Download Introduction - National Tsing Hua University

Part 7
Further Topics
© 2006 Thomson Learning/South-Western
Chapter 15
Pricing in Input
Markets
© 2006 Thomson Learning/South-Western
Profit-Maximizing Behavior and
the Hiring of Inputs


3
A profit-maximizing firm will hire additional
units of any input up to the point at which
the additional revenue from hiring one
more unit is exactly equal to the cost of
hiring that unit.
Let MEK and MEL denote the marginal
expense of hiring capital and labor,
respectively.
Profit-Maximizing Behavior and
the Hiring of Inputs


Let MRK and MRL be the extra revenue that
hiring more units of capital and labor allows the
firm to bring in.
Profit maximizing behavior requires:
ME K  MRK
ME L  MRL .
4
15.1
Price-Taking Behavior

If the firm is a price taker in the capital and labor
market then it can always hire an extra unit of
capital at the prevailing rate (v) and an extra unit
of labor at the wage rate (w).
v  MEK  MRK
w  MEL  MRL .
5
15.2
Marginal Revenue Product



Marginal product is how much output the
additional input can produce.
Marginal revenue (MR) is the extra revenue
obtained from selling an additional unit of output.
Thus, the profit maximizing rules are:
v  ME K  MRK  MPK  MR
w  ME L  MRL  MPL  MR.
6
15.3
A Special Case--Marginal Value
Product


If the firm is also a price taking in the goods
market, marginal revenue equals the price (P) at
which the output sells.
The profit maximizing conditions become
v  MPK  P
w  MPL  P
7
15.3
Marginal Value Product

The marginal value product (MVP) of capital
and labor, respectively, are special cases of
marginal revenue product in which the firm is a
price taker for its output.
v  MVPK
w  MVPL
8
15.5
Responses to Changes in Input
Prices: Single Variable input Case



9
Assume the firm has fixed capital and can
only vary its labor input in the short run.
Labor will exhibit diminishing marginal
physical productivity so labor’s MVP will
decline as more labor is hired.
In Figure 15-1, the profit maximizing firm
will hire L1 labor hours when the wage rate
is w1.
FIGURE 15-1: Change in Labor Input
When Wage Falls: Single Variable Case
MVP
Wage
w1
w2
MVPL
0
10
L1
L2
Labor hours
Responses to Changes in Input
Prices: Single Variable input Case

If the wage rate falls to w2 the firm hires
increased labor out to L2.


11
If the firm continued to hire L1 it would not
be maximizing profit since labor would be
capable of producing more in additional
revenue than hiring additional labor would
cost.
With one variable input, diminishing
marginal productivity results in a
downward sloping demand curve.
TABLE 15-1: Hamburger Heaven’s ProfitMaximizing Hiring Decision
12
Labor
Input
per Hour
Hamburgers
Produced
per Hour
Marginal
Product
(Hamburger)
Marginal
Value Product
($1.00 per
Hamburger)
1
2
3
4
5
6
7
8
9
10
20.0
28.3
34.6
40.0
44.7
49.0
52.9
56.6
60.0
63.2
20.0
8.3
6.3
5.4
4.7
4.3
3.9
3.7
3.4
3.2
$20.00
8.30
6.30
5.40
4.70
4.30
3.90
3.70
3.40
3.20
The Substitution Effect



13
The substitution effect, in the theory of
production, is the substitution of one input for
another while holding output constant in
response to a change in the input’s price.
In Figure 15-2(a), a fall in w will cause the firm to
change from input combination A to B to equate
RTS to the new w/v.
Diminishing RTS leads to more labor hired.
FIGURE 15-2: Substitution and Output
Effects of A Decrease in Price of Labor
Capital
per week
Price
MC
K1
A
P
K2
q1
0
L1
L2
Labor hours
per week
(a) Input Choice
14
0
q1
Output
per week
(b) Output Decision
FIGURE 15-2: Substitution and Output
Effects of A Decrease in Price of Labor
Price
Capital
per week
MC
K1
A
P
K2
B
0
L1
q1
L2
Labor hours
per week
(a) Input Choice
15
0
q1
Output
per week
(b) Output Decision
The Output Effect



16
The output effect is the effect of an input
price change on the amount of the input
that the firm hires that results from a
change in the firm;s output level.
In Figure 15-2(b), the lower w causes the
marginal cost curve to shift to MC’.
The profit maximizing output raises to q2
resulting in more labor hired.
FIGURE 15-2: Substitution and Output
Effects of A Decrease in Price of Labor
Price
Capital
per week
MC
MC’
K1
A
P
K2
B
0
L1
q1
L2
Labor hours
per week
(a) Input Choice
17
0
q1 q2
Output
per week
(b) Output Decision
FIGURE 15-2: Substitution and Output
Effects of A Decrease in Price of Labor
Price
Capital
per week
MC
MC’
K1
A
C
K2
q2
B
0
L1
q1
L2
Labor hours
per week
(a) Input Choice
18
P
0
q1 q2
Output
per week
(b) Output Decision
Responsiveness of Input Demand
to Price Changes

Ease of Substitution


19
The size of the substitution effect will depend
upon how easy it is to substitute other factors
of production for labor.
The size of the substitution effect will also
depend upon the length of time as it becomes
easier to find substitutes in a longer period of
time.
Costs and the Output Effect

The size of the output effect will depend upon



20
How large the increase in marginal costs brought
about by the wage rate increase is, and
How much quantity demanded will be reduced by
a rising price.
The first depend upon how important labor is in
production while the latter depends upon the price
elasticity of demand for the final product.
Input Supply

Resources come from three major sources:




21
Labor is provided by individuals.
Capital equipment is produced which other firms
can buy outright or rent.
Natural resources are extracted from land and can
be used outright or sold to other firms.
As shown in earlier chapters, capital and
natural resources have upward sloping
supply curves.
Labor Supply and Wages



22
Wages represent the opportunity cost of
not working at a paying job for individuals.
For purposes of this analysis, wages
should be interpreted to include all forms
of compensation.
Individuals will balance the monetary
rewards from working against the psychic
benefits of other, nonpaid activities.
Labor Supply and Wages

Labor supply curves will differ based upon
individual preferences.


It is likely that an increase in the wage will
result in more labor supplied to the market.

23
Noneconomic factors such as pleasant working
conditions will affect the location of the supply
curve.
Graphically, the market labor supply curve is likely
to be positively sloped.
Equilibrium Input Price
Determination



24
In Figure 15-3, the market demand for
labor is labeled D, and the market supply
of labor is labeled S.
The equilibrium wage and quantity is
where quantity demanded equals quantity
supplied, [w*, L*].
Other things equal, this equilibrium will
tend to persist from period to period.
FIGURE 15-3: Equilibrium in an
Input Market
Wage
S
w*
D
0
25
L*
Labor hours
per week
Shifts in Demand and Supply


26
Any factor that shifts the firms’ underlying
production function will shift its input
demand curve.
Demand for an input is derived from the
demand for the output, changes in the
prices of the output will shift input demand
curves
Shifts in Demand and Supply


27
In Figure 15-3, the demand curve shifts to
D’ which reduces equilibrium wages from
w* to w’ and equilibrium employment from
L* to L’.
The various factors that shift input demand
and supply curves are summarized in
Table 15-2.
FIGURE 15-3: Equilibrium in an
Input Market
Wage
S
w*
w’
D
D’
0
28
L’
L*
Labor hours
per week
TABLE 15-2: Factors That Shift Input
Demand and Supply Curves
Demand
Demand Shifts Outward
Rise in output price
Increase in marginal
productivity
Demand Shifts Inward
Fall in output price
Decrease in marginal
productivity
29
Labor Supply
Capital Supply
Supply Shifts Outward
Decreased preference
Fall in input costs of
for Leisure
equipment makers
Increased desirability
Technical progress in
of job
making equipment
Supply Shifts Inward
Increased preference
Rise in input costs of
for Leisure
equipment makers
Decreased desirability
of job
Monopsony



30
If the firm is not a price taker in the input
market, it may have to offer a higher wage
to attract more employees.
A monopsony is the condition in which
one firm is the only hirer in a particular
input market.
If the firm is a monopsony, it faces the
entire market supply curve for the input.
Marginal Expense

The marginal expense of an input is the
cost of hiring one more unit of an input.


31
The firm has to offer a higher wage to the
hired worker and to the workers already
employed.
The marginal expense of labor (MEL) will
exceed the price of the input if the firm faces
an upward-sloping supply curve for the input.
A Numerical Illustration



32
Suppose the Yellowstone Park Company
is the only hirer of bear wardens.
The number of people willing to take this
job (L) is given by
1
15.6
L w
2
This relationship is shown in Table 15-3
TABLE 15-3: Labor Costs of Hiring Bear
Wardens in Yellowstone Park
Hourly
Wage
$2
4
6
8
10
12
14
33
Workers
Supplied
per Hour
1
2
3
4
5
6
7
Total Labor
Cost per
Hour
$2
8
18
32
50
72
98
Marginal
Expense
$2
6
10
14
18
22
26
A Numerical Illustration


34
Total labor costs (w·L) is shown in the third
column and the marginal expense of hiring
each warden is shown in the fourth
column.
Since the new warden and the existing
wardens receive the wage increase, the
marginal expense exceeds the wage rate.
A Numerical Illustration

Figure 15-4 shows the supply curve (S) for
wardens.


35
If Yellowstone wishes to hire three wardens it
must pay $6 per hour with total outlays of $18
(point A on the graph).
The wage must be increased to $8 to get a
fourth warden (point B) which results in total
outlays of $32.
FIGURE 15-4: Marginal Expense of
Hiring Bear Wardens
Hourly
wage
S
B
$8
A
6
0
36
3
4
Bear wardens
per hour
A Numerical Illustration

The marginal expense of the fourth
warden, $14 is reflected in the graph.



37
The hourly wage ($8) is shown in gray.
The extra outlay to the three previous workers
($8 per hour versus $6 per hour previously) is
shown in color.
Total outlays exceed the amount for three
wardens by the sum of these two areas.
FIGURE 15-4: Marginal Expense of
Hiring Bear Wardens
Hourly
wage
S
B
$8
A
6
0
38
3
4
Bear wardens
per hour
Monopsonists and Resource Allocation:
A Graphical Demonstration



39
The demand curve in Figure 15-5 is D.
Since marginal expense (MEL) exceeds
the wage, the marginal expense curve is
above the supply curve (S).
L1 is the profit maximizing choice while the
marginal value product is MVP1 and the
wage is w1.
FIGURE 15-5: Pricing in a
Monopsonistic Labor Market
Wage
ME
S
D
0
40
Labor hours
per week
FIGURE 15-5: Pricing in a
Monopsonistic Labor Market
ME
Wage
S
MVP1
D
0
41
L1
Labor hours
per week
FIGURE 15-5: Pricing in a
Monopsonistic Labor Market
ME
Wage
S
MVP1
w1
0
42
D
L1
Labor hours
per week
A Graphical Demonstration


43
L1 is less than L*, the amount hired with
perfect competition.
As with a monopoly, the “demand curve”
for a monopolist actually consists of the
single point given by L1, w1.
FIGURE 15-5: Pricing in a
Monopsonistic Labor Market
ME
Wage
S
MVP1
w*
w1
0
44
D
L1
L*
Labor hours
per week
Monopsonists and Resource
Allocation



45
Since the monopsonist restrict its input
use, it pays an input less than its marginal
value product (w1 < MVP1).
Total output could be increased by
drawing more labor into the market.
The more inelastic the labor supply, the
more the monopsonists can benefit from
this profit opportunity.
Bilateral Monopoly



46
A bilateral monopoly is a market in which both
suppliers and demanders have monopoly power.
In Figure 15-6, “supply” and “demand” intersect
at P*, Q*, but this is not equilibrium since neither
player is a price taker.
The monopoly supplier will operate on its
marginal revenue curve (MR) and prefer pricequantity combination P1, Q1.
FIGURE 15-6: Bilateral Monopoly
ME
Input
price
S
P1
D
MR
0
47
Q1
Quantity per
period
Bilateral Monopoly


48
The monopoly supplier will operate on its
marginal revenue curve (MR) and prefer
price-quantity combination P1, Q1.
The monopsonistic will operate on its
marginal expense curve (ME) and prefer
combination P2, Q2.
FIGURE 15-6: Bilateral Monopoly
ME
Input
price
S
P*
P2
D
MR
0
49
Q2
Quantity per
period
Bilateral Monopoly



50
The monopoly supplier will operate on its
marginal revenue curve (MR) and prefer
price-quantity combination P1, Q1.
The monopsonistic will operate on its
marginal expense curve (ME) and prefer
combination P2, Q2.
The final outcome, after bargaining, will lie
between these two combinations.
FIGURE 15-6: Bilateral Monopoly
ME
Input
price
S
P1
P*
P2
D
MR
0
51
Q2 Q1
Q*
Quantity per
period