Chapter Seven
Costs
© 2008 Pearson Addison Wesley. All rights reserved
無人商店紅什麼？小白店員絕跡
(中央社訊息服務20091127 16:16:13)
• 近年來消費者自主意識抬頭，自助旅行、自助加油站、自
助租片店、自助洗衣店等消費習慣走紅，也讓新一代智慧
型無人商店領導品牌「MiniShop 24H無人商店」趁勢崛起，
還意外成為上班族兼差首選。。
• 創立「MiniShop 24H無人商店」的優活力企業董座縱曜光說
，一般認為「無人商店」最大的優勢，在於零人事、庫存
成本，並能真正做到以「最小成本創造最大獲利」的營運
績效，但MiniShop更要做到用最方便、輕鬆的方式，滿足消
費者最深層的渴望。
資料來源：http://tw.news.yahoo.com/article/url/d/a/091127/5/1vsua.html (Mini Shop)
擴大台廠代工 為日數位相機廠逆境求生活路
(中央社記者韓婷婷台北15日電)
• 金融風暴及日圓強勁升值重擊，「低價、超值」成為數位
相機市場新顯學，台灣代工廠商擁有設計、成本及快速應
變能力優勢，成為日本數位相機廠逆境求生少不了的夥伴
• 日廠為了避免市佔率流失，並且縮減資本支出，紛紛擴大
委外代工比率，以降低成本，尋求利潤最大化。原本一度
傳出退出市場的Fujifilm就是一個鮮明的例子。去年12月下
旬，剛就任Fujifilm電子影像事業部長的 ( 木通)口武常務執
行董事為徹底改革成本構造，要求「從原料採購到生產完
成的前置作業時間要縮短一半，並降低製造成本20%」。
擴大台廠代工 為日數位相機廠逆境求生活路
(中央社記者韓婷婷台北15日電)
• 富士找來台灣最大代工廠華晶科順利完成，推出的Fujifilm A170
數位相機，這款「俗又大碗」的殺手級產品，竟然成為富士逆
轉勝的關鍵球。日本專家認為，A170能夠以低成本，還保留基
本應有功能，主要關鍵應該是「從產品設計到零件採購，大部
份都交給台灣的數位相機代工大廠一手包辦」
• 專家認為，後金融風暴時代，消費行為有了微妙的變化，「品
牌優先」觀念逐漸式微，起而代之的是「不管是誰，給我最好
、最便宜的」，只要誰能推出「便宜又超值」的產品，消費者
就買單。
資料來源：http://tw.news.yahoo.com/article/url/d/a/091115/5/1uzzi.html
Costs
• In this chapter, we examine five main
topics
– Measuring Costs
– Short-Run Costs
– Long-Run Costs
– Lower Costs in the Long Run
– Cost of Producing Multiple Goods
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7-5
Economic Costs
• Economic Cost
– The economic cost or opportunity cost is
the value of the best alternative use of a
resource.
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7-6
Capital Costs
• Two problems may arise in measuring the
cost of capital.
– The first is how to allocate the initial purchase
cost over time.
– The second is what to do if the value of the
capital changes over time.
• Durable Good
– a product that is usable for years
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7-7
Allocating Capital Costs
over Time
• An economist amortizes the cost of the truck
on the basis of its opportunity cost at each
moment of time, which is the amount that the
firm could charge others to rent the truck.
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7-8
Actual and Historical
Costs
• A piece of capital may be worth much more or
much less today than it was when it was
purchased.
• The firm’s current opportunity cost of capital may
be less than what it paid if the firm cannot resell
the capital.
• Sunk Cost
– an expenditure that cannot be recovered
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7-9
Short-Run Costs
• Short-Run Cost Measures
1)
fixed cost (F)
– a production expense that does not vary with
output
2)
variable cost (VC)
– a production expense that changes with the
quantity of output produced
3)
cost (total cost, C)
– the sum of a firm’s variable cost and fixed cost:
C = VC + F
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7-10
Marginal Cost
• A firm’s marginal cost (MC) is the amount by
which a firm’s cost changes if the firm produces
one more unit of output.
• The marginal cost is:
(7.1)
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7-11
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
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7-12
Average Costs
• average coust (AC)
– or average total cost
– The total cost divided by the units of output
produced:
AC=C/q
– Because C = VC + F
(7.2)
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7-13
Short-Run Cost Curves
• The total cost differs from the variable cost by
the fixed cost.
• The marginal cost curve, MC, cuts the average
variable cost, AVC, and average cost, AC,
curves at their minimums.
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7-14
Figure 7.1
Short-Run
Cost Curves
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7-15
Production Functions and
the Shape of Cost Curves
• The production function determines the
shape of a firm’s cost curves.
• The production function shows the amount of
inputs needed to produce a given level of
output.
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7-16
Shape of the Marginal
Cost Curve
• In the short run, capital is fixed, so the only way
the firm can produce more output is to use extra
labor.
• The marginal cost equals the wage times the
extra labor necessary to produce one more unit
of output.
dV (q)
dL
w
MC 
w

dq
dq MPL
(7.3)
• The marginal cost moves in the direction opposite
that of the marginal product of labor.
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7-17
Shape of the Average
Cost Curves
• For the firm, whose only variable input is labor,
variable cost is wL, so average variable is:
AVC 
VC wL
w
w



q
q
q / L APL
(7.4)
• With a constant wage, the average variable cost
moves in the opposite direction of the average
product of labor .
• The average cost curve is the vertical sum of the
average variable cost curve and the average
fixed cost curve.
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7-18
Shape of the Average
Cost Curves
• If the average variable cost curve is U-shaped,
adding the strictly falling average fixed cost makes
the average cost fall more steeply than the
average variable cost curve at low output levels.
• At high output levels, the average cost and
average variable cost curves differ by ever smaller
amounts, as the average fixed cost, F/q,
approaches zero.
• The average cost curve is also U-shaped.
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7-19
Effects of Taxes on Costs
• Taxes applied to a firm shift some or all of
the marginal and average cost curves.
• A specific tax affects the firm’s average cost,
average variable cost, and marginal cost
curves but not its average fixed cost curve.
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7-20
Figure 7.2
Effect of a Specific Tax on Furniture
Firm’s Cost Curves
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7-21
Short-Run Cost Summary
• In the short run, the cost associated with inputs
that cannot be adjusted is fixed, while the cost
from inputs that can be adjusted is variable.
• Given constant input prices, the shapes of the
cost, variable cost, marginal cost, and average
cost curves are determined by the production
function.
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7-22
Short-Run Cost Summary
• Where there are diminishing marginal
returns to a variable input, the variable cost
and cost curves become relatively steep as
output increases, so the average cost,
average variable cost , and marginal cost
curves rise with output.
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7-23
Short-Run Cost Summary
• Both the average cost and average variable
cost curve fall when marginal cost is below
them and rise when marginal cost is above
them, so the marginal cost curve cuts both
of these average cost curves at their
minimum points.
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7-24
Long-Run Costs
• In the long run, the firm adjusts all its inputs so
that its cost of production is as low as possible.
• Although firms may incur fixed costs in the
long run, these fixed costs are avoidable
(rather than sunk, as in the short run).
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7-25
Input Choice
• From among the technologically efficient
combinations of inputs, a firm wants to choose
the particular bundle with the lowest cost of
production, which is the economically efficient
combination of inputs.
• To do so, the firm combines information about
technology from the isoquant with information
about the cost of labor and capital.
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7-26
Isocost Line
• The firm’s total cost is the sum of its labor and
capital cost (where r is the implicit rental rate):
C = wL + rK
(7.6)
• All the combinations of inputs that require the
same (iso-) total expenditure (cost)
(7.7)
• Using Algebra,
(7.8)
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7-27
Isocost Line
• Three properties of isocost lines:
– First, where the isocost lines hit the capital and
labor axes depends on the firm’s cost and on
the input prices.
– Second, isocosts that are farther from the origin
have higher costs than those that are closer to
the origin.
– Third, the slope of each isocost line is the same.
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7-28
Figure 7.3
Cost Minimization
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7-29
Minimizing Cost
• Lowest-isocost rule:
– Pick the bundle of inputs where the lowest
isocost line touches the isoquant.
• Tangency rule:
– Pick the bundle of inputs where the isoquant
is tangent to the isocost line.
• 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.
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7-30
Minimizing Cost
• To minimize its cost of producing a given level of
output, a firm chooses its inputs so that the
marginal rate of technical substitution equals the
negative of the relative input prices.
MPL w
MPL MPK
 

MPK
r
w
r
• Because MRTS = - MPL/MPK
© 2008 Pearson Addison Wesley. All rights reserved.
(7.9)
(7.10-11)
7-31
Using Calculus to
Minimize Cost
• Formally, the firm is minimizing its cost subject
to the information in the production function
contained in the isoquant expression. The
corresponding Lagrangian problem is shown in
Equation (7.12).
• Equation 7.12
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7-32
Using Calculus to
Minimize Cost
• Assuming that we have an interior solution, the
first-order conditions are:
(7.13)
(7.14)
(7.15)
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7-33
Using Calculus to
Minimize Cost
• Dividing Equation 7.13 by Equation 7.14 and
rearranging terms, we obtain:
(7.16)
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7-34
Maximizing Output
• We could equivalently examine the dual
problem of maximizing output for a given level
of cost.
• Here the Lagrangian problem is:
(7.17)
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7-35
Maximizing Output
• Assuming that we have an interior solution
where both L and K are positive, the first-order
conditions are:
(7.18)
(7.19)
(7.20)
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7-36
Figure 7.4
Output Maximization
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7-37
Factor Price Change
• When the wage falls, the firm minimizes its new
cost by substituting away from the now relatively
more expensive input, capital, toward the now
relatively less expensive input, labor.
• The change in the wage does not affect
technological efficiency, so it does not affect the
isoquant.
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7-38
Figure 7.5
Change in Factor Price
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7-39
How Long-Run Cost
Varies with Output
• Expansion Path:
– the cost-minimizing combination of labor and
capital for each output level
• Long-Run Cost Function
– The expansion path contains the same
information as its long-run cost function,
C(q), which shown the relationship between
the cost of production and output.
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7-40
Solved Problem 7.4
• What is the expansion path function for a
constant-return-to-scale Cobb-Douglas
production function q = ALaK1-a?
• Use the tangency condition between the isocost
and isoquant that determines the factor ratio
when the firm is minimizing cost to derive the
expansion path.
(7.21)
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7-41
Figure 7.6(a)
Expansion Path
and Long-Run
Cost Curve
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7-42
Figure 7.6(b)
Expansion Path and Long-Run Cost Curve
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7-43
The Shape of Long-Run
Cost Curves
• The shapes of the average cost and marginal
cost curves depend on the shape of the long-run
cost curve.
• As with the short-run curves, the shape of the
long-run curves is determined by the production
function relationship between output and inputs.
• In the long run, returns to scale play a major
role in determining the shape of the average
cost curve and other cost curves.
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7-44
The Shape of Long-Run
Cost Curves
• Increasing all inputs in proportion may cause
output to increase more than in proportion
(increasing returns to scale) at low levels of
output, in proportion (constant returns to scale)
at intermediate levels of output, and less than in
proportion (decreasing returns to scale) at
high levels of output.
• If a production function has this returns-to-scale
pattern and the prices of inputs are constant,
long-run average cost must be U-shaped.
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7-45
The Shape of Long-Run
Cost Curves
• 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
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7-46
Table 7.1
Shape of Average Cost Curves in
Canadian Manufacturing
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7-47
Lower Costs in the Long Run
• Because the firm cannot vary its capital in the
short run but vary it in the long run, short-run
cost is at least as high as long-run cost and is
higher if the “wrong” level of capital is used in the
short run.
• Long-Run Average Cost as the Envelope of
Short-Run Average Cost Curves
– As a result, the long-run average cost is always
equal to or below the short-run average cost.
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7-48
Figure 7.7(a)
Long-Run Average Cost as the Envelope of
Short-Run Average Cost Curves
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7-49
Figure 7.7(b)
Long-Run Average Cost as the Envelope of
Short-Run Average Cost Curves
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7-50
Application
• 對台灣學生而言，在2009年，採購家用印表機有噴墨式與黑白雷
射式兩種選擇。以印表機第一大廠hp為例，噴墨式印表機可選擇
hp deskjet D1660，其單價為新台幣990元，這款印表機黑白列印每
分鐘可達20頁(黑白墨水匣平均可列印200頁的標準頁面)，彩色列
印則每分鐘16頁(黑白墨水匣平均可列印165頁的標準頁面) ；而雷
射印表機如 hp LaserJet P1006，黑白列印每分鐘可達16頁，其單價
為新台幣3,888元 (碳粉匣平均可列印 1,500 頁的標準頁面)。
資料來源： http://buy.yahoo.com.tw/gdsale/gdsale.asp?gdid=1751946
http://buy.yahoo.com.tw/gdsale/gdsale.asp?gdid=749845
http://h10060.www1.hp.com/pageyield/index.html
© 2008 Pearson Addison Wesley. All rights reserved.
7-51
Application
• Choosing an Ink-Jet or a Laser Printer:
– You decide to buy a printer for your college
assignments. You need to print in black and
white. In 2007, you can buy a personal laser
printer for $150 or an ink-jet printer for $75
that prints 15 pages a minute at 1,200 dots
per inch.
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7-52
Application
• The cost of ink and paper is about 4 cents per
page for a laser compared to about 7 cents per
page for an ink jet.
• The average cost per page of operating a laser is:
$150/q + 0.04
• The average cost per page of operating an ink jet:
$75/q + 0.07
© 2008 Pearson Addison Wesley. All rights reserved.
7-53
Application
Choosing an Ink-Jet or a Laser Printer
20
SRAC
of laser printer
SRAC
10
of ink-jet printer
LRAC
4
0
© 2007 Pearson Addison-Wesley. All rights reserved.
2,500
5,000
q, pages
7–54
Short-Run and Long-Run
Expansion Paths
• Long-run cost is lower than short-run cost
because the firm has more flexibility in the long
run.
• To show the advantage of flexibility, we can
compare the short-run and long-run expansion
paths, which correspond to the short-run and
long-run cost curves.
© 2008 Pearson Addison Wesley. All rights reserved.
7-55
Figure 7.8
Long-Run and Short-Run Expansion Paths
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7-56
How Learning by Doing
Lowers Costs
• Learning by Doing :
– the productive skills and knowledge of better
ways to produce that workers and managers
gain from experience.
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7-57
Figure 7.9(a)
Learning by Doing
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7-58
Figure 7.9(b)
Learning by Doing
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7-59
Cost of Producing Multiple
Goods
• Few firms produce only a single good ─ We
have discussed single-output firms only for
simplicity.
• If a firm produces two or more goods, the cost
of one good may depend on the output level of
the other.
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7-60
Cost of Producing Multiple
Goods
• We say that there are economies of scope if
it is less expense to produce goods jointly than
separately (Panzar and Willig, 1977, 1981).
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7-61
Cost of Producing Multiple
Goods
• A measure of the degree to which there are
economies of scope (SC) is
C (q1 , 0)  C (0, q2 )  C (q1 , q2 )
SC 
C (q1 , q2 )
where C(q1,0) is the cost of producing q1 units of
the first good by itself, C(0, q2) is the cost of
producing q2 units of the second good, and C(q1,
q2) is the cost of producing both goods together.
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7-62
Cost of Producing Multiple
Goods
• Production Possibility Frontier (PPF):
– The maximum amount of outputs that can be
produced from a fixed amount of input.
– The production possibility frontier summarizes
the trade-off someone faces.
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7-63
Figure 7.10
Joint Production
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7-64