Economic Behaviour of
Household:
Theory of Time Allocation
(Gary Becker)
Dwini Handayani
Two time uses in neoclassical economics:
leisure
market work (labor)
Three time uses in the New Homes
Economics:
leisure
market work (labor)
household production
NEO CLASSICAL ECONOMICS
Labor Supply : Theory and Evidence
Labor supply decisions can be roughly divided
into two categories:
(1) Decisions about whether to work at all, if so,
how long to work.
(2) Decisions about the occupation or general class
of occupation in which to seek offers and the
geographical area in which offers should be
sought.
2. A Theory of The Decision to Work
• The decision to work is ultimately a decision about
how to spend time.
Spend time in pleasurable leisure activities
Use time to work (working for pay)
• The discretionary time we have
(24 hours – time spent eating and sleeping)
can be allocated to either work or leisure.
Demand for Leisure
Supply of Labor.
Basically, the demand for a good is a function of
three factors:
1. The opportunity cost of the good.
2. One’s level of wealth.
3. One’s set of preference.
The demand（D） for a normal good can be
characterized as a function of opportunity
cost（C）and wealth（V）
D = f（C, V）
•
Where f depends on preferences.
Demand for Leisure:
(1) The opportunity cost of an hour of leisure is
very closely related to one’s wage rate.
For simplicity, we shall say that leisure’s
opportunity cost is the wage rate.
(2) Economists often use total income as an
indicator of total wealth, since the two are
conceptually so closely related.
Demand for leisure function becomes
DL = f（W, Y）
w
(1) If income increases, holding wages（and f）
constant, the demand for leisure goes up.
If income increases（decreases）, holding
wages constant, hours of work will go down
（up）.
Income effect on hours of work is negative.
Income Effect =
 w <0
(2) If income is held constant, an increase
（decrease）in the wage rate will reduce
（increase）the demand for leisure, thereby
increasing（decreasing）work incentives.
Substitution effect on hours of work is
positive.
Substitution Effect = H W  Y >0
Both Effect Occur When Wages Rise
Income effect: For a given level of work effort,
he/she now has a greater command over
resources than before because more income is
received for any given number of hours of work.
Substitution effect: The wage increase raises
the opportunity costs of leisure, and thereby
increases hours of work.
If income effect is dominant, the person will respond
to a wage increase by decreasing his/her labor supply.
Should the substitution effect dominate, the person’s
labor supply curve will be positively sloped.
Wage
Backward-bending
W*
Desired hours of work
3. A Graphic Analysis of the Labor-Leisure Choice
Two categories of goods: Leisure（L）and Money
Income ( M )
Since both leisure and money can be used to generate
satisfaction, these two goods are to some extent
substitutes for each other.
M
Indifference Curve:
A
B
IC2
C
D
IC1
L
A curve connecting the
various combinations of
money income and leisure
that yield equal utility.
Indifference curves have certain specific characteristics:
1. Any curve that lies to the northeast of another one is
preferred to any curve to the southwest because the
northeastern curve represents a higher level of utility.
2. Indifference curves do not intersect.
3. Indifference curves are negatively sloped.
4. Indifference curves are convex.
When money income is relatively high and leisure
hours are relatively few, leisure is more highly valued
than when leisure is abundant and income relatively
scarce.
5. Different people have different sets of IC’s
M
M
L
Person who place high
value on an extra hour of
leisure
L
Person who place low
value on an extra hour of
leisure
The resources anyone can command are limited.
Budget constraint reflects the combinations of leisure
and income that are possible for the individual.
M
The slope of the budget
constraint is a graphic
representation of the wage
rate.
E
Wage rate = OE/OD
0
D
L
Note: Full income = wage rate * T
→It represents the maximum attainable income.
M
At point B: MUL/MUM>W or
MUL>W*MUM
L should increase
E
B
A*
IC2
At point C: MUL/MUM<W or
MUL<W*MUM
L should reduce, or
H should increase
IC*
C
IC1
D
L
IC2：impossible under current condition
IC1：possible, but higher level of utility
can be attained
IC*：utility-maximized level
A* ：utility-maximization point
•An indifference curve that is
just tangent to the constraint
represents the highest level of
utility that the person can
obtain given his or her
constraint.
The Decision Not to Work
What happens if there is no point of tangency?
M
The person’s IC are at every
point more steeply than the
budget constraint.
Pt. D is not a tangency point.
There can be no tangency if the
IC has no points at which the
slope equals the slope of the
budget constraint.
E
D
L
At this point（D）the person chooses not to be in the labor force.
Recall: Leisure Work Analysis (4)
1. Income effect
income real naik, makin kaya maka mampu
untuk meningkatkan Leisure.
2. Substitution effect
income real naik, artinya harga leisure naik,
mendorong untuk meningkatkan jam kerja
Total effect: dalam keadaan normal akan
meningkatkan jam kerja (SE>IE).
The Income Effect
Nonlabor income: Even if this person worked zero hour per
day, he/she will have this nonlabor income.
M
Note that the new constraint
is parallel to the old one.
E
B
A
IC2
→The increase in nonlabor
income has not changed the
person’s wage rate.
IC1
D
L
Pure income effect: The income effect is negative; as income
goes up, holding wages constant, hours of work goes down.
Income and Substitution Effects with a Wage Increase
The wage increase would cause both an income and a substitution effect;
the person would be wealthier and face a higher opportunity cost of leisure.
N1→N3: income effect
→ L↑, H↓
N3→N2: substitution effect
→L↓, H↑
N1→N2: observed effect
Substitution effect dominates.
L↓, H↑
Income effect: Had the person received nonlabor income, with no change
in the wage, sufficient to reach the new level of utility, he/she would have
reduces work hours from N1 to N3.
N1→N3: income effect
→L↑, H↓
N3→N2: substitution effect
→L↓, H↑
N1→N2: observed effect
Income effect dominates.
L↑, H↓
Note: The differences in the observed effects of a wage
increase are due to differences in the shape of the indifference
curve. i.e., different preference.
Recall: Leisure Work Analysis (1)
Max:
U = u (C, L)
St : PC = WH + V
T=H+L
(2)
PC =WH + V
C = (W/P) H + V/P
(slope budget line =w/p)
...1
...2
...3
Recall: Leisure Work Analysis (2)
Maksimisasi:
£ = u (C, L) + λ (PC- WT + WL –V)
FOC:
∂ £/ ∂ L =
MUL= λ W =0
∂ £/ ∂ C =
MUC = λ P =0
Jadi Optimum ketika:
MUL / MUC = W/P
(slope IC = slope BL)
Recall: Leisure Work Analysis (3)
Keputusan jumlah leisure dan hours for work
optimum saat : MUL / MUC = W/P
Ketika upah naik, terdapat 2 effect:
1. Income effect (L ↑)
2. Substitution effect (L ↓)
Income and Substitution Effects with a Wage Increase
The wage increase would cause both an income and a substitution effect;
the person would be wealthier and face a higher opportunity cost of leisure.
N1→N3: income effect
→ L↑, H↓
N3→N2: substitution effect
→L↓, H↑
N1→N2: observed effect
Substitution effect dominates.
L↓, H↑
Income effect: Had the person received nonlabor income, with no change
in the wage, sufficient to reach the new level of utility, he/she would have
reduces work hours from N1 to N3.
N1→N3: income effect
→L↑, H↓
N3→N2: substitution effect
→L↓, H↑
N1→N2: observed effect
Income effect dominates.
L↑, H↓
Note: The differences in the observed effects of a wage
increase are due to differences in the shape of the indifference
curve. i.e., different preference.
Recall: Leisure Work Analysis (6):
Backward Bending Supply
NEW HOMES ECONOMICS
Allocation of time (1)
Becker (EJ, 1965)
"A Theory of the Allocation of Time“
Becker wrote: households are "assumed to
combine time and market goods to
produce more basic commodities that
directly enter their utility functions.“
Allocation of time (2)
Becker’s Asumptions:
•
•
•
•
•
commodities (outputs) measurable
commodity (shadow) prices
constant returns to scale
single person households
no human capital
Theory of the Allocation of Time (3)
Kegiatan individu/hh:
• market production (work)
• nonmarket production (household
production)
• Leisure
Asumsi: HH memaksimisasi utility
U= U(Z1, Z2, ...., Zn)
HH diasumsikan mengkombinasi time dan
market goods: untuk memproduksi basic
commodities (Zi)
Zi = fi (xi, Ti)
Becker emphasize:
• goods purchase are not immediate source
of utility
• to consume and satisfy utility also require
inputs of HH member’s time → in
producing final commodities that yields
utility
Theory of the Allocation of Time (4)
Dalam memaksimisasi utility, individu/hh
dihadapkan pada kendala:
• Waktu terbatas (T= time)
• Sumber daya terbatas ( S= full income)
yaitu
1. T= tm + ∑ ti
2. y = ∑ Pi xi
Theory of the Allocation of Time (5)
• Full income is time and resources of HH to
earn income (from work and nonlabor
income).
• Dalam makismisasi alokasi waktu:
tidak hanya semata-mata mementingkan
kerja, tetapi harus juga dialokasikan untuk
kegiatan lain.
• Kerja terus ? Tidak tidur ? Mana mungkin
SECARA GRAFIS
goods
•
To formalize this, define
the household’s budget
in terms of both
what they can produce for
themselves, in home
production
home production possibilities frontier
Slope = marginal product of labor in home production
time
Total time
goods
Household utility is defined
over goods and leisure time
(as usual)
Indifference curve: U = u(X,l)
Slope = marginal rate of substitution
of goods for leisure time
w/P
Time
goods
The essence of the model is that an
individual will work at home
as long as the marginal product of
labor in home production exceeds the
marginal return to market work (w/P).
w/P
less steep
Steeper than w/P
Work at home
goods
And will work in the market
w/P
until the return to labor (w/P) is just
exceeded by the marginal rate of
substitution for leisure
market Work at
work home
When wages for market work
are relatively high
goods
all work time will be in the
market, for a cash wage
w/P
And the rest will be leisure time
Market work
Time
When wages for
market work are
relatively low :
w/P
goods
And the rest will be leisure time
all work time will be
in home production
Time
The familiar case:
A little time in home production,
high returns to market work
full-time market work,
and leisure time.
goods
low productivity in most home production
leisure
market
work
home
production
SECARA MATEMATIS
Secara Matematis:
Makimisasi Utility:
U= U(Z1, Z2, ...., Zn)
Subject to:
1. T= tm + ∑ ti
2. y = ∑ Pi xi
Dimana
3. Zi = fi(xi, ti)
4. Z = g (Zi,...,Zm)
(sederhanakan kendala)
...(1)
...(2)
...(3)
...(4)
...(5)
(1) T= tm + ∑ ti
tm= T- ∑ ti
(2) y = ∑ Pi xi = w. tm + V
...(1a)
(1a) & (2)
∑ Pi xi = w. tm + V
∑ Pi xi = w. (T- ∑ ti) + V
∑ Pi xi + w . ∑ ti = w.T + V
(full income=S)
Problem Maksimisasi
Menjadi:
Maksimisasi
U = u( Z1,...., Zn)
Dimana
Zi = fi (xi, ti)
Subject to:
S = ∑ Pi xi + w . ∑ ti
Problem Maksimisasi
ʆ =u[ Z1, Z2,....,Zm]+λ [ S- ∑ Pi xi - w .∑ ti ]
L U Zi

*
 pi  0
xi Zi xi
U
xi
 pi
Zi
Zi
.......(a)
Problem Maksimisasi
ʆ =u[ Z1, Z2,....,Zm]+λ [ S- ∑ Pi xi - w .∑ ti ]
L U Zi

*
 w  0
ti Zi ti
U
ti
 w
Zi
Zi
.......(b)
Alokasi antara 2 kegiatan (commodity)
MU1
MU 2
MU 1

MU 2
x1
t1
 w
Z1
Z1

x2
t 2
p 2
 w
Z 2
Z 2
p1
p1
p 2
x1
t1
 w
Z1
Z1

 1
x2
t 2
2
 w
Z 2
Z 2
Bagaimana jika kegiatan tersebut tidak ada
harganya: gunakan shadow price.
Cost of commodity/activity, consist foregone
earnings (opportunity cost foregone)
Cost of time
Cost of time tends to be less for
commodities that have less opportunity
cost of time (indirectly contribute to
earnings).
Example: sleep, play, price of time during
weekend < price of time during weekday
Treatment of Variables in Household Demand System
1. Personal characteristics
of HH
2. Market for labor
3. Market for goods
4. Physical environment
5. Policy instrument
Exogenous Factor
1. age of women
2. women’s education
3.man’s education
4. couples physical wealth
5. family origin
6. wage rate for women
7. wage rate for man
8. wage rate for children
9. seasonality derive
10. migration oppor
Prices of goods
11. produced for sale
12. produced for home prod
13. purchase input for
market prod
14. purchase input for home
prod
15. variability market price
16. climate
17. geography
18. infrastructure
19. public services
20. technical change
Endogen Outcome
1. matching husb&wife
charact
2. age women at marriage
3. age of women at first
birth
4. timing sequence of birth
5. no of child ever born
6. proportions of births
surviving to a specific age
7. schooling of children
8. production activities
performed by children
9. extent of adult women’s
LF activities
10. migration of family
11. market income
12. expenditure
13. intrafanily allocation of
consumption among fam
members
14. saving behaviour
Labor Supply of Family
Members Models
1. Male Chauvinist
– Husbands does not decide his LS based on
wife’s LS decision
– Wife views husbands earnings as property
income (husband=income producing assets)
2. Family utility-family budget model
– Max utility of all family members respect to
family budget constraint
Labor Supply of Family
Members Models
3. Individual Utility- Family Budget
Constraint
– Every body does their own thing
– Husband and wife’s consumption and LS
maybe inconsistent (may based his LS
decision on an incorrect value of wife’s LS)
– See figure below
Labor Supply of Family
Members Models
3. Individual Utility- Family Budget
– P: wife LS at Hf1, husband Hm1, this will
induce wife to lower LS to Hf2, this will induce
husband to increase his LS to Hm2 dst sd di
titik Q
– This model will be stable:
• Husband’s reaction curve slope exceeds wife’s
reaction curve (necessary condition)
• Consumer goods are normal for both spouses
(sufficient condition)
Labor Supply of Family
Members Models
4. Bargaining Model
– LS between husband and wife are done by
bargaining between them.
– Democracy ?
– Increase of women’s education ?
Men vs Women
• How they differ in allocating their time
• Is it by gender differentiated
• What changes the allocation of time?
– Technology
– Demographic characteristics (education,
health status, nonlabor income,...)
– Taste (workaholic vs a lazy person)
– What else ?
Gender division of labor
• Historically, married women have tended to
specialize in household production and married
males have tended to specialize in market
production.
• Comparative advantage for women in household
production in the past?
• Possible reasons:
– high completed fertility rates,
– high infant mortality rates, and
– labor market discrimination.
Evolving gender roles
• As infant mortality and completed fertility rates
decline and as female wage rates rise, it is
expected that this division of labor between
spouses will be altered.
– In recent years, married women have substantially
increased the amount of time spent in the paid labor
market and have spent slightly less in household
production).
– Married men now spend slightly more time in
household production than in the past.
Specialization or shared activities?
• Both spouses will tend to work together in
household production tasks in which their
time is complementary
• Individuals will specialize (according to
comparative advantage) when one
spouse’s time is a substitute for that of the
other spouse.
Data Empiris
SNA=Sistem of National Accounting
• In general, non-SNA time is devoted to
preparing food, caring for clothes and
maintaining the home, household,
management, shopping etc.