent to the income constraint
at that point. It must be lower than Ub because we are told that they are better off at
the point (40, $150). When worker B is forced to locate at (20, $300), there is an
indifference curve (call it Ub’) that cuts through that point that is lower than Ub. Ub’
intersects Ua at (20, $300), and it is steeper, so the marginal rate of substitution is
higher for worker B than for worker A. This new indifference curve Ub’, however, is
higher than another of worker B’s indifference curves (call it Ub*) cutting though the
point (60, $0), which corresponds to the point of no work. For worker B, the
marginal rate of substitution at the point (20, $ 300) is greater in absolute value than
the slope of the income constraint (which is - 7.5) at the point (20, $300). Since it lies
above Ub*, we know that this worker will prefer working 40 hours per week to
working 0 hours per week, but their unconstrained choice is working 20 hours per
week. One point to note is that the only time that we obtain a tangency equilibrium is
if the worker is not constrained in their choice of hours to work, but does decide to
work a positive number of hours.
b. It is a common practice in the real world for the contractual part-time wage to be
lower than the full-time wage. In this model, note that the indifference curve is flatter
at the equilibrium for part-time work than is the case for full time work. Recall that
the slope of the indifference curve gives the marginal rate of substitution between
income and leisure for the worker in that range of weekly hours. At the part-time
point, the worker values one more hour of leisure less than is the case at the full-time
equilibrium, so consequently they are willing to pay less for that extra hour of leisure
in the form of the forgone wage. This translates into a lower a lower wage as far as
the worker’s choice is concerned. In order to generate a lower market wage,
however, one would still have to analyse the demand side of the labour market, which
, emanates from employers.
4. (LO3, 4) We are given the formula for the marginal rate of substitution of leisure for
income (or consumption, since there is a one-for-one trade-off between the two of them).
The MRS is the slope of the indifference curve. The formula that appears is actually the
absolute value of the MRS, since that expression must be positive (A(x) must always be
positive, and C and l must always be non-negative), and the indifference curves have a
negative slope.
a. As we move from left to right, the amount of leisure increases, while A(x) remains
constant, and the value of C falls. This implies that the value of the MRS decreases.
The interpretation is that as the worker consumes more and more leisure, they value
the marginal hour of leisure less and less, and is willing to trade off less and less
income. The variables (labelled X) which might affect the MRS are the number of
children that the woman has, as well as their ages, her level of education, and her
marital status (tied with her spouse’s income).
b. Recall that the reservation wage is equal to the slope of the indifference curve at the
lower right-hand corner solution, which corresponds to the situation in which no
hours are worked. If h = 0, the number of hours worked, then all of the time
endowment T goes to leisure. We can thus write: MRS = A (x) C / T = w*. In order
for this woman to participate in the labour market, the market wage has to exceed the
reservation wage, so we can write: w > A(x) C / T. Taking the natural logarithm of
both sides of the equation yields: ln w > ln (A(x)) + ln C - ln T. Since the
logarithmic operation is the inverse of the exponential operation, and at the corner
solution, C = non-labour income (y), and we obtain the desired result. The log of the
time endowment T can probably be interpreted as a constant across almost all
women, and so it can probably be ignored at this stage of the problem.
c. We treat Z as a random variable which is distributed normally. That means that it has mean
zero and a variance of unity. The graph has a bell shape on a diagram with the probability
density of the vertical axis and the values of Z on the horizontal axis. Any factor which
raises Z makes labour force participation more likely. The form of that distribution, however,
is not really the focus of this question. An increase (decrease) in non-labour income ln Y
would shift the income constraint upward (downward), making participation less (more)
likely. An increase (decrease) in ln W would rotate the income constraint upward
(downward), making participation more (less) likely. The impact of the taste shifters
depends on whether the sign of the beta coefficient is positive or negative. They have the
effect of changing the slope of the indifference curve.
