Chapter 6
Costs
© 2004 Thomson Learning/South-Western
Basic Concepts of Costs

Opportunity cost is the cost of a good or
service as measured by the alternative uses
that are foregone by producing the good or
service.
–

2
If 15 bicycles could be produced with the materials
used to produce an automobile, the opportunity
cost of the automobile is 15 bicycles.
The price of a good or service often may reflect
its opportunity cost.
Basic Concepts of Costs


3
Accounting cost is the concept that goods or
services cost what was paid for them.
Economic cost is the amount required to keep
a resource in its present use; the amount that it
would be worth in its next best alternative use.
Labor Costs



4
Like accountants, economists regard the
payments to labor as an explicit cost.
Labor services (worker-hours) are purchased
at an hourly wage rate (w): The cost of hiring
one worker for one hour.
The wage rate is assumed to be the amount
workers would receive in their next best
alternative employment.
Capital Costs



5
While accountants usually calculate capital
costs by applying some depreciation rule to the
historical price of the machine, economists
view this amount as a sunk cost.
A sunk cost is an expenditure that once made
cannot be recovered.
These costs do not focus on foregone
opportunities.
Capital Costs



6
Economists consider the cost of a machine to
be the amount someone else would be willing
to pay for its use.
The cost of capital services (machine-hours) is
the rental rate (v) which is the cost of hiring
one machine for one hour.
This is an implicit cost if the machine is owned
by the firm.
APPLICATION 6.1: Stranded Costs and
Electricity Deregulation


7
Until the mid 1990s, the electric power industry
in the United States was heavily regulated.
The expected decline in the wholesale price of
electricity resulting from deregulation has
sparked a debate over “stranded costs”.
The Nature of Stranded Costs


8
When the average costs of generating
electricity exceed the price of electricity in the
open market, the generating facilities become
“uneconomic.”
The historical costs of these facilities have
been “stranded” by deregulation.
The Nature of Stranded Costs



9
To economists, these are sunk costs.
Generating facilities that have become
“uneconomic” have zero market value, a
situation that occurs frequently in many other
business (for example, machines that produce
78 RPM recordings).
Economist Joseph Schumpeter coined such
situations, “creative destruction.”
The Legal Framework--Socking It to
the Consumer


10
Utilities companies argue that they were
promised a “fair” return on their investment, so
they should be compensated for the impact of
deregulation.
Southern California Edison Company was
awarded stranded cost compensation that
exceeded the company’s value on the New
York Stock Exchange.
The Legal Framework--Socking It to
the Consumer

A result of mandated stranded-cost
compensation is the slowing of the pace of
deregulation.
–
–
11
Since consumers see little of the price decline,
they have little incentive to push for deregulation.
Would-be entrants are also not encouraged by
consumers because of the stranded-cost
compensation.
Entrepreneurial Costs


12
Owners of the firm are entitled to the difference
between revenue and costs which is generally
called (accounting) profit.
However, if they incur opportunity costs for
their time or other resources supplied to the
firm, these should be considered a cost of the
firm.
The Legal Framework--Socking It to
the Consumer

A computer programmer that started a software
firm would supply time, the value of which is an
opportunity cost.
–

13
The wages the programmer would have earned if he
or she worked elsewhere could be used as a
measure of this cost.
Economic profit is revenue minus all costs
including these entrepreneurial costs.
Two Simplifying Assumptions

The firm uses only two inputs: labor (L,
measured in labor hours) and capital (K,
measured in machine hours).
–

14
Entrepreneurial services are assumed to be
included in the capital costs.
Firms buy inputs in perfectly competitive
markets so the firm faces horizontal supply
curves at prevailing factor prices.
Economic Profits and Cost
Minimization


15
Total costs = TC = wL + vK.
Assuming the firm produces only one output,
total revenue equals the price of the product
(P) times its total output [q = f(K,L) where f(K,L)
is the firm’s production function].
Economic Profits and Cost
Minimization

Economic profits () is the difference
between a firm’s total revenues and its total
economic costs.
  Total revenues - Total costs
 Pq  wL  vK
 Pf ( K , L)  wL  vK.
16
Cost-Minimizing Input Choice

Assume, for purposes of this chapter, that the
firm has decided to produce a particular output
level (say, q1).
–

17
The firm’s total revenues are P·q1.
How the firm might choose to produce this
level of output at minimal costs is the subject of
this chapter.
Cost-Minimizing Input Choice

Cost minimization requires that the marginal
rate of technical substitution (RTS) of L for K
equals the ratio of the inputs’ costs, w/v:
w
RTS ( of L for K) 
v
18
Graphic Presentation




19
The isoquant q1 shows all combinations of K
and L that are required to produce q1.
The slope of total costs, TC = wL + vK, is w/v.
Lines of equal cost will have the same slope
so they will be parallel.
Three equal total costs lines, labeled TC1,
TC2, and TC3 are shown in Figure 6.1.
FIGURE 6.1: Minimizing the Costs of
Producing q1
Capital
per week
TC1
TC2
TC3
K*
q1
0
20
L*
Labor
per week
Graphic Presentation



21
The minimum total cost of producing q1 is TC1
(since it is closest to the origin).
The cost-minimizing input combination is L*, K*
which occurs where the total cost curve is
tangent to the isoquant.
At the point of tangency, the rate at which the
firm can technically substitute L for K (the RTS)
equals the market rate (w/v).
An Alternative Interpretation
MPL
RTS (of L for K) 
.
MPK

From Chapter 5

Cost minimization requires

or, rearranging
MPL w
RTS 
 ,
MPK v
MPL MPK

.
w
v
22
The Firm’s Expansion Path



23
A similar analysis could be performed for any
output level (q).
If input costs (w and v) remain constant,
various cost-minimizing choices can be
traces out as shown in Figure 6.2.
For example, output level q1 is produced
using K1, L1, and other cost-minimizing points
are shown by the tangency between the total
cost lines and the isoquants.
The Firm’s Expansion Path


24
The firm’s expansion path is the set of costminimizing input combinations a firm will
choose to produce various levels of output
(when the prices of inputs are held constant).
Although in Figure 6.2, the expansion path is a
straight line, that is not necessarily the case.
FIGURE 6.2: Firm’s Expansion Path
Capital
per week
TC1
TC2
TC3
Expansion path
q3
K1
q2
q1
0
25
L1
Labor
per week
Cost Curves



26
A firm’s expansion path shows how minimumcost input use increases when the level of
output expands.
With this it is possible to develop the
relationship between output levels and total
input costs.
These cost curves are fundamental to the
theory of supply.
Cost Curves


27
Figure 6.3 shows four possible shapes for cost
curves.
In Panel a, output and required input use is
proportional which means doubling of output
requires doubling of inputs. This is the case
when the production function exhibits constant
returns to scale.
FIGURE 6.3: Possible Shapes of the
Total Cost Curve
TC
Total
cost
Quantity
per week
(a) Constant Returns to Scale
0
28
Cost Curves



29
Panels b and c reflect the cases of decreasing
and increasing returns to scale, respectively.
With decreasing returns to scale the cost curve
is convex, while the it is concave with
increasing returns to scale.
Decreasing returns to scale indicate
considerable cost advantages from large scale
operations.
FIGURE 6.3: Possible Shapes of the
Total Cost Curve
TC
Total
cost
Total
cost
Quantity
per week
(a) Constant Returns to Scale
0
Total
cost
TC
0
30
Quantity
per week
(c) Increasing Returns to Scale
TC
Quantity
per week
(b) Decreasing Returns to Scale
0
Cost Curves



31
Panel d reflects the case where there are
increasing returns to scale followed by
decreasing returns to scale.
This might arise because internal co-ordination
and control by managers is initially
underutilized, but becomes more difficult at
high levels of output.
This suggests an optimal scale of output.
FIGURE 6.3: Possible Shapes of the
Total Cost Curve
TC
Total
cost
Total
cost
Quantity
per week
(a) Constant Returns to Scale
0
Total
cost
TC
0
32
TC
Quantity
per week
(b) Decreasing Returns to Scale
TC
0
Total
cost
Quantity
per week
(c) Increasing Returns to Scale
0
Quantity
per week
(d) Optimal Scale
Average Costs


TC
Average cost  AC 
q
Average cost is total cost divided by output; a
common measure of cost per unit.
If the total cost of producing 25 units is $100,
the average cost would be
$100
AC 
 $4
25
33
Marginal Cost
Change in TC
Marginal cost  MC 
Change in q


34
The additional cost of producing one more
unit of output is marginal cost.
If the cost of producing 24 units is $98 and
the cost of producing 25 units is $100, the
marginal cost of the 25th unit is $2.
Marginal Cost Curves


35
Marginal costs are reflected by the slope of the
total cost curve.
The constant returns to scale total cost curve
shown in Panel a of Figure 6.3 has a constant
slope, so the marginal cost is constant as
shown by the horizontal marginal cost curve in
Panel a of Figure 6.4.
FIGURE 6.4: Average and Marginal
Cost Curves
AC, MC
AC, MC
Quantity
per week
(a) Constant Returns to Scale
0
36
Marginal Cost Curves


37
With decreasing returns to scale, the total cost
curve is convex (Panel b of Figure 6.3).
This means that marginal costs are increasing
which is shown by the positively sloped
marginal cost curve in Panel b of Figure 6.4.
FIGURE 6.4: Average and Marginal
Cost Curves
AC, MC
AC, MC
MC
AC
AC, MC
Quantity
per week
(a) Constant Returns to Scale
0
38
Quantity
per week
(b) Decreasing Returns to Scale
0
Marginal Cost Curves


39
Increasing returns to scale results in a concave
total cost curve (Panel c of Figure 6.3).
This causes the marginal costs to decrease as
output increases as shown in the negatively
sloped marginal cost curve in Panel c of Figure
6.4.
FIGURE 6.4: Average and Marginal
Cost Curves
AC, MC
AC, MC
MC
AC
AC, MC
Quantity
per week
(a) Constant Returns to Scale
0
AC, MC
0
40
AC
MC
Quantity
per week
(c) Increasing Returns to Scale
Quantity
per week
(b) Decreasing Returns to Scale
0
Marginal Cost Curves


41
When the total cost curve is first concave
followed by convex as shown in Panel d of
Figure 6.3, marginal costs initially decrease but
eventually increase.
Thus, the marginal cost curve is first negatively
sloped followed by a positively sloped curve as
shown in Panel d of Figure 6.4.
FIGURE 6.4: Average and Marginal
Cost Curves
AC, MC
AC, MC
MC
AC
AC, MC
Quantity
per week
(a) Constant Returns to Scale
0
AC, MC
AC, MC
0
42
Quantity
per week
(b) Decreasing Returns to Scale
0
AC
MC
Quantity
per week
(c) Increasing Returns to Scale
MC
0
q*
AC
Quantity
per week
(d) Optimal Scale
Average Cost Curves


43
If a firm produces only one unit of output,
marginal cost would be the same as average
cost
Thus, the graph of the average cost curve
begins at the point where the marginal cost
curve intersects the vertical axis.
Average Cost Curves


44
For the constant returns to scale case,
marginal cost never varies from its initial level,
so average cost must stay the same as well.
Thus, the average cost curve are the same
horizontal line as shown in Panel a of Figure
6.4.
Average Cost Curves


45
With convex total costs and increasing
marginal costs, average costs also rise as
shown in Panel b of Figure 6.4.
Because the first few units are produced at low
marginal costs, average costs will always b
less than marginal cost, so the average cost
curve lies below the marginal cost curve.
Average Cost Curves


46
With concave total cost and decreasing
marginal costs, average costs will also
decrease as shown in Panel c in Figure 6.4.
Because the first few units are produced at
relatively high marginal costs, average is less
than marginal cost, so the average cost curve
lies below the marginal cost curve.
Average Cost Curves


47
The U-shaped marginal cost curve shown in
Panel d of Figure 6.4 reflects decreasing
marginal costs at low levels of output and
increasing marginal costs at high levels of
output.
As long as marginal cost is below average
cost, the marginal will pull down the average.
Average Cost Curves



48
When marginal costs are above average cost,
the marginal pulls up the average.
Thus, the average cost curve must intersect
the marginal cost curve at the minimum
average cost; q* in Panel d of Figure 6.4.
Since q* represents the lowest average cost, it
represents an “optimal scale” of production for
the firm.
APPLICATION 6.2: Findings on Firms’
Costs



49
Entries in Table 1 represent long-run average
cost estimates for different size firms as a
percentage of the minimal average-cost firm
in the industry.
These estimates, except for trucking, suggest
lower average cost for medium and large
firms.
Figure 1 shows the average cost firm
suggested by the data.
FIGURE 1: Long-Run Average Cost
Curve Found in Many Empirical Studies
Average
cost
AC
0
50
q*
Quantity
per period
TABLE 1: Long-Run Average-Cost
Estimates
Firm Size
Industry
Aluminum
Automobiles
Electric power
HMOs
Hospitals
Life insurance
Lotteries (state)
Sewage treatment
Trucking
51
Small
166.6
144.5
113.2
118.0
129.6
113.6
175.0
104.0
100.0
Medium
131.3
122.7
101.1
106.3
111.1
104.5
125.0
101.0
102.1
Large
100.0
100.0
101.5
100.0
100.0
100.0
100.0
100.0
105.6
APPLICATION 6.3: Airlines’ Costs


Costs for airlines have been of interest to
economists because of recent changes such
as deregulation, bankruptcy, and mergers.
Two general findings:
–
–
52
Costs seem to differ substantially among U.S. firms.
Costs for U.S. airlines appear to be significantly
lower than for airlines in other countries.
Reasons for Differences among U.S.
Firms

Airlines that fly longer average distances or
operate a greater number of flights over a
given network tend to have lower costs.
–
53
Firms can spread the fixed costs associated with
terminals, maintenance facilities, and reservation
systems over a larger output volume.
Reasons for Differences among U.S.
Firms


54
Firms that operate older fleets or that operate
fleets with many different types of planes tend
to have higher maintenance and fuel costs.
Wage costs, especially for pilots, also differ
significantly among the airlines.
International Airline Regulation and
Costs


Many foreign carriers’ have not adopted the
“hub and spoke” system which appears to be
more efficient.
Foreign firms are subject to more regulation.
–
55
This situation appears to be changing. For
example, Australia ended rigid controls and costs
fell by 15 to 20 percent.
Distinction between the Short Run
and the Long Run


56
The short run is the period of time in which a
firm must consider some inputs to be
absolutely fixed in making its decisions.
The long run is the period of time in which a
firm may consider all of its inputs to be variable
in making its decisions.
Holding Capital Input Constant


57
For the following, the capital input is assumed
to be held constant at a level of K1, so that,
with only two inputs, labor is the only input the
firm can vary.
As examined in Chapter 5, this implies
diminishing marginal productivity to labor.
Types of Short-Run Costs
Fixed costs; costs associated with
inputs that are fixed in the short run.
 Variable costs; costs associated with
inputs that can be varied in the short
run.

58
Input Inflexibility and Cost
Minimization



59
Since capital is fixed, short-run costs are not
the minimal costs of producing variable output
levels.
Assume the firm has fixed capital of K1 as
shown in Figure 6.5.
To produce q0 of output, the firm must use L1
units of labor, with similar situations for q1, L1,
and q2, L2.
FIGURE 6.5: “Nonoptimal” Input
Choices Must Be Made in the Short Run
Capital
per week
STC0
STC2
STC1
K1
q2
q1
q0
60
0
L0
L1
L2
Labor
per week
Input Inflexibility and Cost
Minimization



61
The cost of output produced is minimized
where the RTS equals the ratio of prices, which
only occurs at q1, L1.
Q0 could be produce at less cost if less capital
than K1 and more labor than L0 were used.
Q2 could be produced at less cost if more
capital than K1 and less labor than L2 were
used.
Per-Unit Short-Run Cost Curves
STC
Short - run average cost  SAC 
q
and
Change in STC
Short - run marginal cost  SMC 
Change in q
62
Per-Unit Short-Run Cost Curves


63
Having capital fixed in the short run yields a
total cost curve that has both concave and
convex sections, the resulting short-run
average and marginal cost relationships will
also be U-shaped.
When SMC < SAC, average cost is falling, but
when SMC > SAC average cost increase.
Relationship between Short-Run and
Long-Run per-Unit Cost Curves



64
Figure 6.6 shows all cost relationships for a
firm that has U-shaped long-run average and
marginal cost curves.
At output level q* long-run average costs are
minimized and MC = AC.
Associated with q* is a certain level of capital,
K*.
FIGURE 6.6: Short-Run and Long-Run Average and
Marginal Cost Curves at Optimal Output Level
AC, MC
MC
AC
SMC
SAC
0
65
q*
Quantity
per week
Relationship between Short-Run and
Long-Run per-Unit Cost Curves



66
In the short-run, when the firm using K* units of
capital produces q*, short-run and long-run
total costs are equal.
In addition, as shown in Figure 6.6
AC = MC = SAC(K*) = SMC(K*).
For output above q* short-run costs are higher
than long-run costs. The higher per-unit costs
reflect the facts that K is fixed.
APPLICATION 6.4: Can We Do Anything
About Traffic Snarls?



67
For any traffic facility (road, bridge, tunnel, and
so forth), output is measured in number of
vehicles per hour.
Capital costs are largely fixed, as depreciation
occurs regardless of the level of traffic.
Variable costs consist primarily of motorists’
time.
APPLICATION 6.4: Can We Do Anything
About Traffic Snarls?


68
Studies, based on people’s willingness to
spend time commuting, indicate travel time
“costs” about $8 per hour.
The marginal cost of producing “one more trip”
is the overall increase in travel time
experienced by all motorists when one more
vehicle uses a traffic facility.
APPLICATION 6.4: Can We Do Anything
About Traffic Snarls?


69
The high costs associated with adding an extra
automobile to an already crowded facility are
not directly experienced by the motorist driving
the car, because these costs are imposed on
other motorists.
This divergence between the private costs and
the total social costs leads to motorists opting
for overutilizeing traffic facilities.
Congestion Tolls



70
The standard economists answer to this
problem is to adopt taxes that bring social and
private marginal costs into agreement.
This implies the adoption of highway, bridge, or
tunnel tolls, that accurately reflect social costs.
Since these costs vary by time of day, tolls
should also vary over the day.
Toll-Collecting Technology


71
This approach was previously not feasible
since collection booths for tolls would add more
to the congestion that in aiding to the solving of
the problem.
However, the development of low-cost
electronic toll collection techniques, now make
it possible using cards with pre-coded
computer chips.
Shifts in Cost Curves


Any change in economic conditions that affects
the expansion path will also affect the shape
and position of the firm’s cost curves.
Three sources of such change are:
–
–
–
72
change in input prices
technological innovations, and
economies of scope.
Changes in Input Prices


73
A change in the price of an input will tilt the
firm’s total cost lines and alter its expansion
path.
For example, a rise in wage rates will cause
firms to use more capital (to the extent allowed
by the technology) and the entire expansion
path will rotate toward the capital axis.
Changes in Input Prices

Generally, all cost curves will shift upward with
the extent of the shift depending upon how
important labor is in production and how
successful the firm is in substituting other
inputs for labor.
–
74
With important labor and poor substitution
possibilities, a significant increase in costs will
result.
Technological Innovation


75
Because technological advances alter a firm’s
production function, isoquant maps as well as
the firm’s expansion path will shift when
technology changes.
Unbiased improvements would shift isoquants
toward the origin enabeling firms to produce
the same level of output with less of all inputs.
Technological Innovation

Technological change that is biased toward the
use of one input will alter isoquant maps, shift
expansion paths, and affect the shape and
location of cost curves.
–
76
For example, if workers became more skilled, this
would save only on labor input.
Economies of Scope

Economies of scope is the reduction in the
costs of one product of a multiproduct firm
when the output of another product is
increased.
–
77
For example, when hospitals do many surgeries of
one type, it may have cost advantages in doing
other types because of the similarities in equipment
and operating personnel used.
APPLICATION 6.5: Economies of Scope
in Banks and Hospitals



78
Banks and hospitals are both complex types of
firms that produce many different products.
Recently, a large number of mergers has
occurred in both of these industries.
One of the primary reasons for expected the
lower costs associated with these mergers is
that the mergers make it possible for firms to
have a broader array of products.
APPLICATION 6.5: Economies of Scope
in Banks and Hospitals


79
If economies of scope are important, the
additional production after mergers, may cause
the costs of these firms’ traditional business
lines to be lower.
Banks represent an industry where for-profit
firms dominate whereas hospitals are more
commonly regarded as nonprofit firms.
APPLICATION 6.5: Economies of Scope
in Banks and Hospitals



80
Banks are financial intermediaries.
Economies of scope can reduce banks’ costs if the
costs associated with any one particular financial
product fall when the bank offers other products.
The possibility of economies of scope has played an
important role in the evolution of banking regulations
(e.g. Glass-Steagall Acts in the U.S. and the more
flexible merger guidelines adopted by the European
Community.)
APPLICATION 6.5: Economies of Scope
in Banks and Hospitals


Although most hospitals are not intended to earn
economic profits, they still face revenue constraints
that push them toward cost-minimization.
Economies of scope arise in a variety of hospital
activities
–
–
81
Facilities for surgical operations tend to have lower costs the
wider the variety of operations that are done
The provision of of outpatient services, running intensive care
units, and establishing hospital owned pharmacies also lead
to economies of scope.
A Numerical Example


82
Assume Hamburger Heaven (HH) can hire
workers at $5 per hour and it rents all of its
grills for $5 per hour.
Total costs for HH during one hour are
TC = 5K + 5L
where K and L are the number of grills and the
number of workers hired during that hour,
respectively.
A Numerical Example


Suppose HH wishes to produce 40
hamburgers per hour.
Table 6.1 repeats the various ways HH can
produce 40 hamburgers per hour.
–

83
This shows that total costs are minimized when
K = L = 4.
Figure 6.10 shows the cost-minimizing
tangency.
TABLE 6.1: Total Costs of Producing 40
Hamburgers per Hour
Output (q)
40
40
40
40
40
40
40
40
40
40
84
Workers (L)
1
2
3
4
5
6
7
8
9
10
Grills (K)
16.0
8.0
5.3
4.0
3.2
2.7
2.3
2.0
1.8
1.6
Total Cost (TC)
$85.00
50.00
41.50
40.00
41.00
43.50
46.50
50.00
54.00
58.00
Figure 6.7: Cost-Minimizing Input
Choice for 40 Hamburgers per Hour
Grills
per hour
8
E
4
2
40 hamburgers per hour
Total cost = $40
0
85
2
4
8
Workers
per hour
Long-Run cost Curves


86
HH’s production function is constant returns to
scale so
As long as w = v = $5, all of the cost
minimizing tangencies will resemble the one
shown in Figure 6.10 and long-run cost
minimization will require K = L.
Long-Run cost Curves



87
This situation, resulting from constant returns
to scale, is shown in Figure 6.8.
HH’s long-run total cost function is a straight
line through the origin as shown in Panel a.
Its long-run average and marginal costs are
constant at $1 per burger as shown in Panel b.
FIGURE 6.8: Total, Average, and
Marginal Cost Curves
Total
costs
Average and
marginal costs
Total
costs
$80
60
40
20
$1.00
0 20 40 60 80 Hamburgers
per hour
(a) Total Costs
88
Average and
marginal costs
0 20
40
60
80
Hamburgers
per hour
(b) Average and Marginal Costs
Short-Run Costs



89
Table 6.2 repeats the labor input required to
produce various output levels holding grills
fixed at 4.
Diminishing marginal productivity of labor
causes costs to rise rapidly as output expands.
Figure 6.9 shows the short-run average and
marginal costs curves.
TABLE 6.2: Short-Run Costs of
Hamburger Production
Output (q)
10
20
30
40
50
60
70
80
90
100
90
Workers
(L)
0.25
1.00
2.25
4.00
6.25
9.00
12.25
16.00
20.25
25.00
Grills
(K)
4
4
4
4
4
4
4
4
4
4
Total Cost
(STC)
$21.25
25.00
31.25
40.00
51.25
65.00
81.25
100.00
121.25
145.00
Average
Cost (SAC)
$2.125
1.250
1.040
1.000
1.025
1.085
1.160
1.250
1.345
1.450
Marginal
Cost (SMC)
$0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
FIGURE 6.12: Short-Run and Long-Run Average and
Marginal Cost Curves for Hamburger Heaven
Average and
marginal costs
$2.50
SMC (4 grills)
2.00
SAC (4 grills)
1.50
1.00
AC, MC
.50
0
91
20
40
60
80
100 Hamburgers
per hour