The Demand and Supply
of Factors of Production
Principles of Microeconomics
Professor Dalton
ECON 202 – Fall 2013
Boise State University
1
Input Prices and Employment
Input prices and their
employment in a market
economy depend on the
functioning of input markets –
the supply of and demand for
the various inputs.
2
The Market for an Input
Derived Demand
 The demand for labor
(and other factors of
production) is a
Derived Demand.
 A firm’s demand for a
factor of production is
derived from its
decision to supply a
good.
3
Production Theory
 Since the demand for inputs is a derived
demand, production theory is relevant
to our consideration of the demand for
inputs.
 Firms will face diminishing returns to
variable inputs, other inputs fixed, – as
output increases the marginal product of
variable factors diminishes.
4
Typology of Markets
 Product markets:
• Price-takers
• Price-searchers
 Input markets:
• (Input-price) “wage”-takers
• (Input-price) “wage”-searchers
5
Typology of Markets
 The four types of relevant factor markets:
• Price-taker, “wage”-taker market
• Price-searcher, “wage”-taker market
• Price-taker, “wage”-searcher market
• Price-searcher, “wage”-searcher
market
6
Output and Factor Markets
 In a Price-taker market the profitmaximizing firm chooses that output level
at which P = MR= MC.
 In a Price-searcher market the profitmaximizing firm chooses that output level
at which P > MR = MC.
 Given the same market demand for
output, a price-searcher market produces
less output.
7
Output and Factor Markets
 In a “Wage-taker” market the profitmaximizing firm has to take the market
price of inputs as given – it is such a small
employer of inputs that its actions alone
do not affect market price of the input.
 In a “Wage-searcher” market the
profit-maximizing firm alters the market
price of inputs as its own demand for
inputs change – it is a large employer of
those inputs.
8
Price-Taker, Wage-Taker Behavior
 In a price-taker, wage-taker market as
firm output expands the marginal
productivity of inputs changes due to
greater employment, but the price of
inputs do not change.
 Changes in the Marginal Cost of
production are due solely to changes in
MP of inputs.
• Marginal costs rise as marginal productivity
falls.
9
The marginal cost [MC] is a “mirror” image of the MP function.
MPL
MPL x w
MPL x w
MPL
L
MC = 1 x w
MPL
$
MC
Q
10
Price-Taker, Wage-Taker Behavior
 The profit-maximizing output of a firm
occurs where Px = MCx, and MCx = w/MPL:
 Px = w/MPL or
 Px (MPL) = w
11
Price-Taker, Wage-Taker Behavior
Px (MPL) = w
 What does this equation mean?
• Px is the price that the output produced by the
input is sold for.
• MPL is the additional output produced when an
additional unit of the input is employed.
• w is the price (cost) of an additional unit of the
input.
12
Price-Taker, Wage-Taker Behavior
Px (MPL) = w
 What does this equation mean?
• Px (MPL) is the marginal benefit (in
dollar terms) from employing an
additional unit of labor.
• w is the marginal cost of employing an
additional unit of labor.
13
Price-Taker, Wage-Taker Behavior
Px (MPL) = w
 What does this equation mean?
• A firm employs an input until the marginal
benefit of employing the input equals the
marginal cost of employing the input.
• For a price-taking, wage-taking firm this occurs
where the Value of Marginal Product [VMPL
= Px (MPL) ] or Marginal Revenue Product
[MRPL = MRx (MPL)] equals the wage-rate.
14
Price-Taker, Wage-Taker Demand
Px (MPL) = w
 Since the firm is a wage-taker, as the
wage varies, the quantity of labor
demanded will vary.
 The demand curve for the firm (other
inputs constant) is the VMPL curve
(MRPL) curve of the firm.
15
Firm Demand for Labor
Price-taker, Wage-taker with other inputs fixed
wage
W2
W1
W3
MRPL = VMPL = dL
L2 L1
L3
Hours of Labor
16
Market Demand for Labor
Price-taker, Wage-taker
 It would seem natural to get the market demand curve
by simply summing the individual firm’s demand curves.
 Is the market demand for an input simply the horizontal
sum of the individual firm’s demand curves?
 NO.
 Why?
 When, for example, the wage decreases, an output
effect occurs – since it is cheaper to produce output (MC
falls), more output will be produced – AND BY ALL FIRMS!
 This means that the market supply increases and price
of output falls…
 Which means in turn that the firm’s demand curves for
input shift to the left (because MRPL) is now smaller!
17
Market Demand for Labor
Price-taker, Wage-taker
wage
firm
market
wage
W1
ΣdL
W2
dL
DL
dL2
L1
L2
I
L
ΣL1
L
ΣL2
18
Market Supply of Labor
 Determinants of
Market Labor
Supply
wage
market
S
• money wage rate (+)
• non-labor income (-)
• Price level
expectations (-)
L
19
Market Wage
 Market Wages are
determined by the
interaction of
market demand
and supply.
wage
market
S
w*
DL
L
20
Market Wage and Firm Employment
firm
wage
market
S
w*
dL
L*
DL
L
L
21
Determinants of
Labor Demand
 Determinants of Labor Demand
• real wage - law of demand
 (increase w reduces QDL)
• expected price of output - changes in the
price of output are positively related to
changes in labor demand
 (increase Px increases DL)
• productivity - changes in productivity are
positively related to changes in labor demand
 (increase productivity increases DL)
22
Labor Demand
Sources of Productivity Change
 Physical Capital : when workers work with a
larger quantity of equipment and structures,
they produce more.
 Human Capital : when workers are more
educated/better trained, they produce more.
 Technology : when workers have access to
more sophisticated technologies, they produce
more.
23
Labor-Market Equilibrium
Comparative Statics
w
SL(Pe0)
An increase in
productivity or
product prices...
w**
w
D 1L
DL
L*
L**
Labor
…increases the
demand for labor...
…increasing the
market wage...
…and increasing the
quantity of labor
employed.
24
Growth Rates in Productivity
and Real Earnings
Annual Growth Rate (%)
Productivity
Real Earnings
1960 - 1970
2.33
2.89
1970 - 1980
0.84
0.79
1980 - 1990
1.38
1.15
1990 - 2000
1.89
1.92
Observations
• Greater growth in labor productivity increases
the demand for labor and causes higher real
wage growth
25
Labor-Market Equilibrium
Comparative Statics
W
SL
S1L
w*
An decrease in nonlabor income or price
level expectations, or
increase in number of
workers...
…increases the supply
of labor...
w**
DL
L*
L**
Labor
…decreasing the
market wage...
…and increasing the
quantity of labor
employed.
26
Profit-maximizing Employment
 For a firm maximizing profits, the least
cost-combination of inputs must be
employed.
 The least cost condition occurs when:
MPK/r = MPL/w
27
Price-Taker, Wage-Taker Behavior
 A price-taker, wage-taker maximizes
profits when it employs resources
such that the MP per dollar spent per
resource is equal to the inverse of
the Marginal Cost of output (equal to
the inverse of the Price of output).
28
Profit-maximizing Employment
 Generalizing, the least-cost combination of
inputs occurs when:
MPK = MPL = MPa = MPb = … = MPn
r
w
Pa
Pb
Pn
29
Explaining the Trends in Real
Wages and Employment
 Why has the gap between the wages of
skilled and unskilled workers widened in
recent years?
30
The Effect of Globalization on the
Demand for Workers in Two Industries
Ssoftware
Real Wage
Stextiles
w’software
w
D’software
w’textiles
Dsoftware
Dtextiles
D’textiles
N’textiles
N textiles
Nsoftware
Employment
Importing industry
N’software
Employment
Exporting industry
Initially, wages are equal
Demand for workers in importing industry (textiles) declines, lowering wages and employment
Demand for workers in exporting industry (software) increases, raising wages and employment.
31
Explaining the Trends in Real
Wages and Employment
 Increasing Wage Inequality: The Effects of
Globalization
• When wages in “losing” industries fall and wages in
“winning” industries rise, wage inequality increases.
• Low-skill industries in the U.S. face the toughest
international competition. High-skill industries in the
U.S. tend to do the best in international competition.
• This relationship between low-skill and high-skill
industries exacerbates the wage inequality created by
increasing trade.
32
Explaining the Trends in Real
Wages and Employment
 Why has the gap between the wages of
less-skilled and higher-skilled workers
widened in recent years?
33
The Effect of Skill-Biased Technological
Change on Wage Inequality
Sskilled
Real Wage
Sunskilled
w’skilled
wunskilled
w’skilled
D’skilled
w’unskilled
Dskilled
Dunskilled
D’unskilled
N’unskilled
N unskilled
Employment
Unskilled workers
Nskilled
N’skilled
Employment
Skilled workers
Initially, wages are equal.
The increase in demand for skilled workers, due to technological change, raises their wages.
The demand for unskilled workers decreases and reduces their wages.
34
Typology of Markets
 The four types of relevant factor markets:
• Price-taker, “wage”-taker market
• Price-searcher, “wage”-taker market
• Price-taker, “wage”-searcher market
• Price-searcher, “wage”-searcher
market
35
Output and Factor Markets
 In a Price-taker market the profitmaximizing firm chooses that output level
at which P = MR= MC.
 In a Price-searcher market the profitmaximizing firm chooses that output level
at which P > MR = MC.
 Given the same market demand for
output, a price-searcher market produces
less output.
36
Output and Factor Markets
 In a “Wage-taker” market the profitmaximizing firm has to take the market
price of inputs as given – it is such a small
employer of inputs that its actions alone
do not affect market price of the input.
 In a “Wage-searcher” market the
profit-maximizing firm alters the market
price of inputs as its own demand for
inputs change – it is a large employer of
those inputs.
37
Price-Searcher, Wage-Taker Behavior
 In a price-searcher, wage-taker market as
firm output expands the marginal
productivity of inputs changes due to
greater employment, but the price of
inputs do not change.
 Changes in the Marginal Cost of
production are due solely to changes in
MP of inputs.
• Marginal costs rise as marginal productivity
falls.
38
Price-Searcher, Wage-Taker Behavior
 The profit-maximizing, least-cost combination of inputs remains:
MPK = MPL = MPa = MPb = 1 = 1
r
w
Pa
Pb
MCx MRx
39
Price-Searcher, Wage-Taker Behavior
 A price-searcher, wage-taker
maximizes profits when it employs
resources such that the MP per dollar
spent per resource is equal to the
inverse of the Marginal Cost of output
(equal to the inverse of the Marginal
Revenue of output).
40
Price-Searcher, Wage-Taker Behavior
MRx (MPL) = w
 What does this equation mean?
• MRx is the marginal revenue obtained from the
output produced by the input.
• MPL is the additional output produced when an
additional unit of the input is employed.
• w is the price (cost) of an additional unit of the
input.
41
Price-Searcher, Wage-Taker Behavior
MRx (MPL) = w
 What does this equation mean?
• MRx (MPL) is the marginal benefit (in
dollar terms) from employing an
additional unit of labor.
• w is the marginal cost of employing an
additional unit of labor.
42
Price-Searcher, Wage-Taker Behavior
MRx (MPL) = w
 What does this equation mean?
• A firm employs an input until the marginal
benefit of employing the input equals the
marginal cost of employing the input.
• For a price-taking, wage-taking firm this occurs
where the Marginal Revenue Product [MRPL
= MRx (MPL)] equals the wage-rate.
43
Price-Searcher, Wage-Taker Demand
MRx (MPL) = w
 Since the firm is a wage-taker, as the
wage varies, the quantity of labor
demanded will vary.
 The demand curve for the firm (other
inputs constant) is the MRPL curve of
the firm.
44
Firm Demand for Labor
Price-searcher, Wage-taker with other inputs fixed
wage
W2
W1
W3
MRPL = dL
L2 L1
L3
Hours of Labor
45
Market Demand for Labor
Price-searcher, Wage-taker
 It would seem natural to get the market demand curve
by simply summing the individual firm’s demand curves.
 Is the market demand for an input simply the horizontal
sum of the individual firm’s demand curves?
 NO.
 Why?
 When, for example, the wage decreases, an output
effect occurs – since it is cheaper to produce output (MC
falls), more output will be produced – AND BY ALL FIRMS!
 This means that the market supply increases and price
of output falls…
 Which means in turn that the firm’s demand curves for
input shift to the left (because MRPL) is now smaller!
46
Market Demand for Labor
Price-searcher, Wage-taker
wage
firm
market
wage
W1
ΣdL
W2
dL
DL
dL2
L1
L2
I
L
ΣL1
L
ΣL2
47
Marshall’s Laws of Derived
Demand
 The demand for a factor of production is
more elastic when
• demand for the final product is more elastic
• the degree of substitutability with other
inputs is higher
• the supply of other factors is more elastic
48
Typology of Markets
 The four types of relevant factor markets:
• Price-taker, “wage”-taker market
• Price-searcher, “wage”-taker market
• Price-taker, “wage”-searcher market
• Price-searcher, “wage”-searcher
market
49
Wage-Searcher Factor Markets
 In a “Wage-searcher” market the
profit-maximizing firm alters the market
price of inputs as its own demand for
inputs change – it is a large employer of
those inputs.
50
Wage-Searcher Factor Markets
 What is the consequence of being a
wage-searcher on the cost of employing
additional units of labor?
 Let’s take the extreme case of wagesearcher activity – a monopsony.
• A monopsony is a single buyer of an item – in
this context a monopsony is the only buyer
of labor.
51
Monopsony Factor Markets
 If the firm is a
monopsony it
faces the
entire
Wage
rate
SL
market
supply curve
of labor.
Hrs. Labor
52
Monopsony Factor Markets
 If the firm
wants to hire H0
hours of labor, it
has to pay w0
per hour.
 If the firm
wants to hire H1
hours of labor it
has to pay w1
per hour.
Wage
rate
SL
w1
w0
H0 H1
Hrs. Labor
53
Monopsony Factor Markets
 What happens to the
marginal cost of hiring
labor (marginal
factor cost) in this
situation?
 When the additional
labor is hired, the firm
not only has to pay w1
to the additional labor,
but also has to
increase the wage
paid to “previous”
units of labor from w0
to w1 also.
Wage
rate
SL
w1
w0
H0 H1
Hrs. Labor
54
Monopsony Factor Markets
 Suppose that H1 = 11
and H0 = 10, and w1
= $10 and w0 = $9 .
 When H1 is hired, the
marginal factor cost of
hiring the 11th hour of
labor is the $10 paid
for the 11th hour plus
the $1 that has to be
paid for each of the
previous 10 hours ( =
$10) so that the
marginal factor cost =
$20!
Wage
rate
SL
$20
$10
$9
H0 H1
Hrs. Labor
55
Monopsony Factor Markets
 For a monopsony
(and for a wagesearcher in
general) the
marginal factor
cost curve will lie
everywhere above
the supply curve of
labor…
MFCL
Wage
rate
SL
$20
$10
$9
H0 H1
Hrs. Labor
56
Monopsony Factor Markets
 … because when a the
amount of labor is
increased the cost of
hiring labor increases
due to 2 reasons – (1)
having to pay a higher
wage to induce
additional labor to be
employed and (2)
having to pay a higher
wage to previous
units.
MFCL
Wage
rate
SL
$20
$10
$9
H0 H1
Hrs. Labor
57
Monopsony Factor Markets
MFC > w
for a
wagesearcher
MFCL
Wage
rate
SL
$20
$10
$9
H0 H1
Hrs. Labor
58
Output and Factor Markets
 In a Price-taker market the profitmaximizing firm chooses that output level
at which P = MR= MC.
 In a Price-searcher market the profitmaximizing firm chooses that output level
at which P > MR = MC.
59
Price-Taker, Wage-Searcher Behavior
 A price-taker’s marginal benefit from
hiring additional labor is the VMPL.
 If the price-taker is also a wage-searcher,
it’s marginal cost of hiring additional labor
is it’s MFCL.
 A price-taker, wage-searcher hires that
amount of labor where VMPL = MFCL.
60
Firm Demand for Labor
Price-taker, Wage-searcher with other inputs fixed
MFCL
wage
SL
MFC = VMP
determines L
L determines w
as read off S
w*
VMPL = dL
L*
Hours of Labor
61
Price-Searcher, Wage-Searcher
Behavior
 A price-searcher’s marginal benefit from
hiring additional labor is the MRPL (and
MR < P).
 If the price-taker is also a wage-searcher,
it’s marginal cost of hiring additional labor
is it’s MFCL.
 A price-taker, wage-searcher hires that
amount of labor where MRPL = MFCL.
62
Firm Demand for Labor
Price-searcher, Wage-searcher with other inputs fixed
MFCL
wage
SL
MFC = MRP
determines L
L determines w
as read off S
VMPL
w*
MRPL = dL
L*
Hours of Labor
63
Comparing Outcomes
with other inputs fixed – the short run
wage
MFCL
SL
In a PTWT market,
VMP = w
wPTWT
wPTWS
In a PTWS market,
VMP = MFC
wPSWS
VMPL In a PSWS market,
MRP = MFC
MRPL
LPSWS LPTWS LPTWT
Hours of Labor
64
Comparing Outcomes
with other inputs fixed – the short run
• Price-searcher behavior reduces the
employment of inputs below that
which a price-taker would employ,
certeris paribus, because MR < P
(marginal benefits are lower).
• Wage-searcher behavior reduces the
employment of inputs below that
which a wage-taker would employ,
ceteris paribus, because MFC > w
(marginal costs are higher).
65