廠商的決策

)()()(max qcQqpqq

QUIZ (0302)

• What explain the slowdown in the labor productivity in the 1970s in US

• What explains the resurgence of labor productivity since 1995 in US

公司的目標 :極大化利潤 ?所有者與經營者

• 目標不同• 資訊不對稱• 公司治理• 當事代理人理論 ~管理經濟學• 員工分紅成本

決定產量決策的因素• 預期市場價格 p(q1+q2+,…)~ 市場競爭結

構• 成本函數 c(q)

市場競爭• 完全競爭 : price taker

• 獨占 : price setter

• 寡占 : 必須猜測對手產量• 同質寡占• 異質寡占 : 水平差異 , 垂直差異

成本函數 ~ch 7在即定生產目標下成本極小

qKLFtosubject

wLrK

questionfollowingtheofsolutiontheisqc

KL

),(:

min

)(

,

生產函數 F(L,K)

• The maximum quantity of outputs a firm can produce given the quantities of inputs that it might employ

• 生產管理問題給定 L,K 如何配置放對的人在對的部門

Why to consider only L, K?

Fix K, one variable input

• F(L, K(fixed)) ~short run

• Technically efficient

FIGURE 6-1 Technical Efficiency and Inefficiency

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-01

勞動邊際產量• 邊際報酬遞增 : 專業分工• 邊際報酬遞減• 總報酬遞減 : 人多手雜

FIGURE 6-2 Total Product Function

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-02

邊際產量與平均產量

LLL

LLL

LLL

LLL

LL

APAPMP

APAPMP

APAPMP

L

APMP

L

QLL

Q

L

AP

L

QAP

L

QMP

"

;

2

FIGURE 6-3 Average and Marginal Product Functions

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-03

FIGURE 6-4 Relationship Among Total, Average, and Marginal

Product Functions

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-04

(Figure continues on next slide)

FIGURE 6-4 (Continued)

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-04 continued

兩投入 (L,K) 生產函數• 等產量曲線 (ISOQUANT)

FIGURE 6-5 Total Product Hill

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-05

FIGURE 6-6 Isoquants and the Total Product Hill

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-06

FIGURE 6-8 Isoquants for the Production Function in Table 6.3

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-08

FIGURE 6-9 Economic and Uneconomic Regions of Production

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-09

非經濟區域

等產量曲線的特性• 邊際技術替代率 (MRTS)

• :The rate of which the quantity of capital can be reduced for every one unit increases in the quantity of labor, holding the quantity constant

FIGURE 6-10 Marginal Rate of Technical Substitution of Labor for Capital (MRTSL,K) Along an Isoquant

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-10

FIGURE 6-11 Input Substitution Opportunities and theShape of Isoquants

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-11

邊際技術替代率遞減:MRTS 與 MP 的關係

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K

L

QQ

MRTSMPMPL

MP

MP

K

QL

Q

L

K

KL

QL

L

QQ

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),(

0

如何描述比較不同產業的要素替代程度 ?

• 不同產業的 MRTS?

替代彈性

LK

LKMRTS

MRTSL

KL

K

)(

FIGURE 6-12 Elasticity of Substitution

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-12

替代彈性的直覺 ?

FIGURE 6-13 Isoquants for Iron and VehicleProduction in Germany

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-13

特殊的生產函數 :完全替代• 完全替代 :替代彈性

無限大• 例子 :不同電腦儲存

容量

bKaLQ

FIGURE 6-14 Isoquants for a Linear Production Function

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-14

特殊的生產函數 :完全互補• 完全互補 :替代彈性

=0• 例子 :一部車需一個

引擎 , 四個輪子

},min{ bKaLQ

FIGURE 6-15 Isoquants for a Fixed-ProportionsProduction Function

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-15

特殊的生產函數 :Cbb-Douglas

• Cbb-Douglas 生產函數

L

K

KAL

KAL

MP

MPMRTS

KALQ

K

LLK 1

1

Cobb-Doulgas 的替代彈性

1)(

)(1

)(

)(

)(

k

kMRTS

k

kMRTS

k

kMRTS

kMRTS

k

MRTSMRTS

L

KL

KL

Kk令

LK

LK

FIGURE 6-16 Isoquants for the Cobb-Douglas Production Function

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-16

CES 生產函數

FIGURE 6-17 Isoquants for the CES Production Function

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-17

Quiz 0317

• What two factors does the throughput of an oil pipeline of a given length depend on ?

規模報酬 (returns to scale)

• 所有要素增加對產量的影響

QKLf

KLfQ

),(

),(

FIGURE 6-18 Increasing, Constant, and DecreasingReturns to Scale

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-18

Increasing returns to scale

QKLf

QKLf

KLfQ

3)2,2(

),(

),(

constant returns to scale

QKLf

QKLf

KLfQ

2)2,2(

),(

),(

decreasing returns to scale

QKLf

QKLf

KLfQ

5.1)2,2(

),(

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練習

規模報酬遞減固定規模報酬規模報酬遞增

KALQ

:1

:1

:1

邊報酬遞減與規模報酬遞減

FIGURE 6-19 Diminishing Marginal Returns versusReturns to Scale

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-19

技術進步• 一定數量投入生產更多產量 :學習效果• 中性技術進步 :

要素價格不變 , 要素投入比不變• 勞動節省 (LABOR-SAVING) 型技術進步 :

邊際資本生產力上升 , 要素價格不變 , 多用資本• 資本節省 (CAPITAL-SAVING) 型技術進步 :

邊際勞動生產力上升 , 要素價格不變 , 多用勞動

FIGURE 6-20 Neutral Technological Progress

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-20

FIGURE 6-21 Labor-Saving Technological Progress

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-21

FIGURE 6-22 Capital-Saving Technological Progress

Besanko & Braeutigam/Microeconomics: An Integrated ApproachChapter 6, Figure 06-22

技術進步與 MRTS

LKKL

LKLK

K

L

QQ

MRTSKL同樣的MPMP改善員工素質技術進步MRTSKL同樣的MPMP改善生產善生技術進步

MP

MP

K

QL

Q

L

K

),(,)(

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0