Diminishing Returns (pp. 199 - 207)
Capital 5
per year
Increasing labor
holding capital
constant (A, B, C)
OR
Increasing capital
holding labor constant
(E, D, C
4
3
A
B
C
D
2
q3 = 90
E
1
q2 = 75
q1 = 55
1
©2005 Pearson Education, Inc.
2
3
Chapter 6
4
5
Labor per year
1
Production: Two Variable Inputs
(pp. 199 -
207)
Substituting Among Inputs
Companies must decide what combination of
inputs to use to produce a certain quantity of
output
There is a trade-off between inputs, allowing
them to use more of one input and less of
another for the same level of output (Do you
know the Luddites in England in the early
19th century?)
©2005 Pearson Education, Inc.
Chapter 6
2
Production: Two Variable Inputs
(pp. 199 -
207)
Substituting Among Inputs
Slope of the isoquant shows how one input
can be substituted for the other and keep the
level of output the same
The negative of the slope is the marginal
rate of technical substitution (MRTS)
Amount
by which the quantity of one input can
be reduced when one extra unit of another input
is used, so that output remains constant
©2005 Pearson Education, Inc.
Chapter 6
3
Production: Two Variable Inputs
(pp. 199 -
207)
The marginal rate of technical
substitution equals:
Change in Capital Input
MRTS = −
Change in Labor Input
MRTS = − ΔK
©2005 Pearson Education, Inc.
ΔL
(for a fixed level of q )
Chapter 6
4
Production: Two Variable Inputs
(pp. 199 - 207)
As labor increases to replace capital
Labor becomes relatively less productive
Capital becomes relatively more productive
Need less capital to keep output constant
Isoquant becomes flatter (convex to the
origin)
q=
©2005 Pearson Education, Inc.
L
K
Chapter 6
5
Marginal Rate of
Technical Substitution (pp. 199 - 207)
Capital
per year
5
4
Negative Slope measures
MRTS;
MRTS decreases as move down
the indifference curve
2
1
3
1
1
2
2/3
Q3 =90
1
Q2 =75
1/3
1
1
1
©2005 Pearson Education, Inc.
2
3
Chapter 6
4
Q1 =55
5
Labor per month
6
MRTS and Marginal Products
(pp. 199 - 207)
If we increase labor and decrease capital
to keep output constant, we can see how
much the increase in output is due to the
increased labor
Amount of labor increased (i.e., ΔL positive)
times the marginal productivity of labor
= ( MPL )(ΔL)
©2005 Pearson Education, Inc.
Chapter 6
7
MRTS and Marginal Products
(pp. 199 - 207)
Similarly, the decrease in output from the
decrease in capital can be calculated
Decrease in output from reduction of
capital(ΔK is negative) times the marginal
produce of capital
= ( MPK )(ΔK )
©2005 Pearson Education, Inc.
Chapter 6
8
MRTS and Marginal Products
(pp. 199 - 207)
If we are holding output constant, the net
effect of increasing labor and decreasing
capital must be zero
Using changes in output from capital and
labor we can see
(MPL )( ΔL) + (MPK )( ΔK) = 0
©2005 Pearson Education, Inc.
Chapter 6
9
MRTS and Marginal Products
(pp. 199 - 207)
Rearranging equation, we can see the
relationship between MRTS and MPs
(MPL )( ΔL) + (MPK )( ΔK) = 0
(MPL )(ΔL) = - (MPK )( ΔK)
(MPL )
ΔL
=−
= MRTS
ΔK
( MPK )
©2005 Pearson Education, Inc.
Chapter 6
10
Isoquants: Special Cases
(pp. 199 - 207)
Two extreme cases show the possible
range of input substitution in production
1. Perfect substitutes
MRTS is constant at all points on isoquant
Same output can be produced with a lot of
capital or a lot of labor or a balanced mix
©2005 Pearson Education, Inc.
Chapter 6
11
Perfect Substitutes (pp. 199 - 207)
Capital
per
month
A
Same output can be
reached with mostly
capital or mostly labor
(A or C) or with equal
amount of both (B)
B
C
Q1
©2005 Pearson Education, Inc.
Chapter 6
Q2
Q3
Labor
per month
12
Isoquants: Special Cases
(pp. 199 - 207)
2. Perfect Complements
Fixed proportions production function
There is no substitution available between
inputs
The output can be made with only a specific
proportion of capital and labor
Cannot increase output unless increase
both capital and labor in that specific
proportion
©2005 Pearson Education, Inc.
Chapter 6
13
Fixed-Proportions
Production Function (pp. 199 - 207)
Capital
per
month
Same output can
only be produced
with one set of
inputs.
Q3
C
Q2
B
K1
Q1
A
Labor
per month
L1
©2005 Pearson Education, Inc.
Chapter 6
14
A Production Function for
Wheat (pp. 199 - 207)
Farmers can produce crops with different
combinations of capital and labor
Crops in US are typically grown with capitalintensive technology
Crops in developing countries grown with
labor-intensive productions
Can show the different options of crop
production with isoquants
©2005 Pearson Education, Inc.
Chapter 6
15
A Production Function for
Wheat: Ex. 6-3 (pp. 199 - 207)
Manager of a farm can use the isoquant
to decide what combination of labor and
capital will maximize profits from crop
production
A: 500 hours of labor, 100 units of capital for
13,800 bushels per year
B: decreases units of capital to 90, but must
increase hours of labor by 260 to 760 hours
This experiment shows the farmer the shape
of the isoquant
©2005 Pearson Education, Inc.
Chapter 6
16
Isoquant Describing the Production
of Wheat : Ex. 6-3 (pp. 199 - 207)
Point A is more
capital-intensive, and
B is more labor-intensive.
Capital
120
100
90
80
A
B
ΔK = - 10
ΔL = 260
Output = 13,800 bushels
per year
40
Labor
250
©2005 Pearson Education, Inc.
500
760
Chapter 6
1000
17
A Production Function for Wheat :
Ex. 6-3 (pp. 199 - 207)
Increase L to 760 and decrease K to 90
the MRTS =0.04 < 1
MRTS = - ΔK
ΔL
= −( −10 / 260) = 0.04
When wage (i.e.,cost of labor) is equal to
cost of running a machine, more capital
should be used
Unless labor is much less expensive than
capital, production should be capital intensive
©2005 Pearson Education, Inc.
Chapter 6
18
Returns to Scale (pp. 207 - 210)
In addition to discussing the tradeoff
between inputs to keep production the
same
How does a firm decide, in the long run,
the best way to increase output?
Can change the scale of production by
increasing all inputs in proportion
If double inputs, output will most likely
increase but by how much?
©2005 Pearson Education, Inc.
Chapter 6
19
Returns to Scale (pp. 207 - 210)
Rate at which output increases as inputs
are increased proportionately
Increasing returns to scale
Constant returns to scale
Decreasing returns to scale
©2005 Pearson Education, Inc.
Chapter 6
20
Returns to Scale (pp. 207 - 210)
Increasing returns to scale: output
more than doubles when all inputs are
doubled
Larger output associated with lower cost
(cars)
One firm is more efficient than many
(utilities)
The isoquants get closer together
©2005 Pearson Education, Inc.
Chapter 6
21
Increasing Returns to Scale
Capital
(machine
hours)
A
(pp. 207 - 210)
The isoquants
move closer
together
4
30
20
2
10
5
©2005 Pearson Education, Inc.
10
Chapter 6
Labor (hours)
22
Returns to Scale (pp. 207 - 210)
Constant returns to scale: output
doubles when all inputs are doubled
Size
does not affect productivity
May
have a large number of producers
Isoquants
©2005 Pearson Education, Inc.
are equidistant apart
Chapter 6
23
Returns to Scale (pp. 207 - 210)
Capital
(machine
hours)
A
6
30
4
20
2
Constant
Returns:
Isoquants are
equally spaced
10
5
©2005 Pearson Education, Inc.
10
Chapter 6
15
Labor (hours)
24
Returns to Scale (pp. 207 - 210)
Decreasing returns to scale: output
less than doubles when all inputs are
doubled
Decreasing
efficiency with large size
Reduction
of entrepreneurial abilities
Isoquants
become farther apart
Exercise: Problem 8 on page 212. (To be
included in your HW)
©2005 Pearson Education, Inc.
Chapter 6
25
Returns to Scale (pp. 207 - 210)
Capital
(machine
hours)
A
Decreasing Returns:
Isoquants get further
apart
4
18
2
10
5
©2005 Pearson Education, Inc.
10
Chapter 6
Labor (hours)
26
Returns to Scale: Carpet Industry
Ex. 6-4 (pp. 207 - 210)
The carpet industry has grown from a small industry to a
large industry with some very large firms
There are four relatively large manufacturers along with a
number of smaller ones
Growth has come from
Increased consumer demand
More efficient production reducing costs
Innovation and competition have reduced real prices
©2005 Pearson Education, Inc.
Chapter 6
27
The U.S. Carpet Industry
©2005 Pearson Education, Inc.
Chapter 6
(pp. 207 - 210)
28
Returns to Scale: Carpet Industry
(pp. 207 - 210)
Some growth can be explained by
returns to scale
Carpet production is highly capital
intensive
Heavy upfront investment in machines for
carpet production
Increases in scale of operating have
occurred by putting in larger and more
efficient machines into larger plants
©2005 Pearson Education, Inc.
Chapter 6
29
Returns to Scale: Carpet Industry
Results (pp. 207 - 210)
1. Large Manufacturers
Increases in machinery and labor
Doubling inputs has more than doubled
output
Economies of scale exist for large
producers
©2005 Pearson Education, Inc.
Chapter 6
30
Returns to Scale: Carpet Industry
Results (pp. 207 - 210)
2. Small Manufacturers
Small increases in scale have little or no
impact on output
Proportional increases in inputs increase
output proportionally
Constant returns to scale for small
producers
©2005 Pearson Education, Inc.
Chapter 6
31
Returns to Scale: Carpet Industry
(pp.
207 - 210)
From this we can see that the carpet
industry is one where:
1. There are constant returns to scale for
relatively small plants
2. There are increasing returns to scale for
relatively larger plants
These are limited, however
Eventually reach decreasing returns
©2005 Pearson Education, Inc.
Chapter 6
32