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