1 chapter 7 technology and production 1. 2 production technologies firms produce products or...
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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
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Production Technologies:An Example
Firm producing garden benches:One worker produces 33 benches in a weekTwo workers can produce different numbers of
benches in a week, depending on how they divide up the assembly tasks
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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
WeekEfficient?
A 1 33 Yes
B 2 66 No
C 2 70 No
D 2 74 Yes
E 4 125 No
F 4 132 Yes
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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
A firm’s efficient production frontier shows the input-output combinations from all of its efficient production methodsCorresponds to the highest point in the production
possibilities set on the vertical line at a given input level
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Production Function
Mathematically, describe efficient production frontier with a production functionOutput=F(Inputs)
Example: Q=F(L)=10LQ is quantity of output, L is quantity of laborSubstitute different amounts of L to see how output
changes as the firm hires different amounts of laborAmount of output never falls when the amount
of input increases Production function shows output produced for
efficient production methods
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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 stage where one or more inputs is fixed
Long run: a stage where all inputs are variable
production process not time 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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Average and Marginal Products
Average product of labor is the amount of output that is produced per worker:
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:
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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
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
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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 addsIf he is more productive than average, he brings the
average upIf he is less productive than average, he drives the
average down
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AP and MP Curves
For any point on a short run production function:AP is the slope of the straight line
connecting the point to the originMP equals the slope of the line tangent to
the production function at that point
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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
Consider a firm that uses two inputs in the long run:Labor (L) and capital (K)Each of these inputs is homogeneousFirm’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 inputsE.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
Firm’s family of isoquants consists of the isoquants for all of its possible output levels
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Properties of Isoquants
Isoquants are thinDo not slope upwardThe 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
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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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MRTS and Marginal Product
Recall the relationship between MRS and marginal utility
Parallel relationship exists between MRTS and marginal product
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 identicalFirm is able to exchange one for another at a fixed
rateEach isoquant is a straight line, constant MRTS
Two inputs are perfect complements whenThey must be used in fixed proportionsIsoquants are L-shaped
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Cobb-Douglas Production Function
Common production function in economic analysis
Introduced by mathematician Charles Cobb and economist (U.S. Senator) Paul Douglas
General form:
Where A, α, and are parameters that take specific values for a given firm
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Cobb-Douglas Production Function
A shows firm’s general productivity levelα and affect relative productivities of labor
and capital
Substitution between inputs:
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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?
ConstantSame proportional change in
outputOutput doubles
IncreasingGreater than proportional
change in outputOutput more than
doubles
DecreasingLess than proportional
change in outputOutput less than doubles
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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 inputsIts production function shifts upward at each
combination of inputsMay be either general change in productivity
of specifically linked to use of one inputProductivity improvement that leaves
MRTS unchanged is factor-neutral34