Same relationship
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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 relationshipSame relationship
Labor Demand in Dollars and NumbersW = 26 - 2*N
05
101520
2530
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Numbers
$
Slope = -2 =(ΔW)/(ΔN)
Labor Demand in Hours and CentsC = 2600 - 25H
0
500
1000
1500
2000
2500
3000
0 20 40 60 80 100 120
Hours
Cents
Slope = -25
Slopes are sensitive to the units
Need a unit free measure of labor demand sensitivity
=(ΔW)/(ΔN)
Own wage elasticity of demand for labor: Percentage change in labor demand caused by a 1% change in the wage
• N: labor
• W: wage
Computing the elasticity
N% change in labor =
NW
% 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 WOwn wage elasticity = /
N W
N W = /
W N
Units cancelUnits cancel
Example of linear demand with different measuresNumbers 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
99 88 72 800
1010 66 80 60011 4 88 400
12 2 96 200
7<>9.5
Labor Demand in Dollars and NumbersW = 26 - 2*N
0
5
10
15
20
25
30
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Numbers
$
Slope = -2
ΔW=2
ΔN=19.5N
7W
N W/
N W
=(1/9.5) / (2/7) = |-.368|
Example of linear demand with different measuresNumbers 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 7272 800800
10 6 8080 60060011 4 88 400
12 2 96 200
>76 700<
Labor Demand in Hours and CentsC = 2600 - 25H
0500
10001500200025003000
0 20 40 60 80 100 120
Hours
Cents
Slope = -25
ΔW=200
ΔN=8
=(8/76) / (200/700) = |-.368|
700W
76N N W
/N W
Relationship between demand slope and elasticity
N WOwn wage elasticity = /
N W
N W = /
W N
Slope of demand curve is Slope of demand curve is ((ΔΔW)/(W)/(ΔΔN)N)
Relationship between demand slope and elasticity
N WOwn wage elasticity = /
N W
N W = /
W N
Elasticity Elasticity = |(1/slope)*(W/N)|= |(1/slope)*(W/N)|
Relationship between demand slope and elasticity
Elasticity Elasticity = |(1/slope)*(W/N)| =>= |(1/slope)*(W/N)| =>As the demand slope As the demand slope gets bigger , the gets bigger , the demand elasticity demand elasticity gets smallergets smaller
N
W
1
2
3
4
Relationship between demand slope and elasticity
Elasticity Elasticity = |(1/slope)*(W/N)|= |(1/slope)*(W/N)|
N
W
1
2
3
4
Extremes: 3: slope = 0 Extremes: 3: slope = 0 ηηNN NN
Relationship between demand slope and elasticity
Elasticity Elasticity = |(1/slope)*(W/N)|= |(1/slope)*(W/N)|
N
W
1
2
3
4
Extremes: 3: slope = 0 Extremes: 3: slope = 0 ηηNN NN
Perfectly EPerfectly E lasticlastic
Relationship between demand slope and elasticity
Elasticity Elasticity = |(1/slope)*(W/N)|= |(1/slope)*(W/N)|
N
W
1
2
3
4
Extremes: 4: slope = -Extremes: 4: slope = -ηηNN NN = 0 = 0
Relationship between demand slope and elasticity
Elasticity Elasticity = |(1/slope)*(W/N)|= |(1/slope)*(W/N)|
N
W
1
2
3
4
Extremes: 4: slope = -Extremes: 4: slope = -ηηNN NN = 0 = 0
Perfectly nelasticPerfectly nelastic
Relationship between demand slope and elasticity
Elasticity Elasticity = |(1/slope)*(W/N)|= |(1/slope)*(W/N)|
N
W
1
2
3
4 Relatively Inelastic Demand
Relatively Elastic Demand
If you are a union representative, which demand curve would you want?
N
W
1
2
3
4
Aim: Maximize the wage bill = W*N
Labor demand elasticity and the wage bill
Labor demand: N: number of workers; W: Wage
Demand
N
W
W1
W0
N1 N0
Wage Bill = W*N; Change in wage bill = W1N1 – W0N0
Labor demand elasticity and the wage bill
Relatively Inelastic Demand
N
W
W1
W0
N1 N0
Change in wage bill
Relatively Inelastic demand, Δ(W*N) = W1N2 – W0N0
Relatively Elastic demand, Δ(W*N) = W1N1 – W0N0
Relatively Elastic Demand
N2
Labor demand elasticity and the wage bill
Relatively Inelastic Demand
N
W
W1
W0
N1 N0
Change in wage bill
Relatively Inelastic demand, Δ(W*N) = W1N2 – W0N0
Relatively Elastic demand, Δ(W*N) = W1N1 – W0N0
Relatively Elastic Demand
N2
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.
(ΔN)/(ΔW) = -1
Demand Schedule Estimated as N = 10 - 1*W
0
2
4
6
8
10
12
0 2 4 6 8 10
W
N .
.........
.
(W = 6; (W = 6; N = 4)N = 4)
Point Elasticity: [(ΔN)/(ΔW)]*(W/N) = | (-1)*(6/4) |
= 1.5
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 substitutesgross substitutes if as the price of K rises, the quantity of N demanded rises
ηNK = ΔN Δr
N r
>0
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 gross complements if as the price of K rises, the quantity of N demanded falls
ηNK = ΔN Δr
N r
<0
Price of IT Indexes of Computer Price and Business Capital Stock, 1960-1996
Source: Ruttan, Technology, Growth and Development: An Induced Innovation Perspective . 2001
0
50
100
150
200
250
300
350
400
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Year
Index
Price
Capital Stock
Demand for
Price of
Physical Capital
Numbers of Workers
Human Capital per Worker
Physical Capital -0.45 1.07 -0.11
Numbers of Workers
0.66 -1.44 0.15
Human Capital per Worker
-0.15 0.35 -0.13
Red: Complements; 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.
Estimated own and cross price elasticities between capital, labor and human capital per worker
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 Covered Private wage and salary workers 8.5 9.3 Mining 8.5 10.0 Construction 17.2 17.8 Manufacturing 14.3 15.1 Transportation and public utilities. 23.0 24.3 Wholesale and retail trade 4.5 4.9 Finance, insurance, real estate 1.9 2.5 Services 5.7 6.7 Government workers 37.5 42
Source: Bureau of Labor Statistics
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