Technology
and
Production
chapter 7
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
Learning Objectives
• Explain how to identify a firm’s efficient
production methods.
• Calculate average product and marginal product
and explain how they measure a firm’s
productivity.
• Discuss input substitution with two variable
inputs.
• Understand the concept of returns to scale and
its causes.
• Discuss the sources of productivity differences
across firms and over time.
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-2
Overview
• Among all possible production technologies, firms
use the most efficient methods
• The simplest production function requires one
input, but usually we encounter two or more
variable inputs
• As firms grow and increase the use of all inputs, the
effect on production may not be proportional –
returns to scale
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-3
Production Technologies
• Outputs: the physical products or services a firm
produces
• Inputs: the materials, labor, land, or equipment that
firms use to produce their outputs
• Production technology: summarizes all possible
methods for producing output
• Efficient: when there is no way for the firm to
produce a larger amount of output using the same
amounts of inputs
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-4
Production Possibilities Set and
Efficient Production Frontier
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-5
Production Possibilities Set and
Efficient Production Frontier
• Production possibilities
set: contains all
combinations of inputs
and outputs that are
possible given the firm’s
technology
• Efficient production
frontier: contains the
combinations of inputs
and outputs that the firm
can achieve using efficient
production methods
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-6
Production Functions
• Production function: states the amount of output a
firm can produce from given amounts of inputs using
efficient production methods
– Output = F(Inputs)
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-7
Production in the Short Run and
the Long Run
• Variable input: can be adjusted over the time period
being considered
• Fixed input: cannot be adjusted over the time period
being considered
• Short run: a period of time over which one or more
inputs is fixed
• Long run: a period of time over which all inputs are
variable
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-8
Average Product
• Average product of labor: the amount of output
divided by the number of workers employed
Q F(L)
– APL = =
L L
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-9
Production Function and Average
Product Curve
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-10
Marginal Product
• Marginal product of labor: the extra output
produced due to the L marginal units of labor, per
unit of labor
–
DQ F(L)- F(L - DL)
MPL = =
DL
DL
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-11
Production Function and Marginal
Product
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-12
Law of Diminishing Marginal
Returns
• Law of diminishing marginal returns: states the
general tendency for the marginal product of an
input to eventually decline as its use is increased
holding all other inputs fixed
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-13
Average and Marginal Product
• If the marginal
worker is more
productive than
average, she brings
the average up. If
she is less
productive than
average, she drives
the average down.
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-14
Optimal Assignment of Workers
between Two Plants
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-15
Production with Two Variable
Inputs
• Two inputs: labor (L) and capital (K)
• Production function: Q = F(L, K)
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-16
Input Substitution
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-17
Isoquants
• Isoquant: identifies
all the input
combinations a firm
can use to efficiently
produce a given
amount of output
• Family of isoquants:
consists of the
isoquants
corresponding to all
possible output
levels
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-18
Productive Input Principle
Increasing the amounts of all inputs strictly increases
the amount of output the firm can produce (using
efficient production methods).
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-19
Properties of Isoquants
• Isoquants are thin
Output in A > B due
to productive input
principle ⇒ B and A
cannot belong in the
same isoquant
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-20
Properties of Isoquants
• Isoquants are thin
• Isoquants do not slope
upward
Output in A > B due
to productive input
principle ⇒ A and B
cannot belong in the
same isoquant
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-21
Properties of Isoquants
• Isoquants are thin
• Isoquants do not slope upward
• An isoquant is the boundary
between input combinations
that produce more than a
given amount of output and
those that produce less
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-22
Properties of Isoquants
• Isoquants are thin
• Isoquants do not slope
upward
• An isoquant is the boundary
between input combinations
that produce more than a
given amount of output and
those that produce less
• Isoquants for the same
technology do not cross
However, this is impossible
since the output in C > B due
to the productive input
principle
ByBytransitivity,
transitivity,BBand
andCCshould
should
produce
producethe
thesame
sameoutput
output
Similarly,
Similarly,bybybeing
beingon
onthe
thesame
same
isoquant,
isoquant,AAand
andCCproduce
producethe
the
same
sameoutput.
output.
CC
ByBybeing
beingon
onthe
thesame
same
isoquant,
isoquant,AAand
andBB
produce
producethe
thesame
same
output.
output.
BB
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-23
Properties of Isoquants
• Isoquants are thin
• Isoquants do not slope
upward
• An isoquant is the boundary
between input combinations
that produce more than a
given amount of output and
those that produce less
• Isoquants for the same
technology do not cross
• Higher-level isoquants lie
farther from the origin
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-24
Substitution between Labor and Capital
Along an Isoquant and the MRTS
Marginal rate of
technical substitution
(MRTS) for input X
with input Y: the rate
at which a firm must
replace units of X
with units of Y to
keep output
unchanged starting at
a given input
combination
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-25
Declining MRTS
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-26
MRTS and Marginal Products
Along the Same Isoquant
(MPL ´DL)+(MPK ´DK) = 0
-DK DL = MPL MPK
MPL
MRTSLK =
MPK
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-27
Input Substitution for Three
Special Production Technologies
• Perfect substitutes
• Perfect complements (fixed proportions)
• The Cobb-Douglas production function
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-28
Perfect Substitutes
• If the functions of
two inputs are
identical, so that a
firm can exchange
one for another at a
fixed rate
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-29
Perfect Complements (Fixed
Proportions)
• When two inputs
must be combined
in a fixed ratio
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-30
The Cobb-Douglas Production
Function
Q = F(L, K) = ALa K b
MPL = a ALa-1K b
MPK = b ALa K b-1
a K
MRTSLK = ( )( )
b L
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-31
Returns to Scale
• Constant returns to scale
• Increasing returns to scale
• Decreasing returns to scale
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-32
Returns to Scale
• Constant returns to
scale: when a
proportional change in
all inputs produces the
same proportional
change in output
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-33
Returns to Scale
• Increasing returns to
scale: when a
proportional change in
all inputs produces a
more than proportional
change in output
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-34
Returns to Scale
• Decreasing returns to
scale: when a
proportional change in
all inputs produces a
less than proportional
change in output
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-35
Implications of Returns to Scale
• With increasing returns to scale, production is most
efficient if there is a single producer
• However, a single producer may not operate in a
manner that would benefit consumers
• More when we discuss natural monopoly in Chapter
17
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-36
Productivity and Technological
Change
Technological change: when a firm’s
ability to turn inputs into output changes
over time
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-37
Productivity Improvement
• Higher productivity:
when a firm can
produce more
output using the
same amounts of
inputs
• Factor-neutral
technical change: a
productivity
improvement that
keeps the MRTS
unchanged at every
input combination
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-38
Reasons for Productivity
Differences
• Firms may be subject to different regulations
or market circumstances
• Examples: labor laws, union contracts
• Firms may have different levels of technical,
organizational knowledge, research and
development; learning by doing
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-39
Review
• A production method is efficient if there is no way to
produce larger amounts of outputs using the same amounts
of inputs
• Production with one variable input: when the marginal
product of labor is (larger than/smaller than/equal to) the
average product of labor, the average product is (increased
by/decreased by/unchanged by) the marginal units of labor.
• A firm has (constant/increasing/decreasing) returns to scale
if a proportional change in all inputs leads to (the same/a
greater than/a less than) proportional change in output.
• A firm is more productive when it can produce more output
using the same amount of inputs.
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-40
Looking Forward
• Next, we will learn how firms put together their
production possibilities, with the cost of individual
inputs, to determine the optimal combination of
inputs for different outputs, and the resulting cost of
production for each level of output
Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
7-41