# Topic 4 Labor Demand by qv98Vk7G

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ECN706

TOPIC 4

THE DEMAND FOR
LABOUR
2

Objectives
• To analyse the part played by labour in the firm’s
production function.
• To define the marginal product of labour and capital
and analyse how they impact on firm’s production
decision and profit maximisation.
• To define Value of Marginal Product and Marginal
Revenue Product and derive the short run labour
demand curve
• To use isocost-isoquant analysis to derive the long-
run labour demand curve.
• To analyse the firm’s decision to an optimal
combination of inputs to maximise profits
3

Objectives
• To distinguish between the short run and long
run demand for labour.
• To explain the scale and substitution effects of a
change in input prices.
• To define and calculate elasticity, cross elasticity
and elasticity of substitution between factor
inputs.
• To analyse the demand for labour when the
product market is not competitive.
• To discuss how adjustment costs impact labour
employment.
4

Introduction

• Firms hire workers because consumers want to
purchase a variety of goods and services
• Demand for workers is derived from the wants
and desires of consumers
• Central questions: how many workers are hired
and how much should they be paid?
5

The Firm’s Production Function

• Describes the technical relationship between the
firm’s uses of inputs in the production of output:
q = f (E, K)
• The firm’s output is produced by any
combination of capital and labor
• Assumption:
“All labor and capital are assumed to be
homogenous”.
6

The Firm’s Production Function

• The marginal product of labor is the change in
output resulting from hiring an additional
worker, holding constant the quantities of other
inputs
• The marginal product of capital is the change in
output resulting from hiring one additional unit
of capital, holding constant the quantities of
other inputs
7

Production Function

• Marginal products of labor and capital are
positive, so as more units of each are hired,
output increases
• When firms hire more workers, total product
rises
• The slope of the total product curve is the
marginal product of labor
8

Production Function
• Law of Diminishing Returns: eventually, the
marginal product of labor declines
▫ Average Product: the amount of output produced
by the typical worker
• measured by the amount of total output divided
by the number of workers used in the production
of that output
• Marginal Product and Average Product of Labor
(holding K constant)
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The Total Product, the Marginal Product,
and the Average Product Curves
140                                             25

120                                                                      Average Product
20
100

Output
Output

80                                             15

60               Total Product
10
Curve
40
5
20                                                          Marginal Product

0                                              0
0   2   4   6    8    10    12                 0   2     4     6     8    10    12

Number of Workers                              Number of Workers

The total product curve gives the relationship between output and the
number of workers hired by the firm (holding capital fixed). The
marginal product curve gives the output produced by each additional
worker, and the average product curve gives the output per worker.
10

Profit Maximization

• Objective of the firm is to maximize profits
• The profit function is:
▫ Profits = pq – wE – rK
▫ Total Revenue = pq
▫ Total Costs = (wE + rk)
• Perfectly competitive firm cannot influence
prices of output or inputs
11

Short Run Hiring Decision –the Short
Run Demand for Labor

• Value of Marginal Product of labor (VMP) is the
dollar value of what each additional worker
produces:

VMP = p x MP

• This indicates the benefit derived from hiring an
12

Short Run Hiring Decision –the Short
Run Demand for Labor
• Value of Average Product is the dollar value of
output per worker:

VAP = p x AP

• Note: For a perfectly competitive firm, the VMP of
labor is equivalent to the Marginal Revenue
Product (MRP) which is the increase (change) in
total revenue resulting from the employment of
•
So the VMP schedule (Figure 4.2) in slide 15 is also
the perfectly competitive firm’s MRP schedule.
13

Firm’s Hiring Decision in the
Short Run
• What is the logic underlying the equality of VMP and
MRP where perfect competition prevails in the
product market?
• Because the competitive firm is a price taker, it can
sell as many units of output as it desires at the
market price (= \$2). The sale of each additional unit
of the product adds the product price (= \$2) to the
firm’s total revenue;
• MR = p (constant)
• the extra revenue to the firm from employing an
additional labour unit (MRP = MR x MP) equals the
value of the extra output (VMP = p x MP)
14

Firm’s Hiring Decision in the Short
Run
Firms should hire the number of workers to the point
the value of extra production from hiring of the last
worker (VMP) equals the wage rate (w) and the
value of marginal product curve is downward
sloping :

VMP = w
15

The Firm's Hiring Decision
in the Short-Run - Fig 4.2

38
A profit-maximizing
firm hires workers up
VAPE                 to the point where the
wage rate equals the
22
value of marginal
VMPE                 product of labor. If the
wage is \$22, the firm
hires eight workers.
8    Number of Workers
1   4
16

The Firm’s Short Run Labor Demand
Curve
• The short-run demand curve for labour is meant to
tell what happens to the firm’s employment decision
as the wage changes, holding capital constant.
Therefore, the VMP schedule and the curve is
the firm’s short run labour demand curve.
• It indicates the amount of labour this firm would
demand at separate competitively determined wage
rates.
17

The Firm’s Short Run Labor Demand
Curve
• The demand curve for labor indicates how the firm
reacts to wage changes, holding capital constant
• The curve is downward sloping
• Because of the Law of Diminishing Returns
(marginal and average production declines) and
therefore VMP decline as more workers are hired
• So if the firm is to employ more workers, the wage
must fall
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The Short-Run Demand Curve for Labor

Because marginal product
eventually declines, the
short-run demand curve for
labor is downward sloping.
A drop in the wage from
22
\$22 to \$18 increases the
18
firm’s employment. An
increase in the price of the
VMPE
output shifts the value of
VMPE
marginal product curve
upward, and increases
8   9          12                       employment.
Number of Workers
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Maximizing Profits: A General Rule
• The profit maximizing firm should produce up to
the point where the cost of producing an
additional unit of output (marginal cost) is equal
to the revenue obtained from selling that output
(marginal revenue)
• Marginal Productivity Condition: this is the
hiring rule, hire labor up to the point when the
cost of hiring the worker (i.e., the wage)
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The Mathematics of Marginal
Productivity Theory
• The cost of producing an extra unit of output:
▫ MC = w x 1/MPe
• The condition: produce to the point when MC =
P (for the competitive firm, P = MR)
▫ w x 1/MPe = P
▫ w = P x MPe
▫ w = VMP
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The Mathematics of Marginal
Productivity Theory
• The firm’s hiring decision:

E*: VMP=w is the same as the firm’s output
decision:

q: P (MR) = MC
22

The Short-Run Demand Curve
for the Industry

Wage                              Wage

T

D
20                                20

10                                10
D

T

15   28 30   Employment                  30   56 60 Employment
23

The Employment Decision in
the Long Run
• In the long run, the firm maximizes profits by
choosing how many workers to hire AND how
much plant and equipment to invest in

• Isoquant:
describes the possible combinations of labor and
capital that produce the same level of output
(the curve “ISOlates the QUANTity of output).
24

The Employment Decision in
the Long Run
• Isoquants…
▫ Must be downward sloping
▫ Do not intersect
▫ Higher isoquants indicate more output
▫ Are convex to the origin
▫ Have a slope that is the negative of the ratio of the
marginal products of capital and labor
▫ MPÉ/MPκ
▫ The value of this slope is called the marginal
rate of technical substitution.
25

Isoquant Curves
Capital

All capital-labor
combinations that lie along
a single isoquant produce
the same level of output.
X
The input combinations at
K                                   points X and Y produce q0
Y
q1
units of output. Input
q0
combinations that lie on
higher isoquants produce
more output.
E                 Employment
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Isocost

• The Isocost line indicates the possible
combinations of labor and capital the firm can
hire given a specified budget
• Isocost indicates equally costly combinations of
inputs
• Higher isocost lines indicate higher costs
27

Isocost Lines
Capital

All capital-labor
C1/r                                          combinations that lie along
a single isocost curve are
Isocost with Cost Outlay C1
C0/r                                          equally costly. Capital-labor
combinations that lie on a
Isocost with Cost Outlay C0
higher isocost curve are
more costly. The slope of an
isoquant equals the ratio of
input prices (-w/r).
C0/w      C1/w       Employment
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Cost Minimization

• Profit maximization implies cost minimization
• The firm chooses a least cost combination of
capital and labor
• This least cost choice is where the isocost line is
tangent to the isoquant
• Marginal rate of substitution equals the price
ratio of capital to labor
• MPE/MPκ = w/r
29

The Firm's Optimal Combination
of Inputs
Capital
A firm minimizes the costs of
C1/r
producing q0 units of output
A                                   by using the capital-labor
C0/r
combination at point P,
where the isoquant is tangent
to the isocost. All other
P
175                                             capital-labor combinations
(such as those given by
B                     points A and B) lie on a
q0
higher isocost curve.
100                Employment
30

The Firm's Optimal Combination
of Inputs
• Cost Minimisation therefore requires that marginal
rate of technical substitution (MPE/MPκ) equal the
ratio of input prices (w/r)
• MPE/w = MPκ/r
• MPE/w gives the output yield of the last dollar
spent on labor.
• MPκ/r gives the output yield of the last dollar spend
on capital.
31

The Firm's Optimal Combination
of Inputs
• Cost Minimisation requires that the last dollar
spent on labor yield as much output as the last
dollar spent on capital.
• Since, we constrain the firm to produce qo units of
output. The firm must produce this level of output
(qo) in a cost minimizing way in order to maximise
profits.
32

The Firm's Optimal Combination
of Inputs
• Long-run Profit max:

w = P x MPE and r = P x MPK

• Profit –maximizing conditions imply cost
minimization

• Note that the ratios of the two marginal
productivity conditions implies that the ratio of
input prices equals the ratio of marginal
products
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Long Run Demand for Labor

•    Consider firm producing profit maximising qo
(qo*: MC = P [MR=P] and

Firm is minimising costs:

(K*,L*: MPE/MPK = w/r)

•    WHAT HAPPENS TO THE FIRM’S LONG
RUN DEMAND FOR LABOUR WHEN WAGE
CHANGES?
34

Long Run Demand for Labor

•     If the wage rate drops, two effects take place:
i) Firm takes advantage of the lower price of
labor by expanding production (scale
effect)
Scale Effect- the change in employment and
output resulting solely from the effect of
the wage change on the employers’ cost
outlays
35

Long Run Demand for Labor

(ii) Firm takes advantage of the wage change
by rearranging its mix of inputs (while
holding output constant; substitution effect)

• Substitution Effect- the change in employment
and input mix resulting solely from the change
in the relative price of labor, output held
constant
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The Impact of A Wage Reduction, Holding
Constant Initial Cost Outlay at Co
Capital

A wage reduction flattens the
isocost curve. If the firm were to
C0/r
hold the initial cost outlay
constant at C0 dollars, the
isocost would rotate around C0
R
75              P                                               and the firm would move from
point P to point R. A profit-

q0                   maximizing firm, however, will
not generally want to hold the
q0                    cost outlay constant when the
Wage is w0
Wage is w1   wage changes.

25       40
37
The Impact of a Wage Reduction on the
Output and
Employment of a Profit-Maximizing Firm
Dollars                                Capital

MC0      MC1

p                                                              R
P

150

100
100        150    Output             25       50       Employment

•A wage cut reduces the marginal cost of production and encourages the firm
to expand (from producing 100 to 150 units).
•The firm moves from point P to point R, increasing the number of workers
hired from 25 to 50.
38

Substitution and Scale Effects
Capital
A wage cut generates
D
substitution and scale effects.
C1/r
The scale effect (the move from
Q                                              point P to point Q) encourages
C0/r                                                                 the firm to expand, increasing
R
the firm’s employment. The
P                                                       substitution effect (from Q to
200
R) encourages the firm to use a
D
more labor-intensive method of
production, further increasing
100
employment.
Wage is w1
Wage is w0

25       40       50                                Employment
39

The Short- and Long-Run Demand
Curves for Labor
Dollars

Short-Run
Demand Curve                      In the long run, the firm can
economic opportunities
introduced by a change in
Long-Run
Demand Curve       the wage. As a result, the
long-run demand curve is
more elastic than the short-
run demand curve.
Employment
40

Elasticity of Substitution

• Intuitively, elasticity of substitution is the
percentage change in capital to labor (a ratio)
given a percentage change in the input price
ratio (wages to real interest)
• %∆K/L%∆w/r
• This is the percentage change in the capital:labor
ratio given a 1% change in the relative price of
the inputs
41

Elasticity of Substitution

• For eg as the relative price of labour (w/r) increases,
substitution effect tells us the that K/L ratio increases
(firm replaces labour with capital)
• Elasticity of substitution measures the curvature of the
isoquant.
• When two inputs can be substituted at a constant rate
(MRTS is constant), the two inputs are called perfect
substitutes ;isoquant is linear: σ = α (infinite)
• The substitution effect is large when the two inputs are
perfect substitutes
42

Elasticity of Substitution
• If σ = 0, there would be no change in the relative
amounts of K and L when there is a change in the
relative input prices w/r. The isoquant is right
angled and therefore inputs are perfect
complements in production
• There is no substitution effect when the inputs are
perfect complements (since both inputs are
required for production)
• If σ = 3, a 1% rise in the relative price of labor
(w/r) would lead to a 3% rise in the K/L ratio. The
isoquant is strictly convex and inputs are
substitutes in production.
43
Isoquants: When inputs are either
perfect substitutes or perfect
complements
Capital                             Capital

100

q 0 Isoquant                     q 0 Isoquant
5

200 Employment        20                    Employment

Capital and labor are perfect substitutes if the isoquant is linear (so that two
workers can always be substituted for one machine). The two inputs are perfect
complements if the isoquant is right-angled. The firm then gets the same output
when it hires 5 machines and 20 workers as when it hires 5 machines and 25
workers.
44

Factor Demand with Many Inputs

• There are many different inputs and categories
of workers
▫ Skilled and unskilled labor
▫ Old and young
▫ Old and new machines
What will happen to the demand for unskilled
labour if the price of skilled labour increases?
45

Factor Demand with Many Inputs

• Cross-elasticity of factor demand:
• Gives the percentage change in the demand for
input i resulting from a 1% change in the price of
input j

% Δ Li
ηij=
% Δ wj
46

Factor Demand with Many Inputs
• ηij > 0 – if the price of unskilled labor (j) rises, the
employer will consequently use more skilled labor
(i); inputs i and j are said to be substitutes in
production
• ηij < 0 – if the price of factor (j) rises, the
employer would use less of factor (i).
▫ two inputs are complements in production
47

The Demand Curve for a Factor of Production
is Affected by the Prices of Other Inputs
Price of                                Price of
input i                                 input i

(a)
(b)

D1                                      D0
D0                                      D1

Employment of                           Employment of
input i                                 input i

The labor demand curve for input i shifts when the price of another input changes.
(a) If the price of a substitutable input rises, the demand curve for input i shifts up.
(b) If the price of a complement rises, the demand curve for input i shifts down.
48

Marshall’s Rules –Determinants of
Elasticity
• Labor Demand is more elastic when:
▫ Elasticity of substitution is greater
▫ Elasticity of demand for the firm’s output is
greater
▫ The greater labor’s share in total costs of
production
▫ The greater the supply elasticity of other factors of
production (such as capital)
49

The Demand for Labor in Non
competitive Product Market
• What is the logic underlying the equality of VMP
and MRP where perfect competition prevails in
the product market?
• Because the competitive firm is a price taker, it
can sell as many units of output as it desires at
the market price (= \$2). The sale of each
price (= \$2) to the firm’s total revenue;
• MR = p (constant)
• the extra revenue to the firm from employing an
additional labor unit (MRP = MR x MP) equals
the value of the extra output (VMP = p x MP)
50

The Demand for Labor in Non
competitive Product Market
• Because of product uniqueness or
differentiation, the imperfectly competitive
seller’s product demand curve is downward
sloping rather than perfectly elastic. This means
that the firm must lower its price to sell the
output contributed by each successive worker.
• It must lower the price not only on the last unit
produced but also on all other units which would
otherwise have commanded a higher price.
• The sale of an extra unit of output therefore does
not add its full price to the firm’s marginal
revenue.
51

The Demand for Labor in Non
competitive Product Market

• Because the marginal revenue is les than the
product price, the imperfectly competitive sellers
Marginal Revenue Product is less than that of
the perfectly competitive seller .
• Recall that perfectly competitive firm suffers no
decline in marginal revenue as it sells the extra
52

The Demand for Labor in Non
competitive Product Market
• To see how the demand for labor would change if
the product market is non-competitive, let’s turns
to an example.
• The MRP or labor demand curve of the purely
competitive seller falls for a single reason –
marginal product diminishes as more units of labor
are employed.
• But the MRP or labor demand of the imperfectly
competitive seller declines for two reasons –
marginal product falls as more units of labor are
employed and product price declines as output
increases.
53

The Demand for Labor in Non
competitive Product Market
The lower price accompanying each increase in
output applies not only to the output produced by
each additional worker but also to all prior units
that otherwise could have been sold at a higher
price.
For example, the 5th worker’s marginal product is 12
units, and these 12 units can be sold at \$2.40 each
(\$28.80).
54

The Demand for Labor in Non
competitive Product Market
• This is the value of VMP- value of added output
from the society’s perspective. But the MRP of the
5th worker is only \$25.80.
• Why the \$3.00 difference? Because in order to sell
the 12 units associated with the 5th worker, the firm
must accept a \$0.20 price cut on each of the 15 units
produced by the previous workers – units that could
have been sold for \$2.60 each. Thus, the MRP of the
5th worker is only (\$25.80) [\$28.80 – (15x 0.20)].
• So for a firm in non-competitive product market,
the VMP no longer measures the true worth of the
marginal worker but the MRP.
55

The Demand for Labor in Non
competitive Product Market

Therefore, for a non competitive seller the
application of the MRP = w rule to the MRP will
yield the conclusion that the MRP curve is the
imperfectly competitive seller’s labour demand
curve.
56

The Demand for Labor in Non
competitive Product Market
• Comparing the MRP curves, all else being equal, the
imperfectly competitive sellers labor demand curve is
less elastic than that of a purely competitive seller.
Thus a firm that has monopoly power is less
responsive to wage rate changes.
• This is merely the labor market reflection of the firm’s
reduction in output in the product market (as
compared to perfectly competitive seller).
• In producing less output, the seller with monopoly
power will employ fewer workers.
• Therefore, the marginal revenue accruing to an
imperfectly competitive seller from hiring an
additional unit of labor is less then the market value of
the extra output the unit of labor helps produce [(MRP
= MR x MP) < (VMP = P x MP).
57

THE END

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