Labour Economics

Bino Paul G D,

School of Management & Labour Studies

Tata Institute of Social Sciences, Mumbai

System of Labour Market

Wage

Supply of Labour

Equilibrium

Wage

Demand for Labour

Labour Demand/Supply

Supply of Labour

The system of Labour Supply

Population

Labour

Employed Unemployed

Not in Labour

The system of Labour Supply

Employed

Self

Employed

Regular Salaried/

Wage

Casual

Employment

The system of Labour Supply

Self

Employed

Own Account

Workers

Employer Helper

Estimating the trend growth rate of

Labour Supply

L1 = L0 + L0r = L0(1 + r), L2 = L1(1 + r) = L0(1 + r)2

Lt = L0(1 + r)t

Ln Lt = Ln L0 + t Ln(1 + r)

Ln Lt = β0+ β1 t , β0 = Ln L0 , β1 = Ln (1 + r)

r *100 = (e β1 - 1)*100

L = Labour Supply, Subscript ‘t’ = Time, Ln = Natural Logarithm,

β0 = Intercept, β1 = Slope

Labour Force in India (15 years and above) (1990-2013)

Source: ILO (2014), Key Indicators of Labour Market, 8th Edition

0

5,00,00,000

10,00,00,000

15,00,00,000

20,00,00,000

25,00,00,000

30,00,00,000

35,00,00,000

40,00,00,000

45,00,00,000

50,00,00,000

1990 1995 2000 2005 2010

La

bo

ur

Fo

rce

Year

Labour Force in India (15 years and above)

(1990-2013) Estimate

We apply Ordinary Least Square Regression to estimate

Ln Lt = β0+ β1 t

Ln Lt = -15.96 + 0.018 t Standard Error (1.5) (0.001)

Statistical Significance (1%) (1%)

R Square = 0.93, Durbin Watson (DW) =.17

r *100 = (e 0.018 - 1)*100 = 1.82%

However, this regression suffers from positive autocorrelation.

DW below 2 indicates positive auto correlation. DW 2 to 2.6 is a

desirable range

Estimate with lagged values of dependent variable

An option is estimate Ln Lt = β0+ β1 t + β2 Ln Lt -1

However, DW remains less one.

So, one more lag

Ln Lt = β0+ β1 t + β2 Ln Lt -1+ β3 Ln Lt -2

For the above model, DW increases to 2.3 (no auto correlation)

since lagged values of dependent variable account for large

chunk of explanation. However, r reduces to 0.3%.

Labour Force Particpation Rate (LFPR) in India (15 years and above)

(1990-2013) [LFPR = Labour/Population]

Source: ILO (2014), Key Indicators of Labour Market, 8th Edition

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0 1

99

0

19

92

19

94

19

96

19

98

20

00

20

02

20

04

20

06

20

08

20

10

20

12

La

bo

ur

Fo

rce

Pa

rtic

ipa

tio

n R

ate

(L

FP

R)

Year

India Male and Female 15+

India Male 15+

India Female 15+

‘O’ Level Microeconomics

Y

X

U = f (X, Y)

dU = (U/X) dX + (U/Y) dY

U/X = fx , U/Y = fY

If dU = 0, then

fxdX + fy dY = 0

(-) fx/fy = dY/dX

Same

utility

Same

utility

‘O’ Level Microeconomics

Y

X

U = f (X, Y)

dU = (U/X) dX + (U/Y) dY

U/X = fx , U/Y = fY

If dU = 0, then

fxdX + fy dY = 0

(-) fx/fy = dY/dX

(-) fx/fy = dY/dX = MUx/MUy

‘O’ Level Microeconomics

Y

X

U (Y1 + Y2 (1- ), X1+(1- )X2) > U(Y1, X1);

U (Y1 + Y2 (1- ), X1+(1- )X2) > U(Y2, X2);

+ (1- ) = 1, 0 < < 1

X2 X1

Y1

Y2

Work Leisure Model

Co

nsu

mp

tion

( C )

Leisure (L)

Y =C= hw ; w = Wage Rate, Y =Income

h = C/w ;

T = h + L ; T = Time, L=Leisure

T = (C/w) + L

If C= 0, L max = T

If L = 0, Cmax = Tw

Slope = Cmax/Lmax = Tw/ T = w

Work (h)

Cmax

Lmax

Work Leisure Model with Autonomous Income

C

Leisure (L)

C = hw + V ; w = Wage Rate,

V= Autonomous Income

h = (C-V)/w ;

T = h + L

T = ((C-V)/w) + L

If C= 0, L = T + V/w = (Tw + V)/w

If L = 0, C = Tw + V

Slope = Cmax/Lmax = [Tw + V] / [(Tw + V)/w]

= w

Work (W)

Cmax

Lmax V

Work Leisure Model with Autonomous Income

C

Leisure (L)

C = wh + V; h = T - L

C= w (T-L) + V C = (wT + V )- wL

Work (W)

Cmax

Lmax V

C/ L

=w

Slope of Budget Line

Work Leisure Model

Consumption (C)

Leisure (L)

Work (h)

Utility = f(C, L)

C

L

C/ L =

MU Leisure / MU Cons

(U/ L) / (U/ C)

w = MU leis /MU cons C

L

Work Leisure Model: leisure as a normal good

Consumption

( C )

Leisure (L)

Work (h)

V

A B C

a

b c

AC = (-) BC + AB

AC = Wage Effect,

BC = Substitution Effect

AB = Income Effect

Sign of AB is positive

Sign of BC is negative

Sign of AC is positive

Here, INCOME EFFECT is greater than

SUBSTITUTION EFFECT. This implies

Wage Effect is positive

h

w

Work Leisure Model: leisure as an inferior good

Consumption

( C )

Leisure (L)

Work (h)

V

A

B

C

a

b c

AC= BC + AB

AC = Wage Effect,

BC = Substitution Effect

AB = Income Effect

Sign of AC is negative

Sign of BC is negative

Sign of AB is negative

h

w

Backward bending

Labour Supply

Consumption

Leisure

Work

Labour Supply

Wage

An application

Screenshot of the application

Reservation Wage

Scenario Decision

Market Wage > Reservation Wage To Work for a Pay

Market Wage = Reservation Wage Indifferent between to work and not to work

Market Wage < Reservation Wage Not to Work

Market Wage > Reservation Wage

Market Wage

Reservation Wage

L

C

Market Wage < Reservation Wage

Reservation Wage

Market Wage

C

L

Market Wage < Reservation Wage

C

Reservation Wage = Market Wage

L

Impact of Cash Grant

Cash Grant

C

L

U0

U1

Life Cycle Path of Wage

Wage Hours of Work

Age Age

Wage increase and Retirement

Consumption

U1

U0

Years of Retirement

Household Scenario

A B

MARKET ACTIVITY (M) 5 4

NON MARKET ACTIVITY (N) 2 6

PERSONS

Household Scenario

Ma Na Mb Nb Va + Vb Va Vb3 0 3 0 27 15 12

2 1 3 0 24 12 12

1 2 3 0 21 9 12

0 3 3 0 18 6 12

3 0 2 1 29 15 14

2 1 2 1 26 12 14

1 2 2 1 23 9 14

0 3 2 1 20 6 14

3 0 1 2 31 15 16

2 1 1 2 28 12 16

1 2 1 2 25 9 16

0 3 1 2 22 6 16

3 0 0 3 33 15 18

2 1 0 3 30 12 18

1 2 0 3 27 9 18

0 3 0 3 24 6 18

Va = 5 Ma + 2 Na; Vb = 4 Mb + 6 Nb

Supposing disposable time is 3 hours

Equivalent Figures

C Earnings

L Hours of work

Fixed Salary

Earning

Hours of Work

Demand for Labour

(Short run)

An Exercise

PRICE 5 WAGE 3

OUTPUT 1 F 10

REVENUE 5 LABOUR 1

COST 13

PROFIT -8

A 0.1

B 0.01

OUTPUT LABOUR REVENUE COST PRICE LABOUR MPL PRICE *MPL WAGE

0 0 0 10 2 0 1 2 3

1.09 1 5.45 13 5 1 1.17 5.85 3

2.32 2 11.6 16 5 2 1.28 6.4 3

3.63 3 18.15 19 5 3 1.33 6.65 3

4.96 4 24.8 22 5 4 1.32 6.6 3

6.25 5 31.25 25 5 5 1.25 6.25 3

7.44 6 37.2 28 5 6 1.12 5.6 3

8.47 7 42.35 31 5 7 0.93 4.65 3

9.28 8 46.4 34 5 8 0.68 3.4 3

9.81 9 49.05 37 5 9 0.37 1.85 3

10 10 50 40 5 10 0 0 3

9.79 11 48.95 43 5 11 -0.43 -2.15 3

9.12 12 45.6 46 5 12 -0.92 -4.6 3

Q = L + A L^2 -B L^3

FIRST ORDER DERIVATIVE

DATA

MPL =1 + 2 A L - 3 B L^2

OUTPUT FUNCTION

An Exercise

PRICE

PRICE 9 WAGE 3 LET OUTPUT = Q

OUTPUT 1 F 10 REVENUE

REVENUE 9 LABOUR 1 A 10 AQ -B Q^2

COST 13 B 1 MARGINAL REVENUE

PROFIT MR = A-2BQ

C 0.1

D 0.01

OUTPUT LABOUR REVENUE COST MR LABOUR MPL MR *MPL WAGE

0 0 0 10 10 0 1 10 3

1.09 1 9.7119 13 7.82 1 1.17 9.1494 3

2.32 2 17.8176 16 5.36 2 1.28 6.8608 3

3.63 3 23.1231 19 2.74 3 1.33 3.6442 3

4.96 4 24.9984 22 0.08 4 1.32 0.1056 3

6.25 5 23.4375 25 -2.5 5 1.25 -3.125 3

7.44 6 19.0464 28 -4.88 6 1.12 -5.4656 3

8.47 7 12.9591 31 -6.94 7 0.93 -6.4542 3

9.28 8 6.6816 34 -8.56 8 0.68 -5.8208 3

9.81 9 1.8639 37 -9.62 9 0.37 -3.5594 3

10 10 0 40 -10 10 0 0 3

PRICE = A-B OUTPUT

DATA

OUTPUT FUNCTION FIRST ORDER DERIVATIVE

Q = L + C L^2 -D L^3

MPL =1 + 2 A L - 3 B L^2

When product and labour market are competitive

0

1

2

3

4

5

6

7

0 5 10 15

PR

ICE

*MP

L =

VM

P

LABOUR

PRICE *MPL

WAGE

While product market is imperfectly competitive, labour

market is perfectly competitive

-4

-2

0

2

4

6

8

10

12

0 1 2 3 4 5 6

MR

*MP

L

LABOUR

MR *MPL

WAGE

Both product and labour markets are imperfectly competitive

-4

-2

0

2

4

6

8

10

12

0 1 2 3 4 5 6

MR

P,M

E,A

E

LABOUR

MRP

ME

AE

Demand for Labour

(Longrun)

Production Function

max Q = f(E, K)

Subject to C ≥ wE + rK

Q = Output – Raw Material = Value Added

C = Cost, w = Wage rate , r = Rate of interest

E = Labour, K = Capital

Production Function

Z = f(K, E) + λ (C- wE - rK)

𝟃 Z/ 𝟃 K = (𝟃Q/ 𝟃K)- r = 0

𝟃 Z/ 𝟃 E = (𝟃Q/ 𝟃E)- w = 0

𝟃 Z/ 𝟃 λ = C- wE - rK = 0

𝟃Q/ 𝟃K = MPk ; 𝟃Q/ 𝟃E = MPe

MPk = Marginal Product of Capital

MPe = Marginal Product of Labour

MPe/MPk = w/r (generating equilibrium E, K, and Q)

Production Function: an example

Let Q = KE

Z = KE + λ (C- wE - rK)

𝟃 Z/ 𝟃 K = E- r = 0

𝟃 Z/ 𝟃 E = K- w = 0

𝟃 Z/ 𝟃 λ = C-wE-rK = 0

K/E = w/r ; K = E (w/r),

E = K (r/w) (Demand function of labour)

Thank you