Topics to be Discussed
The Technology of Production
Production with One Variable Input
(Labor)
Isoquants
Production with Two Variable Inputs
Returns to Scale
©2005 Pearson Education, Inc.
Chapter 6
1
Production Decisions of a Firm
(pp. 187-8)
1. Production Technology
2. Cost Constraints
3. Input Choices
©2005 Pearson Education, Inc.
Chapter 6
2
Production Decisions of a Firm
(pp. 187-8)
If a firm is a cost minimizer, we can also
study
How total costs of production vary with
output (Ch. 7)
How the firm chooses the quantity to
maximize its profits (Ch. 8)
We can represent the firm’s production
technology in the form of a production
function
©2005 Pearson Education, Inc.
Chapter 6
3
The Technology of Production
(pp. 188-90)
Production Function:
Indicates the highest output (q) that a firm
can produce for every specified combination
of inputs with its technological knowledge
given
For simplicity, we will consider only labor (L
for labor) and capital (K for kapital in German)
Shows what is technically feasible when the
firm operates efficiently
©2005 Pearson Education, Inc.
Chapter 6
4
The Technology of Production
(pp. 187-8)
The production function for two inputs:
q = F(K,L)
Output (q) is a function of capital (K) and labor (L)
The production function is true for a given technology
If technology progresses, more output can be
produced for a given level of inputs (for instance,
printing technology from movable type (J. Gutenberg
?); xerographic technology (Xerox); Surely you can
list up more. )
©2005 Pearson Education, Inc.
Chapter 6
5
The Technology of Production
(pp. 187-8)
Short Run versus Long Run
Consider a hotel for example. It uses more utilities like
water, electric power when it is busy in a season. How
about the number of rooms? In a longer period it may
expand the building to accommodate more for
increasing demand (more visitors).
It takes time for a firm to adjust production from one
set of inputs to another
Firms must consider not only what inputs can be
varied but over what period of time that can occur
We must distinguish between long run and short run
©2005 Pearson Education, Inc.
Chapter 6
6
The Technology of Production
(pp. 187-8)
Short Run
Period of time in which quantities of one or more
production factors cannot be changed
These inputs are called fixed inputs
Long Run
Amount of time needed to make all production inputs
variable (called as variable inputs)
Short run and long run are not time specific
©2005 Pearson Education, Inc.
Chapter 6
7
Production: One Variable Input
(pp. 190
- 99)
©2005 Pearson Education, Inc.
Chapter 6
8
Production: One Variable Input
(pp. 190 - 99)
Observations:
1. When labor is zero, output is zero as well
2. With additional workers, output (q)
increases up to 8 units of labor
3. Beyond this point, output declines
Increasing labor can make better use of
existing capital initially
After a point, more labor is not useful and can
be counterproductive
©2005 Pearson Education, Inc.
Chapter 6
9
Production: One Variable Input
(pp. 190 - 99)
Firms make decisions based on the
benefits (revenues) and costs of
production
Sometimes useful to look at benefits and
costs on an incremental basis
How much more can be produced when at
incremental units of an input?
Sometimes useful to make comparison
on an average basis
©2005 Pearson Education, Inc.
Chapter 6
10
Production: One Variable Input
(pp. 190 - 99)
Average product of Labor - Output per
unit of a particular product with other
inputs being constant
Measures the productivity of a firm’s
labor in terms of how much, on average,
each worker can produce
Output
q
APL =
=
Labor Input L
©2005 Pearson Education, Inc.
Chapter 6
11
Production: One Variable Input
(pp. 190 - 99)
Marginal Product of Labor – additional
output produced when labor increases by
one unit with other inputs being constant
Change in output divided by the change
in labor
ΔOutput
Δq
MPL =
=
ΔLabor Input ΔL
©2005 Pearson Education, Inc.
Chapter 6
12
Production: One Variable Input: Table 6-1
(pp. 190 - 99)
©2005 Pearson Education, Inc.
Chapter 6
13
Production: One Variable Input
(pp. 190 - 99)
We can graph the information in Table
6.1 to show
How output varies with changes in labor
Output
is maximized at 112 units
Average and Marginal Products
Marginal
Product is positive as long as total
output is increasing
Marginal Product crosses Average Product at its
maximum
©2005 Pearson Education, Inc.
Chapter 6
14
Production: One Variable Input
Output
per
Month
(pp. 190 - 99)
D
112
Total Product
C
60
At point D, output
is maximized.
B
A
0 1
2
©2005 Pearson Education, Inc.
3
4
5 6
7
Chapter 6
8
9
10 Labor per Month
15
Production: One Variable Input
Output
per
Worker
(pp. 190 - 99)
•Left of E: MP > AP & AP is increasing
•Right of E: MP < AP & AP is decreasing
•At E: MP = AP & AP is at its maximum
•At 8 units, MP is zero and output is at max
30
Marginal Product
E
20
Average Product
10
0 1
2
©2005 Pearson Education, Inc.
3
4
5 6
7
Chapter 6
8
9
10 Labor per Month
16
Marginal and Average Product
(pp. 190 - 99)
When marginal product is greater than the
average product, the average product is
increasing
When marginal product is less than the average
product, the average product is decreasing
When marginal product is zero, total product
(output) is at its maximum
Marginal product crosses average product at its
maximum
The above is an established relation between
“average” and “marginal” quantities in general.
©2005 Pearson Education, Inc.
Chapter 6
17
Product Curves (pp. 190 - 99)
We can show a geometric relationship
between the total product and the
average and marginal product curves
Slope of line from origin to any point on the
total product curve is the average product
At point B, AP = 60/3 = 20 which is the same
as the slope of the line from the origin to
point B on the total product curve
©2005 Pearson Education, Inc.
Chapter 6
18
Product Curves (pp. 190 - 99)
q
q/L
AP is slope of line from
origin to point on TP
curve
112
TP
C
60
30
20
B
AP
10
MP
0 1 2 3 4 5 6 7 8 9 10
Labor
©2005 Pearson Education, Inc.
Chapter 6
0 1 2 3 4 5 6 7 8 9 10
Labor
19
Product Curves (pp. 190 - 99)
Geometric relationship between total
product and marginal product
The marginal product is the slope of the
line tangent to any corresponding point on
the total product curve
For 2 units of labor, MP = 30/2 = 15 which is
slope of total product curve at point A
©2005 Pearson Education, Inc.
Chapter 6
20
Product Curves (pp. 190 - 99)
q
q
MP is slope of line tangent to
corresponding point on TP
curve
112
TP 30
15
60
30
10
A
MP
0 1 2 3 4 5 6 7 8 9 10
Labor
©2005 Pearson Education, Inc.
AP
Chapter 6
0 1 2 3 4 5 6 7 8 9 10
Labor
21
Production: One Variable Input
(pp. 190 - 99)
From the previous example, we can see
that as we increase labor the additional
output produced declines
Law of Diminishing Marginal Returns
(Products): As the use of an input
increases with other inputs fixed, the
resulting additions to output will
eventually decrease
©2005 Pearson Education, Inc.
Chapter 6
22
Law of Diminishing Marginal
Returns (pp. 190 - 99)
When the use of labor input is small and
capital is fixed, output increases
considerably since workers can begin to
specialize and MP of labor increases
When the use of labor input is large,
some workers become less efficient and
MP of labor decreases
©2005 Pearson Education, Inc.
Chapter 6
23
Law of Diminishing Marginal
Returns (pp. 190 - 99)
Assumes a constant technology
Changes in technology will cause shifts in the total
product curve
More output can be produced with same inputs
(technological progress)
Labor productivity can increase if there are
improvements in technology, even though any given
production process exhibits diminishing returns to
labor (Have PCs improved labor productivity? Or, Has
IT improved labor productivity?)
©2005 Pearson Education, Inc.
Chapter 6
24
The Effect of Technological
Improvement (pp. 190 - 99)
Output
Moving from A to B to
C, labor productivity is
increasing over time
C
100
O3
B
A
O2
50
O1
0 1
2
©2005 Pearson Education, Inc.
3
4
5 6
7
Chapter 6
8
9
10
Labor per
time period
25
Malthus and the Food Crisis
(pp. 190 - 99)
Malthus predicted mass hunger and
starvation as diminishing returns limited
agricultural output and the population
continued to grow
Why did Malthus’ prediction fail?
Did not take into account changes in
technology
Although he was right about diminishing
marginal returns to labor
©2005 Pearson Education, Inc.
Chapter 6
26
Malthus and the Food Crisis
(pp. 190 - 99)
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©2005 Pearson Education, Inc.
Chapter 6
27
Labor Productivity (pp. 190 - 99)
Macroeconomics are particularly
concerned with labor productivity
The average product of labor for an entire
industry or the economy as a whole
Links macro- and microeconomics
Can provide useful comparisons across time
and across industries
q
Average Productivity =
L
©2005 Pearson Education, Inc.
Chapter 6
28
Labor Productivity (pp. 190 - 99)
Link between labor productivity and
standard of living
Consumption can increase only if
productivity increases
Growth of Productivity
Growth in stock of capital – total amount of
capital available for production
2. Technological change – development of new
technologies that allow factors of production to
be used more efficiently
1.
©2005 Pearson Education, Inc.
Chapter 6
29
Labor Productivity (pp. 190 - 99)
Trends in Productivity
Labor productivity and productivity growth have
differed considerably across countries
U.S. productivity is growing at a slower rate than other
countries
Productivity growth in developed countries has been
decreasing (A convergence hypothesis)
Given the central role of productivity in
standards of living, understanding differences
across countries is important
©2005 Pearson Education, Inc.
Chapter 6
30
Labor Productivity in Developed
Countries (pp. 190 - 99)
©2005 Pearson Education, Inc.
Chapter 6
31
Productivity Growth in US
(pp. 190 - 99)
Why has productivity growth slowed
down?
1. Growth in the stock of capital is the
primary determinant of the growth in
productivity
2. Rate of capital accumulation (US) was
slower than other developed countries
because they had to rebuild after WWII
3. Depletion of natural resources
4. Environmental regulations
©2005 Pearson Education, Inc.
Chapter 6
32
Production: Two Variable Inputs
(pp. 199 -
207)
Firm can produce output by combining
different amounts of labor and capital
In the long run, capital and labor are both
variable
We can look at the output we can
achieve with different combinations of
capital and labor – Table 6.4
©2005 Pearson Education, Inc.
Chapter 6
33
Production: Two Variable Inputs: Table 64 (pp. 199 - 207)
©2005 Pearson Education, Inc.
Chapter 6
34
Production: Two Variable Inputs
(pp. 199 -
207)
The information can be represented graphically
using isoquants
Curves showing all possible combinations of inputs
that yield the same output (Compare with indifference
curves in consumer demand)
Curves are smooth to allow for use of fractional
inputs
Curve 1 shows all possible combinations of labor and
capital that will produce 55 units of output
©2005 Pearson Education, Inc.
Chapter 6
35
Isoquant Map (pp. 199 - 207)
E
Capital 5
per year
Ex: 55 units of output
can be produced with
3K & 1L (pt. A)
OR
1K & 3L (pt. D)
4
3
A
B
C
2
q3 = 90
D
1
q2 = 75
q1 = 55
1
©2005 Pearson Education, Inc.
2
3
Chapter 6
4
5
Labor per year
36
Production: Two Variable Inputs
(pp. 199 -
207)
Diminishing Returns to Labor with
Isoquants
Holding capital at 3 and increasing labor
from 0 to 1 to 2 to 3
Output increases at a decreasing rate (0, 55,
20, 15) illustrating diminishing marginal
returns from labor in the short run and long
run
©2005 Pearson Education, Inc.
Chapter 6
37
Production: Two Variable Inputs
(pp. 199 -
207)
Diminishing Returns to Capital with
Isoquants
Holding labor constant at 3 increasing
capital from 0 to 1 to 2 to 3
Output increases at a decreasing rate (0, 55,
20, 15) due to diminishing returns from
capital in short run and long run
©2005 Pearson Education, Inc.
Chapter 6
38
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
39
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
40
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
41
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
42
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
©2005 Pearson Education, Inc.
Chapter 6
43
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
1/3
1
Q2 =75
1
Q1 =55
1
©2005 Pearson Education, Inc.
2
3
Chapter 6
4
5
Labor per month
44
MRTS and Isoquants (pp. 199 - 207)
We assume there is diminishing MRTS
Increasing labor in one unit increments from 1 to 5
results in a decreasing MRTS from 1 to 1/2
Productivity of any one input is limited
Diminishing MRTS occurs because of
diminishing returns and implies isoquants are
convex
There is a relationship between MRTS and
marginal products of inputs
©2005 Pearson Education, Inc.
Chapter 6
45
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 times the
marginal productivity of labor
= ( MPL )(ΔL)
©2005 Pearson Education, Inc.
Chapter 6
46
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
times the marginal produce of capital
= ( MPK )(ΔK )
©2005 Pearson Education, Inc.
Chapter 6
47
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
48
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
49
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
50
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
51
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
52
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
53
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
54
A Production Function for
Wheat (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
B: decreases unit 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
55
Isoquant Describing the
Production of Wheat (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
56