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Chapter 2 (& 9)

Labor Supply



2- 3

Introduction to Labor Supply

Individual decision to work (or not)

and conditional on work ing, how many hour s to work

Allows to rationalize a number of stylized facts



2- 4

Measuring the Labor Force

Curr ent population sur vey (CPS) = Br itish LFS

P = civilian adult population 16 year s or older not in institutions

- Labor For ce = Employed + Unemployed LF = E + U (does not tell us about ³intensity´ of work)

E: at a job with pay for at least one hour or work ed for at least 15 hour s on an un paid job

U: on a temporary layoff or not having a job but actively look ing for in 4 week s pr eceding sur vey

- Labor For ce Partici pation Rate LFPR = LF/P

- Employment: Population Ratio (per cent of population that is employed) EPR = E/P

- Unemployment Rate UR = U/LF



2- 5

Measurement Issues

Labor For ce measur ement r elies on subjectivity and lik elyunder states the eff ects of a r ecession

Hidden unemployed: per sons who have left the labor for ce, giving upin their sear ch for work

EPR is a better measur e of fluctuations in economic activity than the UR

UR Might even be pro-cyclical (discouraged work er s)

dUR/dGDP=(E dU/dGDP ± U dE/dGDP)/LF2

(>0 if dlnU/dGDP>dlnE/dGDP)>0)



2- 6

Facts about labour supply (in the USA)



2- 7




2- 8

Average hours worked/week, 1900-2005

30

35

40

45

50

55

60

1900 1920 1940 1960 1980 2000 2020

Year

W e e k l y h o u r s



2- 9


- Work ing men: decline in labor for ce partici pation from 90% in

1947 to 75% in 1990

- Work ing women: r ise in labor for ce partici pation from 32% in

1947 to 60% in 1990

- Work hour s f ell from 40 to 35 per week dur ing the same time

per iod



2- 10




2- 11


- Mor e women than men work part-time

- Mor e men who ar e high school drop outs work than women who

ar e high school drop outs

- White men have higher partici pation rates and hour s of work than

black men



2- 12

Worker Performance

Neo-Classical Model of Labor -Leisur e Choice

Classical consumer problem with 2 caveats- Work is µ bad¶ (leisur e is a good)- Unear ned income deliver s a discontinuity in the budget constraint

Building bock s:- utility function- budget constraint

- time constraint

Solve for :- inter ior solution (intensive mar gin)- Partici pation (extensive mar gin)



2- 13

Utility function and Indifference Curves

U=f(C, L)

- C: consumption ($ value)

- L=Leisur e

Indiff er ence cur ves

- Downwar d sloping (indicates the trade off between consumption

and leisur e)

Higher cur ves = higher utility

Do not inter sect

Convex to the or igin (indicating that opportunity costs incr ease)



2- 14

Indifference Curves

Consumption ($)

500

450

400

40,000 Utils

25,000 Utils

Hour s of

Leisur e150125100+Hour s of

work



2- 15

Indifference Curves Do Not Intersect

U 0

U 1

Y

Z

0 Leisur e

Consumption ($)



2- 16

Differences in Preferences across Workers

Stee p and flat indiff er ence cur ves:

Lazy Workaholic

U 0U 0

U 1

U 1

Consumption ($) Consumption ($)

Hour s of

Leisur eHour s of

Leisur e



2- 17

MRS between C and L

MRS=| xC/xL|U |= MUL/MUC>0

- U(C,L)=const

- MULdL+MUCdC=0

Diminishing mar ginal rate of substitution



2- 18

The Budget ad Time Constraints

Budget constraint

C = wh + V Note: p=1 (a rise in p corresponds to a

fall in both w and V).- V=nonlabor (unear ned) income

- w=wage rate

- h=hour s of work

Time constraint T=h+L

- T=time endowment

C +w L= wT + V = full income



2- 19

Depicting the Budget Constraint

T

E

V

wT+V

0

Hour s of

Leisur e

Consumption ($)

Budget Line

Endowment

point

Hour s of work

0T



2- 20

The Hours of Work Decision

O ptimal consumption is given by the point wher e the budget

line is tangent to the indiff er ence cur ve

MRS =w

Max U(C,L)

s.t. C +w L= wT + V

FOC: MUC= P

MUL= P w



2- 21

Optimal Consumption and Leisure

$1100

$1200

A Y

$500P

U 1

$100

U 0

U *

E

110

110

40

70

0

0

Hour s of

Work

Hour s of

Leisur e



2- 22

Optimal Consumption and Leisure

At A: subjective evaluation of C-L tradeoff > mark et

evaluation

MRS=2W=1

Work er willing to give up 2 units of C for one extra unit of L

Able to cut his C by 1 unit for 1 extra unit of L

Not optimal: it pays to work less (consume mor e L)

w=pr ice of leisur e



2- 23

The Effect of a Change in Nonlabor Income on

Hours of Work

An increase in nonlabor income leads to a parallel, upward shift in the budget line, moving the

worker from point P0 to point P1. If leisure is a normal good, hours of work fall.

F 1

P 1

$200

U 1

U 0E 1

E 0

P 0

70 80 110

F 0

$100

Hour s of Leisur e

Consumption ($)



2- 24

The Effect of a Change in Nonlabor Income on Hours of

Work

An increase in nonlabor income leads to a parallel, upward shift in the budget line, moving the

worker from point P0 to point P1. If leisure is an INFERIOR good, hours of work increase.

F 1

P 1

$200

U 1

U 0

E 1

E 0

P 0

7060 110

F 0

$100

Consumption ($)



2- 25

The Effect of a Change in Nonlabor Income

on Hours of Work

Incr ease in nonlabor income allows work er to ³ jump´ to higher

indiff er ence cur ve, indicating the Income Effect

- Leisur e can be tr eated as a normal good or as an inf er ior good

- R easonable to assume that is a NORMAL good



2- 26

More Leisure at a Higher Wage

When the Income Eff ect dominates:

G

U 1

Q D

D

R

P

U 0

V

F

E

8575 1100 70 Hour s of

Leisur e

Consumption ($)



2- 27

More Work at a Higher Wage

When the Substitution Eff ect dominates:

G

D

D

F

E

U 1

Q

R

P

U 0

V

8070 1100 65 Hour s of

Leisur e

Consumption ($)



2- 28

Ambiguous Relationship: Hours Worked and Wage

Rates

As wages change holding real income constant, changes in

consumption-leisur e bundle indicate the Substitution Effect

If the Substitution Eff ect is gr eater than the Income Eff ect, then

hour s of work incr ease when the wage rate r ises

If the Income Eff ect is gr eater than the Substitution Eff ect, then hour s of work decr eases when the wage rate r ises.



2- 29

Ambiguous Relationship: Hours Worked and

Wage Rates

At optimum

h*=g(w, V+wh)

xh*/xw = xg/x w|U* + (xg/xV) h ><0 ? (1)

subst. inc.

>0 <0 IF L is NORMAL!!!!!!!!

The flatter the IC, the mor e lik ely the subst eff ect dominates



2- 30

To Work or Not to Work?

Ar e the ³terms of trade´ suff iciently attractive to br i be a work er to enter the labor mark et?

R eser vation wage: the minimum level of wages that would mak e the per son indiff er ent between work ing and not work ing

- Rule 1: if the mark et wage is less than the r eser vation wage, then the per son will not work

- Rule 2: the r eser vation wage incr eases as nonlabor income incr eases



2- 31

The Reservation Wage

H

Y

G X

U H

E

U 0

Hour s of

Leisur e

T 0

Has Slope -w high

Has Slope -w b

Consumption

($)



2- 32

For standar d budget lines

w*=MRS |L=T

Cor ner solution (work er would lik e to buy mor e leisur e than C)

If V incr eases , w* r ises

Stee per IC associated to higher w*

(w* inde pendent of w)

For individuals out of work a r ise in w only induces a

substitution eff ect

The Reservation Wage



2- 33

Labor Supply Curve

h*=T-L*=h(w,V)

Hour s of

Work

0

Wage Rate ($)

4020 30

10

20

25



2- 34

Labor Supply Curve

R elationshi p between hour s work ed and the wage rate

- For w slightly above w*, the labor supply cur ve is

positively sloped (substitution eff ect dominates)

- If the income eff ect begins to dominate, hour s of work decline as wage rates incr ease (a negatively sloped labor supply cur ve)



2- 35

Labor Supply Elasticity

Elasticity of (individual LS) = % change in hours work ed/% change in wage rate =

W=[xh/xw] w/h = [xh/h] w/ xw = x lnh / xlnw

Labor supply elasticity <1 means ³inelastic´

If elasticity of LS negative income eff ect dominates and ear nings grow less than proportionally as wages incr ease

x ln wh / xln w = W +1



2- 36

Estimating Elasticity

From equation (1)

xh/xw = xh/xw|U + [xh/xV] h

[xh/xw] w/h = [xh/xw|U] w/h + [xh/xV] V/h (wh/V)

[x ln h/x lnw] = x lnh/x ln w|U + x lnh/x lnV (K)

total subst. inc.

(K = wh/V)e = e* + ev K

><0 >0 <0

uncompensated compensated income



2- 37

Estimating Elasticity

ln h= E0 +E1 ln w + E2 lnV

E1= e E2= eV

e*= e-ev K =E1-E2K



2- 38

Labor Supply of Women

Labor supply tends to be inelastic

For men income eff ect typically dominates:

e*=10% = 0.10 substitution

K eV=20%= - 0.20 income

e= -10% small

For women, substitution eff ect typically dominates

e = [0.6 , 1.10]



2- 39

Derivation of the Market Labor Supply Curve from

the Supply Curves of Individual Workers

0 0 0

w ~ B

w ~ A

w ~ B

w ~ A

h A

h A +

h B

( a) Alice ( b) Br enda ( c) Mark et

Wage Rate ($) Wage Rate ($) Wage Rate ($)

Hour s of Work

h A

h B

Note: when we discuss elasticity of aggr egate labor supply we

generally r ef er to % change in PARTICIPATION for a 1% change in

wages

2 40



2- 40

Cross-Country Relationship: Growth in Female

Labor Force and the Wage, 1960-1980

Sour ce: Jacob Mincer , ³Inter country Compar isons of Labor For ce Tr ends and of R elated Developments:

An Over view,´ J ournal of Labor E conomics 3 (January 1985, Part 2): S2, S6.

1 2 3 4 5 6 7 8 9

Percentage Change in Wage

0

1

2

3

4

5

6

7

F e m a l e P a r t i c i p a t i o n

G r o w t h R a t e o f

n te tates

Israel Britain

rance

we en

Germany

Italy

ustra a

pa n

Japan

et er an s

2 41



2- 41

Policy Application: Welfare Programs and Work

Incentives

Cash grants r educe wage incentives

Welfar e programs cr eate work disincentives

Welfar e r educes supply of labor by granting nonlabor income,

which raises r eser vation wage

2 42



2- 42

Effect of a Cash Grant on Work Incentives

F

Consumption($)

500

Hour s of

Leisur e

0 11070

G

U 1

U 0 P

Infinite tax rate

Effect will depend on market wage and on preferences

100% tax rate does not solve problem (because of shape of IC)

2 43



2- 43

$500 cash grant

taxed at 50% for every $ ear ned (up to when exhausted)

Effect of a Welfare Program on Hours of

Work

2 44



2- 44


Work

Hour s of

Leisur e

$500

U 0 U 1

G

E

P

F

R

Q

H

D

D

0 11010070

slope = -$5This part never

attained

slope = -$10

Consumption ($)

2 45



2- 45


Work

Income and substitution eff ects act in same dir ection

In pr inci ple work er s to the left of inter section btw 2 budget lines

can work less

2 46



2- 46

Policy Application: The Earned-Income Tax

Credit

Cr edit of 40 % on labor ear nings as long she ear ns < $10,350. w(1.4)

Cr edit capped at $4,140 = (0.40 * 10,350)

At that point work er mak es 14,490

This maximum amount can be r etained as long as work er ear ns no mor e that $13,520

At that point work er mak es 17,760

Tax cr edit phased out at rate 21.06% Cr edit is exhausted when work er mak es $33,178

[17,660-13,520*(1-.2106)]/.2106

2- 47



2- 47

The EITC and the Budget Line

Hour s

of

Leisur e

Consumption($)

110

10,350

13,520

14,490

17,660

33,178

E

J

H

G

F

Net wage is 40% above the actual wage

Net wage equals the actual wage

Net wage is 21.06% below the actual wage

2- 48



2- 48

Policy Application: The Earned-Income Tax

Credit

2- 49



2 49

The Impact of the EITC on Labor Supply

EITC incr eases LFP of non-work er s produces an income eff ect - hour s work ed should

change (even among non tar get group)

2- 50



2 50

Taxation and labor supply

The wage rate that is r elevant for labor supply decisions

is the tak e home wage.

Labor supply function de pends on the net wage.

Proportional taxation: flatter budget line

Progr essive tax: k ink ed budget line

O ptimum can be at k ink for many work er s (cor ner

solution)

2- 51



2 51

Laff er cur ve

Gover nment tax r evenues R=twh non monotonic function of t

(incentive eff ects)

xlnR/xlnt = 1 + xlnh/xlnt

w N=w(1-t)

xlnR/xlnt = 1 + xlnh/xlnw N xlnw N/xlnt

xlnw N/xlnt= xln(1-t)/ xlnt = -t/(1-t)

xlnR/xlnt = 1 -t/(1-t) xlnh/xlnw N

If xlnh/xlnw N=0, xlnR/xlnt=1

If xlnh/xlnw N>0, xlnR/xlnt<1 (in pr inci ple even <0)

2- 52



2 52

Extensions

³Static´ model is not a complete de piction of how we allocate

our time

We extend the basic model to consider:- The long run

- Hus band-wif e joint-decisions to supply labor

2- 53



Labor Force Participation Rates over the Life

Cycle in 2005

30

40

50

60

70

80

90

100

15 25 35 45 55 65

Age

L a

b o r f o r c e p a r t i c i p a t i o n r a t e

Male

Female

2- 54



Hours of Work over the Life Cycle, 2005

500

1,000

1,500

2,000

2,500

15 25 35 45 55 65

Age

A n n u a l h o u r s o f w o

r k

Male

Female

2- 55



Labor supply over the life cycle

Wage rates change over the work er ¶s lif e cycle

- Wages ar e low when young

- Wages r ise with time and peak around age 50- Wages decline or r emain stable after the age of 50

Change in wage over the lif e cycle is an ³evolutionary´ wage

change alter ing the pr ice of leisur e

2- 56



The Life Cycle Path of Wages and Hours for a

Typical Worker

Age

Wage

Rate

50 Age

Hour s of

work

50

2- 57



Theoretical issues of evolutionary wages

Max U(C1,L1) +A U(C2,L2)

A=(1+r)-1

s.t. w1L1+AW2L2+C1+AC2 = V1+AV2 +w1T+ Aw2T

(no cr edit constraints!)

FOC: MRSL2,L1=MUL1/MUL2=w1/w2

w1>w2 L1<L2 only substitution eff ect

2- 58



Theoretical issues of evolutionary wages

Positive r elationshi p between changes in hour s or work and changes in the wage rate

The prof ile of hour s of work over the lif e cycle will have the same shape as the age-ear nings prof ile

Intertemporal substitution hypothesis: people substitute their time over the lif e cycle to tak e advantage of changes in the

pr ice of leisur e

2- 59



Hours of Work over the Life Cycle for Two

Workers with Different Wage Paths

Age

Jack

t * Age t *

Joe

Wage Rate Hour s of Work

Jack

Joe (if substitution eff ect

dominates)

Joe (if income eff ect

dominates)

Joe¶s wage exceeds Jack ¶s at every age. Although both Joe and Jack work mor e

hour s when the wage is high, Joe work s mor e hour s than Jack only if the

substitution eff ect dominates. If the income eff ect dominates, Joe work s f ewer

hour s than Jack .

2- 60



Retirement

Work er aged 60 ± lif e ex pectancy =80

O ptimal r etir ement decision (year s)

Each additional year of work yields w

Each year of pension yields B (<w, naturally!)

Work until age 80: V80=w (1+A +A2 + «+A19)

R etir es now: V60= B (1+A +A2 + «+A1 9)< V80

Max U(C, YR) st C=V60 + (20-YR)(V80-V60)/20(linear ized BC)

2- 61



The retirement decision

Consumption ($)

20

P

U 0

U 1

V 60

V 80

R etir ement

F

100

E

2- 62



Effect of an increase in the wage on the

retirement decision

wo V80o

rotates budget line around E

both income eff ects and substitution eff ects

ambiguous

R

P

20105

U 1

U 0

G

F

E

Consumption ($)

Year s of

R etir ement

2- 63



Effect of an increase in pension benefits on

retirement decision

2010 15

R

U 1

U 0

F

Consumption ($)

Year s of

R etir ement

Bo V60o

rotates budget line around F

both income eff ects and substitution eff ects

Same dir ection, YR incr eases

2- 64



Policy Application: the decline in work

attachment among older workers

Older work er s have lower partici pation rates

Work disincentives/ Disability benef its

Social Secur ity Ear nings Test

Assume r etir ement benef it = 10K

r etir ees can ear n <=$17K without losing r etir ement benef its

If ear nings>$17K every $3 of income r educes benef its by $1 R etir ee exhaust r etir ement benef it when he ear ns 47K

2- 65



The Impact of the Social Security Earnings

Test on Hours of Work

$47,000

$10,000

$27,000

Consumption ($)

H

H R2

P1

R3

P 3

T 0 Hour s of

Leisur e

W orker 2

W orker 1

W orker 3

Eff ect on hour s of work

ambiguous

Partici pation might decr ease

2- 66



Allocation of Weekly Hours to Various Activities,

By Gender and Marital Status

40.2

32.9

16.7

22.2

14.3

12

34.9

23.5

77.6

76.9

78.7

79.4

22.4

24.2

22

23.8

13.5

22

15.7

19.1

0 24 48 72 96 120 144 168

Married Men

Unmarried Men

Married Women

Unmarried Women

Mark et

Work Household

Work

Per sonal Car e Passive

Leisur e

Other

2- 67



Household Production

Leisur e includes many forms of nonmark et work , including

household production

Why do some household member s s pecialize in the mark etsector and other member s s pecialize in the household sector?

Why marr ied women have an incentive to s pecialize in

household production?

2- 68



Household Production Function

Household problem Assume no leisur e!

Max U(C,Z)

s.t. C=C1+C2=w1h1+w2h2 mark et produced goods

Z=Z1+Z2=a1(T1-h1)+a2(T2-h2) home produced goods

- a1, a2= mar ginal productivity in home production

Assume w1/a1>w2/a2

Individual 1 r elatively mor e productive in mark et

(comparative advantage)

2- 69



(1) + (2) individual opportunity sets

200

100 Household

Goods ($)

Mark et

Goods ($)

(a) 1¶s Budget Line

slope = -w1/a1150

250 Household

Goods ($)

Mark et

Goods ($)

(b) 2¶s Budget Line

slope = -w2/a2

C1=w1h1, Z1=a1(T-h1)

C1= w1T1 ±(w1/a1)Z1

C2=w2h2, Z2=a2(T-h2)

C2= w2T2 ±(w2/a2)Z2

2- 70



Opportunity Frontier of Couple

G350

F 200

1

2

E ¡

E

250100 350340 Household

Goods ($)

150 slope = -w1/a1

1 shar es time btw M and Home2 only home

slope = -w2/a2

2 shar es time btw Mkt and Home

1 only Mkt

Perf ect s pecialization

Mark et

Goods ($)

2- 71



Solution to household problem

G350

F 200

E ¢

E

250100 350340 Household

Goods ($)

150

O ptimal (unattainable)

H

Work er 1 devotes his entir e time to

Mkt if w1/a1>MRSC,Z|F

Wher e MRSC,Z= MUZ/MUC

Mark etGoods ($)

2- 72




G350

F 200

E £

E

250100 350340 Household

Goods ($)

150 O ptimal H

Work er 1 shar es his time btw Mkt

and home if w1/a1<MRSC,Z|F

Mark etGoods ($)

2- 73




0<h1<T1, h2=0 if w2/a2<w1/a1=MRSC,Z<MRS

C,Z|F

h1=T

1, h

2=0 if w

2/a

2<MRS

C,Z|F

<w1/a

1

h1=T1, 0<h2<T2 if MRSC,Z|F<MRS

C,Z=w2/a2<w1/a1

2- 74



Increases in the Wage Rate or Household

Productivity Lead to Specialization

Household

Goods ($)

Mark et

Goods ($)

P ¤

U d

U P

w1 o

2- 75



Increases in the Wage Rate or Household

Productivity Lead to Specialization

Household

Goods ($)

Mark et

Goods ($)

U d

P d P

U

a2 o

2- 76



End of Chapter 2 (&9)

Documents

Chap002 Modified