Chapter 7
Technology and Production
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.
Main Topics
Production technologies
Production with one variable input
Production with two variable inputs
Returns to scale
Productivity differences and
technological change
7-2
Production Technologies
Firms produce products or services, outputs
they can sell profitably
A firm’s production technology summarizes
all its production methods for producing its
output
Different production methods can use the
same amounts of inputs but produce different
amounts of output
A production method is efficient if there is no
other way for the firm to produce more output
using the same amounts of inputs
7-3
Production Technologies:
An Example
Firm producing garden benches
Assembles benches from pre-cut kits
Hired labor is only input that can be varied
One worker produces 33 benches in a week
Two workers can produce different numbers of
benches in a week, depending on how they
divide up the assembly tasks
Each work alone, produce total of 66 benches
Help each other, produce more
7-4
Production Technologies: An
Example
Table 7.1: Inputs and Output for Various Methods of Producing
Garden Benches
Production
Method
Number of
Assembly Workers
Benches
Produced Per
Week
Efficient?
A
1
33
Yes
B
2
66
No
C
2
70
No
D
2
74
Yes
E
4
125
No
F
4
132
Yes
7-5
Production Possibilities Set
A production possibilities set contains all
combinations of inputs and outputs that are
possible given the firm’s technology
Output on vertical axis, input on horizontal axis
A firm’s efficient production frontier shows
the input-output combinations from all of its
efficient production methods
Corresponds to the highest point in the production
possibilities set on the vertical line at a given input
level
7-6
Figure 7.2: Production Possibility
Set for Garden Benches
Q  F L   2 L3  10 L2  25L
7-7
Production Function
Mathematically, describe efficient production
frontier with a production function
Output=F(Inputs)
Example: Q=F(L)=10L
Q is quantity of output, L is quantity of labor
Substitute different amounts of L to see how output
changes as the firm hires different amounts of labor
Amount of output never falls when the amount
of input increases
 Production function shows output produced for
efficient production methods
7-8
Short and Long-Run Production
An input is fixed if it cannot be adjusted over
any given time period; it is variable if it can be
Short run: a period of time over which one or
more inputs is fixed
Long run: a period over time over which all
inputs are variable
Length of long run depends on the production
process being considered
Auto manufacturer may need years to build a new
production facility but software firm may need only a
month or two to rent and move into a new space
7-9
Average and Marginal Products
Average product of labor is the amount of
output that is produced per worker:
Q F L 
APL  
L
L
Marginal product of labor measures how
much extra output is produced when the firm
changes the amount of labor it uses by just a
little bit:
Q F L   F L  L 
MPL 

L
L
7-10
Diminishing Marginal Returns
Law of diminishing
marginal returns:
eventually the
marginal product for
an input decreases
as its use increases,
holding all other
inputs fixed
Table 7.3: Marginal Product of
Producing Garden Benches
Number of
Workers
Benches
Produced
Per Week
MPL
0
0
--
1
33
33
2
74
41
3
111
37
4
132
21
7-11
Relationship Between AP and MP
Compare MP to AP to see whether AP rises or
falls as more of an input is added
MPL shows how much output the marginal
worker adds
If he is more productive than average, he brings the
average up
If he is less productive than average, he drives the
average down
Relationship between a firm’s AP and MP:
When the MP of an input is (larger/smaller/the
same as) the AP, the marginal units
(raise/lower/do not affect) the AP
7-12
AP and MP Curves
When labor is finely divisible, AP and MP
are graphed as curves
For any point on a short run production
function:
AP is the slope of the straight line
connecting the point to the origin
MP equals the slope of the line tangent to
the production function at that point
7-13
Figure 7.4: Marginal Product of
Labor
7-14
Figure 7.6: Average and Marginal
Product Curves
AP curve slopes
upward when it is
below MP
AP slopes downward
when it is above MP
AP is flat where the
two curve cross
7-15
Production with Two Variable Inputs
Most production processes use many variable
inputs: labor, capital, materials, and land
Capital inputs include assets such as physical
plant, machinery, and vehicles
Consider a firm that uses two inputs in the long
run:
Labor (L) and capital (K)
Each of these inputs is homogeneous
Firm’s production function is Q = F(L,K)
7-16
Production with Two Variable Inputs
When a firm has more than one variable
input it can produce a given amount of
output with many different combinations
of inputs
E.g., by substituting K for L
Productive Inputs Principle: Increasing
the amounts of all inputs strictly
increases the amount of output the firm
can produce
7-17
Isoquants
An isoquant identifies all input
combinations that efficiently produce a
given level of output
Note the close parallel to indifference curves
Can think of isoquants as contour lines for
the “hill” created by the production function
Firm’s family of isoquants consists of
the isoquants for all of its possible output
levels
7-18
Figure 7.8: Isoquant Example
7-19
Properties of Isoquants
Isoquants are thin
Do not slope upward
The boundary between input
combinations that produce more and less
than a given amount of output
Isoquants from the same technology do
not cross
Higher-level isoquants lie farther from the
origin
7-20
Figure 7.10: Properties of
Isoquants
7-21
Figure 7.10: Properties of
Isoquants
7-22
Substitution Between Inputs
 Rate that one input can be substituted for another is an
important factor for managers in choosing best mix of
inputs
 Shape of isoquant captures information about input
substitution
 Points on an isoquant have same output but different input mix
 Rate of substitution for labor with capital is equal to negative
the slope
 Marginal Rate of Technical Substitution for input X
with input Y: the rate as which a firm must replace
units of X with units of Y to keep output unchanged
starting at a given input combination
7-23
Figure 7.12: MRTS
7-24
MRTS and Marginal Product
Recall the relationship between MRS and
marginal utility
Parallel relationship exists between MRTS
and marginal product
MRTS LK
MPL

MPK
The more productive labor is relative to
capital, the more capital we must add to
make up for any reduction in labor; the larger
the MRTS
7-25
Figure 7.13: Declining MRTS
Often assume
declining MRTS
Here MRTS declines
as we move along
the isoquant,
increasing input X
and decreasing input
Y
7-26
Extreme Production Technologies
Two inputs are perfect substitutes if their
functions are identical
Firm is able to exchange one for another at a fixed
rate
Each isoquant is a straight line, constant MRTS
Two inputs are perfect complements when
They must be used in fixed proportions
Isoquants are L-shaped
7-27
Figure 7.14: Perfect Substitutes
7-28
Figure 7.15: Fixed Proportions
7-29
Cobb-Douglas Production
Function
Common production function in economic
analysis
Introduced by mathematician Charles Cobb
and economist (U.S. Senator) Paul Douglas
General form:
a
b
Q  F L, K   AL K
Where A, a, and b are parameters that take
specific values for a given firm
7-30
Cobb-Douglas Production Function
Q  F L, K   AL K
a
b
A shows firm’s general productivity level
a and b affect relative productivities of labor
and capital
a 1
MPL  aAL K
a
MPK  bAL K
b
b 1
Substitution between inputs:
 a  K 
MRTS LK    
 b  L 
7-31
Figure: 7.16: Cobb-Douglas
Production Function
7-32
Returns to Scale
Types of Returns to Scale
Proportional change in
ALL inputs yields…
What happens when all
inputs are doubled?
Constant
Same proportional change in
output
Output doubles
Increasing
Greater than proportional
change in output
Output more than
doubles
Decreasing
Less than proportional
change in output
Output less than doubles
7-33
Figure 7.17: Returns to Scale
7-34
Productivity Differences and
Technological Change
A firm is more productive or has higher
productivity when it can produce more
output use the same amount of inputs
Its production function shifts upward at each
combination of inputs
May be either general change in productivity
of specifically linked to use of one input
Productivity improvement that leaves
MRTS unchanged is factor-neutral
7-35