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![Page 1: Slide 1 2002 South-Western Publishing Cost Analysis Chapter 8 The meaning and measurement of cost Short-run Cost Functions Long-run Cost Functions Scale.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d635503460f94a46290/html5/thumbnails/1.jpg)
Slide 12002 South-Western Publishing
Cost AnalysisChapter 8
• The meaning and measurement of cost
• Short-run Cost Functions
• Long-run Cost Functions
• Scale Economies and Cost• Appendix 8A: Cobb-Douglas & Long Run
Cost
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Slide 21999 South-Western College Publishing
The Object of Cost Analysis
• Managers seek to produce the highest quality products at the lowest possible cost.
• Firms that are satisfied with the status quo find that competitors arise that can produce at lower costs.
• The advantages once assigned to being large firms (economies of scale and scope) have not provided the advantages of flexibility and agility found in some smaller companies.
• Cost analysis is helpful in the task of finding lower cost methods to produce goods and services.
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Slide 3
Managerial Challenge:US Airways
• US Airways created in mergers with Allegheny, Mohawk, Lake Central, Pacific Southwest and Piedmont Airways.
• Mostly in the East, with high cost but high yields (most seats were filled).
• But, this situation invites entry by competitors by Continental or others.
• The key to US Airways’ survival lays in managing its high cost.
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Slide 4
Meaning of Cost There an Many Economic Cost Concepts
• Opportunity Cost -- value of next best alternative use.
• Explicit vs. Implicit Cost -- actual prices paid vs. opportunity cost of owner supplied resources.
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Slide 5
機會成本 (Opportunity Cost)
• 定義» 在所有被放棄的可能方案中,所能帶來的最大可能淨收益
• 揭露相關的成本有兩種方式» 直接把所有可能的方案都列出來» 利用機會成本的概念
• 機會成本帶有相關性,但可能不反映在會計報表中» 必須透過分析才能發現
• 機會成本是財務上非常重要的概念» 支撐「附加價值」的概念,如今常出現在公司的年報中
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Slide 6
案例 8-5 機會成本• 永安集團在香港上市,旗下百貨公司擁有很久歷史
• 百貨公司總店,香港 Des Voeux Road» 底層: 25,000平方英尺» 其他層面: 64,000平方英尺
• 永安集團該對旗下百貨公司收多少房租?» 製造壓縮機有規模經濟
• 變成製造空調和冰箱的多樣化經濟» 另外,顧客是一樣,所以在銷售方面,用同一品牌即可得到多樣化經濟
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Slide 7
案例 8-5 機會成本(續)
收入 $2,236
成本 $2,210
利潤 $26
機會成本 $53
單位:百萬港幣
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Slide 8
案例 8-5 機會成本(續 1)• 零售地產市場是競爭性的:永安應該收取市場租金» 假設永安將零售場地租給其他承租人並賺取了 5,30
0萬港幣» 某種程度上,永安有向百貨公司收取租金,但沒有達到市場租金
» 除了市場租金,永安集團應考慮其他因素• 從百貨公司到辦公樓承租人有什麼外部性?
• 另外考慮» 飯店、咖啡店和停車場對百貨公司有什麼外部性?
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Slide 9
Examples of Relevant Cost Concepts
• Depreciation Cost Measurement. Accounting depreciation (e.g., straight-line depreciation) tends to have little relationship to the actual loss of value» To an economist, the actual loss of value is the
true cost of using machinery. • Inventory Valuation. Accounting valuation
depends on its acquisition cost» Economists view the cost of inventory as the
cost of replacement.
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Slide 10
• Unutilized Facilities. Empty space may appear to have "no cost”» Economists view its alternative use (e.g.,
rental value) as its opportunity cost.• Measures of Profitability. Accountants and
economists view profit differently. » Accounting profit, at its simplest, is revenues
minus explicit costs. » Economists include other implicit costs (such as a
normal profit on invested capital).
Economic Profit = Total Revenues - Explicit Costs - Implicit Costs
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Slide 11
相關性原則• 只應考慮相關成本,忽略其他成本
» 整個行動過程中,哪些成本是相關的» 相關成本可能很隱蔽» 不相關成本極可能出現在報表裡
• 會計原理» 注重客觀而確定的數字» 可以被缺少商業知識的獨立審計師批准» 會計報表不一定能為管理決策提供最有用的訊息
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Slide 12
• Sunk Costs -- already paid for, or there is already a contractual obligation
to pay• Incremental Cost - - extra cost of
implementing a decision = TC of a decision
• Marginal Cost -- cost of last unit produced = TC/Q
SHORT RUN COST FUNCTIONS1. TC = FC + VC fixed & variable costs
2. ATC = AFC + AVC = FC/Q + VC/Q
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Slide 13
沉沒成本 (Sunk Cost)
• 定義» 已經(或承諾)支出而無法挽回的成本
• 另外的行動» 先前的承諾
• 較少承諾→較少沉沒成本» 計畫期的長短
• 較長的計畫期→較少沉沒成本
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Slide 14
沉沒成本 (Sunk Cost)(續)• 沉沒成本是商業策略的重要概念
» Qwest光纖網絡的沉沒成本阻止了新進入者• 技術密集型產業:高沉沒成本
» 與傳統投資相比,研發成本不易回收
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Slide 15
案例 8-9 蘋果公司的訂價策略• 1988年夏天
» 以每顆 38 美元的價格買下共計幾億美元的百萬位元的 DRAM
• 1989年元月» 市場價格跌到 23 美元» 為給Macintosh 訂價,百萬位元的 DRAM 庫
存該是多少成本
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Slide 16
案例 8-9 蘋果公司的訂價策略(續)
• 蘋果電腦沒有將 15 美元的差異作為沉沒成本» 將最終產品訂價在較高的位置上
• 無法銷售高階產品,只能銷售低階產品• 毛利從 1988年的 51.5%下降到 1989年第二季的 46.2%
• 蘋果電腦應該不理會沉沒成本» 極端情形:假使蘋果電腦的市場部從現貨市場購買
存儲器• 價錢是 23 美元,這就比倉庫存貨來得便宜
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Slide 17
沉沒成本:策略影響• 在第九章詳細分析這些策略影響
» 鎖定顧客• Microsoft 讓學生以特價購買軟體,目的就是使他們習慣這些軟體
• 推廣牛奶與孕婦• 台灣例子
» 驅逐競爭對手• 減少未來的邊際成本,例如 Qwest
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Slide 18
沉沒成本與固定成本
成本
沉沒
相關固定
變動• 並非所有沉沒成本都是固定的• Qwest 鋪設 48 束 10GBPS的光纖:一旦發生就沉沒
» 但最初也可以選擇較少的束數
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Slide 19
沉沒成本與固定成本(續)• 假設,簽訂三年的勞動合約來滿足全職生產工人» 所有勞動報酬成本是沉沒的» 但是事先可以談判若干不同的工資或更具彈性的條
件• 並非所有固定成本都是沉沒的• 例如,所有商用飛機必須要有一位飛行員和領
航員,這就是固定成本» 但不是沉沒成本,因為從這個線路轉移到另一條線
路,可以辭退飛行員
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Slide 20
Short Run Cost Graphs
AFC
Q
Q
1.
2. AVC
3.
QAFC
AVC
ATCMC
MC intersects lowest pointof AVC and lowest point ofATC.
When MC < AVC, AVC declinesWhen MC > AVC, AVC rises
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Slide 21
邊際成本與平均成本• 邊際成本
» 每增加一單位產出所須增加的生產成本• 平均成本
» 又稱為單位成本» 總成本除以總產量
• 總成本曲線» 變動成本曲線平行上移,移動量為固定成本
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Slide 22
圖 4-2 短期邊際成本與平均成本
0
0.50
1.00
1.50
2.00
2 4 6 8
生產量(千個 / 週)
2.50
3.00
邊際成本平均成本平均變動成本
•邊際產量遞減 (diminishing marginal product) 使邊際成本曲線和平均成本曲線上升
成本(千元)
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Relation of Cost & Production Functions in SR
• AP & AVC are inversely related. (ex: one input)
• AVC = WL /Q = W/ (Q/L) = W/ APL
» As APL rises, AVC falls
• MP and MC are inversely related
• MC = dTC/dQ = W dL/dQ = W / (dQ/dL) = W / MPL
» As MPL declines, MC rises
prod. functions
cost functions
MPL
MC
AP
AVC
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Slide 24
短期邊際成本、平均變動成本和平均成本
• 邊際產量» 每增加一單位投入所增加的產出
• 從生產量= 0 開始» 平均變動成本隨著產量增加而下降
• 因為被 divide by 愈大生產率» 平均(總)成本類似
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Slide 25
短期邊際成本、平均變動成本和平均成本(續)
• 邊際產量遞減 (diminishing marginal product)» 平均變動成本隨著產量增加而上升» 平均(總)成本隨著生產率的增加而增加
• 邊際成本、平均變動成本與平均成本三條曲線都顯現出「 U」字型
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Slide 26
Problem• Let there be a cubic VC function:
VC = .5 Q3 - 10 Q2 + 150 Q » find AVC from VC function» find minimum variable cost output» and find MC from VC function
• Minimum AVC, where dAVC/dQ = 0
» AVC = .5 Q 2 -10 Q + 150» dAVC / dQ = Q - 10 = 0» Q = 10, so AVC = 100 @ Q = 10
• MC= dVC/dQ= 1.5 Q2 - 20 Q + 150
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Slide 27
Long Run Costs
• In Long Run, ALL inputs are variable
• LRAC » long run average cost» ENVELOPE of
SRAC curves
• LRMC is FLATTER than SRMC curves
Q
LRAC
LRMCSRAC1
SRMC1
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Slide 28
個別廠商的長期供給曲線• 和短期相似
» 從會計科目數據開始» 分析並確認邊際成本和平均成本» 利潤極大化原則
• 價格等於邊際成本是確定產量» 長期和短期的原則相同
• 但使用長期價格和長期邊際成本
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Slide 29
個別廠商的長期供給曲線(續)• 對製造業和服務業的分析是相同的
» 製造業—生產量,比如對汽車生產商來說,就是每年的汽車生產數量
» 服務業—運轉量,比如對電信營運商來說,就是每月通訊的分鐘數
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Slide 30
Long Run Cost Functions: Envelope of SRAC curves
Q
SRAC-small capital
SRAC-med. capital
SRAC-big capital
LRAC--Envelopeof SRAC curves
Ave Cost
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Slide 31
Economists think that the LRAC is U-shaped
• Downward section due to:» Product-specific economies which include
specialization and learning curve effects.» Plant-specific economies, such as economies
in overhead, required reserves, investment, or interactions among products (economies of scope).
» Firm-specific economies which are economies in distribution and transportation of a geographically dispersed firm, or economies in marketing, sales promotion, or R&D of multi-product firms.
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Slide 32
• Flat section» Constant returns to scale
• Upward rising section of LRAC is due to:» diseconomies of scale. These include transportation
costs, imperfections in the labor market, and problems of coordination and control by management.
» The minimum efficient scale (MES) is the smallest scale at which minimum per unit costs are attained.
» Modern business management offers techniques to avoid diseconomies of scale through profit centers, transfer pricing, and tying incentives to performance.
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Slide 33
Equi-marginal Principle in LR
• Since, LR costs are least cost, they must be efficient; that is, obey the equi-marginal principle:
MPX/CX = MPY/CY.• That is, the marginal product per dollar
in each use is equal.
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Slide 34
Cost Functions and Production Functions: LR Relationships and the Importance of Factor Costs
A. CRS & Constant Factor Prices:
TC AC
Q 2Q
B. IRS & Constant Factor Prices:
Q 2Q
TCAC
C. DRS & Constant Factor Prices
Q 2Q
AC
D. CRS & Rising Factor Prices -- looks like “C”
More than doubles output
Doesn’t quite double output
Constant cost
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Slide 35
Problem: Let TC & MC be:• TC = 200 + 5Q - .4Q2 + .001Q3
• MC = 5 - .8Q + .003 Q2
a. FIND fixed cost
FIND AVC function
b. FIND minimum average variable cost point
c. If FC rises $500, what happens to minimum average variable cost?
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Slide 36
TC = 200 + 5Q - .4Q2 + .001Q3
MC = 5 - .8Q + .003 Q2
a. FIND fixed cost
FIND AVC function
Answer: FC = 200 and AVC = 5 - .4Q + .001Q2.
b. FIND minimum average variable cost point
Answer: First find dAC/dQ = 0: From (a) that is:
-.4 + .002Q = 0, so Q = 2,000
c. If FC rises $500, what happens to minimum average variable cost?
Answer: No change, since AVC doesn’t change.
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Slide 37
Cobb-Douglas Production Function and the Long-Run Cost Function:
Appendix 8A
• Long Run Costs & Production Functions: 1 Input
» In the long run, total cost is: TC = w·L, where w is the wage rate.
» production function is Cobb-Douglas: Q = Lß. » Solving for L in the Cobb-Douglas production
function, we find: L = Q1/ß.» Substituting this into the total cost function, we get:
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Slide 38
One Input Case
• TC = w·Q1/ß. • This also demonstrates that
if the production function were constant returns to scale (ß=1), then TC rises linearly with output and average cost is constant.
• If the production function is increasing returns to scale (ß >1), then TC rises at a decreasing rate in output and average cost is declining.
• If the production function is decreasing returns to scale (ß<1), then TC rises at an increasing rate in output and average cost rises.
![Page 39: Slide 1 2002 South-Western Publishing Cost Analysis Chapter 8 The meaning and measurement of cost Short-run Cost Functions Long-run Cost Functions Scale.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d635503460f94a46290/html5/thumbnails/39.jpg)
Slide 39
TWO Input Case
• With two inputs, long run cost is: TC = w·L + r·K,» where w is the wage rate
and r is the cost of capital, K.
• Cobb-Douglas: Q = K·Lß.• The manager attempts to
minimize cost, subject to an output constraint. This is a Lagrangian Multiplier problem.
• Min L = w·L + r·K + ·[ K·Lß - Q ]
• Taking derivatives and solving yields a total cost:
• TC = w·L* + r·K* = • TC = w·Q(1/(+ß))·(·w/ß·r)(ß/(+ß)) +
r·Q(1/(+ß))·(·w/ß·r)(/(+ß))
• If (+ß>1), then 1/(+ß) less than 1, and total cost rises at a decreasing rate in output. That means that average cost declines.
![Page 40: Slide 1 2002 South-Western Publishing Cost Analysis Chapter 8 The meaning and measurement of cost Short-run Cost Functions Long-run Cost Functions Scale.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d635503460f94a46290/html5/thumbnails/40.jpg)
Slide 40
長期收支平衡• 是否進入 / 退出
» 價格≧平均成本• 營業規模
» 邊際成本=價格• 環境條件和短期決策的十分相似
» 關鍵區別為所有變量是對長期而言的• 長期邊際成本可能和短期的不同• 長期價格可能和短期的不同
![Page 41: Slide 1 2002 South-Western Publishing Cost Analysis Chapter 8 The meaning and measurement of cost Short-run Cost Functions Long-run Cost Functions Scale.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d635503460f94a46290/html5/thumbnails/41.jpg)
Slide 41
圖 4-6 長期產量
0
0.70
3.4
長期邊際成本
長期平均成本
邊際收益 =價格收支平衡點
產量(千個 / 週)
成本/收益(元
/
個)
![Page 42: Slide 1 2002 South-Western Publishing Cost Analysis Chapter 8 The meaning and measurement of cost Short-run Cost Functions Long-run Cost Functions Scale.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d635503460f94a46290/html5/thumbnails/42.jpg)
Slide 42
案例 4-4 富士通:杜翰市與格力斯翰市• 已投資英國杜翰市 5.9 億美元
» 現有設備僅能生產 4和 16百萬位元 DRAM
» 需投資 10 億美元才可生產 64百萬位元 DRAM )» 長期價格<平均成本(包括重置成本)
• 格力斯翰市» 平均變動成本<長期價格<平均成本
• 註釋» 這只是作者對真實情況的解釋,不包含有關成本的
內部訊息
![Page 43: Slide 1 2002 South-Western Publishing Cost Analysis Chapter 8 The meaning and measurement of cost Short-run Cost Functions Long-run Cost Functions Scale.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d635503460f94a46290/html5/thumbnails/43.jpg)
Slide 43
案例 4-5 石油:該不該生產呢?
• 原油價格上升時,油井平台的數量增加• 原油價格下降時,油井平台的數量減少
![Page 44: Slide 1 2002 South-Western Publishing Cost Analysis Chapter 8 The meaning and measurement of cost Short-run Cost Functions Long-run Cost Functions Scale.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d635503460f94a46290/html5/thumbnails/44.jpg)
Slide 44