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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 relationship
               Labor Demand in Dollars and Numbers
                          W = 26 - 2*N

  30
  25
  20                           Slope = -2 =(ΔW)/(ΔN)
$ 15
  10
   5
   0
       0   1   2   3   4   5    6   7    8   9   10   11   12   13
                               Numbers
                 Labor Demand in Hours and Cents
                          C = 2600 - 25H

      3000
      2500
      2000                              Slope = -25 =(ΔW)/(ΔN)
Cents 1500
      1000
       500
         0
             0       20         40        60         80     100         120
                                        Hours




                 Slopes are sensitive to the units
                 Need a unit free measure of labor demand sensitivity
          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

     9               8           72            800
      >9.5      7<
    10               6           80            600
     11              4            88             400
     12              2            96             200
                    Labor Demand in Dollars and Numbers
                               W = 26 - 2*N

       30
       25
                                    Slope = -2
       20
     $ 15
ΔW=2   10
 W 7 5
        0
            0   1   2   3   4   5    6    7      8   9   10    11   12   13
                                    Numbers          ΔN=1
                                                     N  9.5

     N   W 
        /     =(1/9.5) / (2/7) = |-.368|
      N   W 
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
                                  >76 700<
    10              6            80       600
     11              4            88             400
     12              2            96             200
                     Labor Demand in Hours and Cents
                              C = 2600 - 25H

          3000
          2500
          2000                           Slope = -25
    Cents 1500
ΔW=200 1000
W  700 500
             0
                 0      20      40         60          80    100   120
                                         Hours     ΔN=8
                                                   N  76
         N   W 
            /            =(8/76) / (200/700) = |-.368|
          N   W 
 Relationship between demand slope and
                 elasticity




                           N   W 
    Own wage elasticity =     /     
                           N   W 
Slope of demand curve is
(ΔW)/(ΔN)                  N   W 
                         =    / 
                           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
                                    As the demand slope
Elasticity = |(1/slope)*(W/N)| =>   gets bigger , the
                                    demand elasticity
 W                       4          gets smaller




                                          3

                                          2


                                     1
                                                N
  Relationship between demand slope and
                  elasticity
                                     Extremes: 3: slope = 0
Elasticity = |(1/slope)*(W/N)|       ηNN
 W                       4




                                      3

                                      2


                                 1
                                            N
  Relationship between demand slope and
                  elasticity
                                       Extremes: 3: slope = 0
Elasticity = |(1/slope)*(W/N)|         ηNN
 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)|       Extremes: 4: slope = -
                                     ηNN = 0
 W                       4




                                            Perfectly nelastic
                                        3

                                        2


                                 1
                                                N
  Relationship between demand slope and
                  elasticity

Elasticity = |(1/slope)*(W/N)|
 W                       4               Relatively Inelastic
                                         Demand




                                     3      Relatively
                                            Elastic Demand
                                     2


                                 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                    N

Change in wage bill
Relatively Inelastic demand, Δ(W*N) = W1N2 – W0N0
Relatively Elastic demand, Δ(W*N) = W1N1 – W0N0
      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         Bigger
Relatively Elastic demand, Δ(W*N) = W1N1 – W0N0
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      10
                                       W

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 substitutes if as the price of
  K rises, the quantity of N demanded rises

                  ηNK = ΔN           Δr
                                        >0
                         N           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          Δr
                                      <0
                        N          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            1985            1990        1995   2000
                                                                       Year
    Estimated own and cross price elasticities between capital,
               labor and human capital per worker
                                                  Price of
                                                           Human
                            Physical            Numbers of Capital per
    Demand for              Capital             Workers    Worker
    Physical Capital             -0.45             1.07              -0.11
    Numbers of
                                 0.66              -1.44              0.15
    Workers
    Human Capital
                                 -0.15             0.35              -0.13
    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):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       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

				
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