Post on 09-Feb-2016
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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)
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