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Chapter 22
The Firm:
Cost and Output
Determination

Introduction
The most expensive component of a hybrid or all-electric
passenger vehicle is its set of battery packs.
Automakers have found that the cost of producing a
battery pack declines as more are produced.
Yet, the volume of electric cars is not great enough to
make use of the scale of operation that would minimize
the cost of producing a battery pack.
Reading this chapter will help you understand why the
per-unit cost of battery packs varies with the scale of
production of these items.

Copyright ©2014 Pearson Education, Inc. All rights reserved.

22-2

Learning Objectives
• Discuss the difference between the short
run and the long run from the perspective
of a firm
• Understand why the marginal physical
product of labor eventually declines as more
units of labor are employed
• Explain the short-run cost curves a typical
firm faces


22-3

Learning Objectives (cont’d)
• Describe the long-run cost curves a typical
firm faces
• Identify situations of economies and
diseconomies of scale and define a firm’s
minimum efficient scale


22-4

Chapter Outline
• Short Run versus Long Run
• The Relationship Between Output and
Inputs
• Diminishing Marginal Product
• Short-Run Costs to the Firm
• The Relationship Between Diminishing
Marginal Product and Cost Curves


22-5

Chapter Outline (cont’d)
• Long-Run Cost Curves
• Why the Long-Run Average Cost Curve is UShaped
• Minimum Efficient Scale


22-6

Did You Know That ...
• Utilization of apps is growing more rapidly in the
business world than among consumers?
• Firms are employing apps to manage travel plans,
track equipment, and monitor employees working
time.
• Businesses find that digital apps enable them to
better organize the diverse resources they use to
produce goods and services.


22-7

Short Run versus Long Run
• Short Run
– A time period when at least one input, such as
plant size, cannot be changed
– Plant Size
• The physical size of the factories that a firm owns and
operates to produce its output


22-8

Short Run versus Long Run (cont'd)
• Long Run
– The time period in which all factors of production
can be varied


22-9

Short Run versus Long Run (cont'd)
• Managers take account of both the shortrun and long-run consequences of their
behavior
• While making decisions about what to do
today, tomorrow, and next week—they
keep an eye on the long-run benefits


22-10

The Relationship Between Output
and Inputs
• A firm takes numerous inputs, combines
them using a technological production
process and ends up with output
• We classify production inputs in two broad
categories—labor and capital


22-11

and Inputs (cont'd)

Output per time period = some function of capital and labor inputs

or
Q = ƒ(K,L)
Q = output / time period
K = capital
L = labor


22-12

and Inputs (cont'd)
• Production
– Any activity that results in the conversion of
resources into products that can be used in
consumption


22-13

and Inputs (cont'd)
• Production Function
– The relationship between maximum physical
output and the quantity of capital and labor used
in the production process
– The production function is a technological
relationship between inputs and output.


22-14

Example: 3D Printers Shift from Design to
Production
• 3D printers have been in use since the late 1990s.
Printing physical models is less expensive than
paying skilled workers to construct models by
hand.
• In recent years, some firms have used 3D printing
to produce goods such as airline parts and dental
crowns in their final forms.
• Materials used to create fine layers in 3D-print
production include nylon, plastic, carbon fiber,
stainless steel, and titanium.


22-15

and Inputs (cont'd)
• Average Physical Product
– Total product divided by the variable input


22-16

and Inputs (cont'd)
• Marginal Physical Product
– The physical output that is due to the addition of
one more unit of a variable factor of production
– The change in total product occurring when a
variable input is increased and all other inputs
are held constant
– Also called marginal product


22-17

Figure 22-1 The Production
Function and Marginal
Product: A Hypothetical
Case, Panel (a)


22-18

Figure 22-1 The Production Function and Marginal
Product: A Hypothetical Case, Panel (b)


22-19

Figure 22-1 The Production Function and Marginal
Product: A Hypothetical Case, Panel (c)


22-20

Diminishing Marginal Product
• The marginal product of labor may increase
very rapidly at the beginning
• Beyond some point, marginal product must
begin to diminish as more workers are hired
• This is not because additional workers are
less qualified, but rather because each
worker has, on average, fewer machines to
work with


22-21

(cont'd)
• Law of Diminishing Marginal Product
– The observation that after some point,
successive equal-sized increases in a variable
factor of production, such as labor, added to
fixed factors of production, will result in smaller
increases in output


22-22

(cont’d)
• Production of computer servers as an
example of the law of diminishing marginal
profit:
• We have a fixed amount of factory space,
assembly equipment, and quality control
diagnostic software
– So the addition of more workers eventually
yields successively smaller increases in output


22-23

Diminishing Marginal Product (cont'd)
• After a while, when all the assembly
equipment and quality-control diagnostic
software are being used, additional workers
will have to start assembling and
troubleshooting quality problems manually
• The marginal physical product of an
additional worker, given a specified amount
of capital, must eventually be less than that
for the previous workers


22-24

Diminishing Marginal Product (cont’d)
• Point of saturation
– Given the amount of fixed inputs, there is no
further positive use for more of the variable
input.


22-25

Example: Evaluating the Marginal
Physical Product of Oil Drilling
• Chevron uses a sonic boom technology to
determine which potential drilling locations
in the Gulf of Mexico will yield the most oil.
• By observing energy shifts in different
areas, scientists can distinguish solid rock
from ridges that line pools of oil.
• In this way, Chevron’s geophysicists can
identify locations that will most likely result
in the highest increase in the company’s
marginal physical product.

22-26

Figure 22-2 Cost of Production: An
Example, Panel (a)


22-27

Example, Panel (b)


22-28

Example, Panel (c)


22-29

Policy Example: How the U.S. Army Uses
Virtual Warfare to Cut Variable Costs
• The U.S. Army has long relied on war games to
keep soldiers trained for combat.
• These practice battles, however, are costly in terms
of wear and tear on equipment as well as with
regard to inadvertent injuries.
• To reduce its training expenses, the Army is now
using digital devices such as smartphones and
tablet computers that simulate field exercises with
electronic games, apps, and avatars.
• This approach has slashed the variable costs of
training soldiers.


22-30

Short-Run Costs to the Firm
• Total Costs
– The sum of total fixed costs and total variable costs

• Fixed Costs
– Costs that do not vary with output and are fixed for a
certain period of time, i.e. rent on a building

• Variable Costs
– Costs that vary with the rate of production, i.e. wages
paid to workers and purchases of materials

Total costs (TC) = TFC + TVC

22-31

Short-Run Costs to the Firm (cont'd)
• Average Total Costs (ATC)
– Also called average per-unit total costs

Average total costs (ATC) =


total costs (TC)
output (Q)

22-32

• Average Variable Costs (AVC)

Average variable costs (AVC) =


total variable costs (TVC)
output (Q)

22-33

• Average Fixed Costs (AFC)

Average fixed costs (AFC) =


total fixed costs (TFC)
output (Q)

22-34

International Example: Using Cheap Power from
the Sun to Reduce Average Total Costs
• A number of petroleum companies are now using
heat waves from the sun to extract small pools of
oil that remain after traditional drilling operations.
• Mirrors are used to focus energy waves from the
sun into pipes that will direct steam into remaining
pockets of oil.
• The steam pushes the oil into a position where it
can be extracted.
• This method reduces the average total cost of
extracting oil from the fields.


22-35

• Marginal Cost
– The change in total costs due to a one-unit
change in production rate

Marginal costs (MC) =


change in total cost
change in output

22-36

• Question
– What do you think—is there a predictable
relationship between the production function and
AVC, ATC, and MC?


22-37

• Answer
– As long as marginal physical product rises,
marginal cost will fall, and when marginal
physical product starts to fall (after reaching the
point of diminishing marginal product), marginal
cost will begin to rise


22-38

Short-Run Costs to the Firm (cont’d)
• The relationship between average and
marginal costs:
– When marginal costs are less than average
variable costs, the latter must fall
– When marginal costs are greater than average
variable costs, the latter must rise


22-39

• There is also a relationship between
marginal costs and average total costs
– Average total cost is equal to total cost divided
by the number of units produced
– Marginal cost is the change in total cost due to a
one-unit change in the production rate


22-40

Figure 22-3 The Relationship Between Output
and Costs, Panel (a)


22-41

and Costs, Panel (b)


22-42

and Costs, Panel (c)


22-43

and Costs, Panel (d)


22-44

The Relationship Between Diminishing Marginal
Product and Cost Curves

• Firms’ short-run cost curves are a reflection
of the law of diminishing marginal product
• Given any constant price of the variable
input, marginal costs decline as long as the
marginal product of the variable resource is
rising


22-45

Product and Cost Curves (cont'd)

• At the point at which diminishing marginal
product begins, marginal costs begin to rise
as the marginal product of the variable
input begins to decline


22-46


• If the wage rate is constant, then the labor
cost associated with each additional unit of
output will decline as long as the marginal
physical product (MPP) of labor increases


22-47


• Of course, the average total cost curve and
average variable cost curve are also
affected.
• They will have their familiar U shape in the
short run.


22-48

Long-Run Cost Curves
• Planning Horizon
– The long run, during which all inputs are variable


22-49

Long-Run Cost Curves (cont'd)
• Long-Run Average Cost Curve
– The locus of points representing the minimum
unit cost of producing any given rate of output,
given current technology and resource prices

• Planning Curve
– The long-run average cost curve.


22-50

Figure 22-4 Preferable Plant Size and the
Long-Run Average Cost Curve


22-51

Long-Run Cost Curves (cont'd)
• Observation
– Only at minimum long-run average cost curve is
short-run average cost curve tangent to longrun average cost curve.

• Question
– Why do you think the long-run average cost
curve U-shaped?


22-52

Why the Long-Run Average Cost
Curve is U-Shaped
• Economies of scale
• Constant returns to scale
• Diseconomies of scale


22-53

Curve is U-Shaped (cont'd)
• Economies of Scale
– Decreases in long-run average costs resulting
from increases in output
• These economies of scale do not persist indefinitely,
however.
• Once long-run average costs rise, the curve begins to
slope upwards.


22-54

• Reasons for economies of scale
– Specialization
• Division of tasks or operations

– Dimensional factor
• Large-scale firms often require proportionately less
input per unit of output

– Improved productive equipment
• The larger the enterprise, the more the firm can take
advantage of larger-volume types of machinery.


22-55

Figure 22-5 Economies of Scale, Constant Returns to
Scale, and Diseconomies of Scale Shown with the
Long-Run Average Cost Curve


22-56

• Explaining why a firm might experience
diseconomies of scale
– Limits to the efficient functioning of
management
– Coordination and communication is more of a
challenge as firm size increases


22-57

Example: Diseconomies of Scale at
One of the World’s Top Airlines
• American Airlines is the world’s fourth largest airline
company.
• It operates at a higher long-run cost per passenger
mile than most other airlines. The reason is
because its scale is so large.
• The company is contemplating reducing its number
of flights, selling off regional routes operated by a
subsidiary, and cutting back on the size of its fleet.
• At the current level of operations, American Airlines
is experiencing diseconomies of scale.


22-58

Minimum Efficient Scale
• Minimum Efficient Scale (MES)
– The lowest rate of output per unit time at which
long-run average costs for a particular firm are
at a minimum


22-59

Figure 22-6 Minimum Efficient Scale


22-60

Minimum Efficient Scale (cont'd)
• Small MES relative to industry demand
– There is room for many efficient firms.
– High degree of competition

• Large MES relative to industry demand
– There is room for only a small number of
efficient firms.
– Small degree of competition


22-61

What if . . .the government required firms to
reduce their long-run scales of operation to cut
overall U.S. energy use?

• Requiring firms to reduce their scales of
operation would compel firms to operate
below minimum efficient scale.
• Consequently, average total cost would
increase, and goods and services would be
provided at higher costs per unit.


22-62

You Are There: Cutting Costs by Replacing Pilot
Projects with Simulations

• Schneider National, a large U.S. trucking
firm, has relied on pilot projects to
investigate whether cost-cutting ideas
actually translate into cost savings.
• Since there was a cost involved in running
the pilots, there were instances where no
cost-saving methods were discovered, and
costs actually increased due to conducting
the pilot.


22-63

You Are There: Cutting Costs by Replacing Pilot
Projects with Simulations (cont’d)

• Ted Gifford, an operations research
scientist, developed software to simulate
the pilots, thereby eliminating the need to
actually conduct the pilot projects.
• This has reduced Schneider’s total costs by
tens of millions of dollars per year.


22-64

Issues & Applications: Can Electric Car
Production Attain Minimum Efficient Scale?
• A significant portion of the cost of an electric or
hybrid passenger vehicle is the battery pack.
• To reduce average battery cost, car companies are
expanding their productive capabilities.
• This is an attempt to move down along the average
cost curve to a minimum efficient scale.
• But the number of battery packs consistent with
minimum efficient scale is more than what is
needed to supply the number of electric cars
operating in the U.S.
• Consequently, average costs will remain high.


22-65

Summary Discussion of Learning
Objectives
• The short run versus the long run from a
firm’s perspective
– Short run—a period in which at least one input is
fixed
– Long run—a period in which all inputs are
variable


22-66

Objectives (cont'd)
• The law of diminishing marginal product
– As more units of a variable input are employed with a
fixed input, marginal physical product eventually begins to
decline

• A firm’s short-run cost curves
– Fixed and average fixed cost
– Variable and average variable cost
– Total and average total cost
– Marginal cost


22-67

Objectives (cont'd)
• A firm’s long-run cost curve
– Planning horizon
– All inputs are variable including plant size

• Economies and diseconomies of scale and a firm’s
minimum efficient scale
– Along the down-ward sloping range of the firm’s long-run
average cost curve, the firm experiences economies of
scale
– Along the upward sloping portion, the firm encounters
diseconomies of scale


22-68

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