Example of linear demand with different measures
Numbers
Wage ($)
Hours
Wage (Cents)
1
24
8
2400
2
22
16
2200
3
20
24
2000
4
18
32
1800
5
16
40
1600
6
14
48
1400
7
12
56
1200
8
10
64
1000
9
8
72
800
10
6
80
600
11
4
88
400
12
2
96
200
Same relationship
Labor Demand in Dollars and Numbers
W = 26 - 2*N
30
25
20
$ 15
10
5
0
Slope = -2 =(ΔW)/(ΔN)
0
1
2
3
4
5
6
7
Numbers
8
9
10
11
12
13
Labor Demand in Hours and Cents
C = 2600 - 25H
3000
2500
2000
Cents 1500
1000
500
0
Slope = -25 =(ΔW)/(ΔN)
0
20
40
60
80
100
Hours
Slopes are sensitive to the units
Need a unit free measure of labor demand sensitivity
120
Computing the elasticity
Own wage elasticity of demand for labor:
Percentage change in labor demand caused by
a 1% change in the wage
• N: labor
• W: wage
N
% change in labor =
N
W
% change in wage =
W
Computing the elasticity
Own wage elasticity of demand for labor:
Percentage change in labor demand caused by
a 1% change in the wage
 N   W 
Own wage elasticity = 
/

 N   W 
 N   W 
Units cancel
=
/ 
 W   N 
Example of linear demand with different measures
Numbers
Wage ($)
Hours
Wage (Cents)
1
24
8
2400
2
22
16
2200
3
20
24
2000
4
18
32
1800
5
16
40
1600
6
14
48
1400
7
12
56
1200
8
10
64
1000
8
72
800
6
80
600
11
4
88
400
12
2
96
200
9
>9.5
10
7<
Labor Demand in Dollars and Numbers
W = 26 - 2*N
30
25
Slope = -2
20
$ 15
10
ΔW=2
W 7 5
0
0
1
2
3
4
5
6
7
Numbers
 N   W 

/
 =(1/9.5) / (2/7) = |-.368|
N

  W 
8
9
10
ΔN=1
N  9.5
11
12
13
Example of linear demand with different measures
Numbers
Wage ($)
Hours
Wage (Cents)
1
24
8
2400
2
22
16
2200
3
20
24
2000
4
18
32
1800
5
16
40
1600
6
14
48
1400
7
12
56
1200
8
10
64
1000
9
8
10
6
11
4
88
400
12
2
96
200
72
800
>76 700<
80
600
Labor Demand in Hours and Cents
C = 2600 - 25H
3000
2500
2000
Cents 1500
ΔW=200 1000
W  700 500
0
Slope = -25
0
20
40
60
Hours
 N   W 

/

N

  W 
80
ΔN=8
N  76
=(8/76) / (200/700) = |-.368|
100
120
Relationship between demand slope and
elasticity
 N   W 
Own wage elasticity = 
/

 N   W 
Slope of demand curve is
 N   W 
(ΔW)/(ΔN)
=
/ 
 W   N 
Relationship between demand slope and
elasticity
 N   W 
Own wage elasticity = 
/

 N   W 
Elasticity = |(1/slope)*(W/N)|
 N   W 
=
/ 
 W   N 
Relationship between demand slope and
elasticity
Elasticity = |(1/slope)*(W/N)| =>
W
4
As the demand slope
gets bigger , the
demand elasticity
gets smaller
3
2
1
N
Relationship between demand slope and
elasticity
Extremes: 3: slope = 0
ηNN
Elasticity = |(1/slope)*(W/N)|
W
4
3
2
1
N
Relationship between demand slope and
elasticity
Extremes: 3: slope = 0
ηNN
Elasticity = |(1/slope)*(W/N)|
W
4
Perfectly E
lastic
3
2
1
N
Relationship between demand slope and
elasticity
Elasticity = |(1/slope)*(W/N)|
W
4
Extremes: 4: slope = ηNN = 0
3
2
1
N
Relationship between demand slope and
elasticity
Elasticity = |(1/slope)*(W/N)|
W
Extremes: 4: slope = ηNN = 0
4
3
Perfectly nelastic
2
1
N
Relationship between demand slope and
elasticity
Elasticity = |(1/slope)*(W/N)|
W
4
Relatively Inelastic
Demand
3
2
Relatively
Elastic Demand
1
N
If you are a union representative, which
demand curve would you want?
W
4
Aim: Maximize the wage bill = W*N
3
2
1
N
Labor demand elasticity and the wage bill
Labor demand: N: number of workers; W: Wage
W
W1
W0
Demand
N1
N0
N
Wage Bill = W*N; Change in wage bill = W1N1 – W0N0
Labor demand elasticity and the wage bill
W
Relatively Inelastic
Demand
W1
W0
Relatively
Elastic Demand
N1 N2 N0
Change in wage bill
Relatively Inelastic demand, Δ(W*N) = W1N2 – W0N0
Relatively Elastic demand, Δ(W*N) = W1N1 – W0N0
N
Labor demand elasticity and the wage bill
W
Relatively Inelastic
Demand
W1
W0
Relatively
Elastic Demand
N1 N2 N0
N
Change in wage bill
Relatively Inelastic demand, Δ(W*N) = W1N2 – W0N0
Relatively Elastic demand, Δ(W*N) = W1N1 – W0N0
Bigger
Precise relationship between demand
elasticity and the wage bill
ED = Elasticity of demand =
% change in employment
% change in wage
0 < ED < 1: inelastic demand
ED = 1: unitary elastic demand
ED > 1: elastic demand
Wage increase with inelastic demand will raise the
wage bill
Wage increase with elastic demand will lower the
wage bill
EXAMPLE
ED = Elasticity of demand = 0.3 < 1, inelastic
% change in employment = 3%
% change in wage = 10%
W1 = W0 (1.10)
N1 = N0 (0.97)
Change in wage bill = W1N1 – W0N0
= W0 (1.10)* N0 (0.97) - W0N0
= 0.067*W0N0
So wage bill rises when wage rises when the elasticity of demand is
below 1.
.
Demand Schedule Estimated as N = 10 - 1*W
12
10
8
(ΔN)/(ΔW) = -1
N
.
6
.
(W = 6; N = 4)
4
2
0
0
2
4
6
8
W
Point Elasticity: [(ΔN)/(ΔW)]*(W/N) = | (-1)*(6/4) |
= 1.5
10
Cross price elasticity of demand
Cross-price elasticity of demand for labor: Percentage
change in labor demand caused by a 1% change in the
price of another input
Two inputs N and K are gross substitutes if as the price of
K rises, the quantity of N demanded rises
ηNK = ΔN
N
Δr
>0
r
Cross price elasticity of demand
Cross-price elasticity of demand for labor: Percentage
change in labor demand caused by a 1% change in the
price of another input
Two inputs N and K are gross complements if as the price
of K rises, the quantity of N demanded falls
ηNK = ΔN
N
Δr
<0
r
Price of IT
Indexes of Computer Price and Business Capital Stock, 1960-1996
Source: Ruttan, Technology, Growth and Development: An Induced Innovation Perspective . 2001
Index
400
350
300
250
200
Capital Stock
150
100
50
Price
0
1955
1960
1965
1970
1975
1980
Year
1985
1990
1995
2000
Estimated own and cross price elasticities between capital,
labor and human capital per worker
Price of
Demand for
Physical Capital
Numbers of
Workers
Human Capital
per Worker
Red: Complements;
Physical
Capital
Human
Numbers of Capital per
Workers
Worker
-0.45
1.07
-0.11
0.66
-1.44
0.15
-0.15
0.35
-0.13
Blue: Substitutes
Note: Based on share-weighted elasticities of substitution reported in Table 6 of Huang.
Hallam, Orazem and Paterno, "Empirical Tests of Efficiency Wage Models."Economica
65 (February 1998):125-143.
Laws of Derived Demand:
Relating the size of the scale and the substitution
effects to the own wage elasticity of demand
1) The more elastic is the demand for
the product, the more elastic is the
demand for labor.
Union affiliation of employed wage and salary workers by industry,
2002
Members
Private wage and salary
workers
Mining
Construction
Manufacturing
Transportation and public
utilities.
Wholesale and retail trade
Finance, insurance, real
estate
Services
Government workers
Source: Bureau of Labor Statistics
Covered
8.5
8.5
17.2
14.3
9.3
10.0
17.8
15.1
23.0
4.5
24.3
4.9
1.9
5.7
37.5
2.5
6.7
42
Source: OECD, Employment Outlook, 2004.
Laws of Derived Demand:
Relating the size of the scale and the substitution
effects to the own wage elasticity of demand
2) The more substitutable are other inputs
for labor, the more elastic is the demand
for labor
3) The more readily available are
substitutes for labor, the more elastic is
the demand for labor
Laws of Derived Demand:
Relating the size of the scale and the substitution
effects to the own wage elasticity of demand
4) ‘The importance of being unimportant’
The greater is labor’s share of total cost,
the greater is the elasticity of demand for
labor