Ebook Managerial economics - Foundations of business analysis and strategy (12th edition): Part 2

Chapter

9

www.downloadslide.com

Production and Cost
in the Long Run
After reading this chapter, you will be able to:
9.1 Graph a typical production isoquant and discuss the properties of isoquants.
9.2 Construct isocost curves for a given level of expenditure on inputs.
9.3 Apply optimization theory to find the optimal input combination.
9.4 Construct the firm’s expansion path and show how it relates to the firm’s longrun cost structure.
9.5 Calculate long-run total, average, and marginal costs from the firm’s expansion
path.
9.6 Explain how a variety of forces affects long-run costs: scale, scope, learning,
and purchasing economies.
9.7 Show the relation between long-run and short-run cost curves using long-run
and short-run expansion paths.

N

o matter how a firm operates in the short run, its manager can always
change things at some point in the future. Economists refer to this
future period as the “long run.” Managers face a particularly important constraint on the way they can organize production in the short run: The
usage of one or more inputs is fixed. Generally the most important type of fixed
input is the physical capital used in production: machinery, tools, computer
hardware, buildings for manufacturing, office space for administrative operations, facilities for storing inventory, and so on. In the long run, managers can
choose to operate with whatever amounts and kinds of capital resources they
wish. This is the essential feature of long-run analysis of production and cost.
In the long run, managers are not stuck with too much or too little capital—

or any fixed input for that matter. As you will see in this chapter, long-run
311


www.downloadslide.com
312  C H A P T E R 9   Production and Cost in the Long Run

flexibility in resource usage usually creates an opportunity for firms to reduce
their costs in the long run.
Since a long-run analysis of production generates the “best-case” scenario for
costs, managers cannot make tactical and strategic decisions in a sensible way
unless they possess considerable understanding of the long-run cost structure available to their firms, as well as the long-run costs of any rival firms they might face.
As we mentioned in the previous chapter, firms operate in the short run and plan for
the long run. The managers in charge of production operations must have accurate
information about the short-run cost measures discussed in Chapter 8, while the
executives responsible for long-run planning must look beyond the constraints imposed by the firm’s existing short-run configuration of productive inputs to a future
situation in which the firm can choose the optimal combination of inputs.
Recently, U.S. auto manufacturers faced historic challenges to their survival, forcing executive management at Ford, Chrysler, and General Motors to examine every
possible way of reorganizing production to reduce long-run costs. While shortrun costs determined their current levels of profitability—or losses in this case—it
was the flexibility of long-run adjustments in the organization of production and
structure of costs that offered some promise of a return to profitability and economic
survival of American car producers. The outcome for U.S. carmakers depends
on many of the issues you will learn about in this chapter: economies of scale,
economies of scope, purchasing economies, and learning economies. And, as you
will see in later chapters, the responses by rival auto producers—both American and
foreign—will depend most importantly on the rivals’ long-run costs of producing
cars, SUVs, and trucks. Corporate decisions concerning such matters as adding new
product lines (e.g., hybrids or electric models), dropping current lines (e.g., Pontiac
at GM), allowing some divisions to merge, or even, as a last resort, exiting through
bankruptcy all require accurate analyses and forecasts of long-run costs.

In this chapter, we analyze the situation in which the fixed inputs in the short
run become variable inputs in the long run. In the long run, we will view all ­inputs
as variable inputs, a situation that is both more complex and more i­ nteresting than
production with only one variable input—labor. For clarification and c­ ompleteness,
we should remind you that, unlike fixed inputs, quasi-fixed inputs do not become
variable inputs in the long run. In both the short- and long-run periods, they are
indivisible in nature and must be employed in specific lump amounts that do not
vary with output—unless output is zero, and then none of the quasi-fixed inputs
will be employed or paid. Because the amount of a quasi-fixed input used in the
short run is generally the same amount used in the long run, we do not include
quasi-fixed inputs as choice variables for long-run production ­decisions.1 With this
distinction in mind, we can say that all inputs are variable in the long run.
1
An exception to this rule occurs when, as output increases, the fixed lump amount of input
eventually becomes fully utilized and constrains further increases in output. Then, the firm must add
another lump of quasi-fixed input in the long run to allow further expansion of output. This exception is not particularly important because it does not change the principles set forth in this chapter
or other chapters in this textbook. Thus, we will continue to assume that when a quasi-fixed input is
required, only one lump of the input is needed for all positive levels of output.


www.downloadslide.com
C H A P T E R 9   Production and Cost in the Long Run   313

9.1  PRODUCTION ISOQUANTS
isoquant
A curve showing all
possible combinations of
inputs p
­ hysically capable
of p

­ roducing a given
fixed level of output.

An important tool of analysis when two inputs are variable is the production
isoquant or simply isoquant. An isoquant is a curve showing all possible combinations of the inputs physically capable of producing a given (fixed) level of output.
Each point on an isoquant is technically efficient; that is, for each combination
on the isoquant, the maximum possible output is that associated with the given
isoquant. The concept of an isoquant implies that it is possible to substitute some
amount of one input for some of the other, say, labor for capital, while keeping
output constant. Therefore, if the two inputs are continuously divisible, as we will
assume, there are an infinite number of input combinations capable of producing
each level of output.
To understand the concept of an isoquant, return for a moment to Table 8.2 in
the preceding chapter. This table shows the maximum output that can be produced by combining different levels of labor and capital. Now note that several
levels of output in this table can be produced in two ways. For example, 108 units
of output can be produced using either 6 units of capital and 1 worker or 1 unit of
capital and 4 workers. Thus, these two combinations of labor and capital are two
points on the isoquant associated with 108 units of output. And if we assumed
that labor and capital were continuously divisible, there would be many more
combinations on this isoquant.
Other input combinations in Table 8.2 that can produce the same level of
output are
Q 5 258: using K 5 2, L 5 5orK 5 8, L 5 2
Q 5 400: using K 5 9, L 5 3orK 5 4, L 5 4
Q 5 453: using K 5 5, L 5 4orK 5 3, L 5 7
Q 5 708: using K 5 6, L 5 7orK 5 5, L 5 9
Q 5 753: using K 5 10, L 5 6or K 5 6, L 5 8
Each pair of combinations of K and L is two of the many combinations
associated with each specific level of output. Each demonstrates that it is possible
to increase capital and decrease labor (or increase labor and decrease capital)

while keeping the level of output constant. For example, if the firm is producing
400  units of output with 9 units of capital and 3 units of labor, it can increase
labor by 1, decrease capital by 5, and keep output at 400. Or if it is producing 453
units of output with K 5 3 and L 5 7, it can increase K by 2, decrease L by 3, and
keep output at 453. Thus an isoquant shows how one input can be substituted for
another while keeping the level of output constant.
Characteristics of Isoquants
We now set forth the typically assumed characteristics of isoquants when labor,
capital, and output are continuously divisible. Figure 9.1 illustrates three such
isoquants. Isoquant Q1 shows all the combinations of capital and labor that yield
100 units of output. As shown, the firm can produce 100 units of output by u
­ sing
10 units of capital and 75 of labor, or 50 units of capital and 15 of labor, or any other


www.downloadslide.com
314  C H A P T E R 9   Production and Cost in the Long Run
F I G U R E 9.1
A Typical Isoquant Map

Units of capital (K )

50
40

20

Q2 = 200
T

10

0

Q3 = 300

A

15 20

40

Q1 = 100

75

Units of labor (L)

isoquant map
A graph showing a
group of isoquants.

combination of capital and labor on isoquant Q1. Similarly, isoquant Q2 shows the
various combinations of capital and labor that can be used to produce 200 units
of output. And isoquant Q3 shows all combinations that can produce 300 units
of output. Each capital–labor combination can be on only one isoquant. That is,
isoquants cannot intersect.
Isoquants Q1, Q2, and Q3 are only three of an infinite number of isoquants that
could be drawn. A group of isoquants is called an isoquant map. In an isoquant
map, all isoquants lying above and to the right of a given isoquant indicate higher

levels of output. Thus in Figure 9.1 isoquant Q2 indicates a higher level of output
than isoquant Q1, and Q3 indicates a higher level than Q2.
Marginal Rate of Technical Substitution

marginal rate of
technical substitution
(MRTS)
The rate at which one
input is substituted
for another along an
isoquant
DK
​2​  ___  ​  ​.
DL

1

2

As depicted in Figure 9.1, isoquants slope downward over the relevant range of
production. This negative slope indicates that if the firm decreases the amount of
capital employed, more labor must be added to keep the rate of output constant.
Or if labor use is decreased, capital usage must be increased to keep output
constant. Thus the two inputs can be substituted for one another to maintain a
constant level of output. The rate at which one input is substituted for another
along an isoquant is called the marginal rate of technical substitution (MRTS)
and is defined as
DK ​ 
MRTS 5 2​ ___
DL

The minus sign is added to make MRTS a positive number because DK/DL, the
slope of the isoquant, is negative.


www.downloadslide.com
C H A P T E R 9   Production and Cost in the Long Run   315

Over the relevant range of production, the marginal rate of technical substitution diminishes. As more and more labor is substituted for capital while holding
output constant, the absolute value of DK/DL decreases. This can be seen in
Figure 9.1. If capital is reduced from 50 to 40 (a decrease of 10 units), labor must be
increased by 5 units (from 15 to 20) to keep the level of output at 100 units. That is,
when capital is plentiful relative to labor, the firm can discharge 10 units of capital
but must substitute only 5 units of labor to keep output at 100. The marginal rate
of technical substitution in this case is 2DK/DL 5 2(210)/5 5 2, meaning that for
every unit of labor added, 2 units of capital can be discharged to keep the level of
output constant. However, consider a combination where capital is more scarce
and labor more plentiful. For example, if capital is decreased from 20 to 10 (again
a decrease of 10 units), labor must be increased by 35 units (from 40 to 75) to keep
output at 100 units. In this case the MRTS is 10/35, indicating that for each unit of
labor added, capital can be reduced by slightly more than one-quarter of a unit.
As capital decreases and labor increases along an isoquant, the amount of
capital that can be discharged for each unit of labor added declines. This relation
is seen in Figure 9.1. As the change in labor and the change in capital become
extremely small around a point on an isoquant, the absolute value of the slope of
a tangent to the isoquant at that point is the MRTS (2DK/DL) in the neighborhood
of that point. In Figure 9.1, the absolute value of the slope of tangent T to isoquant
Q1 at point A shows the marginal rate of technical substitution at that point. Thus
the slope of the isoquant reflects the rate at which labor can be substituted for
capital. As you can see, the isoquant becomes less and less steep with movements
downward along the isoquant, and thus MRTS declines along an isoquant.

Relation of MRTS to Marginal Products
For very small movements along an isoquant, the marginal rate of technical
substitution equals the ratio of the marginal products of the two inputs. We will
now demonstrate why this comes about.
The level of output, Q, depends on the use of the two inputs, L and K. Since Q
is constant along an isoquant, DQ must equal zero for any change in L and K that
would remain on a given isoquant. Suppose that, at a point on the isoquant, the
marginal product of capital (MPK) is 3 and the marginal product of labor (MPL)
is 6. If we add 1 unit of labor, output would increase by 6 units. To keep Q at
the original level, capital must decrease just enough to offset the 6-unit increase
in output generated by the increase in labor. Because the marginal product of
capital is 3, 2 units of capital must be discharged to reduce output by 6 units.
In this case the MRTS 5 2DK/DL 5 2(22)/1 5 2, which is exactly equal to
MPL/MPK  5 6/3 5 2.
In more general terms, we can say that when L and K are allowed to vary
slightly, the change in Q resulting from the change in the two inputs is the ­marginal
product of L times the amount of change in L plus the marginal product of K times
its change. Put in equation form
DQ 5 (MPL)(DL) 1 (MPK)(DK)


www.downloadslide.com
316  C H A P T E R 9   Production and Cost in the Long Run

To remain on a given isoquant, it is necessary to set DQ equal to 0. Then, solving
for the marginal rate of technical substitution yields
DK MPL
MRTS 5 2​ ___ ​ 5 _____
 
 ​

​ 
DL MPK

Now try Technical
Problem 1.

Using this relation, the reason for diminishing MRTS is easily explained. As
additional units of labor are substituted for capital, the marginal product of labor
diminishes. Two forces are working to diminish labor’s marginal product: (1) Less
capital causes a downward shift of the marginal product of labor curve, and
(2) more units of the variable input (labor) cause a downward movement along the
marginal product curve. Thus, as labor is substituted for capital, the marginal product of labor must decline. For analogous reasons the marginal product of capital
increases as less capital and more labor are used. The same two forces are present
in this case: a movement along a marginal product curve and a shift in the location
of the curve. In this situation, however, both forces work to increase the marginal
product of capital. Thus, as labor is substituted for capital, the marginal product of
capital increases. Combining these two conditions, as labor is substituted for capital, MPL decreases and MPK increases, so MPL/MPK will decrease.

9.2  ISOCOST CURVES

isocost curve
Line that shows the
various combinations of
inputs that may be purchased for a given level
of expenditure at given
input prices.

Producers must consider relative input prices to find the least-cost c­ ombination of
inputs to produce a given level of output. An extremely useful tool for analyzing
the cost of purchasing inputs is an isocost curve. An isocost curve shows all

combinations of inputs that may be purchased for a given level of total expenditure
at given input prices. As you will see in the next section, isocost curves play a key
role in finding the combination of inputs that produces a given output level at the
lowest possible total cost.
Characteristics of Isocost Curves
Suppose a manager must pay $25 for each unit of labor services and $50 for each
unit of capital services employed. The manager wishes to know what combinations of labor and capital can be purchased for $400 total expenditure on inputs.
Figure 9.2 shows the isocost curve for $400 when the price of labor is $25 and
the price of capital is $50. Each combination of inputs on this isocost curve costs
$400 to purchase. Point A on the isocost curve shows how much capital could be
purchased if no labor is employed. Because the price of capital is $50, the manager
can spend all $400 on capital alone and purchase 8 units of capital and 0 units of
labor. Similarly, point D on the isocost curve gives the maximum amount of labor—
16 units—that can be purchased if labor costs $25 per unit and $400 are spent on
labor alone. Points B and C also represent input combinations that cost $400. At
point B, for example, $300 (5 $50 3 6) are spent on capital and $100 (5 $25 3 4)
are spent on labor, which represents a total cost of $400.
If we continue to denote the quantities of capital and labor by K and L, and
denote their respective prices by r and w, total cost, C, is C 5 wL 1 rK. Total cost is


www.downloadslide.com
C H A P T E R 9   Production and Cost in the Long Run   317
F I G U R E 9.2
An Isocost Curve
(w 5 $25 and r 5 $50)

Capital (K )

10

8

A
B

6

K=8–

C

4

1
2

L

2
0

D
2

4

6

8

10

12

14

16

18

20

Labor (L)

simply the sum of the cost of L units of labor at w dollars per unit and of K units of
capital at r dollars per unit:
C 5 wL 1 rK
In this example, the total cost function is 400 5 25L 1 50K. Solving this equation for
400 ___
25
K, you can see the combinations of K and L that can be chosen: K 5 ​ ____
50 ​ 2 ​  50  ​L 5
__
1  ​ L. More generally, if a fixed amount ​C​  is to be spent, the firm can choose
8 2 ​ __
2
among the combinations given by
__
C​
​   ​  w ​L

__
K 5 ​ r ​  2 __
r 
__
If ​C​  is the total amount to be spent__on inputs, the most capital that can be
purchased (if no labor is purchased) is ​C​ /r units__of capital, and the most labor that
can be purchased (if no capital is purchased) is C​
​  /w units of labor.
The slope of the isocost curve is equal to the negative of the relative input price
ratio, 2w/r. This ratio is important because it tells the manager how much capital
must be given up if one more unit of labor is purchased. In the example just given
and illustrated in Figure 9.2, 2w/r 5 2$25/$50 5 21/2. If the manager wishes
to purchase 1 more unit of labor at $25, 1/2 unit of capital, which costs $50, must
be given up to keep the total cost of the input combination constant. If the price of
labor happens to rise to $50 per unit, r remaining constant, the slope of the isocost
curve is 2$50/$50 5 21, which means the manager must give up 1 unit of capital
for each additional unit of labor purchased to keep total cost constant.
Shifts in Isocost Curves
If the constant level of total cost associated with a particular isocost curve changes,
the isocost curve shifts parallel. Figure 9.3 shows how the isocost curve shifts


www.downloadslide.com
318  C H A P T E R 9   Production and Cost in the Long Run
F I G U R E 9.3
Shift in an Isocost Curve
12

Capital (K )

10
8
6

K = 10 –

1
2

L

4
K=8–

2
0

2

4

1
2

6

L

8

10

12

14

16

18

20

Labor (L)

__

when the total expenditure on resources (​C​ ) increases from $400 to $500. The isocost curve shifts out parallel, and the equation for the new isocost curve is
K 5 10 2 __
​  1 ​ L
2
The slope is still 21/2 because 2w/r does not change. The K-intercept is now 10,
indicating that a maximum of 10 units of capital can be purchased if no labor is
purchased and $500 are spent.
In general, an increase in cost, holding input prices constant, leads to a parallel
upward shift in the isocost curve. A decrease in cost, holding input prices constant,
leads to a parallel downward shift in the isocost curve. An infinite number of
isocost curves exist, one for each level of total cost.
__

Relation  At constant input prices, w and r for labor and capital, a given expenditure on inputs (C )  will

purchase any combination of labor and capital given by the following equation, called an isocost curve:
__

​   __
C​
w
K 5 __
​ r ​ 2
  ​  r  ​  L

Now try Technical
Problem 2.

  

9.3  FINDING THE OPTIMAL COMBINATION OF INPUTS
We have shown that any given level of output can be produced by many
combinations of inputs—as illustrated by isoquants. When a manager wishes
to produce a given level of output at the lowest possible total cost, the manager
chooses the combination on the desired isoquant that costs the least. This is a
constrained m
­ inimization problem that a manager can solve by following the rule
for constrained optimization set forth in Chapter 3.


www.downloadslide.com
C H A P T E R 9   Production and Cost in the Long Run   319

Although managers whose goal is profit maximization are generally and primarily concerned with searching for the least-cost combination of inputs to produce a
given (profit-maximizing) output, managers of nonprofit organizations may face

an alternative situation. In a nonprofit situation, a manager may have a budget or
fixed amount of money available for production and wish to maximize the amount
of output that can be produced. As we have shown using isocost curves, there are
many different input combinations that can be purchased for a given (or fixed)
amount of expenditure on inputs. When a manager wishes to maximize output for
a given level of total cost, the manager must choose the input combination on the
isocost curve that lies on the highest isoquant. This is a constrained maximization
problem, and the rule for solving it was set forth in Chapter 3.
Whether the manager is searching for the input combination that minimizes
cost for a given level of production or maximizes total production for a given level
of expenditure on resources, the optimal combination of inputs to employ is found
by using the same rule. We first illustrate the fundamental principles of cost minimization with an output constraint; then we will turn to the case of output maximization given a cost constraint.
Production of a Given Output at Minimum Cost
The principle of minimizing the total cost of producing a given level of output
is illustrated in Figure 9.4. The manager wants to produce 10,000 units of output
F I G U R E 9.4
Optimal Input Combination to Minimize Cost for
a Given Output
140
134

Capital (K )

120
100

KЈ

K'
100

K''

KЉ
Kٞ

A
B

90

A

L'
L''

B

60 66
E

60

C

40

Q1 = 10,000

Lٞ
0

60

90

150
Labor (L)

180

LЉ
201

LЈ
210


www.downloadslide.com
320  C H A P T E R 9   Production and Cost in the Long Run

at the lowest possible total cost. All combinations of labor and capital capable of
producing this level of output are shown by isoquant Q1. The price of labor (w) is
$40 per unit, and the price of capital (r) is $60 per unit.
Consider the combination of inputs 60L and 100K, represented by point A on
isoquant Q1. At point A, 10,000 units can be produced at a total cost of $8,400,
where the total cost is calculated by adding the total expenditure on labor and the
total expenditure on capital:2
C 5 wL 1 rK 5 ($40 3 60) 1 ($60 3 100) 5 $8,400
The manager can lower the total cost of producing 10,000 units by moving down
along the isoquant and purchasing input combination B, because this combination

of labor and capital lies on a lower isocost curve (K0L0) than input combination A,
which lies on K9L9. The blowup in Figure 9.4 shows that combination B uses 66L
and 90K. Combination B costs $8,040 [5 ($40 3 66) 1 ($60 3 90)]. Thus the manager
can decrease the total cost of producing 10,000 units by $360 (5 $8,400 2 $8,040) by
moving from input combination A to input combination B on isoquant Q1.
Since the manager’s objective is to choose the combination of labor and capital
on the 10,000-unit isoquant that can be purchased at the lowest possible cost, the
manager will continue to move downward along the isoquant until the lowest
possible isocost curve is reached. Examining Figure 9.4 reveals that the lowest cost
of producing 10,000 units of output is attained at point E by using 90 units of labor and 60 units of capital on isocost curve K'''L''', which shows all input combinations that can be purchased for $7,200. Note that at this cost-minimizing input
combination
C 5 wL 1 rK 5 ($40 3 90) 1 ($60 3 60) 5 $7,200
No input combination on an isocost curve below the one going through point E is
capable of producing 10,000 units of output. The total cost associated with input
combination E is the lowest possible total cost for producing 10,000 units when
w 5 $40 and r 5 $60.
Suppose the manager chooses to produce using 40 units of capital and 150 units
of labor—point C on the isoquant. The manager could now increase capital and
reduce labor along isoquant Q1, keeping output constant and moving to lower and
lower isocost curves, and hence lower costs, until point E is reached. Regardless
of whether a manager starts with too much capital and too little labor (such as
point A) or too little capital and too much labor (such as point C), the manager can
move to the optimal input combination by moving along the isoquant to lower
and lower isocost curves until input combination E is reached.
At point E, the isoquant is tangent to the isocost curve. Recall that the slope
(in absolute value) of the isoquant is the MRTS, and the slope of the isocost curve
2
Alternatively, you can calculate the cost associated with an isocost curve as the maximum
amount of labor that could be hired at $40 per unit if no capital is used. For K9L9, 210 units of labor
could be hired (if K 5 0) for a cost of $8,400. Or 140 units of capital can be hired at $60 (if L 5 0) for a

cost of $8,400.


www.downloadslide.com
C H A P T E R 9   Production and Cost in the Long Run   321

(in absolute value) is equal to the relative input price ratio, w/r. Thus, at point E,
MRTS equals the ratio of input prices. At the cost-minimizing input combination,
w
MRTS 5 __
​ r ​ 
Now try Technical
Problem 3.

To minimize the cost of producing a given level of output, the manager employs
the input combination for which MRTS 5 w/r.
The Marginal Product Approach to Cost Minimization
Finding the optimal levels of two activities A and B in a constrained optimization problem involved equating the marginal benefit per dollar spent on each
of the activities (MB/P). A manager compares the marginal benefit per dollar
spent on each activity to determine which activity is the “better deal”: that
is, which activity gives the higher marginal benefit per dollar spent. At their
optimal levels, both activities are equally good deals (MBA/PA 5 MBB/PB) and
the constraint is met.
The tangency condition for cost minimization, MRTS 5 w/r, is equivalent to
the condition of equal marginal benefit per dollar spent. Recall that MRTS 5 MPL/
MPK; thus the cost-minimizing condition can be expressed in terms of marginal
products
MPL __
w
MRTS 5 ​ _____

 ​ 5 ​  r ​ 
MP  
K

After a bit of algebraic manipulation, the optimization condition may be
expressed as
MPL _____
MPK
 
 5 ​  r ​
 
 
​ ____
w ​
The marginal benefits of hiring extra units of labor and capital are the marginal
products of labor and capital. Dividing each marginal product by its respective
input price tells the manager the additional output that will be forthcoming if
one more dollar is spent on that input. Thus, at point E in Figure 9.4, the marginal
product per dollar spent on labor is equal to the marginal product per dollar spent
on capital, and the constraint is met (Q 5 10,000 units).
To illustrate how a manager uses information about marginal products and
­input prices to find the least-cost input combination, we return to point A in
Figure 9.4, where MRTS is greater than w/r. Assume that at point A, MPL 5 160
and MPK 5 80; thus MRTS 5 2 (5 MPL/MPK 5 160/80). Because the slope of the
isocost curve is 2/3 (5 w/r 5 40/60), MRTS is greater than w/r, and
MPK
MPL ____
80 _____
160
___

​ ____
 
 5 ​ 
 
 
 
 
 ​
5
4
.
1.33
5
​ 
 ​
5
​ 
r ​
w ​
60
40
The firm should substitute labor, which has the higher marginal product per
dollar, for capital, which has the lower marginal product per dollar. For example,
an additional unit of labor would increase output by 160 units while increasing
labor cost by $40. To keep output constant, 2 units of capital must be released,


www.downloadslide.com
322  C H A P T E R 9   Production and Cost in the Long Run

causing output to fall 160 units (the marginal product of each unit of capital
released is 80), but the cost of capital would fall by $120, which is $60 for each
of the 2 units of capital released. Output remains constant at 10,000 because the
higher output from 1 more unit of labor is just offset by the lower output from
two fewer units of capital. However, because labor cost rises by only $40 while
capital cost falls by $120, the total cost of producing 10,000 units of output falls
by $80 (5 $120 2 $40).
This example shows that when MPL/w is greater than MPK/r, the manager
can reduce cost by increasing labor usage while decreasing capital usage just
enough to keep output constant. Because MPL/w . MPK/r for every input
combination along Q1 from point A to point E, the firm should continue to
substitute labor for capital until it reaches point E. As more labor is used, MPL
falls because of diminishing marginal product. As less capital is used, MPK rises
for the same reason. As the manager substitutes labor for capital, MRTS falls
until equilibrium is reached.
Now consider point C, where MRTS is less than w/r, and consequently MPL/w
is less than MPK/r. The marginal product per dollar spent on the last unit of labor
is less than the marginal product per dollar spent on the last unit of capital. In
this case, the manager can reduce cost by increasing capital usage and decreasing labor usage in such a way as to keep output constant. To see this, assume that
at point C, MPL 5 40 and MPK 5 240, and thus MRTS 5 40/240 5 1/6, which is
less than w/r (5 2/3). If the manager uses one more unit of capital and 6 fewer
units of labor, output stays constant while total cost falls by $180. (You should
verify this yourself.) The manager can continue moving upward along isoquant
Q1, keeping output constant but reducing cost until point E is reached. As capital
is increased and labor decreased, MPL rises and MPK falls until, at point E, MPL/w
equals MPK/r. We have now derived the following:
Principle  To produce a given level of output at the lowest possible cost when two inputs (L and K) are
variable and the prices of the inputs are, respectively, w and r, a manager chooses the combination of inputs
for which
MPL

w
MRTS 5 ____
​   ​  5  ​ __
r ​  
MP
which implies that

Now try Technical
Problem 4.

K

MPL ____
MPK
____
  ​  r ​
  
​ w ​  5

The isoquant associated with the desired level of output (the slope of which is the MRTS) is tangent
to the isocost curve (the slope of which is w/r) at the optimal combination of inputs. This optimization
condition also means that the marginal product per dollar spent on the last unit of each input is the
same.

Production of Maximum Output with a Given Level of Cost
As discussed earlier, there may be times when managers can spend only a fixed
amount on production and wish to attain the highest level of production consistent


www.downloadslide.com

C H A P T E R 9   Production and Cost in the Long Run   323
F I G U R E 9.5
Output Maximization for
a Given Level of Cost

Capital (K )

K

E

KE

KS

Q2 = 1,000

R

KR
0

Q3 = 1,700

S

Q1 = 500
LE

LS

LR

L

Labor (L)

with that amount of expenditure. This is a constrained maximization problem the
optimization condition for constrained maximization is the same as that for constrained minimization. In other words, the input combination that maximizes the
level of output for a given level of total cost of inputs is that combination for which
MPK
MPL _____
w
MRTS 5 __
​ r ​    or  ____
 
 5 ​  r ​
 
 
​  w ​
This is the same condition that must be satisfied by the input combination that
minimizes the total cost of producing a given output level.
This situation is illustrated in Figure 9.5. The isocost line KL shows all possible
combinations of the two inputs that can be purchased for the level of total cost (and
input prices) associated with this isocost curve. Suppose the manager chooses point
R on the isocost curve and is thus meeting the cost constraint. Although 500 units of
output are produced using LR units of labor and KR units of capital, the manager could
produce more output at no additional cost by using less labor and more capital.
This can be accomplished, for example, by moving up the isocost curve to
point S. Point S and point R lie on the same isocost curve and consequently cost

the same amount. Point S lies on a higher isoquant, Q2, allowing the manager to
­produce 1,000 units without spending any more than the given amount on inputs
(represented by isocost curve KL). The highest level of output attainable with the


www.downloadslide.com
324  C H A P T E R 9   Production and Cost in the Long Run

given level of cost is 1,700 units (point E), which is produced by using LE labor and
KE capital. At point E, the highest attainable isoquant, isoquant Q3, is just tangent
to the given isocost, and MRTS 5 w/r or MPL/w 5 MPK/r, the same conditions
that must be met to minimize the cost of producing a given output level.
To see why MPL/w must equal MPK/r to maximize output for a given level
of expenditures on inputs, suppose that this optimizing condition does not hold.
Specifically, assume that w 5 $2, r 5 $3, MPL 5 6, and MPK 5 12, so that
MPK
MPL __
6
12 _____
___
____
​  w ​
 
 5 ​   ​  5 3 , 4 5 ​   ​ 5 ​  r ​
 
 
2
3
The last unit of labor adds 3 units of output per dollar spent; the last unit
of capital adds 4 units of output per dollar. If the firm wants to produce the

maximum output possible with a given level of cost, it could spend $1 less
on labor, thereby reducing labor by half a unit and hence output by 3 units.
It could spend this dollar on capital, thereby increasing output by 4 units.
Cost would be unchanged, and total output would rise by 1 unit. And the
firm would continue taking dollars out of labor and adding them to capital
as long as the inequality holds. But as labor is reduced, its marginal product
will increase, and as capital is increased, its marginal product will decline.
Eventually the marginal product per dollar spent on each input will be equal.
We have established the following:
Principle  In the case of two variable inputs, labor and capital, the manager of a firm maximizes output
for a given level of cost by using the amounts of labor and capital such that the marginal rate of technical
substitution (MRTS) equals the input price ratio (w/r). In terms of a graph, this condition is equivalent to
choosing the input combination where the slope of the given isocost curve equals the slope of the highest
attainable isoquant. This output-maximizing condition implies that the marginal product per dollar spent on
the last unit of each input is the same.

We have now established that economic efficiency in production occurs when
managers choose variable input combinations for which the marginal product per
dollar spent on the last unit of each input is the same for all inputs. While we have
developed this important principle for the analysis of long-run production, we
must mention for completeness that this principle also applies in the short run
when two or more inputs are variable.
9.4  OPTIMIZATION AND COST
Using Figure 9.4 we showed how a manager can choose the optimal (least-cost)
combination of inputs to produce a given level of output. We also showed how
the total cost of producing that level of output is calculated. When the optimal
input combination for each possible output level is determined and total cost is
calculated for each one of these input combinations, a total cost curve (or schedule)
is generated. In this section, we illustrate how any number of optimizing points
can be combined into a single graph and how these points are related to the firm’s

cost structure.


www.downloadslide.com
C H A P T E R 9   Production and Cost in the Long Run   325
F I G U R E 9.6
An Expansion Path
250

Capital (K )

200
150

KЉ
KЈ

B

126
91

Expansion
path

C

K

Q3 = 900

A

Q2 = 700
Q1 = 500
L

0

118 148

200

300

LЈ

LЉ

400

500

Labor (L)

An Expansion Path

expansion path
The curve or locus of
points that shows the

cost-­minimizing input
combination for each
level of output with the
input/price ratio held
constant.

In Figure 9.4 we illustrated one optimizing point for a firm. This point shows the
optimal (least-cost) combination of inputs for a given level of output. However, as
you would expect, there exists an optimal combination of inputs for every level
of output the firm might choose to produce. And the proportions in which the
inputs are used need not be the same for all levels of output. To examine several
optimizing points at once, we use the expansion path.
The expansion path shows the cost-minimizing input combination for each
level of output with the input price ratio held constant. It therefore shows how
input usage changes as output changes. Figure 9.6 illustrates the derivation of an
expansion path. Isoquants Q1, Q2, and Q3 show, respectively, the input combinations of labor and capital that are capable of producing 500, 700, and 900 units of
output. The price of capital (r) is $20 and the price of labor (w) is $10. Thus any
isocost curve would have a slope of 10/20 5 1/2.
The three isocost curves KL, K'L', and K0L0, each of which has a slope of 1/2,
represent the minimum costs of producing the three levels of output, 500, 700, and
900 because they are tangent to the respective isoquants. That is, at optimal input
combinations A, B, and C, MRTS 5 w/r 5 1/2. In the figure, the expansion path
connects these optimal points and all other points so generated.
Note that points A, B, and C are also points indicating the combinations
of inputs that can produce the maximum output possible at each level of
cost given by isocost curves KL, K'L', and K0L0. The optimizing condition, as
­emphasized, is the same for cost minimization with an output constraint and


www.downloadslide.com

326  C H A P T E R 9   Production and Cost in the Long Run

­ utput ­maximization with a cost constraint. For example, to produce 500 units
o
of output at the lowest possible cost, the firm would use 91 units of capital
and 118 units of labor. The lowest cost of producing this output is therefore
$3,000 (from the vertical intercept, $20 3 150 5 $3,000). Likewise, 91 units of
capital and 118 units of labor are the input combination that can produce the
maximum possible output (500 units) under the cost constraint given by $3,000
(isocost curve KL). Each of the other optimal points along the expansion path
also shows an input combination that is the cost-minimizing combination for
the given output or the output-maximizing combination for the given cost. At
every point along the expansion path,
MPL __
w
MRTS 5 ​ _____
 ​ 5 ​  r ​ 
MP  
K

and
MPK
MPL _____
____
 
 5 ​   ​
 
 
​   ​
w

r

Therefore, the expansion path is the curve or locus of points along which the marginal rate of technical substitution is constant and equal to the input price ratio. It
is a curve with a special feature: It is the curve or locus along which the firm will
expand output when input prices are constant.

Now try Technical
Problem 5.

Relation  The expansion path is the curve along which a firm expands (or contracts) output when input prices remain constant. Each point on the expansion path represents an efficient (least-cost) input
combination. Along the expansion path, the marginal rate of technical substitution equals the constant
input price ratio. The expansion path indicates how input usage changes when output or cost changes.

The Expansion Path and the Structure of Cost
An important aspect of the expansion path that was implied in this discussion
and will be emphasized in the remainder of this chapter is that the expansion
path gives the firm its cost structure. The lowest cost of producing any given level
of output can be determined from the expansion path. Thus, the structure of the
relation between output and cost is determined by the expansion path.
Recall from the discussion of Figure 9.6 that the lowest cost of producing
500  units of output is $3,000, which was calculated as the price of capital,
$20, times the vertical intercept of the isocost curve, 150. Alternatively, the cost
of producing 500 units can be calculated by multiplying the price of labor by
the amount of l­ abor used plus the price of capital by the amount of capital used:
wL 1 rK 5 ($10 3 118) 1 ($20 3 91) 5 $3,000
Using the same method, we calculate the lowest cost of producing 700 and
900 units of output, respectively, as
($10 3 148) 1 ($20 3 126) 5 $4,000

www.downloadslide.com
C H A P T E R 9   Production and Cost in the Long Run   327

and
($10 3 200) 1 ($20 3 150) 5 $5,000
Similarly, the sum of the quantities of each input used times the respective input
prices gives the minimum cost of producing every level of output along the expansion path. As you will see later in this chapter, this allows the firm to relate its
cost to the level of output used.
9.5  LONG-RUN COSTS
Now that we have demonstrated how a manager can find the cost-minimizing
input combination when more than one input is variable, we can derive the cost
curves facing a manager in the long run. The structure of long-run cost curves
is determined by the structure of long-run production, as reflected in the expansion path.
Derivation of Cost Schedules from a Production Function

long-run average cost
(LAC)
Long-run total cost
divided by output (LAC 5
LTC/Q).

We begin our discussion with a situation in which the price of labor (w) is $5 per
unit and the price of capital (r) is $10 per unit. Figure 9.7 shows a portion of the
firm’s expansion path. Isoquants Q1, Q2, and Q3 are associated, respectively, with
100, 200, and 300 units of output.
For the given set of input prices, the isocost curve with intercepts of 12 units of
capital and 24 units of labor, which clearly has a slope of 25/10 (5 −w/r), shows
the least-cost method of producing 100 units of output: Use 10 units of labor and
7 units of capital. If the firm wants to produce 100 units, it spends $50 ($5 3 10) on

labor and $70 ($10 3 7) on capital, giving it a total cost of $120.
Similar to the short run, we define long-run average cost (LAC) as
Long-run total cost (LTC)
LAC 5 _______________________
   
​ 
  
 ​
Output (Q)

F I G U R E 9.7
Long-Run Expansion
Path
Capital (K )

20

14
12
10

Expansion Path

8
7

Q 2 = 200

Q 3 = 300

Q 1 = 100
0

10 12

20

24

Labor (L)

28

40


www.downloadslide.com
328  C H A P T E R 9   Production and Cost in the Long Run

I L L U S T R AT I O N 9 . 1
Downsizing or Dumbsizing
Optimal Input Choice Should Guide
­Restructuring Decisions
One of the most disparaged strategies for cost cutting
has been corporate “downsizing” or, synonymously,
corporate “restructuring.” Managers downsize a
firm by permanently laying off a sizable fraction of
their workforce, in many cases, using across-theboard layoffs.
If a firm employs more than the efficient amount
of labor, reducing the amount of labor employed can

lead to lower costs for producing the same amount
of output. Business publications have documented
dozens of restructuring plans that have failed to realize the promised cost savings. Apparently, a successful ­restructuring requires more than “meat-ax,”
across-the-board cutting of labor. The Wall Street Journal reported that “despite warnings about downsizing
becoming dumbsizing, many companies continue to
make flawed ­decisions—hasty, across-the-board cuts—
that come back to haunt them.”a
The reason that across-the-board cuts in labor do
not generally deliver the desired lower costs can be
seen by applying the efficiency rule for choosing inputs that we have developed in this chapter. To either
minimize the total cost of producing a given level of
output or to maximize the output for a given level of
cost, managers must base employment decisions on
the marginal product per dollar spent on labor, MP/w.
Across-the-board downsizing, when no consideration
is given to productivity or wages, cannot lead to an efficient reduction in the amount of labor employed by
the firm. Workers with the lowest MP/w ratios must
be cut first if the manager is to realize the greatest possible cost savings.
Consider this example: A manager is ordered
to cut the firm’s labor force by as many workers as
it takes to lower its total labor costs by $10,000 per
month. The manager wishes to meet the lower level
of labor costs with as little loss of output as possible.
The manager examines the employment performance
of six workers: workers A and B are senior employees, and workers C, D, E, and F are junior employees.
The accompanying table shows the productivity and

wages paid monthly to each of these six workers. The
senior workers (A and B) are paid more per month
than the junior workers (C, D, E, and F), but the senior

workers are more productive than the junior workers.
Per dollar spent on wages, each senior worker contributes 0.50 unit of output per month, while each dollar spent on junior workers contributes 0.40 unit per
month. Consequently, the senior workers provide the
firm with more “bang per buck,” even though their
wages are higher. The manager, taking an across-theboard approach to cutting workers, could choose to
lay off $5,000 worth of labor in each category: lay off
worker A and workers C and D. This across-the-board
strategy saves the required $10,000, but output falls by
4,500 units per month (5 2,500 1 2 3 1,000). Alternatively, the manager could rank the workers according to the marginal product per dollar spent on each
worker. Then, the manager could start by sequentially
laying off the workers with the smallest marginal
product per dollar spent. This alternative approach
would lead the manager to lay off four junior workers.
Laying off workers C, D, E, and F saves the required
$10,000 but reduces output by 4,000 units per month
(5 4 3 1,000). Sequentially laying off the workers that
give the least bang for the buck results in a smaller
reduction in output while achieving the required labor
savings of $10,000.
This illustration shows that restructuring decisions should be made on the basis of the production
theory presented in this chapter. Input employment
decisions cannot be made efficiently without using

Worker

Marginal
product (MP)

Wage
(w)

MP/w

A

2,500

$5,000

0.50

B

2,500

$5,000

0.50

C

1,000

$2,500

0.40

D

1,000

$2,500

0.40

E

1,000

$2,500

0.40

F

1,000

$2,500

0.40


www.downloadslide.com
C H A P T E R 9   Production and Cost in the Long Run   329

“dumbsizing” if a firm is employing more than the
efficient amount of labor. Dumbsizing occurs only
when a manager lays off the wrong workers or too
many workers.

information about both the productivity of an input and the price of the input. Across-the-board approaches to restructuring cannot, in general, lead to
efficient reorganizations because these approaches
do not consider information about worker productivity per dollar spent when making the layoff decision. Reducing the amount of labor employed is not

long-run marginal
cost (LMC)
The change in longrun total cost per unit
change in output
(LMC 5 DLTC/DQ).

Alex Markels and Matt Murray, “Call It Dumbsizing: Why
Some Companies Regret Cost-Cutting,” The Wall Street
­Journal, May 14, 1996.

a

and long-run marginal cost (LMC) as
DLTC
LMC 5 ______
​ 
 
 
 ​
DQ
Therefore at an output of 100,
$120
LTC _____
 
 5 ​ 
LAC 5 ____

​   ​
100 ​ 5 $1.20
Q
Since there are no fixed inputs in the long run, there is no fixed cost when output
is 0. Thus the long-run marginal cost of producing the first 100 units is
$120 2 0
DLTC ________
 
 5 ​ 
LMC 5 ​ ______
 ​
5 $1.20
100 2 0 ​ 
DQ
The first row of Table 9.1 gives the level of output (100), the least-cost combination
of labor and capital that can produce that output, and the long-run total, average,
and marginal costs when output is 100 units.
Returning to Figure 9.7, you can see that the least-cost method of producing
200 units of output is to use 12 units of labor and 8 units of capital. Thus producing

T A B L E 9.1
Derivation of a Long-Run
Cost Schedule

(1)

(2)

(3)
Least-cost

combination of

(4)

(5)

(6)

Output

Labor
(units)

Capital
(units)

Total cost
(LTC)
(w 5 $5, r 5 $10)

Long-run
average
cost
(LAC )

Long-run
marginal
cost
(LMC )

100
200
300
400
500
600
700

10
12
20
30
40
52
60

 7
 8
10
15
22
30
42

$120
140
200
300
420
560

720

$1.20
0.70
0.67
0.75
0.84
0.93
1.03

$1.20
0.20
0.60
1.00
1.20
1.40
1.60


www.downloadslide.com
330  C H A P T E R 9   Production and Cost in the Long Run

200 units of output costs $140 (5 $5 3 12 1 $10 3 8). The average cost is $0.70
(5 $140/200) and, because producing the additional 100 units increases total cost
from $120 to $140, the marginal cost is $0.20 (5 $20/100). These figures are shown
in the second row of Table 9.1, and they give additional points on the firm’s longrun total, average, and marginal cost curves.
Figure 9.7 shows that the firm will use 20 units of labor and 10 units of capital to
produce 300 units of output. Using the same method as before, we calculate total,
average, and marginal costs, which are given in row 3 of Table 9.1.
Figure 9.7 shows only three of the possible cost-minimizing choices. But, if

we were to go on, we could obtain additional least-cost combinations, and in the
same way, we could calculate the total, average, and marginal costs of these other
outputs. This information is shown in the last four rows of Table 9.1 for output
levels from 400 through 700.
Thus, at the given set of input prices and with the given technology, column 4
shows the long-run total cost schedule, column 5 the long-run average cost
­schedule, and column 6 the long-run marginal cost schedule. The corresponding
long-run total cost curve is given in Figure 9.8, Panel A. This curve shows the
least cost at which each quantity of output in Table 9.1 can be produced when no
F I G U R E 9.8
Long-Run Total, Average, and Marginal Cost
1.60

LTC
700
Average and marginal cost (dollars)

1.40

Total cost (dollars)

600
500
400
300
200
100

0

LMC

1.20

LAC

1.00
0.80
0.60
0.40
0.20

100

200

300

400

500

600

700

0

100

200

300

400

500

Units of output

Units of output

Panel A

Panel B

600

700


www.downloadslide.com
C H A P T E R 9   Production and Cost in the Long Run   331

input is fixed. Its shape depends exclusively on the production function and the
input prices.
This curve reflects three of the commonly assumed characteristics of LTC.
First, because there are no fixed costs, LTC is 0 when output is 0. S
­ econd, cost
and output are directly related; that is, LTC has a positive slope. It costs more

to produce more, which is to say that resources are scarce or that one never
gets something for nothing. Third, LTC first increases at a decreasing rate, then
increases at an increasing rate. This implies that marginal cost first decreases,
then increases.
Turn now to the long-run average and marginal cost curves derived from
­Table 9.1 and shown in Panel B of Figure 9.8. These curves reflect the characteristics of typical LAC and LMC curves. They have essentially the same shape as
they do in the short run—but, as we shall show below, for different reasons. Longrun average cost first decreases, reaches a minimum (at 300 units of output), then
increases. Long-run marginal cost first declines, reaches its minimum at a lower
output than that associated with minimum LAC (between 100 and 200 units), and
then increases thereafter.
In Figure 9.8, marginal cost crosses the average cost curve (LAC) at approximately the minimum of average cost. As we will show next, when output and cost
are allowed to vary continuously, LMC crosses LAC at exactly the minimum point
on the latter. (It is only approximate in Figure 9.8 because output varies discretely
by 100 units in the table.)
The reasoning is the same as that given for short-run average and marginal
cost curves. When marginal cost is less than average cost, each additional unit
produced adds less than average cost to total cost, so average cost must decrease.
When marginal cost is greater than average cost, each additional unit of the good
produced adds more than average cost to total cost, so average cost must be
increasing over this range of output. Thus marginal cost must be equal to average
cost when average cost is at its minimum.
Figure 9.9 shows long-run marginal and average cost curves that
reflect the typically assumed characteristics when output and cost can vary
continuously.
Relations  As illustrated in Figure 9.9, (1) long-run average cost, defined as
LTC
LAC 5 ____
​   ​  
Q
first declines, reaches a minimum (here at Q2 units of output), and then increases. (2) When LAC is at its

minimum, long-run marginal cost, defined as
DLTC
LMC 5 _____
​   ​ 
 
DQ
Now try Technical
Problem 6.

equals LAC. (3) LMC first declines, reaches a minimum (here at Q1, less than Q2), and then increases. LMC
lies below LAC over the range in which LAC declines; it lies above LAC when LAC is rising.


www.downloadslide.com
332  C H A P T E R 9   Production and Cost in the Long Run

Average and marginal cost (dollars)

F I G U R E 9.9
Long-Run Average and
Marginal Cost Curves

LMC
LAC

Q1

Q2
Output

9.6  FORCES AFFECTING LONG-RUN COSTS
As they plan for the future, business owners and managers make every effort to
avoid undertaking operations or making strategic plans that will result in losses
or negative profits. When managers foresee market conditions that will not generate enough total revenue to cover long-run total costs, they will plan to cease
production in the long run and exit the industry by moving the firm’s resources
to their best alternative use. Similarly, decisions to add new product lines or enter
new geographic markets will not be undertaken unless managers are reasonably
sure that long-run costs can be paid from revenues generated by entering those
new markets. Because the long-run v
­ iability of a firm—as well as the number of
product lines and geographic markets a firm chooses—depends crucially on the
likelihood of covering long-run costs, managers need to understand the various
economic forces that can affect long-run costs. We will now examine several important forces that affect the long-run cost structure of firms. While some of these
factors cannot be directly controlled by managers, the ability to predict costs in the
long run requires an understanding of all forces, internal and external, that affect
a firm’s long-run costs. Managers who can best forecast future costs are likely to
make the most profitable decisions.
economies of scale
Occurs when long-run
average cost (LAC) falls
as output increases.

Economies and Diseconomies of Scale
The shape of a firm’s long-run average cost curve (LAC) determines the range
and strength of economies and diseconomies of scale. Economies of scale occur when


www.downloadslide.com
C H A P T E R 9   Production and Cost in the Long Run   333
F I G U R E 9.10

Economic and
Disecomies of Scale.
Average and marginal cost (dollars)

Economies
of scale

Diseconomies
of scale

LMC

LAC

LACmin

Q2
Quantity

diseconomies of scale
Occurs when long-run
average cost (LAC ) rises
as output increases.

Now try Technical
Problem 7.

specialization and
division of labor
Dividing production into

separate tasks allows
workers to specialize and
become more productive,
which lowers unit costs.

long-run average cost falls as output increases. In Figure 9.10, economies of scale
exist over the range of output from zero up to Q2 units of output. Diseconomies
of scale occur when long-run average cost rises as output increases. As you can
see in the figure, diseconomies of scale set in beyond Q2 units of output.
The strength of scale economies or diseconomies can been seen, respectively, as
the reduction in unit cost over the range of scale economies or the increase in LAC
above its minimum value LACmin beyond Q2. Recall that average cost falls when
marginal cost is less than average cost. As you can see in the figure, over the output range from 0 to Q2, LAC is falling because LMC is less than LAC. Beyond Q2,
LMC is greater than LAC, and LAC is rising.
Reasons for scale economies and diseconomies  Before we begin discussing
reasons for economies and diseconomies of scale, we need to remind you of two
things that cannot be reasons for rising or falling unit costs as quantity increases
along the LAC curve: changes in technology and changes in input prices. Recall
that both technology and input prices are held constant when deriving expansion
paths and long-run cost curves. Consequently, as a firm moves along its LAC
curve to larger scales of operation, any economies and diseconomies of scale the
firm experiences must be caused by factors other than changing technology or
changing input prices. When technology or input prices do change, as we will
show you later in this section, the entire LAC curve shifts upward or downward,
perhaps even changing shape in ways that will alter the range and strength of
existing scale economies and diseconomies.
Probably the most fundamental reason for economies of scale is that larger-scale
firms have greater opportunities for specialization and division of labor. As an

www.downloadslide.com
334  C H A P T E R 9   Production and Cost in the Long Run

example, consider Precision Brakes, a small-scale automobile brake repair shop servicing only a few customers each day and employing just one mechanic. The single
mechanic at Precision Brakes must perform every step in each brake repair: moving
the car onto a hydraulic lift in a service bay, removing the wheels, removing the
worn brake pads and shoes, installing the new parts, replacing the wheels, moving
the car off the lift and out of the service bay, and perhaps even processing and collecting a payment from the customer. As the number of customers grows larger at
Precision Brakes, the repair shop may wish to increase its scale of operation by hiring more mechanics and adding more service bays. At this larger scale of operation,
some mechanics can specialize in lifting the car and removing worn out parts, while
others can concentrate on installing the new parts and moving cars off the lifts and
out of the service bays. And, a customer service manager would probably process
each customer’s work order and collect payments. As you can see from this rather
straightforward example, large-scale production affords the opportunity for dividing a production process into a number of specialized tasks. Division of labor allows
workers to focus on single tasks, which increases worker productivity in each task
and brings about very substantial reductions in unit costs.
A second cause of falling unit costs arises when a firm employs one or more
quasi-fixed inputs. Recall that quasi-fixed inputs must be used in fixed amounts in
both the short run and long run. As output expands, quasi-fixed costs are spread
over more units of output causing long-run average cost to fall. The larger the contribution of quasi-fixed costs to overall total costs, the stronger will be the downward pressure on LAC as output increases. For example, a natural gas pipeline
company experiences particularly strong economies of scale because the quasifixed cost of its pipelines and compressor pumps accounts for a very large portion
of the total costs of transporting natural gas through pipelines. In contrast, a trucking company can expect to experience only modest scale economies from spreading the quasi-fixed cost of tractor-trailer rigs over more transportation miles,
because the variable fuel costs account for the largest portion of trucking costs.
A variety of technological factors constitute a third force contributing to economies of scale. First, when several different machines are required in a production
process and each machine produces at a different rate of output, the operation
may have to be quite sizable to permit proper meshing of equipment. Suppose
only two types of machines are required: one that produces the product and one
that packages it. If the first machine can produce 30,000 units per day and the
second can package 45,000 units per day, output will have to be 90,000 units per
day to fully utilize the capacity of each type of machine: three machines making

the good and two machines packaging it. Failure to utilize the full capacity of
each machine drives up unit production costs because the firm is paying for some
amount of machine capacity it does not need or use.
Another technological factor creating scale economies concerns the costs of
capital equipment: The expense of purchasing and installing larger machines is
usually proportionately less than for smaller machines. For example, a printing
press that can run 200,000 papers per day does not cost 10 times as much as one
that can run 20,000 per day—nor does it require 10 times as much building space,


www.downloadslide.com
C H A P T E R 9   Production and Cost in the Long Run   335

10 times as many people to operate it, and so forth. Again, expanding size or scale
of operation tends to reduce unit costs of production.
A final technological matter might be the most important technological factor
of all: As the scale of operation expands, there is usually a qualitative change in the
optimal production process and type of capital equipment employed. For a simple
example, consider ditch digging. The smallest scale of operation is one worker
and one shovel. But as the scale expands, the firm does not simply continue to add
workers and shovels. Beyond a certain point, shovels and most workers are replaced by a modern ditch-digging machine. Furthermore, expansion of scale also
permits the introduction of various types of automation devices, all of which tend
to reduce the unit cost of production.
You may wonder why the long-run average cost curve would ever rise. After
all possible economies of scale have been realized, why doesn’t the LAC curve
become horizontal, never turning up at all? The rising portion of LAC is generally
attributed to limitations to efficient management and organization of the firm. As
the scale of a plant expands beyond a certain point, top management must necessarily delegate responsibility and authority to lower-echelon employees. Contact
with the daily routine of operation tends to be lost, and efficiency of operation
­declines. Furthermore, managing any business entails controlling and coordinating a wide variety of activities: production, distribution, finance, marketing, and

so on. To perform these functions efficiently, a manager must have accurate information, as well as efficient monitoring and control systems. Even though information technology continues to improve in dramatic ways, pushing higher the scale
at which diseconomies set in, the cost of monitoring and controlling large-scale
businesses eventually leads to rising unit costs.
As an organizational plan for avoiding diseconomies, large-scale businesses
sometimes divide operations into two or more separate management divisions so
that each of the smaller divisions can avoid some or all of the diseconomies of scale.
Unfortunately, division managers frequently compete with each other for allocation
of scarce corporate resources—such as workers, travel budget, capital outlays, office
space, and R & D expenditures. The time and energy spent by division managers
trying to influence corporate allocation of resources is costly for division managers,
as well as for top-level corporate managers who must evaluate the competing claims
of division chiefs for more resources. Overall corporate efficiency is sacrificed when
lobbying by division managers results in a misallocation of resources among divisions. Scale diseconomies, then, remain a fact of life for very large-scale enterprises.

constant costs
Neither economies nor
diseconomies of scale
occur, thus LAC is flat
and equal to LMC at all
output levels.

Constant costs: Absence of economies and diseconomies of scale  In some
cases, firms may experience neither economies nor diseconomies of scale,
and instead face constant costs. When a firm experiences constant costs in the
long run, its LAC curve is flat and equal to its LMC curve at all output levels.
Figure  9.11 illustrates a firm with constant costs of $20 per unit: Average and
marginal costs are both equal to $20 for all output levels. As you can see by the
flat LAC curve, firms facing constant costs experience neither economies nor
diseconomies of scale.