Chapter 6
SHORT-RUN LABOUR SUPPLY II:
HOUSEHOLD PRODUCTION AND
SECONDARY WORKERS
I. Introduction
Not all output is produced by business firms which hire workers in the labour market. A
substantial proportion of national output is produced inside the household itself, by members of the
household. Since this output is produced within the household; it is called “household production”.
And, since it is produced within the “home”, it is also sometimes called “homework”. It is also
consumed within the household and is part of the households real income.
Household production generates output which consists of services like child-rearing, clotheswashing, food purchase and preparation, dish washing, house cleaning, home maintenance, lawn
care, snow shovelling, … . In some households it may include automobile maintenance or significant
home renovation. In some households it may include the production of goods, such as food from a
home a garden, or the construction of outbuildings or additions to the house, or various useful home
furnishings, like bookshelves or kitchen cabinets, as “do-it-yourself” projects. You can undoubtedly
add to the list.
This output does not go through a market, so isn’t normally counted by the national income
accountants. But the fact that this output doesn’t normally go through a market doesn’t mean that it
doesn’t have a market value. All of the services listed in the paragraph above can be purchased in a
market, so a market value that can be attributed to them, and they can be valued in market prices.
Estimates of the level of household production range from 20% to 25% of GDP in countries like
Canada and the US.
II. Types of Workers
We begin the analysis with the assumption that households differentiate between a “primary”
worker and another, “secondary” worker (or workers). We assume that this decision is based on
maximizing income. “Income” now includes both earned income and household production. The
assumption of maximizing household income immediately produces two results: 1) The primary
worker will be the member of the household who faces the highest wage in the labour market. (See
the chapters on long-run labour supply for where this wage comes from.) 2) The primary worker
works only in the labour market. All household production is done by the secondary worker(s).
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The secondary worker (or workers) are all other potential workers in the household that are not
the primary worker. In the typical North American household, which is a nuclear family rather than
an extended family, this is usually a spouse. Indeed, the propositions derived here will be tested by
observing the labour market behaviour of married women. This isn’t because we’re sexist, it simply
reflects the reality of North America in the relatively recent past. Later we will show why incomemaximizing behaviour of households, interacting with rational behaviour by employers, can cause the
primary worker to be more frequently the husband.
Teenagers and students living at home are also (potential) secondary workers. But it is our
(cynical?) observation that they are rarely perform much household production. This doesn’t mean
that the analysis here doesn’t necessarily apply. See the box on the student production function.
(NOTE: THIS IS NOT HERE YET: ECON 3600 STUDENTS, DON’T WORRY ABOUT THIS.)
The secondary worker produces real income working in the household. Thus, the secondary
worker’s work/leisure choice set is different from the primary worker’s. The secondary worker’s
work/leisure choice set includes the value of homework, as well as the value of work in the labour
market.
II. The Secondary Worker’s Choice Constraint
A. The Household Production Function
The secondary worker’s choice set begins with the Household Production Function (the HPF).
Figure 6-1 shows the household production function. The horizontal axis is hours. The vertical axis
is the market value of the goods and services produced in the household.
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Figure 6-1
Household Production Function
HPF
$Value of Goods and Services
Y2
I2
Y1
I1
V2
V1
O
H2
H1
2 1 A
Hours
NOTE: ALL REFERENCES TO DISTANCES ON THE FIGURES ARE IN LINE SEGMENTS.
FOR EXAMPLE, 100 HOURS IS O,A.
The slope of the HPF at any given hour represents the value of output of the homework done in
that hour. On Figure 6-1 (exaggerating the scale somewhat), one hour of homework – the hour from
A to 1 – produces output of value of O,V1. Two hours of homework – the hours from A to 2 –
produces output of value of O,V2. Thus, the first hour of homework produces a value of O,V1, and
the second hour of homework – the hour from 1 to 2 – produces output of value of V1,V2.
The HPF is similar to the production function of Chapter 2, with two exceptions. The first
difference is that the HPF is reversed, increasing from right to left. This is because, as in the primary
worker’s work/leisure choice space, leisure is the good, and leisure increases as we move right from
point O. Hours of work, which here are hours of homework, therefore increase as we move left from
point A. With the production function of Chapter 2, work increased as we moved from left to right
from the origin.
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The second difference between the household production function and the production function of
Chapter 2, is that there is no range of increasing returns in the HPF. The HPF always increases, and
always at a decreasing rate. This is because “homework” is normally done by a single person
working alone. We assume that person allocates his time rationally. That is, we assume he does the
most valuable homework first, the second most valuable homework second, etc. This causes the HPF
to increase at a decreasing rate, showing diminishing returns immediately as it moves left from point
A. So, on Figure 1, V1,V2 is less than O,V1.
In the absence of a labour market, the secondary worker, the “homeworker”, would divide the
hours available for work or leisure into either household production or leisure, depending on where
his highest indifference curve was tangent to the HPF. On Figure 6-1, for the individual represented
by indifference curve I1, this would be H1,A hours of homework, producing output in the household
with a value of O,Y1, and taking O,H1 hours of leisure. For the individual represented by
indifference curve I2, this would be H2,A hours of homework, producing output in the household with
a value of O,Y2, and taking O,H2 hours of leisure.
B. Unearned Income and a Labour Market
The next part of the choice set is unearned income (UY). For a secondary worker this will usually
be quite a bit larger than with a primary worker, because the secondary worker will normally share a
substantial amount of the primary worker’s earned income. For example, the will usually share a
residence, which may be fully paid for by the primary worker. Since one option for the secondary
worker – the one we concentrate on here – is not working in the labour market, all things that must be
purchased for a decent existence will usually be paid for by the primary worker, who shares her
income with her spouse. So, for many (but not all) secondary workers, UY is quite large.
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Figure 6-2
Secondary Worker Choice Set
Value of Goods and Services
HPF
W
T
W
UY
O
HT
A Hours
Figure 6-2 shows the different parts of the secondary worker’s choice set, including unearned
income As with primary workers, we will model a single week. And as before we take 100 hours
per week to be available for work, in homework and the labour market, or leisure. So O,A is 100
hours. Unearned income is available even if the secondary worker does no work. So now any value
created by homework is value that is added on top of unearned income. Thus, the HPF now starts at
the level of UY on the right-hand vertical axis.
A labour market and a wage exist for the secondary worker’s skill, so the secondary worker’s
choice set must also include the existence of this wage. Figure 6-2 shows the addition of the labour
market and its wage to the choice set. The secondary worker possesses a skill, and, in the short-run,
he faces a wage in that particular skill-market. On Figure 6-2, his potential wage is W. It is shown,
as with primary workers, increasing as it moves left from point A. As with primary workers, the
hourly real wage is the slope of the wage line.
For the secondary worker, the HPF begins with some income – the UY—already available. So,
on Figure 6-2, the HPF starts on the right-hand axis at the level of UY, and then increases as the
amount of homework increases – that is, as we move from right to left. The slope of the HPF over
any given hour is the value of the homework done during that hour. Since the secondary worker does
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at least some homework, his HPF must begin with a slope that is steeper than his wage line, W. This
means that for at least some hours of work, the secondary worker can produce more value doing
homework than he can working in the market for wage W. The individual shown on Figure 6-2
produces more value doing homework for the first HT,A hours of work than he would earn in the
labour market.
But, because the HPF is increasing at a decreasing rate, eventually its slope can become less
steep that the wage. A secondary worker always maximizes the value he receives for his work by
working where his time has the most value. This is homework where the slope of the HPF is steeper
than the slope of the wage line, and it is market-work when the slope of the wage line is steeper than
the slope of the HPF. To determine the outer boundary of the secondary worker’s choice set, take
the slope of the wage he faces in his skill market, and find where this is Tangent to the HPF. This is
point T on Figures 6-2 and 6-3.
To the right of T, that is for hours of work less than HT,A, the HPF has a steeper slope than does
the wage line. This means that for the first HT,A, hours of work, the secondary worker will produce
more value in the homework than in market-work. So his first HT,A hours of work will be in
homework. But to the left of T, that is for hours of work greater than HT,A, the wage line has a
steeper slope than does the HPF. This means that, if this secondary worker is going to work more
hours than HT,A, he will produce more value in the market-work than in homework during those
additional hours. Thus, the boundary of the choice set – the choice constraint – is the HPF for hours
moving left from A to HT, and is the slope of the wage line for hours to the left of HT. The choice
constraint is the solid line in Figure 6-3.
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Figure 6-3
Secondary Worker Choice Constraint
and Equilibrium
Value of Goods and Services
W
2
Y2
HPF
I2
YT
T
Y1
1
I1
W
HPF
UY
O
H2
HT
H1
AHours
C. The Choice Constraint and Work/Leisure Equilibrium
The secondary worker’s equilibrium is the point where he has an indifference curve tangent to
the choice constraint. These points are labelled : on Figure 6-3 there are two of these, 1 and 2 ,
one for each of two different workers. These points yield the highest utility possible given the
constraints faced by the worker. For the secondary worker these constraints are: the number of hours
physically available, A; the Household Production Function; his unearned income; and the wage in
his skill market. The first, and main, question we are interested in with the secondary worker is: Will
he do any work at all in the labour market? That is, will he be a labour force participant?
Using the secondary worker’s choice constraint, and the definition of his equilibrium, we can
now easily answer that question. If the worker has an indifference curve tangent to the choice
constraint to the right of the point where the slope of the wage is tangent to the HPF, the secondary
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worker will not participate in the labour market. That is, if his  is to the right of his T, the
secondary worker will not participate in the labour market. But if the worker has an indifference
curve tangent to the choice constraint to the left of the point where the slope of the wage is tangent to
the HPF, the secondary worker will participate in the labour market. That is, if his  is to the left of
his T, the secondary worker will participate in the labour market.
On Figure 6-3, the equilibrium of individual 1, represented by indifference curve I1, is point 1.
1 is to the right of T, so he will not participate in the labour market.
He will work H1,A hours in
household production, produce output of UY,Y1, and take O,H1 hours of leisure. (lazy fellow) The
equilibrium of individual 2, represented by indifference curve I2, is point 2.
2 is to the left of T, so
he will participate in the labour market. He will work HT,A hours in household production, produce
output of UY,YT at home, then will work H2,HT hours in the labour market. He will earn income of
YT,Y2 in the labour market, and will take O,H2 hours of leisure.
D. Comparative Statics and Labour Force Participation:
The formal analysis of the choice of secondary workers allows us to derive a number of testable
hypotheses. The question of the labour force participation (LFP) of an individual secondary worker
depends exclusively on whether he has an indifference curve tangent to the choice constraint to the
left or to the right of the point where the slope of his wage is tangent to his HPF. That is, it depends
on whether his  is to the left of T or to the right of T. We can show that points T systematically
shift given changes in constraints. These shifts generate changes in the probabilities that secondary
workers will participate in the labour market. While we can’t say how any particular individual will
act, we can say how a change in his point T will affect the probability of his individual choice, and
we can use the observations on groups to test those probability statements.
The first type of observations are cross-section. Here we observe the labour force participation
rates of two different groups of secondary workers at a given time, where we have good reasons to
believe that the groups systematically differ in their location of points T. The second type of
observations are time-series. Here we observe the LFP rates of the same group at different points in
time, where we have good reason to believe that constraints will have changed over time and shifted
points T.
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All the tests reported here use the labour force participation rates of married wives in North
America as the proxy variable for the probability of labour force participation by secondary workers.
This may be offensive to some readers who don’t think we should make judgements on the basis of
sex. But in North American culture until recently, the norm was that the wife was the secondary
worker. That we use this cultural norm to test our hypotheses should in no way be seen as support for
this particular condition. Indeed, this norm appears to be changing, and we welcome the change.
Nevertheless, we think the use of married women to test the hypotheses about the LFP of secondary
workers is valid, especially given that our data is not especially recent.
D-1. Wage Rates and Labour Force Participation
Figure 6-4
Secondary Worker Choice
Wage Increase
W2
Value of Goods and Services
HPF
W1
1
'
T1
0
T2
2
UY
O
H0
H1
A Hours
Figure 6-4 shows the variation in the choice set for secondary workers as the wage in the
particular skill-market increases from W1 to W2, holding all other things constant; particularly, here,
holding the HPF function constant. As the wage increases, point T shifts to the right, from T1 to T2.
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We can’t observe indifference curves, so we can’t predict individual behaviour. But we can say
that an increase in the wage they face in their skill-market will cause some secondary workers to enter
the labour market, other things equal. And we can say that an increase in the wage they face in their
skill-market will cause no individuals to leave the labour market, other things equal. Thus, an
increase in the wage in a given skill-market can only increase labour force participation rates.
All individuals have a tangency of their highest indifference curve with the choice constraint –
that is they have a . (Note that to reduce clutter in Figure 6-4 I have left out the indifference curves.
Three individuals are modeled there: each has different indifference curves, causing each to have a
different . I have only the ’s on Figure 6-4.) There are three possible locations of that
 at wage
W1:
1) An individual has a

that is to the left of T1,
1 on Figure 6-4.
That individual will already be
working some hours in the labour market before the wage increase. The tangency of his highest
indifference curve to the new choice constraint – the HPF plus W2 – must also be to the left of T2,
because T2 is to the right of T1. So that worker will continue to work in the labour market. (But he
may change the number of hours he works. See Section D-2. below.)
2) An individual has a  that is to the right of T2, 2 on Figure 6-4. That individual will not work any
hours in the labour market either before or after the wage increase. The tangency of that individual’s
highest indifference curve to the new choice constraint – the HPF plus W2 – doesn’t change.
3) An individual has a  that is between T1 and T2, 0 on Figure 6-4. Facing W1 in the labour
market, that individual will not work any hours in the labour market: 0 is to the right of T1. But the
shift of T to the right has caused 0 to be to the left of T2. The new tangency of his highest
indifference curve to the new choice constraint –  on Figure 6-4 – must be to the left of T2 and
therefore on the wage line. So that worker will now work in the labour market. In this case, with W1,
the worker works H0,A hours in household production, does no work in the labour market, and takes
O,H0 hours of leisure. With Wage W2, he works H1,A hours in household production, works H0,H1
hours in the labour market, and takes O,H0 hours of leisure. It is clear that all individuals with a 
between T1 and T2 will enter the labour market as the wage increases from W1 to W2.
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In cases 1) and 2), nothing changes as the wage increases. In case 3), the worker moves into the
labour market as the wage increases. These three cases exhaust all possibilities. Thus, as a
secondary worker faces a higher wage in the labour market, the probability that he will work in the
labour market unambiguously increases.
The intuition behind this is sensible. As the wage faced in the skill market rises, an individual
maximizing real income may find himself in the position where the value of some of the homework
he had been doing is now less valuable than what he could purchase with what he can earn in the
labour market during the same length of time. Thus, the probability that he will shift to labour
market work increases.
One can test this in cross-section by observing LPF rates of different groups, where the wage in
the labour market is relatively constant within the group, and where the wage in the labour market is
different between the groups. There is, however, a problem: one cannot observe the wage of
someone not in the labour market. Thus we need a proxy – a variable that we can observe for all
individuals that is correlated with wages. Here we use the level of education which we know is
highly correlated with market wage.
Table 6-1 shows the LFP rates for married women in Canada in 1996, by level of education.
Table 6-1
LEVEL OF EDUCATION
Less than Grade 9
Grade 9-13
Some university/Trades
College certificate or diploma
University degree
LFP RATE: %
29.4
58.5
74.0
77.2
83.4
ADJUSTED DIFFERENCE
base
13.3
23.1
27.3
30.5
If education is a good proxy variable for the wage faced in the skill market, the figures
unequivocally support the analysis. As education rises – and, we assume, the wage in the relevant
skill markets rise – the LFP rates also rise.
There is, however, a possible problem with the conclusion above. The figures in Column 2 of
Table 6-1 do not hold “all other things” equal. For example, women with higher levels of education
have fewer children and are likely to be married to men with higher levels of income. The first will
increase the probability of labour force participation; the second will reduce that probability. To
isolate the various influences we need regression analysis. Regression analysis implicitly holds other
things equal.
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The figures in Column 3 are differences in participation rates, computed using the results of a
regression analysis. The differences in Column 3 monotonically increase, giving even better support
to the prediction that an increase in wages will increase labour force participation.
D-2. Wage rates and Number of Hours
As with primary workers, what happens to total hours of leisure depends on the relative size of
the income and substitution effects. But now there is another type of substitution, and this makes it
almost certain that the secondary worker will increase number of hours of work in response to a wage
increase.
Figure 6-5
Secondary Worker Choice
Wage Increase and Hours
W2
2
Value of Goods and Services
HPF
W1
1
T1
T2
UY
O
H0
H T1
H T2
A Hours
Figure 6-5 shows the effect of an increase in wage for a secondary worker who was already in
the labour market before the wage increase, and whose substitution effect equals his income effect.
As the wage in his skill market increases from W1 to W2, he continues to take O,H0 hours of leisure.
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Nevertheless his hours in market-work increase, from HT1 to HT2. This is because of the second type
of substitution – substituting work in the labour market for homework.
As the wage increases, leisure is constant. But, as the wage increases, the hours between HT1
and HT2 have become more valuable in market-work than in homework. The slope of the HPF
between T2 and T1 is steeper than the slope of wage line W1; but the slope of the HPF between T2 and
T1 is less steep than the slope of the wage line W2. This secondary worker, therefore, substitutes
market-work for homework over this range. This unambiguously increases labour market hours of
work. Thus, a secondary worker is much more likely to increase labour market hours of work when
wages increase than is a primary worker. The short-run labour supply curve for secondary workers,
therefore, is much more likely to be positively sloped.
The intuition behind this is fairly clear. The secondary worker has three choices: homework,
market-work, and leisure. On Figure 6-5, in the labour market the worker’s substitution effect just
offsets his income effect! He takes the same amount of leisure with the higher wage, W2 as with the
lower wage, W1. But there is a second substitution effect that operates because of the three choices: a
substitution of market-work for homework. The worker shown in Figure 6-5 works more hours in the
labour market because, in the range between T2 and T1, only this second substitution effect operates.
6-3. Number, and Ages, of Children and Labour Force Participation:
We make two special assumptions here, although we test these assumptions implicitly later. The
first assumption is that child-rearing is, for most households, the most valuable homework they can
perform. The second assumption is that the value of time spent in child-rearing is greater the younger
is the child. These two assumptions are used to construct Figure 6-6.
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Figure 6-6
Secondary Worker Choice
Child Added
2
HPF2
Value of Goods and Services
T2
W
4
1
W
HPF1
3
X'
T1
X
X
UY
child-rearing
O
H0
H T2
H3
H T1
A Hours
Figure 6-6 can be used with two different interpretations. In the first interpretation, HPF1 is for
the household without children, and HPF2 is for the household with a child. In the second
interpretation, HPF1 is for a household with a school age child, and HPF2 is for a household with a
pre-school age child.
HPF2 is constructed by taking the value of child-rearing and adding it to HPF1. Child-rearing has
greater value than anything on HPF1, so it is added at the beginning – that is, at the right-hand edge.
That is, HPF2 is constructed as follows. Take the value of child-rearing and add it to the value of
unearned income, UY. Then add HPF1 to that by putting point X on HPF1 onto point X on “childrearing”, which becomes point X´ on HPF2 . This means that HPF2 has household production of
greater value than HPF1 over its whole range.
HPF2 is the sum of the two homework functions and contains HPF1, since the homework
without a child must still be done after adding a child to the household (or the homework with a
school age child must be still be done after adding a pre-school age child). But in HPF2, the value of
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homework without a child has been shifted up and to the left. This must also shift point T up and to
the left.
Once again, we can’t observe indifference curves, so we can’t predict individual behaviour. But
we can say that as point T shifts to the left, the probability that the secondary worker’s indifference
curve will be tangent to the choice constraint to the right of point T falls.
In this case we have the opposite effect of Section 6-2. above. The second type of substitution
effect is occurring, but it now works in the opposite direction. The addition of a child to the
household increases the value of household production relative to work in the labour market. So the
secondary worker substitutes homework – the homework of child-rearing – for market-work. This is
shown on Figure 6-6, where the value of household production shifts up at every value of Hours,
while the wage in the labour market remains constant. (Again note that I have left out the
indifference curves to reduce clutter.) There are three possibilities:
1) An individual does not work in the labour market before the addition of a child to the
household. That is, he has a  that is to the right of T1. That individual does not work any hours
in the labour market after the addition of a child to the household. This is obvious and I don’t
bother to show it.
2) An individual has a  that is to the left of T1 and works in the labour market before the
addition of a child. After the addition of a child to the household his  is still to left of T2. This
individual is shown on Figure 6-6 as moving from 1 to2. His substitution effect equals his
income effect in the labour market, so his leisure remains constant at O,H0. That individual still
works some hours in the labour market after the addition of a child to the household, but he
reduces his hours of work in the labour market because of the second substitution effect:
substituting the now more valuable homework for work in the labour market. When on HPF1
(before the child), he spent HT1,A hours in homework, and spent H0,HT1 hours in market-work.
After the child, on HPF2 , he spends HT2,A hours in homework, and spends H0,HT2 hours in
market-work, substituting HT2,HT1 hours of homework for market-work. The number of hours of
market-work is unambiguously reduced.
3) An individual has a  that is between T1 and T2. This individual is shown on Figure 6-6 as
moving from 3 to 4. His substitution effect equals his income effect in the labour market, so
Household Production
leisure remains constant at O,H3.
page 16
That individual spent HT1,A hours in homework, and spent
H3,HT1 hours in market-work before the addition of a child to the household. He drops out of the
labour market after the addition of a child to the household, and spends HT2,A hours in
homework.
Thus, as a child is added to a household, the probability that the secondary worker will work in
the labour market unambiguously falls, and the number of hours provided by the secondary worker
who remains in the labour market unambiguously falls. Also, the probability that the secondary
worker will work in the labour market is unambiguously lower, and the number of hours provided by
the secondary worker who remains in the labour market is unambiguously lower, as the ages of the
children in the household is younger. The intuition behind this is that, as in the situation described in
Section D-2, the second type of substitution effect is occurring, but now in the opposite direction.
Here the addition of a child to a household raises the value of household production, in the range
between T2 and T1. So the secondary worker substitutes the now higher value of homework – childrearing – for the unchanged value of market-work.
Table 6-2 shows the LFP rates for married wives in Canada in 1971 and in 1996, by age and
number of children.
Table 6-2
A: MARRIED WOMEN AGES 15 TO 64 IN 1971
NUMBER AND AGES
LFP RATE: %
OF CHILDREN
None
57
School-age only
42
Pre-school only
30
Both pre-school and school age
25
B: MARRIED WOMEN AGES 15 TO 74 IN 1996
NUMBER OF CHILDREN
LFP RATE
ADJUSTED DIFFERENCE
None
56.5
base
One
76.8
-4.6
Two
75.7
-8.4
Three
69.0
-14.9
Four or more
57.9
-24.4
The figures in Table 6-2A support the analysis unambiguously. The LFP rates decline
monotonically precisely as Figure 6-6 predicts. But the figures in Table 6-2B show one anomalous
result, which requires some explanation. For one child and more, the LFP rates decline
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page 17
monotonically as the number of children increases, as predicted. But the lowest LFP rate in Table 62B is for wives with no children. The reason for this is that there are other factors involved.
Probably most important here is that the LFP rates are for all married women up to the age of 74. By
looking at women to the age of 74, the analysis shown on Table 6-2B has created a serious selection
problem.
The selection problem with these data is that women young enough to have children at home are
young enough to be in the labour market, but this is not true of the women without children. The
women without children in Table 6-2B can be placed into three groups. One large group is women
who have retired and are, therefore, out of the labour market. Another large group, which will
overlap the first, is women who have children, but those children have grown to be adults and have
left home. These women were out of the labour market because of their children and have stayed out.
The third group is women who were, or would be, in the labour market but left because children were
added to the household. The model of choice here applies only to the third group. Thus the figures in
the first row of Table 6-2B cannot be considered as evidence against that model.
The adjusted differences are based on a regression analysis, which control for the women’s age
and overcomes most of the selection problem. These are, in fact, rank-ordered just as the analysis
predicts.
D-4. Household Production Technology and Labour Force Participation
The last of the comparative static exercises involves what is a rather complex issue. The labour
force participation (LFP) rates of married women have risen enormously in recent history. The
increase, as shown in Table 6-3, began at the beginning of the twentieth century, and accelerated after
1970. Note that the numbers rise monotonically in each column.
Table 6-3
YEAR
1954
1967
1977
1987
LFP RATES FOR WOMEN BY AGE – USA
AGES 25 – 34
AGES 35 – 44
AGES 45 – 54
32
39
40
36
44
48
63
63
57
73
75
68
There are a number of reasons for this increase in the LFP rates of married women. We have just
seen that having fewer children increases the labour force participation of married women, and the
number of children per family has fallen throughout the twentieth century, a drop that has also
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accelerated with the “baby-bust” era after 1970. We have also seen that increasing married women’s
level of education increases their labour force participation, and the level of education of women has
risen in the twentieth century, a rise that has become quite dramatic in the second half of the century.
For example, in the US, population increased by less than 100% from 1951 to 2000. The number
of men in colleges and universities increased from 1,390,000 to 6,300,000 in the same period, an
increase of 460%. The number of women in colleges and universities increased from 710,000 to
8,160,000 in that period, an increase of 1150%. In the second half of the twentieth century, in the
US, the proportions of men to women attending colleges and universities went from men:women =
2:1 to men:women =4:5. In Canada in 1998, the average level of education of married women was
13.3 years; for single women it was 14.0 years. (For married men it was 13.5 years; for single men it
was 13.6 years.) This has raised the wage that married women face in the labour market
substantially, which should, as we have seen, increase the LFP rate of married women.
Nevertheless, there is another influence that has almost certainly played a role in this dramatic
increase in married women’s LFP rates. That is the equally dramatic increase in Household
Production technology.
Think back to the beginning of the twentieth century. Heating was with wood or coal stoves and
fireplaces; this required a source of wood or coal. Cooking was the same. Washing clothes was done
with primitive washers, often with home-made soap. Most food served began was raw ingredients,
much of it raised in home gardens. And so on. Today we go to a grocery store about once a week,
buy food, much of it prepared and frozen, take it home and put it in the electric refrigerator. We cook
with microwaves or gas or electric stoves. Gas is piped into the house and used for heating. After
dinner we put the dishes in the dishwasher, add detergent we bought at the grocery store, turn on the
dishwasher and walk away. And so on.
What this means is that a lot of the output of household production takes less time than it used to.
This is illustrated in Figure 6-7. There HFP1 is the household production function before the
technological change; HFP2 is the household production function after the technological change.
After the introduction of the new technology, the amount of homework done in H0,A hours can now
be done in HT2,A hours.
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Figure 6-7
Secondary Worker Choice
Increase in HHP technology
2
T2
Value of Goods and Services
T1
1
W
W
HPF2
HPF1
UY
O
H0
H T2
A Hours
HFP2 has a steeper slope than HFP1 for at least part of the range from A to O. It does not have a
steeper slope over the whole range. That is because, with household production, there is a limit to the
value that can be added to the household with homework. Once that limit is reached – once the house
in clean and warm, the food prepared, the clothes washed, etc – the slope of the HPF normally
becomes quite flat. After the new household production technology is added, that limit is reached
with fewer hours of work. So HPF2 has a steeper slope than HFP1 for some hours of homework, but
after those hours of homework are performed, HPF2 has a less steep slope than HPF1. On Figure 6-7,
HPF2 has a steeper slope than does HPF1 for HT2,A hours, and a less steep slope for O,HT2 hours.
On Figure 6-7, the individual faces wage W in the labour market. This individual’s income effect
again equals his substitution effect in the labour market:  is directly above , and the individual
has the same amount of leisure both before and after the change, O,H0. On Figure 6-7  is to the
right of T1. This means that with older household production technology, this individual spent H0,A
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hours in homework, and did no market-work. After the introduction of the new technology, because
the slope of HPF2 is greater than the slope of HPF1, the tangency of the wage line, W, with HPF2 is
pushed to the right, to T2. Point  is to the left of T2. So this individual will now spend HT2,A hours
doing homework, spend H0,HT2 hours in market-work, and continue to take O,H0 hours of leisure.
The analysis shows that technological improvements in household production will unambiguously
increase the labour force participation of secondary workers.
That an increase in labour force participation must happen as household production technology
improves is easier to see if we simplifies the analysis a bit. We aggregate all homework into two
parts. The first part are the basics: food, clothing and comfortable shelter. The second part are
“extras”, less essential things like mowing and watering lawns, hanging wallpaper, etc. We now also
aggregate the HPF, treating each part of homework as equally valuable. So the HHP becomes two
straight lines, rather than a curve. The line for the basics, HPB, has a steeper slope than the line for
the extas, HPE, since the basics are more valuable than the “extras”. Figure 6-8 shows two HPFs.
With HPF1 the basics require more time to produce than HPF2, so the shift from HPF1 to HPF2 shows
an improvement in household production technology.
There are three possibilities for W: 1) The slope of W can be less than HPE, in which case the
secondary worker will not do market work either before or after the improvement in household
production technology. 2)The slope of W can be greater than HPB, in which case the secondary
worker will do market work, and no homework, both before or after the improvement in household
production technology. 3) The slope of W can be less than HPB and greater than HPE. This
possibility is shown in Figure 6.8.
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Figure 6-8
Secondary Worker Choice
Increase in HHP Technology
HPE2
W
T1
Value of
Basics
T2
HPE1
HPF2
W
Value of
Goods
and
Services
HPF1
HPB2
HPB1
UY
0
H1
H2
A
Hours
If we assume that the first type of substitution effect equals the income effect, the individual will
have the same number of hours of leisure before and after the improvement in household production
technology.
That means that his  after the improvement will be directly above his  before the
improvement. Three possibilities exist: 1) Both s are to the left of H1. The individual is in the
labour market both before and after the improvement in household production technology, so there is
no change in labour force participation, but there is a large increase in the number of hours of marketwork. Market-work increases by H1,H2 hours, and homework decreases by the same number of
hours. The improvement in household production technology causes a large second type of
substitution: the substitution of market-work for homework.
2) Both s are between H1 and H2. The individual does not work in the labour market before the
improvement, and does work in the labour market after the improvement. There is an increase in
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labour force participation. 3) Both s are to the right of H2. The individual does not work in the
labour market either before or after the improvement in household production technology.
Given these three possibilities, and given a number of individuals with varying preferences for
leisure, improvements in household production technology will unambiguously increase the labour
force participation of secondary workers, and it will unambiguously increase the number of hours
worked in the labour market for secondary workers.
D-5. Unearned Income and Labour Force Participation:
When Unearned Income rises there is only an income effect, all other things held equal. Thus an
increase in UY will reduce the probability of labour force participation. Here we won’t bother with
an indifference curve analysis. (We note that it would be possible to have an indifference curve
analysis which showed that an increase in unearned income would increase the probability of labour
force participation. But those indifference curves would be incorporating an assumption that Leisure
is an inferior good. We have assumed all along that Leisure is a normal good.)
Table 6-4 shows the LFP rates for married women in Canada in 1971 by family income minus
wife’s earnings, and for married women in Canada in 1996 by husband’s income level. In
interpreting Table 6-4B, we assume that husband’s income is a proxy for total unearned income.
This is not a perfect proxy – it ignores inherited wealth, pension income for retired people, and
various other sources of unearned income.
Table 6-4
A: MARRIED WOMEN AGES 15 TO 64 IN 1971
FAMILY INCOME MINUS
LFP RATE
WIFE’S EARNINGS
LESS THAN $3000
47
$3000 – $6000
44
$6000 – $9000
44
$9000 – $12,000
38
$12,000 – $15,000
33
GREATER THAN $15,000
27
B: MARRIED WOMEN AGES 15 TO 74 IN 1996
HUSBAND’S INCOME
LFP RATE
ADJUSTED DIFFERENCE FROM BASE
Less than $20,000
55.1
base
$20,000 – $30,000
62.9
5.3
$30,000 – $40,000
69.6
6.0
$40,000 – $60,000
71.8
4.2
$60,000 – $100,000
71.5
2.0
Greater than $100,000
66.6
-1.5
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Table 6-4A supports the prediction unambiguously. As unearned income rises, the LFP rate of
married women falls. This means that Table 6-3A also shows that Leisure is a normal good.
However, something appears to have changed between 1971 and 1996. In 1996 we now have,
even with the rates adjusted using regression analysis, an increase in LFP rates for married women as
husband’s income rises up to around $40,000. Only as it increase above $40,000 do increases in
husband’s income reduce the LFP rates of married women, using the adjusted differences, and then
not by much. While some of this can be explained by the selection problem introduced by including
women age 65-74 in the later data, the shift is too big for this to explain it all. Clearly there has been
a major cultural shift between 1971 and 1996.
There are three ways to “explain” this cultural shift. The first explanation is that household
production has become less valuable for families with higher incomes. Since LFP rates rise with
husbands’ incomes over most of the range, if married women are taking the same number of hours of
leisure, they are doing fewer hours of homework. This effect could reflect that higher income
families can afford more household production technology. But this still seems inadequate.
The second interpretation is that leisure has become an inferior good for families where the
husband earns up to $60,000. Because in this range, assuming household income is positively
correlated with husband’s income, as household income rises, married women are taking less leisure
if they are doing the same number of hours of homework. This seems unlikely.
The third interpretation is that as we move from 1971 to 1996, our assumption that married
women are secondary workers has become incorrect. As I mentioned in class, in a substantial
proportion of all Canadian households, the woman is the primary worker. If this is the case,
observing married women’s LFP rates is not the same as observing secondary worker LFP rates.
This is clearly an important effect, but it still seems inadequate. The full explanation of the cultural
shift remains a bit of a mystery.
END OF CHAPTER SIX