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Introduction to Labor Economics


									Labor Demand

   Chapter 4
Labor Demand Questions
Which workers should a firm hire?
How many workers should a firm hire? How
much capital?
How will firms respond to employment
How should firms respond to policy changes
such as minimum wages, affirmative action,
    Production Function
Describes the technology used to produce goods
and services
   q = f(E,K) where
      q = output
      E = number of employee hours hired
         = number of workers x average hours per worker
      K = capital – land, machines, other physical inputs
      Assume homogenous workers (ignore education, etc)

   Output is a function of the number of employee hours
    hired by the firm and the quantity of capital employed
Production Function, cont.
Recall: q = f(E,K)
Marginal Product:

   MPE =

   MPK =

   MP = slope of total product curve
        Interpretation:
    Production Function Example
E   q    MPE   APE   VMPE
0   0                         MPE 
1   10                              E
2   22
3   33                         APE 
4   41                               E
5   48                      VMPE  P  MPE
6   53                            let P 3
7   56
     Example, cont.
0   0   -   -    -
1   10 10  10   30
2   22 12  11   36
3   33 11  11   33
4   41  8 10.25 24
5   48  7  9.6  21
6   53  5 8.83  15
7   56  3   8   9
    Production Function Characteristics
TP increases rapidly, then at a decreasing rate
   When TP increases at an increasing rate, MP
   When TP increases at a decreasing rate, MP
   When TP decreases, MP
Law of Diminishing Marginal Returns:

MP, AP relationship
   AP increases when MP AP
   AP decreases when MP AP
   MP = AP at
    Short Run Employment Decision

Firms goal:                             where
 w = cost of hiring an additional worker
                                            taken as given
 r = price of capital                      for PC firms
 p = output price

Short run:

E*: Choose E* such that
   VMPE=P·MPE 
   SR Employment Decision Example
                Let w = $32, P=$3
E TP VMPE   π   If E = 2, VMP = $33, but
0 0    -        w = $32, so 3rd worker
1 10  30
                If E = 3, VMP = $24, but
2 22  36        w = $32, so 4th worker
3 33  33
                w = $32 falls between
4 41  24        VMP(E=1)=30 and VMP(E=2)=36,
5 48  21
                If law of diminishing MP did not
6 53  15        hold, E* would have no bounds, so
                diminishing MP ensures firm can-
7 56  9         not influence market                9
    SR Employment Decision, cont.
 APE increases when MPE APE
 APE decreases when MPE APE
 MPE = APE at

VAPE = P∙APE is a “blown-up” version of APE,
 E* only valid if
 If VMP(E*) = w > VAP(E*),
   Individual Firm Demand Curve
     E       0    1 2           3    4    5    6    7
    VMP      -    30 36         33   24   21   15   9
Demand curve: Allow price
(wage) to vary and determine
how many employees the
firm demands
If w = $15, E* =
If w = $21, E* =
If w = $24, E* =
SR demand curve for labor is:

Individual Firm Demand Curve, cont.
                VMP curve drawn for a particular
                price, so when output price
                changes, VMP (labor demand)
                curve shifts

                Positive relationship between P
                and the short-run demand for labor
                    Capital costs (r) constant, and when
                     P↑, revenue ↑
                    Firms only increase E* when revenue
                     from new worker exceeds cost of
                     worker (VMP > w)
    Labor Market Demand Curve

Recall: Market labor supply curve derived by

Market Demand Curve
   Roughly

   Caveat:

Labor Market Demand Curve, cont.
Because of the caveat, the true labor market demand curve is
______ than the horizontal sum of individual demand curves

Profit Maximization Approach
Recall: Profit maximizing firms choose q* such
that MR = MC, where
MC         and MR          and TC 
For a fixed K (short run condition),
MC 

For a PC firm, P = MR, so operating at MR = MC

    Objections to MP Theory
   MP Theory: Choose E* such that w = VMPE
   E* implies q* based on the production function
Employers do not really calculate VMPE and find where
w = VMPE

Adding employees to the production process while
holding K constant will not increase marginal productivity
Elasticity of SR Labor Demand
How responsive is labor demand to changes in wages?

               SR 

__________ (by definition): When wages increase, firms
demand ______ workers

   Elastic (_____ responsive) when |δSR| 1
   Inelastic (_____ responsive) when |δSR| 1

    Long Run Employment Decision
Long run:

   The firm can choose E* and K*

   Note: “iso” = equal, “quant”
    derived from quantity, so isoquant =
    “equal quantity”
Characteristics of Isoquants
                  Do not intersect

                  Higher isoquants represent
                  _______ levels of output
                  Convex to the origin
                     When E is large, a _____ ∆K
                      could replace many workers
                      and maintain the same q
                     When E is small, a _____ ∆K
                      would be required to maintain
                      the same q
Characteristics of Isoquants, cont.
              Slope: Move from point X to Y
                 Gain:
                 Loss:
                 To remain on the same isoquant, MPE∙∆E
                  + MPK∙∆K = 0
              Slope = Marginal Rate of Technical
              Substitution (MRTS)
                 Interpretation:

                 Convexity implies diminishing MRTS

   Isocosts (Constraint)

Isocosts further away from
the origin imply _____ costs
Cost = wE + rK
K 
  Slope     
           E                  21
    Profit Max/Cost Min
Profit max  Cost min
   Choose q* and produce at the
    lowest cost (isocost closest to
    origin) combination of K, E
   Isocost-Isoquant tangency:
             MPE      w
                 
             MPK      r
        MPE MPK
          
         w   r

   Profit Max/Cost Min, cont.
To profit max, firms choose q* such that MR=MC,
then choose K* and E* to minimize costs
Recall: MR = MC implied w = P∙MPE;
analogously, it also implies r = P∙MPK
      P      and P       


Therefore, profit max implies cost min       23
Profit Max/Cost Min, cont.
So far, profit maximization implies cost minimization
Does cost minimization imply profit maximization?

Profit maximization Cost minimization, but
Cost minimization Profit maximization
    Long Run Demand Curve for Labor
Recall: Demand curve is derived
by allowing price (wage) to vary
and determine how many
employees the firm demands
Suppose initially, q*=q0 with C=C0
and w=w0
Cost effect of w↓
   If w↓, firm may buy more labor and
    incur C=C0,

   If C↑ to C1, holding constant r, the
    entire budget line
Long Run Demand Curve for Labor
                Cost effect of w↓, cont.
                   With new cost (C1), new
                    intercept =
                Production effect of w↓
                   When w↓, MC of production
                    likely ________ (additional
                    cost of producing one more
                    unit )
                   With _MC, MR _ MC at q0, so
                    firm responds by _q
                When w↓, E*_, K*_
    Scale and Substitution Effects
So far, we’ve seen that when wages decrease, production
costs (MC) __crease, so firms have an incentive to
__crease production and hire _____ workers (E* )
Substitution Effect
   Capital is now a relatively ______________ input, so firms
    SUBSTITUTE away from ________ and toward a more
    _______-intensive production process (K* and E* )
Scale Effect (eliminates the change in relative prices)
   When firms produce more output (because of decreased MC of
    production), they may hire _____ employees and _____ capital
    simply because the SCALE of production changes (K* and
    E* )                                                      27
      Decomposing the Scale
      and Substitution Effects
To isolate the scale effect, draw
a hypothetical isocost with same
slope as original isocost and
tangent to new isoquant
   Scale Effect: __ to __
   Substitution Effect: __ to __
As drawn, ___________ effect
dominates, and K*
Note: Scale and substitution
effects both suggest E*_, but the
dominant effect determines how
K* changes
    Long Run Demand Curve for Labor
Recall: Both scale and
substitution effects suggest
E*_ when w↓
   Scale effect: When q↑, firm
    demands more K and more E
   Substitution effect: Firms
    demand more of the relatively
    less expensive input when w↓
Therefore, the LR demand
curve for labor is _________
sloping (E*_ when w↓)
       Elasticity of Labor Demand
         %E LR E LR w 1
 LR           LR 
          %w    E1   w
δLR _ 0 because of the ______
relationship between w and E
δLR vs δSR: δLR _ δSR because
firms can be more responsive
to wage changes with fewer
constraints (K not fixed in the
long run)
Therfore, the LR demand
curve for labor is ______ than
the SR demand curve curve
for labor
    Elasticity of Labor Demand
Short-run elasticity of labor demand:
   -0.5 < δSR < -0.4

Long-run elasticity of labor demand:
   δLR ≈ -1

   1/3 due to the substitution effect, 2/3 due to the
    scale effect                                         31
      Elasticity of Substitution
Perfect Substitutes
   Here, 2K = 1E
   Recall: Convexity of a “normal”
    isoquant implied

   Here, inputs can be substituted
    at a ___________ rate
   _________ substitution effect
        One of the two extremes will be
         chosen (K = 100 OR E = 50,
         depending upon w and r)
      Elasticity of Substitution, cont.
Perfect Complements
   If E = 5, K = 5, can produce
    just as much output as E = 5
    and K = 25
   To increase output, must add

   Always use ____________
    for q0, regardless of w and r
   _____ substitution effect
    (___ substitutability) between
    K and E

    Elasticity of Substitution, cont.

Elasticity of Substitution=                   _0

   Measure of

   When labor becomes relatively more expensive (w/r)↑,
    relatively ______ capital will be used (K/E)
   Large elasticity of substitution means firms are _________
    responsive to changes in relative input prices
   More curved isoquants have _______ elasticities of
Policy Application: Affirmative Action

Affirmative action encourages firms to alter
the race, ethnicity, or gender of workforce by
hiring relatively more of the workers typically
under-represented in past hiring
 Two types of inputs – black and white workers
 Black and white workers may have different
  education levels, skills, etc.
 wB = black wage, wW = white wage

Policy Application, cont.
                 Case 1
                     Note: Intercepts suggest
                      wW _ wB
                     Point _ would be profit-
                      maximizing (cost-minimizing)
                      for a “color blind”, non-
                      discriminating firm
                     A discriminating firm might
                      choose point _ to have fewer
                      black employees
                     A fine-tuned AA program

Policy Application, cont.
                 Case 2
                     Note: Again, intercepts suggest wW
                      > wB
                     Firm may be non-discriminating
                      and still hire relatively more whites
                      (point _), perhaps because of
                      productivity differences, etc.
                     An AA program may force the firm
                      to hire relatively more blacks (point
                      _), which is no longer profit-
                 Therefore, AA programs may
                 improve profitability if the firm is
                 ________________, but will
                 reduce profits if firms are _____
                 __________________              37
Marshallian Rules of Derived Demand

Derived Demand:

   What happens in the market for the good itself directly
    influences demand for labor (for instance, when P
    changes, VMPE (DE) shifts)
Marshallian rules describe factors which are likely to
generate an elastic demand for labor
    Marshallian Rules of Derived Demand

Rule 1: Greater elasticity of substitution between
labor and capital (less curved isoquants)

Rule 2: Greater elasticity of demand for output
   When wages ↑, the MC of production ↑, so supply ↓
    and output P↑

    Marshallian Rules of Derived Demand

Rule 3: Greater labor’s share of total costs of
   When labor is a large share of production costs, a
    wage change has a substantial impact on MC, on
    market supply (of output), and ultimately, on P

     Marshallian Rules of Derived Demand
Rule 4: Greater supply elasticity of other inputs to
   When w↑, the firm will want to

   If the price of that input increases dramatically when more is
    demanded, the incentive to replace labor with other inputs is
   If the supply of the other input is ________ (relatively _____
    supply curve), the increase in demand will result in only a
    moderate price increase, so firms will be more likely to make
    substantial changes in the relative share of inputs in the production
    Factor Demand with many inputs
So far, q =f(E,K)
Can add to the production function different types of workers,
machines, etc.
   q = f(x1,x2,…,xi,…xm) where
        xi = quantity of input i
   xi* determined by: wi=P∙MPi where
        wi = cost per unit of input i (wage, rental rate, etc)
Results in the 2-input case hold in this more general set-up
Empirically, labor demand for unskilled workers is more elastic
than the demand for skilled workers  Labor market much more
unstable for unskilled workers
   Cross-Price Elasticity of Demand
How does the demand for input i (xi) respond to a change
in the price of input j (wj)?
Cross-price elasticity of input demand
                       0 if inputs are
       X  P       
                       0 if inputs are
If inputs are substitutes (ηX-P _ 0), demand curve for
input i shifts _____ in response to an increase in the price
of good j)  ____________ effect dominates
If inputs are complements (ηX-P _ 0), demand curve for
input i shifts _____ in response to an increase in the price
of good j)  ___________ effect dominates                 43
    Empirical Evidence
Skilled and unskilled labor
   Empirically, skilled and unskilled labor are _________ (ηX-P _ 0)
Unskilled labor and capital
   Empirically, unskilled labor and capital are ________ (ηX-P _ 0)
   Cross-price elasticity of input demand ≈ 0.5
Skilled labor and capital
   Empirically, skilled labor and capital are __________ (ηX-P _ 0)
   Cross-price elasticity of input demand ≈ -0.5

Labor Market Equilibrium
                Intersection of supply,
                demand defines (E*,w*)
                If w > w*, QS _ QD
                 competition drives w_
                to w*
                If w < w*, QS _ QD
                 competition for
                workers drives w_ to w*
      Application: Minimum Wages
Fair Labor Standards Act
   Established in 1938
   Created a minimum wage,
    established overtime laws, child
    labor laws, etc.
Minimum wage: price ______
on wages (min w _ w*)
Higher wage has two effects

Unemployed =
Application: Minimum Wages, cont.
                  Recall: UR 
                  With minimum wage,

                     Depends upon minimum
                      wage, elasticities of S, D
                     UR higher when S, D more
                      ________ (______ curves)
                       suggests firms and/or
                      workers are responsive to
                      wage changes
Application: Minimum Wages, cont.

Empirical Evidence
   Approximately 40% of workers who qualify for
    minimum wage are not paid it
      Firms that are caught can delay paying a portion of
       payroll for two years (like an interest-free loan) and
       typically do not pay fines
      Not all workers work in sectors covered by the
       minimum wage law (~10% in 1990)

   Application: Minimum Wage, cont.

Workers in covered sector displaced by the minimum wage may
move to the uncovered sector.
The equilibrium wage in the uncovered sector would __crease.
Note that the wage in the covered sector would also __crease due
to ________ workers supplying their services to that market (not
   Application: Minimum Wage, cont.

Workers in uncovered sector may leave their current jobs to try to
find new work in the covered sector to take advantage of minimum
The equilibrium wage in the uncovered sector would __crease.
Note that the wage in the covered sector would also __crease due
to an _________ in the number of workers supplying their services
to that market (not shown).                                      50
    Application: Minimum Wage, cont.
Wages will eventually equate in the two sectors (covered
and uncovered)
E(wC) = πwmin + (1- π)(0) =       , where
   π = probability of holding a job in the covered sector
E(wU) = wU
When wages equate, E(wC) = E(wU)
Pattern of migration (movement from covered sector to
uncovered sector, or vice versa) will depend upon π, such
as the average tenure at jobs in the covered sector, etc.
    Application: Minimum Wage, cont.
Empirical Evidence
   In 1987,
        1/3 of workers age 16-19 earned w ≤ wmin
        5% over the age of 25 earned w ≤ wmin
   Elasticity of teenage employment with regard to changes in the
    minimum wage is between -0.1 and -0.3, and the minimum wage
    rose 27% ($3.35  $4.25) between 1990 and 1991
        If the elasticity were -0.15, teenage employment would have decreased by
   More recent studies using fast food restaurants find no impact of
    the minimum wage on teenage employment
   Minimum wage laws may not effectively help poor families
        Many teenagers affected by the law are themselves poor, but may not come
         from families in need

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