# Introduction to Labor Economics

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```					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
subsidies?
How should firms respond to policy changes
such as minimum wages, affirmative action,
etc?
2
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
3
Production Function, cont.
Recall: q = f(E,K)
Marginal Product:

   MPE =

   MPK =

   MP = slope of total product curve
   Interpretation:
4
Production Function Example
E   q    MPE   APE   VMPE
q
0   0                         MPE 
1   10                              E
2   22
q
3   33                         APE 
4   41                               E
5   48                      VMPE  P  MPE

6   53                            let P 3
7   56
5
Example, cont.
E   q MPE APE VMPE
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
6
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
7
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 
8
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,
but
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.
Recall:
 APE increases when MPE APE
 APE decreases when MPE APE
 MPE = APE at

VAPE = P∙APE is a “blown-up” version of APE,
so
VMPE = VAPE at
 E* only valid if
 If VMP(E*) = w > VAP(E*),
10
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:

11
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)
12
Labor Market Demand Curve

Recall: Market labor supply curve derived by

Market Demand Curve
   Roughly

   Caveat:

13
Labor Market Demand Curve, cont.
Because of the caveat, the true labor market demand curve is
______ than the horizontal sum of individual demand curves

14
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),
ΔTC
MC 
Δq

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

15
Objections to MP Theory
Note:
   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
16
Elasticity of SR Labor Demand
How responsive is labor demand to changes in wages?

SR 

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

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

17
Long Run Employment Decision
Long run:

   The firm can choose E* and K*
Isoquants:

   Note: “iso” = equal, “quant”
derived from quantity, so isoquant =
“equal quantity”
18
Characteristics of Isoquants
Do not intersect
Downward-sloping

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
19
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

20
Isocosts (Constraint)
Isocosts:

Isocosts further away from
the origin imply _____ costs
Cost = wE + rK

K 
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

22
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
24
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
25
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
cost of producing one more
unit )
   With _MC, MR _ MC at q0, so
firm responds by _q
When w↓, E*_, K*_
26
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
28
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↓)
29
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
30
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)
32
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

33
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
substitution
34
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
Assume:
 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

35
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
could

36
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-
maximizing
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
38
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↑


39
Marshallian Rules of Derived Demand

Rule 3: Greater labor’s share of total costs of
production
   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


40
Marshallian Rules of Derived Demand
Rule 4: Greater supply elasticity of other inputs to
production
   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
process
41
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
42
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

44
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*
45
Application: Minimum Wages
Fair Labor Standards Act
(FLSA)
   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 =
46
Application: Minimum Wages, cont.
U
Recall: UR 
LF
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
47
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)

48
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
shown).
49
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
wage.
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.
51
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
240,000
   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
52

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