Economic Behaviour of Household: Theory of Time Allocation (Gary Becker)

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Economic Behaviour of Household Theory of Time
Allocation (Gary Becker)

• Dwini Handayani

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• Two time uses in neoclassical economics
• leisure
• market work (labor)
• Three time uses in the New Homes Economics
• leisure
• market work (labor)
• household production

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NEO CLASSICAL ECONOMICS
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Labor Supply Theory and Evidence

• Labor supply decisions can be roughly divided
  into two categories
• 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.

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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.

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• Basically, the demand for a good is a function of
• three factors
• The opportunity cost of the good.
• Ones level of wealth.
• Ones 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)

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• Where f depends on preferences.
• Demand for Leisure
• (1) The opportunity cost of an hour of leisure is
  very closely related to ones wage rate.
  For simplicity, we shall say that leisures
  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)

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• (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 lt0

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• (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 ? Y gt0

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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.
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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 persons labor supply curve will be
positively sloped.
Wage
Backward-bending
W
Desired hours of work
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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 curve connecting the
various combinations of money income and leisure
that yield equal utility.
A
B
IC2
C
D
IC1
L
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• Indifference curves have certain specific
  characteristics
• 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.
• Indifference curves do not intersect.
• Indifference curves are negatively sloped.
• 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 ICs

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M
M
L
L
Person who place high value on an extra hour of
leisure
Person who place low value on an extra hour of
leisure
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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. Wage rate
OE/OD
E
L
0
D
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Note Full income wage rate T ?It
represents the maximum attainable income.
M
At point B MUL/MUMgtW or
MULgtWMUM L should
increase At point C MUL/MUMltW or
MULltWMUM L should reduce,
or H should increase
E
B
A
IC2
IC
C
IC1

• 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.

L
D
IC2impossible under current condition
IC1possible, but higher level of utility
can be attained ICutility-maximized level A
utility-maximization point
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The Decision Not to Work
What happens if there is no point of tangency?
M
The persons 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
L
D
At this point(D)the person chooses not to be in
the labor force.
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Recall Leisure Work Analysis (4)

• 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 (SEgtIE).

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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. ?The increase in nonlabor income has
not changed the persons wage rate.
E
B
A
IC2
IC1
L
D
Pure income effect The income effect is
negative as income goes up, holding wages
constant, hours of work goes down.
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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.
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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.
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Recall Leisure Work Analysis (1)

• Max U u (C, L) ...1
• St PC WH V ...2
• T H L ...3
• (2) PC WH V
• C (W/P) H V/P
• (slope budget line w/p)

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Recall Leisure Work Analysis (2)

• Maksimisasi
• u (C, L) ? (PC- WT WL V)
• FOC
• ? / ? L MUL ? W 0
• ? / ? C MUC ? P 0
• Jadi Optimum ketika
• MUL / MUC W/P
• (slope IC slope BL)

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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 ?)

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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.
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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.
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Recall Leisure Work Analysis (6) Backward
Bending Supply
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NEW HOMES ECONOMICS
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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.

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Allocation of time (2)

• Beckers Asumptions
• commodities (outputs) measurable
• commodity (shadow) prices
• constant returns to scale
• single person households
• no human capital

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Theory of the Allocation of Time (3)

• Kegiatan individu/hh
• market production (work)
• nonmarket production (household production)
• Leisure

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• 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)

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• Becker emphasize
• goods purchase are not immediate source of
  utility
• to consume and satisfy utility also require
  inputs of HH members time ? in producing final
  commodities that yields utility

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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

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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

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Secara grafis
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goods

• To formalize this, define the households 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
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Indifference curve U u(X,l) Slope
marginal rate of substitution of goods for
leisure time
goods
Household utility is defined over goods and
leisure time (as usual)
w/P
Time
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goods
The essence of the model is that an individual
will work at home
w/P
as long as the marginal product of labor in home
production exceeds the marginal return to market
work (w/P).
less steep
Steeper than w/P
Work at home
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goods
And will work in the market until the return to
labor (w/P) is just exceeded by the marginal rate
of substitution for leisure
w/P
Work at home
market work
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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
Time
Market work
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When wages for market work are relatively low
w/P
goods
And the rest will be leisure time
Time
all work time will be in home production
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The familiar case
A little time in home production,
high returns to market work
full-time market work,
goods
and leisure time.
low productivity in most home production
home production
market work
leisure
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Secara matematis
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Secara Matematis

• Makimisasi Utility
• U U(Z1, Z2, ...., Zn) ...(1)
• Subject to
• 1. T tm ? ti ...(2)
• 2. y ? Pi xi ...(3)
• Dimana
• 3. Zi fi(xi, ti) ...(4)
• 4. Z g (Zi,...,Zm) ...(5)
• (sederhanakan kendala)

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• T tm ? ti
• tm T- ? ti ...(1a)
• (2) y ? Pi xi w. tm V
• (1a) (2)
• ? Pi xi w. tm V
• ? Pi xi w. (T- ? ti) V
• ? Pi xi w . ? ti w.T V
• (full incomeS)

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Problem Maksimisasi

• Menjadi
• Maksimisasi
• U u( Z1,...., Zn)
• Dimana
• Zi fi (xi, ti)
• Subject to
• S ? Pi xi w . ? ti

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Problem Maksimisasi

• ? u Z1, Z2,....,Zm? S- ? Pi xi - w .? ti
• .......(a)

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Problem Maksimisasi

• ? u Z1, Z2,....,Zm? S- ? Pi xi - w .? ti
• .......(b)

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Alokasi antara 2 kegiatan (commodity)
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• Bagaimana jika kegiatan tersebut tidak ada
  harganya gunakan shadow price.
• Cost of commodity/activity, consist foregone
  earnings (opportunity cost foregone)

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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 lt price of time during weekday

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Treatment of Variables in Household Demand System
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Labor Supply of Family Members Models

• Male Chauvinist
• Husbands does not decide his LS based on wifes
  LS decision
• Wife views husbands earnings as property income
  (husbandincome producing assets)
• Family utility-family budget model
• Max utility of all family members respect to
  family budget constraint

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Labor Supply of Family Members Models

• 3. Individual Utility- Family Budget Constraint
• Every body does their own thing
• Husband and wifes consumption and LS maybe
  inconsistent (may based his LS decision on an
  incorrect value of wifes LS)
• See figure below

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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
• Husbands reaction curve slope exceeds wifes
  reaction curve (necessary condition)
• Consumer goods are normal for both spouses
  (sufficient condition)

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Labor Supply of Family Members Models

• 4. Bargaining Model
• LS between husband and wife are done by
  bargaining between them.
• Democracy ?
• Increase of womens education ?

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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 ?

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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.

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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.

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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 spouses time is
  a substitute for that of the other spouse.

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Data Empiris
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SNASistem of National Accounting
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• In general, non-SNA time is devoted to preparing
  food, caring for clothes and maintaining the
  home, household, management, shopping etc.

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