Economic Behaviour of Household:

Theory of Time Allocation (Gary Becker)

Dwini Handayani

Two time uses in neoclassical economics:leisuremarket work (labor)

Three time uses in the New Homes Economics:

leisuremarket 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 ）

(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

ww

(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 >0W

H

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

Desired hours of work

Backward-bendingW*

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

L

IC1

IC2

A

B

CD

Indifference Curve:

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

L

M

L

Person who place high value on an extra hour of leisure

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

L0

E

D

The slope of the budget constraint is a graphic representation of the wage rate.

Wage rate = OE/OD

Note: Full income = wage rate * T →It represents the maximum attainable income.

M

L

IC1

IC*IC2

E

D

A*

B

C

At point B: MUL/MUM>W or MUL>W*MUM L should increase

At point C: MUL/MUM<W or MUL<W*MUM L should reduce, or H should increase

•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.

IC2 ： impossible under current condition IC1 ： possible, but higher level of utility can be attainedIC* ： utility-maximized levelA* ： utility-maximization point

The Decision Not to WorkWhat happens if there is no point of tangency?

M

L

E

D

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.

At this point （ D ） the person chooses not to be in the labor force.

Recall: Leisure Work Analysis (4)

1. Income effectincome 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

L

IC1

IC2

E

D

AB

Note that the new constraint is parallel to the old one.

→The increase in nonlabor income has not changed the person’s wage rate.

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 IncreaseThe 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) ...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)

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 IncreaseThe 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

• To formalize this, define the household’s budget in terms of both

what they can produce for themselves, in home production

time

goods

Total time

home production possibilities frontier

Slope = marginal product of labor in home production

Household utility is defined over goods and leisure time(as usual)

Time

goods

w/P

Indifference curve: U = u(X,l) Slope = marginal rate of substitution of goods for leisure time

The essence of the model is that an individual will work at home

Work at home

goods

w/P

as long as the marginal product of labor in home production exceeds the marginal return to market work (w/P).

Steeper than w/P

less steep

And will work in the market

until the return to labor (w/P) is just exceeded by the marginal rate of substitution for leisure

Work at home

goods

w/P

market work

When wages for market work are relatively high

Time

goods

w/P

all work time will be in the market, for a cash wage

And the rest will be leisure time

Market work

When wages for market work are relatively low :

Time

goods

w/P

all work time will be in home production

And the rest will be leisure time

The familiar case:

home production

goods

market work

full-time market work,

and leisure time.

leisure

low productivity in most home production

high returns to market workA little time in home production,

SECARA MATEMATIS

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)

(1) T= tm + ∑ titm= 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 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 ]

.......(a)

0*

pixi

Zi

Zi

U

xi

L

Zi

xipi

Zi

U

Problem Maksimisasi

ʆ =u[ Z1, Z2,....,Zm]+λ [ S- ∑ Pi xi - w .∑ ti ]

.......(b)

0*

wti

Zi

Zi

U

ti

L

Zi

tiw

Zi

U

Alokasi antara 2 kegiatan (commodity)

2

1

2

2

2

22

1

1

1

11

2

1

Z

tw

Z

xp

Z

tw

Z

xp

MU

MU

2

2

2

22

1

1

1

11

2

1

Z

tw

Z

xp

Z

tw

Z

xp

MU

MU

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 Exogenous Factor Endogen Outcome 1. Personal characteristics of HH

1. age of women 2. women’s education 3.man’s education 4. couples physical wealth 5. family origin

2. Market for labor 6. wage rate for women 7. wage rate for man 8. wage rate for children 9. seasonality derive 10. migration oppor

3. Market for goods 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

4. Physical environment 16. climate 17. geography

5. Policy instrument 18. infrastructure 19. public services 20. technical change

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.