Example of linear demand with different measures NumbersWage ($)HoursWage (Cents) Same relationship

=(ΔW)/(ΔN)

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

Own wage elasticity of demand for labor: Percentage change in labor demand caused by a 1% change in the wage Units cancel

Example of linear demand with different measures NumbersWage ($)HoursWage (Cents) <>9.5

ΔW=2 ΔN=1 =(1/9.5) / (2/7) = |-.368|

Example of linear demand with different measures NumbersWage ($)HoursWage (Cents) >76700<

ΔW=200 ΔN=8 =(8/76) / (200/700) = |-.368|

Relationship between demand slope and elasticity Slope of demand curve is (ΔW)/(ΔN)

Relationship between demand slope and elasticity Elasticity = |(1/slope)*(W/N)|

Relationship between demand slope and elasticity Elasticity = |(1/slope)*(W/N)| => As the demand slope gets bigger, the demand elasticity gets smaller N W

Relationship between demand slope and elasticity Elasticity = |(1/slope)*(W/N)| N W Extremes: 3: slope = 0 η NN

Relationship between demand slope and elasticity Elasticity = |(1/slope)*(W/N)| N W Extremes: 3: slope = 0 η NN Perfectly Elastic

Relationship between demand slope and elasticity Elasticity = |(1/slope)*(W/N)| N W Extremes: 4: slope = - η NN = 0

Relationship between demand slope and elasticity Elasticity = |(1/slope)*(W/N)| N W Extremes: 4: slope = - η NN = 0 Perfectly nelastic

Relationship between demand slope and elasticity Elasticity = |(1/slope)*(W/N)| N W Relatively Inelastic Demand Relatively Elastic Demand

If you are a union representative, which demand curve would you want? N W 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 W1W1 W0W0 N1N1 N0N0 Wage Bill = W*N; Change in wage bill = W 1 N 1 – W 0 N 0

Labor demand elasticity and the wage bill Relatively Inelastic Demand N W W1W1 W0W0 N1N1 N0N0 Change in wage bill Relatively Inelastic demand, Δ(W*N) = W 1 N 2 – W 0 N 0 Relatively Elastic demand, Δ(W*N) = W 1 N 1 – W 0 N 0 Relatively Elastic Demand N2N2

Labor demand elasticity and the wage bill Relatively Inelastic Demand N W W1W1 W0W0 N1N1 N0N0 Change in wage bill Relatively Inelastic demand, Δ(W*N) = W 1 N 2 – W 0 N 0 Relatively Elastic demand, Δ(W*N) = W 1 N 1 – W 0 N 0 Relatively Elastic Demand N2N2 Bigger

Precise relationship between demand elasticity and the wage bill E D = Elasticity of demand = % change in employment % change in wage 0 < E D < 1: inelastic demand E D = 1: unitary elastic demand E D > 1: elastic demand Wage increase with inelastic demand will raise the wage bill Wage increase with elastic demand will lower the wage bill

EXAMPLE E D = Elasticity of demand = 0.3 < 1, inelastic % change in employment = 3% % change in wage = 10% W 1 = W 0 (1.10) N 1 = N 0 (0.97) Change in wage bill = W 1 N 1 – W 0 N 0 = W 0 (1.10)* N 0 (0.97) - W 0 N 0 = 0.067*W 0 N 0 So wage bill rises when wage rises when the elasticity of demand is below 1.

(ΔN)/(ΔW) = -1 (W = 6; 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 gross substitutes Two inputs N and K are gross substitutes if as the price of K rises, the quantity of N demanded rises η NK = 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 gross complements Two inputs N and K are gross complements if as the price of K rises, the quantity of N demanded falls η NK = ΔN Δr N r <0

Price of IT

Demand for Price of Physical Capital Numbers of Workers Human Capital per Worker Physical Capital Numbers of Workers Human Capital per Worker 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): 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.

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