Transcript Chapter 7

Chapter 7
Technology and Production
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.
Production Decisions
The chapters we covered before the
midterm were focused on how
consumers decided which products to
purchase.
The next 3 chapters will focus on how
firms make decisions on what to produce
and how to produce it.
Ch 7 – Production Technology
Ch 8 – Production Costs
Ch 9 – How a firm maximizes its profit and
chooses production quantities and prices
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Main Topics
Production technologies
Dif. production methods = dif. product quant.
Production with one variable input
Short-run capabilities with 1 variable input
Production with two variable inputs
Input substitution
Returns to scale
Scale of production leads to more/less efficiency
Productivity differences and technological
change
Dif. firms have dif. outcomes
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Production Technologies
Firms produce products or services (outputs)
which they can sell profitably.
These outputs are produced from inputs or
materials, labor, land and equipment (capital)
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
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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
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Example: Production Technologies
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
Remember…efficiency is the method that maximizes
output for the amt. of inputs.
What might be a reason that F isn't 148 benches?
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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
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Figure 7.2: Production Possibility
Set for Garden Benches
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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
 However, the amount of output will produce less and less marginal
quantities. Will discuss later in this chapter.
 Note: The bench making example production function is:
Q  F L  2L3  10L2  25L
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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
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In-Text Exer. 7.3
Suppose that a firm uses both labor (L)
and capital (K) as inputs and has the
long-run production function.
F (L, K )  Q  10 L 10
If its capital is fixed at K=10 in the short
run, what is its short-run production
function? How much does it produce in
the short run if it hires 1 worker? 2
workers?
What is an assumption also made here?
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In-Text Exer. 7.3
What is an assumption also made here?
The firm uses efficient production methods!
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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
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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
Why do you think this is the case?
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Example: Dim. Marginal Returns
Output
per worker
1
2. When the economy has a
high level of capital, an
extra unit of capital leads to
a small increase in output.
1. When the economy has a low level of capital, an
extra unit of capital leads to a large increase in output.
1
In this example, what is the input? What
happens as the amount of capital is increased?
Capital per
worker
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
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AP and MP Curves
When labor is finely divisible, AP and MP
are graphed as curves (otherwise, graph
will look like stairs…)
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
Remember….the formula for slope is…
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Figure 7.3/.4: Products of Labor
Average Product
Marginal Product
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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
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Production with Two Variable Inputs
Most production processes use many variable
inputs: labor, capital, materials, and land
The “complete” example production function
is Y = A F(L, K, H, N)
Y = quantity of output
A = available production technology
L = quantity of labor
K = quantity of physical capital
H = quantity of human capital
N = quantity of natural resources
F( ) is a function that shows how the inputs are
combined.
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Production with Two Variable Inputs
In our example here, we will use a 2
variable model.
Consider a firm that uses two inputs in the
long run:
Labor (L) and capital (K)
Capital inputs include assets such as physical plant,
machinery, and vehicles
Each of these inputs is homogeneous
Firm’s production function is Q = F(L,K)
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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
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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
A firm’s family of isoquants consists of
the isoquants for all of its possible output
levels
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Figure 7.8: Isoquant Example
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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
7-25
Figure 7.10: Properties of
Isoquants
Think the Productive Inputs Principle…increasing
the amts. of all inputs strictly increases the
amount of output the firm can produce. Possible
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with the examples above?
Figure 7.10: Properties of
Isoquants
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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
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Figure 7.12: MRTS
So…the rate of substitution for labor with capital is ½.
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MRTS and Marginal Product
Recall the relationship between MRS and
marginal utility
Parallel relationship exists between MRTS
and marginal product
MRTSLK
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
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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
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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
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Figure 7.14: Perfect Substitutes
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Figure 7.15: Fixed Proportions
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Cobb-Douglas Production Function
 Common production function in economic analysis and is
widely used to represent the relationship of an output to
inputs
 Introduced by mathematician Charles Cobb and
economist (U.S. Senator) Paul Douglas
 For production, the function is
Q  F L, K   AL K


 Q = total production (the monetary value of all goods
produced in a year)
 L = labor input
 K = capital input
 A, α and β are the general productivity level, and output
elasticities of labor and capital, respectively. These
values are constants determined by available technology
and take specific values for a given firm.
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Cobb-Douglas Production Function
Q  F L, K   AL K


A shows firm’s general productivity level
 and  affect relative productivities of labor
and capital
MPL  AL 1 K 
MPK   AL K  1
Substitution between inputs:
   K 
MRTSLK    
   L 
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Figure: 7.16: Cobb-Douglas
Production Function
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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
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Figure 7.17: Returns to Scale
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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
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