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Labor Demand

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					Labor Demand




               1
                      Labor Demand
• A firm’s decision about how much labor to use in production is
  driven by the firm’s desire to maximize profits.
    – Derived demand

• Firm’s thinking about whether to hire a worker
    –   Each worker can produce a certain amount to output per hour
    –   That output can be sold for money
    –   Thus, each worker generates a certain amount of revenue per hour.
    –   If that hourly revenue is greater than the hourly wage, then hire the
        worker.

• Just another way of saying marginal benefit must be greater than
  marginal cost

• Now let’s look at this formally.


                                                                                2
                     Labor Demand
•   Production Function: q=f(E,K)

•   Some variable definitions
     q = output
     E = labor
     K = capital

•   Example: q=E1/4K1/2

•   Marginal Product of Labor: Change in the physical output resulting
    from a hiring an additional worker.
      – MPE = Δq / ΔE
      – For our example: MPE = 1/4(E-3/4K1/2)
      – Note that the MPE is decreasing in labor
      – Intuition



                                                                         3
         Labor Demand

q                MPE




    E’       E         E’   E


                                4
    Profit Maximization in a Perfectly
           Competitive Market
•   Profits = pq-wE-rK
     w = wage rate
     r = price of capital
     p = price of output

•   Labor demand in the short run (capital is fixed)

•   Marginal Revenue: Change in revenue resulting from a one-unit increase
    in output.
      – In a perfectly competitive market: MR=p

•   Value of the Marginal Product of Labor: The additional revenue a firm
    receives from hiring an additional worker.
     – VMPE = p × MPE


                                                                             5
    Profit Maximization in a Perfectly
           Competitive Market

•   Marginal Cost of Labor            VMPE
     – MCE=w
                                             VMPE=p×MPE
•   Decision making rule of profit
    maximizing firm
     – VMPE>w hire more               w*
     – VMPE<w hire fewer
     – VMPE=w stop

•   Labor demand curve in the short
    run is the downward sloping
    portion of the VMPE curve.                        E*   E




                                                               6
                             Example
Variables
• q = K1/3L1/2
• w=2
• p = 12
• K = 8 (fixed)

How many hours of labor should the firm employ?
• Capital is fixed so we can re-write the production function as:

                              q = (8)1/3E1/2 = 2 E1/2

•   MPE = E-1/2
•   VMPE=12E-1/2
•   Profit Maximization: VMPE=w
                                    12E-1/2=2
                                     E1/2=6
                                     E*=36
                                                                    7
                 Hey Wait
Econ 1   Econ 139
p = MC   VMPE = w
         p × MPE = w

         MPE = Δq / ΔE

         Δq / ΔE : how much more output I can get from another unit
         of labor.

         ΔE / Δq: how much more labor I need to produce an
         additional unit of output.

         p × (Δq / ΔE) = w
         p = w × (ΔE / Δq) = MC (So it’s exactly the same thing)


                                                                   8
    Labor Demand in the Long Run
•   Two factors of production: capital and labor.
•   Both capital and labor can be varied.
•   Labor demand curve downward sloping in the long run too.
•   Demand for labor more responsive to wage changes in the long run.
              W




                                             DLR
                                     DSR
                                                   E                9
   Elasticity of Labor Demand
How sensitive is the quantity of labor demanded to a change in wages?

         w




                                             D

                                                 E

                                         E
                % change in employment
                                         E
                   % change in wage      w
                                            w                           10
          Diagram of Economy
     Many markets influence the labor market

             supply
 Land
Capital
            demand             supply
                                         Consumers
                      Firms
                               demand
             supply
Workers
            demand


                                                     11
    The Scale and Substitution Effects
•   How does a firm’s labor demand respond to changes in the price of labor?

•   Substitution effect: Describes how input demand changes as the relative
    price of the inputs changes, holding output fixed.
     – If labor becomes more expensive, you may want to substitute out of
        labor and into capital.

•   Scale effect: Describes how input demand changes as output changes,
    holding input prices fixed.
     – If labor becomes more expensive, you may have to scale back
        production.




                                                                               12
         Remember from Econ 1
                                                  MC2
         $                                               MC1




        p




                                                          q
                                         q2*   q1*

A wage increase will increase the marginal cost of producing an extra unit of
output. This will lead the firm to produce less.


                                                                                13
Summary of Scale and Substitution
            Effects

                Increase in the Decrease in the
                 Price of Labor Price of Labor
 Substitution   Quantity of labor   Quantity of labor
   Effect         demanded            demanded
                 DECREASES           INCREASES
 Scale Effect   Quantity of labor   Quantity of labor
                  demanded            demanded
                 DECREASES           INCREASES


                                                    14
  Marshall’s Four Rules of Derived Demand

Own-wage elasticity is high when:

RULE 1: Relates to the output market. When the price elasticity of
demand for the product is high, the scale effect is big.

            Output Market                          Output Market
           Price Elasticity of                P   Price Elasticity of
    P
            Demand is High                         Demand is Low
                                 S2                                     S2

                                  S1                                         S1




                                                                         D
                                      D
           Q2    Q1                       Q           Q2 Q1                       Q
                                                                                      15
    Marshall’s Four Rules of Derived
         Demand, Continued
RULE 2: Relates to the production technology. When the technology is such
that easy to substitute for labor in production, then the substitution effect is big.

                                                % change in K
                  Elasticity of substitution=                   L
                                                % change in w
                                                                r

       perfect                                                          perfect
    complements                                                       substitutes
                                 In most cases, inputs                elasticity of
     elasticity of               are somewhere in the
   substitution = 0                                                 substitution → ∞
                                        middle



RULE 3: When the cost of employing labor is a large share of total costs.
                                                                                   16
   Marshall’s Four Rules of Derived
        Demand, Continued
RULE 4: When the supply of other factors of production is highly
elastic, then the substitution effect is big. Increases in the demand for
capital do not drive the price of capital up.



                        r               Capital
                                        Market



                                                  S




                                                      D
                                                          K
                                                                            17
Changes in the Demand for Labor
     Wage




            Decrease     Increase

            in demand   in demand




                                    D

                                        Quantity


                                                   18
     Three Factors that Affect Labor Demand

1.   Change in the price of output. For example, this could happen if there
     were an increase in demand for the output.


            w
                                    Case of an increase in output prices.




                                                VMPE=p2 × MPE


                                             VMPE=p1 × MPE


                                                            E               19
       Factors that Affect Labor Demand

2.   Firm’s technology choice. For example, the firm could switch to a
     technology for which the marginal productivity in labor is higher.


          w
                                Case of an increase in the MPE




                                                VMPE=p × MPE’


                                              VMPE=p × MPE


                                                             E            20
           Factors that Affect Labor Demand

                                     Capital Market
3. Change in the price of        $               S2       S1
   other inputs. For example,
   this could happen if there                                       Supply decreases
   were a change in the
   supply of other inputs like                        D

   capital and labor.                            K                                Output Market
                                                                                                 S2
                                                                             $                        S1
                                               Substitution effect
   Example: Supply of                     (increases demand for labor)
   capital decreases.
   Ambiguous affect on                                                                                D
                                       Labor Demand
   the demand for labor.         $
                                                                                                      Q

                                                                           Scale effect
                                                                  (decreases demand for labor)
                                                 D

                                                      L

                                                                                                      21
Gross Substitutes and Gross Complements

                Labor demand         Labor demand
                  increases            decreases
 r increases   Gross substitutes   Gross complements
                  (SE>SCE)             (SE<SCE)

               Capital demand       Capital demand
                   increases           decreases
w increases    Gross substitutes   Gross complements
                  (SE>SCE)             (SE<SCE)

                                                       22
     Labor Demand When the Labor
    Market Is Not Perfectly Competitive
•    If a market is characterized by monopsony, it means that there are many
     sellers and only one buyer.

•    In the case of the labor market, it means that there’s only one firm that buys
     labor.
       – Prototypical example is a coal mine in a remote location.
       – However, the most important feature of a monopsony is that if they want
          to hire more workers, they can only do so by raising wages.

•    This could happen if there were a large number of employers but you also
     had
      – Mobility costs
      – Firms may to pay workers higher and higher wages as the firm gets
         bigger to prevent the workers from slacking off.


                                                                                 23
 Differences in Labor Supply Curves Under
   Perfectly Competition and Monopsony
                   Competitive
                                               Monopsony
          $        Labor Market         $
                                                               S


                                  S=W




                                    L                      L



Note: in this class, we will examine the case of a monopsonist who cannot
price discriminate. What does that mean?

It means that the monopsonist must pay all of it’s workers the same wage.
                                                                            24
     The Marginal Cost of Hiring For
            Monopsonists
•   Intuitively, profit maximization is the same for a monopsonist as it is for a
    perfectly competitive firm.

     – Each firm’s profit maximizing demand for labor is the quantity of labor
       such that: VMPE = MC of hiring a worker

•   However, the MC of hiring a worker will not be equal to w.
•   Why? Because when the monopsonist hires an additional unit of labor, it
    must increase the wages.

•   Example:
     – Labor supply curve: w=10+2E
     – 10 workers, w = 30     Total Cost = 10 × 30 = 300
     – 11 workers, w = 32     Total Cost = 11 × 32 = 352
     – Marginal Cost of 11th worker = 52
     – (=$32 for 11th worker plus $20 for extra $2 paid to 10 original workers)

                                                                                    25
    Graphically

w
             MCE



                   S




                       E
                           26
     Profit Maximization

w
                 MCE

                                   How do you draw the
                                   labor demand curve for
                           S       a monopsonist?

                                   The monopsonist
                                   simultaneously picks
w*                                 w* and E* so there is
                                   no labor demand curve
                                   for a monopsonist.
                    VMPE

       E*                      E
            VMPE = MCE                                  27
     Comparison with Perfect
         Competition
                                     In a monopsony, fewer
w
                        MCE          people are hired than in a
                                     perfectly competitive
                                     market and wages are
                                     lower.
                                 S
                                     This is because the
                                     marginal cost of hiring an
w*                                   additional worker is higher
w*                                   for a monopsonist than for
                                     a perfectly competitive firm.

                              VMPE   Workers worse off relative
                                     to perfectly competitive
         E*   E*                 E   labor market.

                   VMPE = MCE                                 28
 Monopsony in Professional Sports
• Sports owners are a small and interconnected group.

• Possibly can band together and act as monopsonists.

• Main issue here is that the owners can set wages—that is, wages
  are not determined by perfect competition.

• Two implications




                                                                    29
Salaries of Major League Baseball
       Players, 1876-1920




                                30
        Evidence on the Degree of
        Monopsonistic Exploitation
• If an employer is a monopsony, then workers are paid less than their
  marginal product

• How does a player’s marginal revenue product (or value of marginal
  product of labor) compare with that player’s salary?

• Two steps
   – Calculate how various measures of player performance affect a team’s
     winning percentage (MPE)
   – Calculate how a team’s winning percentage affects revenue (p)


• Estimates
   – Late 1960s: players paid 15-20% of VMPE.
   – Late 1980s: players paid 29-45% of VMPE.
   – Reserve clause effectively ends in 1976.

                                                                        31
Labor Demand Application:
  Minimum Wage Laws




                            32
             Minimum Wage Laws
Basic Facts
 Federal minimum wage is.
 California minimum wage is
 Not all sectors are covered.
    Farmworkers employed on small farms
    Employees of season recreational establishments
    Salespeople at automobile dealerships
 In 2001, 3.1 percent of workers earned at or below the Federal
  minimum wage, and 71 percent of those workers earned below
  $5.15 per hour.




                                                                   33
Value of the Federal Miniumum Wage
              (1970-2000)
        Nominal Min. Wage        Real Min Wage


 6.00
 5.00
 4.00
 3.00
 2.00
 1.00
 0.00
  70

        74

             78

                  82

                       86

                               90

                                    94

                                         98
 19

        19

             19

                  19

                       19

                            19

                                    19

                                         19
                        Year




                                                 34
          Minimum Wage Laws
Perfect Competition:                w

Minimum wages are a type
   of price floor.
                                                      S
Effectively change supply
   curve.                   min w

Decrease employment.          wC




                                                  D

                                        Emin EC           E
                                                              35
       Monopsony and Minimum Wages

  $       New MCE     MCE

                            S

                                Note that when minimum
                                wage laws are implemented in
                                a monopsonistic market, then

wmin
 w*


                       VMPE

            E* Emin    Employment
                                                           36
      Criticisms of the Minimum Wage
• It causes unemployment.
• It only helps teenagers.

• Are these criticisms valid?




                                       37
     Who Earns the Minimum Wage?
             (Age Groups)
 One third are
  teenagers.

 Almost one half
  are over the
  age of 25.




                                   38
      Who Earns the Minimum Wage?
       (Relationship in Household)
 About 25% are
  heads of a
  households.

 About 35% are
  children.




                                     39
          Who Earns the Minimum Wage?
               (Race and Gender)

Mostly women.
    63.7% of minimum wage earners are women.

Mostly White.
    80% of minimum wage earners are ―white‖.




                                                40
     What is the Effect of the Minimum
          Wage on Employment
Issues to consider:
1.    We observe employment and the timing of minimum wage
      increases.
2.    Looking at what happens in a small number of firms can be
      misleading.

                     McDonald’s                 KFC

                                  S                        S


       WMIN

          W



                             D                         D
                                                                   41
                                  E                            E
     What is the Effect of the Minimum
          Wage on Employment
3.    Other changes in the economy also affect employment.

            w
                                                 S

      min wage

             w0


                                                         D

                                                     D

                                                         E
                        Emin      E* E’
                                                             42
                  Need Variation!
Sources of Minimum Wage Variation:

            variation in the nominal and real value of the minimum wage

            variation in nominal and real minimum wage




                                                                           43
     Time Series Variation
Real Value of Minimum Wage and Average Wages of
         Manufacturing Production Workers




                                                  44
 Teenage Employment Rate With
Dates of Minimum Wage Changes




  Problem:


                            45
     Study by Card and Krueger
                       Study Design
Natural Experiment
• Ideally, we would randomize.

• Alternatively, we can look for ―natural experiments‖.
    Prior to April 1992, the minimum wage in NJ and PA is
      $4.25/hour
    April 1, 1992 NJ raises its minimum wage to $5.05/hour
    Other states nearby didn’t (for example, PA)




                                                              46
     Study by Card and Krueger
                     Data Collection

• Survey
    Burger King, Roy Rogers, KFC, Wendy’s etc.
    New Jersey and Pennsylvania
• Asked them number of full-time and part-time employees
• Before:
• After:




                                                           47
    Difference-in-Difference
           Estimation
   Number of Full-Time Equivalent       Non-
            supervisory Employees

                 NJ        PA       Difference
 March 1992     20.4      23.3
                 (A)       (B)
December 1992   21.0      21.2
                (C)       (D)
  Difference


                                             48
  Difference-in-Difference
         Estimation
Number of Full-Time Equivalent         Non-
         supervisory Employees
                Before     After   Difference
   NJ            20.4      21.0        .6
                  (A)      (B)       (B-A)
   PA            23.3      21.2       -2.1
                 (C)       (D)       (D-C)
Difference       2.9        .02
                (C-A)      (D-B)



                                                49
Suggests that employment
  Implications of Card and Krueger
                Study
• Suggests that the labor demand curve is upward sloping.

• Monopsony?




                                                            50
    Criticisms of the Card and Krueger
                    Study
•   No attempt to collect data on hours worked.
•   Big drop in employment in PA over 8 month time period.
•   Overall increase masks huge variation in both directions.
•   Hungry teenager theory




                                                                51

				
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