Chapter 7
Costs
Topics
•  The Nature of Costs.
•  Short-Run Costs.
•  Long-Run Costs.
•  Lower Costs in the Long Run.
•  Cost of Producing Multiple Goods.
7-2
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The Nature of Costs
•  Economists measure all relevant costs.
w Explicit costs – direct, out-of-pocket
payments for inputs to its production process
within a given time period
w Implicit costs – reflect only a forgone
opportunity rather than an explicit, current
expenditure.
•  Accountants measure costs in ways that
are more consistent with tax laws and
other laws.
7-3
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Opportunity Cost
•  Economic cost or opportunity cost the value of the best alternative use of a
resource.
7-4
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Solved Problem 7.1
•  Meredith’s firm sends her to a conference for managers
and has paid her registration fee. Included in the
registration fee is free admission to a class on how to
price derivative securities such as options. She is
considering attending, but her most attractive alternative
opportunity is to attend a talk by Warren Buffett about
his investment strategies, which is scheduled at the
same time. Although she would be willing to pay $100 to
hear his talk, the cost of a ticket is only $40. Given that
there are no other costs involved in attending either
event, what is Meredith’s opportunity cost of attending
the derivatives talk?
7-5
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Solved Problem 7.1 (cont.)
•  Answer:
w To calculate her opportunity cost, determine
the benefit that Meredith would forgo by
attending the derivatives class.
7-6
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Costs of Durable Goods
•  Durable good- a product that is usable
for years.
•  Two issues arise with measuring the cost
of durable goods:
w How to allocate the initial purchase cost over
time.
w What to do if the value of the capital changes
over time.
7-7
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Sunk Costs
•  Sunk cost – a past expenditure that
cannot be recovered.
7-8
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Short-Run Cost Measures
•  Fixed cost (F) - a production expense that does
not vary with output.
•  Variable cost (VC) - a production expense that
changes with the quantity of output produced.
•  Cost (total cost, C) - the sum of a firm’s
variable cost and fixed cost:
C = VC + F
7-9
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Marginal Cost
•  Marginal cost (MC) - the amount by which a
firm’s cost changes if the firm produces one
more unit of output.
ΔC
MC =
Δq
w  And since only variable costs change with output:
ΔVC
MC =
Δq
7 - 10
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Average Costs
•  Average fixed cost (AFC) - the fixed cost
divided by the units of output produced:
AFC = F/q.
•  Average variable cost (AVC) - the variable
cost divided by the units of output produced:
AVC = VC/q.
•  Average cost (AC) - the total cost divided by
the units of output produced:
AC = C/q
AC = AFC + AVC.
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Table 7.1 Variation of Short-Run
Cost with Output
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Cost, $
Figure 7.1 ShortRun Cost Curves
(a)
400
C
VC
216
48
0
(b)
60
A
B
120
1
4
6
8
Quantity
,10
q,
Units per da
y
Cost per unit, $
2
MC
20
a
0
b
8
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27
20
1
F
28
27
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AVC
AC
10
8
Quantity
,
q,
Units per da
y
AFC
2
4
6
Cost per unit, $
Relationship Between Average and
Marginal Cost Curves
60
20
When MC is
lower than AC,
When
ACMC
is is
lower
than
decreasing…
AVC, AVC is
decreasing…
and when MC is
andlarger
whenthan
MCAC,
is
AC is
increases
larger
than
AVC,
a
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b
AVC
AC
0
2
4
AVC is increases
28
27
8
MC
6
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…so MC = AC, at the
lowest point of the
AC curve!
…so MC = AVC, at
the lowest point of
the AVC curve!
10
8
Quantit y, q, Units per d ay
Figure 7.2 Variable Cost and Total
Product of Labor
7 - 15
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Shape of the Marginal Cost Curve
= DVC/Dq.
MC
•  But in the short run,
DVC = wDL
(can you tell why?)
w  Therefore,
MC
= wDL/Dq
•  The additional output created by every additional unit
of labor is:
w  Therefore,
Dq/ DL = MPL
MC = w/ MPL
7 - 16
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Shape of the Average Cost Curves
AVC = VC/q.
w But in the short-run, with only labor as an
input:
AVC = VC/q = wL/q
w And since q/L = APL, then
AVC = VC/q = w/APLL
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Application: Short-Run Cost Curves for a
Furniture Manufacturer
7 - 18
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Effects of Taxes on Costs
•  Taxes applied to a firm shift some or all of
the marginal and average cost curves.
7 - 19
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Table 7.2 Effect of a Specific Tax of
$10 per Unit on Short-Run Costs
7 - 20
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Costs per unit, $
Figure 7.3 Effect of a Specific Tax on
Cost Curves
80
M
C
b
A $10.00 tax shifts
both the AVC and
MC by exactly
$10…
MC a = MC b + 10
$10
37
27
0
7 - 21
a
b
AC
=
AC
+ 10
$10
5
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8
10
ACb
15
q, Units per d ay
Solved Problem 7.2
•  What is the effect of a lump-sum franchise
tax on the quantity at which a firm’s after
tax average cost curve reaches its
minimum? (Assume that the firm’s beforetax average cost curve is U-shaped.)
7 - 22
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Solved Problem 7.2
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Long-Run Costs
•  Fixed costs are avoidable in the long run.
w In the long F = 0.
w As a result, the long-run total cost equals:
C = VC
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Input Choice
•  Isocost line - all the combinations of
inputs that require the same (iso-) total
expenditure (cost).
•  The firm’s total cost equation is:
C = wL + rK.
Capital
Labor Costs
Costs
7 - 25
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Input Choice (cont.)
•  The firm’s total cost equation is:
C = wL + rK.
w We get the Isocost equation by setting
fixing the costs at a particular level:
C = wL + rK.
w And then solving for K (variable along yaxis):
w
C
K = 7 - 26
r
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- r
L Table 7.3 Bundles of Labor and
Capital That Cost the Firm $100
7 - 27
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Figure 7.4 A Family of Isocost Lines
K, Units of capital per year
Isocost Equation
w
C
K = r - r L Initial Values
C = $100
w = $5
r = $10
For each extra unit of
capital it uses, the
firm must use two
fewer units of labor to
hold its cost constant.
e
$100
$10
10 =
5
2.5
d
7.5
c
DK = 2.5
Slope = -1/2 = w/r
b
DL = 5
$100 isocost
$100
=
20
$5
L,
Units of labor per
year
a
5
7 - 28
10
15
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K, Units of capital per year
Figure 7.4 A Family of Isocost Lines
$150
$10
15 =
e
$100
$10
10 =
Isocost Equation
C
- w
L K = r
r
An increase in C….
Initial Values
C = $150
w = $5
r = $10
$100 isocost
$150 isocost
$100
$150
=
20
=
30
$5
$5
L,
Units of labor per
year
a
7 - 29
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K, Units of capital per year
Figure 7.4 A Family of Isocost Lines
$150
$10
15 =
e
$100
$10
10 =
Isocost Equation
w
C
K = r - r L A decrease in C….
Initial Values
C = $50
w = $5
r = $10
$50
$10
5=
$50 isocost
$100 isocost
$100
$150
=
20
=
30
$5
$5
L,
Units of labor per
year
a
$50
= 10
$5
7 - 30
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$150 isocost
Combining Cost and Production
Information
•  The firm can choose any of three equivalent
approaches to minimize its cost:
w  Lowest-isocost rule - pick the bundle of inputs
where the lowest isocost line touches the isoquant.
w  Tangency rule - pick the bundle of inputs where
the isoquant is tangent to the isocost line.
w  Last-dollar rule - pick the bundle of inputs where
the last dollar spent on one input gives as much
extra output as the last dollar spent on any other
input.
7 - 31
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K, Units of capital per hour
Figure 7.5 Cost Minimization
q = 100 isoquant
$3,000
isocost
Which of these three
Isocost would allow
the firm to produce
the 100 units of
output at the lowest
possible cost?
$2,000
isocost
100
0
7 - 32
$1,000
isocost
x
50
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Isocost Equation
w
C
K = r - r L Isoquant Slope
MPL
= MRTS
- MPK
Initial Values
q = 100
C = $2,000
w = $24
r = $8
L,
Units of labor per hour
Isocost Equation
w
C
K = r - r L Isoquant Slope
MPL
= MRTS
- MPK
q = 100 isoquant
$3,000
isocost
K, Units of capital per hour
Figure 7.5 Cost Minimization
303
y
$2,000
isocost
100
0
$1,000
isocost
x
28
7 - 33
24
50
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Initial Values
q = 100
C = $2,000
w = $24
z
r = $8
116
L,
Units of labor per hour
Cost Minimization
•  At the point of tangency, the slope of the
isoquant equals the slope of the isocost.
Therefore,
w
MRTS = −
r
MPL
MRTS = −
MPK
MPL w
=
MPK
r
MPL MPK
=
w
r
7 - 34
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last-dollar rule: cost is
minimized if inputs are
chosen so
that the last dollar spent
on labor adds as much
extra output as the last
dollar spent on capital.
$3,000
isocost
303
y
1.2
MPL
MPK
= = r
w
24
$2,000
isocost
100
0
$1,000
isocost
q = 100
C = $2,000
w = $24
r = $8
0.4
= 8
= 0.05 Spending one more dollar on
labor at x gets the firm as much
extra output as spending the
same amount on capital.
x
116
z
28
7 - 35
Initial Values
MPL = 0.6q/L
MPK = 0.4q/K q = 100 isoquant
K, Units of capital per hour
Figure 7.5 Cost Minimization
24
50
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L, Units of labor per hour
Figure 7.5 Cost Minimization
q = 100 isoquant
$3,000
isocost
K, Units of capital per hour
Initial Values
q = 100
C = $2,000
MPL = 0.6q/L
w = $24
MPK = 0.4q/K r = $8
303
y
$2,000
isocost
100
0
$1,000
isocost
x
116
z
28
7 - 36
if So
the…the
firm shifts
firm one
dollar
should
from
shift
capital to
labor,
evenoutput
more falls by
0.017
resources
because
from
there is
less
capital
capital
to labor—
but also
increases
which increases
by 0.1 the
because
marginal
there
product
is more
labor
of capital
for a net
andgain of
0.083
decreases
more the
output at
the
marginal
same cost….
product
of labor.
2.5
MPL
= 24 = 0.1 w
MPK
0.13
r
= 8
= 0.017
24
50
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L, Units of labor per hour
K, Units of capital per hour
Figure 7.6 Change in Factor Price
Or
iginal
isocost,
$2,000
Minimizing Cost Rule
q = 100 isoquant
A decrease in w….
New isocost,
$1,032
100
52
0
7 - 37
x
v
50
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77
MPL
MPK
w
= r
Initial Values
q = 100
C = $2,000
w = $24
r = $8
w2 = $8
C2 = $1,032
L, Workers per hour
Solved Problem 7.3
•  If it manufactures at home, a firm faces
input prices for labor and capital of wˆ and
rˆ and produces qˆ units of output using Lˆ
units of labor and Kˆ units of capital.
Abroad, the wage and cost of capital are
half as much as at home. If the firm
manufactures abroad, will it change the
amount of labor and capital it uses to
produce qˆ? What happens to its cost of
producing qˆ?
7 - 38
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Solved Problem 7.3
•  Answer:
w Determine whether the change in factor
prices affects the slopes of the isoquant or
the isocost lines.
w Using a rule for cost minimization, determine
whether the firm changes its input mix.
w Calculate the original cost and the new cost
and compare them.
7 - 39
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How Long-Run Cost Varies with Output
•  Expansion path - the cost-minimizing
combination of labor and capital for each
output level
7 - 40
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K, Units of capital per hour
Figure 7.7(a) Expansion Path and
Long-Run Cost Curve
$4,000
isocost
$3,000
isocost
Expansion path
$2,000
isocost
150
100
z
200
0
7 - 41
y
x
q = 150 Isoquant
q = 100 Isoquant
L,
Wo
r
k
ers
per hour
q = 200 Isoquant
50
75
100
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Figure 7.7(b) Expansion Path and
Long-Run Cost Curve
7 - 42
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Solved Problem 7.4
•  What is the long-run cost function for a
fixed-proportions production function
(Chapter 6) when it takes one unit of labor
and one unit of capital to produce one unit
of output? Describe the long-run cost
curve.
•  Answer:
w Multiply the inputs by their prices, and sum to
determine total cost.
7 - 43
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The Shape of Long Run Cost Curves
•  The shape of long run cost curves is
determined by the production function
relationship between output and inputs.
7 - 44
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Figure 7.8 LongRun Cost Curves
7 - 45
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Economies of Scale
•  Economies of scale - property of a cost
function whereby the average cost of
production falls as output expands.
•  Diseconomies of scale - property of a
cost function whereby the average cost of
production rises when output increases.
7 - 46
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Table 7.4 Returns to Scale and
Long-Run Costs
7 - 47
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Table 7.5 Shape of Average Cost
Curves in Canadian Manufacturing
7 - 48
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Lower Costs in the Long Run
•  In its long-run planning, a firm chooses a
plant size and makes other investments
so as to minimize its long-run cost on the
basis of how many units it produces.
w Once it chooses its plant size and equipment,
these inputs are fixed in the short run.
•  Thus, the firm’s long-run decision determines its
short-run cost.
7 - 49
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Average cost, $
Figure 7.9 Long-Run Average Cost as the
Envelope of Short-Run Average Cost Curves
LRA
C
SRAC 3
SRAC 1
10
b
12
a
d
7 - 50
SRAC 2
c
e
0
SRAC 3
q1
q2
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q, Output per day
Application: Long-Run Cost Curves in
Furniture Manufacturing and Oil Pipelines
7 - 51
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Application: Long-Run Cost Curves in
Furniture Manufacturing and Oil Pipelines
7 - 52
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Application: Choosing an Ink-Jet or a
Laser Printer
7 - 53
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Figure 7.10 Long-Run and
Short-Run Expansion Paths
7 - 54
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How Learning by Doing Lowers Costs
•  Learning by doing - the productive skills
and knowledge that workers and
managers gain from experience
7 - 55
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Figure 7.11 Learning by Doing
7 - 56
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Why Costs Fall over Time
•  Technological or organizational progress
may increase productivity.
•  Operating at a larger scale in the long run
may lower average costs due to
increasing returns to scale.
•  The firm’s workers and managers may
become more proficient over time due to
learning by doing.
7 - 57
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Cost of Producing Multiple Goods
•  Economies of scope - situation in which
it is less expensive to produce goods
jointly than separately.
•  Production possibility frontier - the
maximum amount of outputs that can be
produced from a fixed amount of input.
7 - 58
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Figure 7.12 Joint Production
7 - 59
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Figure 7.13 Technology Choice
7 - 60
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