長期成本

Long run cost minimization

長期成本函數QrwrKQrwwLrwQC

長期要素需求QrwKQrwL

QKLFtosubject

wLrKKL

),,(*),,(*),;(

),,(*),,,(*

),(:

min,

邊學邊做 8.1

長期成本函數QwrQrwrKQrwwLrwQC

r

wQQrwK

w

rQQrwL

Qr

wLL

r

wLK

r

w

L

K

KL

KL

MP

MPMRTS

QKLLKKLFtosubject

wLrK

K

LLK

KL

25),,(*),,(*),;(

)50

(),,(*,)50

(),,(*

)(50

,*

25

25

5050),(:

min

2/12/1

2/12/1

2/12/1

2/12/1

,

FIGURE 8-2 Long-Run Total Cost Curve for Learning-By-Doing Exercise 8.1

W=25, r=100

FIGURE 8-1 Cost Minimization and the Long-Run Total Cost Curve for a Producer of Television Sets

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 8, Figure 08-01

(Figure continues on next slide)

FIGURE 8-1 (Continued)

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 8, Figure 08-01 continued

How does the long-run total cost curve shift when input prices

change?• Just one input price changes

• All input prices change proportionately

FIGURE 8-3 How a Change in the Price of Capital Affects the Optimal Input Combination and Long-Run Total Cost for a Producer

of Television Sets

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 8, Figure 08-03

FIGURE 8-4 How a Change in the Price of Capital Affects the Long-Run Total Cost Curve for a Producer of Television Sets

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 8, Figure 08-04

FIGURE 8-5 How a Proportionate Change in the Prices of All Inputs Affects the Cost-Minimizing Input Combination

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 8, Figure 08-05

Application 8.1

• The long-run cost of Trucking , 2

FIGURE 8-6 Long-Run Total Cost Curve for a Trucking Firm

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 8, Figure 08-06

FIGURE 8-7 Deriving Average and Marginal Cost from theTotal Cost Curve

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 8, Figure 08-07

(Figure continues on next slide)

FIGURE 8-7 (Continued)

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 8, Figure 08-07 continued

FIGURE 8-9 Relationship Between the Average andMarginal Cost Curves

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 8, Figure 08-09

長期平均成本與邊際成本

)(25

)(

25),,(*),,(*),;(

QMCwr

QAC

長期成本函數

QwrQrwrKQrwwLrwQC

FIGURE 8-8 Long-Run Average and Marginal Cost Curves for Learning-By-Doing Exercise 8.2

W=25, r=100

FIGURE 8-10 The Average and Marginal Cost Curves for University Education at U.S. Universities

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 8, Figure 08-10

Quiz (0331)

• In the study of Rajindar and Manjulika Koshal (1005) how school size affects the average and marginal cost of higher education ?

• 為何大學的邊際成本遞減 ?

• 學生增加 , 圖書館會增蓋 ?

• 範例 8.2 中提到學校額外增加一名學生的邊際成本會低於位學生的平均成本，因此增加學生人數可以降低學生的平均成本，如果是這樣為何碩士在職專班人數只有 20 人一班，似乎有些規模不經濟，是否應該要增加成一班至少 30-40 人，降低平均成本 !

Economies of scale

• Economies of scale :

average cost decreases as output goes up

• diseconomies of scale :

average cost increases as output goes up

Causes of economies of scale

• Increasing returns to scale

• Indivisible inputs available only in a certain

minimum size. Its quantity cannot be scaled down as the firm’s output goes to zero

生產線機器 就長期考慮也是需要最小的設備規模• Specialization of labor

Causes of diseconomies of scale

• decreasing returns to scale• Managerial diseconomies : a given percentage

increase in output forces the firm to increases its spending on the services of the managers by more than this percentage

• Key individual’s contribution cannot be replicated

• 宏碁 vs 華碩

FIGURE 8-11 實證研究結果 :Real-World Average Cost Curve

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 8, Figure 08-11

MES

• MES: minimum efficient scale :

the smallest quantity at which the long run average cost curve attains it minimum point

• MES and industry structure : 表 8.1 p276

• MES 愈大表示 : 市場愈不競爭

Economies of scale and returns to scale

• Increasing returns to scale : economies of scale

• decreasing returns to scale : diseconomies of scale

• 表 8.3 (p277) 自行練習

Application 8.2

• The costs of higher education, 2

Application 8.3

• Economies of Scale in Refining Alumina

Application 8.4

• 為何而併 ?

• Economies of scale or

• Reduce competition

FIGURE 8-12 醫院合併 Average Cost Curves for “Backoffice 後勤” Activities

in a Hospital

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 8, Figure 08-12

Measure the extent of economies of scale ~ 表 8.5

1

1

)(

)(

,

,

,

QTC

QTC

QTC

ACMC

ACMC

QAC

QMC

QTC

QTC

QQTC

TC

短期成本

L

L

MP

w

Q

wQL

Q

QTVC

Q

QSTCQSMC

AP

w

Q

wQL

Q

QTVCQAVC

Q

QSTCQSAC

TFCQTVCQSTC

)()()()(

*)()()(

)()(

)()(

FIGURE 8-16 Short-Run Marginal and Average Cost Curves

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 8, Figure 08-16

FIGURE 8-13 Short-Run Total Cost Curve

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 8, Figure 08-13

短期成本與長期成本

)();( 1 QTCKQSTC

FIGURE 8-14 Why Total Costs Are Higher in the Short Runthan in the Long Run

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 8, Figure 08-14

FIGURE 8-15 Relationship Between Short-Run and Long-RunTotal Cost Curves

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 8, Figure 08-15

FIGURE 8-17 The Long-Run Average Cost Curve as anEnvelope Curve

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 8, Figure 08-17

FIGURE 8-18 The Relationship Between the Long-Run Average and Marginal Cost Curves and the Short-Run Average and

Marginal Cost Curves

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 8, Figure 08-18

短期最適化 : 邊學邊做 8.4~ 圖8.19

:w=25, r=100

KrQTFC

K

QwQTVC

短期成本函數KrK

QwKrQKwLrwQSTC

K

QQKL

QKLLFtosubject

wLKrKL

)(

2500)(

2500),(*),;(

2500),(*

50),(:

min

2

2

2

2/12/1

1,

Application 8.5

• Tracking Railroad Costs, 2, 3

• BDT(1984)(JIE)

Quiz (0421)

• Why did US shipping freight by the train in the 1990s take longer than it have 30 years earlier ?

FIGURE 8-20 Long-Run and Short-Run Average Cost Curvesfor a Railroad

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 8, Figure 08-20

Economies of scope

)0,0(),0()0,(),(

),0()0,(),(

2121

2121

TCQTCQTCQQTC

QTCQTCQQTC

例子• 範疇經濟也就是多樣化經濟，即企業在

生產不同的產品時，若出現成本遞減的現象，則就可稱之為範疇經濟。例如聯合報系在出刊報合報以後，還可以利用同樣的印報機器來出刊民生報、聯合晚報，此即範疇經濟的表現；此外，美語補習班除了教美語以外，還可代辦申請赴美念書或辦理旅遊等等。

Reasons

• A firm’s ability to use a common input to make and sell more than one output

• ~ 金控的範疇經濟

Application 8.6

• Economies of Scope for the Swoosh , 2

• Swoosh

Economies of experience

• Cost advantages that result from accumulated experience

• Learning by doing

• Experience curve : a relationship between average variable costs and cumulative production volume

• Why not “average fixed costs?”

Economies of scale and economies of experience

• 排課 : 9 學分都教個體 ~economies of scale

• 一直都教個體 : 累積經驗 ~ economies of experience

• 製程改善 ,….

Experience elasticity

BAN

ABN

NNAVC

NNAVC

NN

NAVCNAVC

ANNAVC

B

B

B

1

1

)(

)()(

)(

)(

SLOPE OF the experience curve

)(

)2(

2)2(

)(

)2(

NAVC

NAVCB

AN

NA

NAVC

NAVC BB

B

FIGURE 8-21 Experience Curves with Different Slopes

Application 8.7

• Experience Reduces Costs of Computer Chips

Estimating cost functions

• Total cost function

),,( rwQTC

How to estimate cost functions?

• 1. cross-section data

Estimating cost functionsconstant elasticity cost function

(CECF)

rdwcQbaTC

bwhere

rwaQwrQTC

QTC

dcb

lnlnlnlnln

),,(

,

Why constant ?

brwaQ

rwabQ

QAC

QMC

QTC

QTC

QQTC

TC

rwaQwrQTC

dcb

dcb

QTC

dcb

1

1

, )(

)(

),,(

Problems of CECF

• Does not allow for the possibility of AC(Q) that first decreases and then increases as Q increases

Estimating cost functionstranlog cost function

fucntionstofformgeneral

rwb

rbwbQb

rbwbQbaTC

CURVECOSTSHAPEU

cos`

,...))(ln(ln

)(ln)(ln)(ln

lnlnlnlnln

7

26

25

24

321

Translog cost function

• 碩博士論文