Download Chapter3

Chapter 3
Labor Demand
McGraw-Hill/Irwin
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
2010/10/03 工商時報
台灣歐肯係數 四小龍最小 u = a -0.1(Y/Y )
• 主計處研究:現階段我國歐肯係數約在0.10～0.16之間，
即經濟成長每提升1%，只能降低失業率0.10%～0.16%。
亞洲四小龍最小，顯示台灣GDP成長對改善失業的效果，
相對較低:
• 金融海嘯前（97年第1季）台灣的歐肯係數為0.11，
係數低於美、德、英等14個先進國家。
• 97年第1季新加坡的歐肯係數為0.17、香港0.23、南韓0.35。
• 台灣致力發展高科技產業，雖能創造GDP，但由於所能提
供的就業機會非常有限。
3-2
Firm: Profit Optimization
• Assume: Supply of each factor is fixed.
• Assume markets are competitive:
each firm takes W, Re, and P as given.
P = price of output, W = nominal wage,
Re= nominal rental rate
W /P = real wage (measured in units of output),
/P= real rental rate
Re
Max   PF ( K , N )  Re K  WN
FOC wrt K: P  MPk  Re
FOC wrt N: P  MPN  W
3
3-3
Demand for labor: A derived demand
hire workers if P MPN  W
Value of Marginal Product (VMPN )
VMPN  P MPN : Demand for labor
W
in real terms : MPN 
w
P
Pr ofit Maximization (FOC Y): P  ?  MC
4
3-4
Total Product, Marginal Product,
and Average Product Curves
140
25
Average Product
120
20
Output
Output
100
80
Total Product
Curve
60
15
10
40
5
20
0
Marginal Product
0
0
2
4
6
8
10
Number of Workers
12
0
2
4
6
8
10
12
Number of Workers
3-5
Labor Demand Curve =VMPE
38
VAPE
22
VMPE
1
4
8
Number of Workers
3-6
SR Hiring Decision (summary)
• Value of Marginal Product:
VMPE= P*MPE
• A profit-maximizing firm hires workers up to the point where
the wage rate equals the value of marginal product of labor.
• The demand curve for labor indicates how many workers the
firm hires for each possible wage, holding capital constant.
• The labor demand curve is downward sloping.
This reflects the fact that additional workers are costly
due to the law of diminishing returns.
3-7
P ↑  SR Labor Demand
↑
22
18
VMPE
VMPE
8
9
12
Number of Workers
3-8
Critiques of Marginal Productivity Theory
• A common criticism is that the theory bears little
relation to the way that employers make hiring
decisions.
• Another criticism is that the assumptions of the
theory are not very realistic.
• However, employers act as if they know the
implications of marginal productivity theory (hence,
they try to make profits and remain in business).
3-9
SR Demand Curve for the Industry
Wage
Wage
T
D
20
20
10
10
D
T
15
Firm
28
30
Employment
30
56
60
Employment
Industry
3-10
LR Employment Decision
• In LR, firm maximizes profits by choosing
how many workers to hire AND how much
plant and equipment to invest in.
3-11
Isoquant Curves
Capital
X
K
Y
q1
q0
E
Employment
3-12
Isocost Lines
Capital
C1/r
C0/r
Isocost with Cost Outlay C1
Isocost with Cost Outlay C0
C0/w
C1/w
Employment
3-13
Firm's Optimal Combination of Inputs:
minimize costs
Capital
C1/r
A
C0/r
P
175
B
q0
100
Employment
3-14
Cost Minimization
• Profit maximization implies cost minimization.
• The firm chooses the least-cost combination of capital
and labor.
• This least-cost choice is where the isocost line is
tangent to the isoquant.
• Marginal rate of technical substitution equals the
ratio of input prices, w / r, at the least-cost choice.
3-15
LR Demand for Labor: (-)vely sloped
• wage↓: two effects
1. Substitution Effect:
the firm utilizes cheaper labor to substitute more expensive
factor K even if holding output constant.
→ N↑, K↓
2. Scale Effect:
the firm expanding production
→ N↑, K↑
Total effect: W↓ → N↑
3-16
SR vs LR Demand Curves for Labor
Dollars
Short-Run
Demand Curve
Long-Run
Demand Curve
Employment
3-17
2 Special Cases of Isoquants
Capital
Capital
100
q 0 Isoquant
q 0 Isoquant
5
200 Employment
20
Employment
Fig Left: Capital and labor are perfect substitutes if the isoquant is linear
Fig: Right: The two inputs are perfect complements if the isoquant is rightangled.
3-18
The Demand Curve for a Factor of Production
is Affected by the Prices of Other Inputs
Price of
input i
Price of
input i
(a)
(b)
D0
D1
D0
Employment of
input i
D1
Employment of
input i
The labor demand curve for input i shifts when the price of another input changes.
(a) If the price of a substitutable input rises, the demand curve for input i shifts up.
(b) If the price of a complement rises, the demand curve for input i shifts down.
3-19
Elasticity of Substitution
• Elasticity of substitution：替代彈性

( K
N
)
 (W )
r
• Cross-elasticity of factor demand：交叉彈性

(K
(W
K
W
)
)
3-20
Affirmative Action
Black Labor
Q
P
q*
White Labor
3-21
Marshall’s Rules
• Labor Demand is more elastic when:
– The elasticity of substitution is greater.
– The elasticity of demand for the firm’s output is
greater.
– Labor’s share in total costs of production is greater.
– The elasticity of supply of other factors of
production such as capital is greater.
3-22
Factor Demands given several inputs
• many different inputs:
– Skilled and unskilled labor
– Taiwan and foreign labor
– Old and new machines
Capital-skill complementarity hypothesis:
If subsidies to investment: DK ↑
 Demand for skilled vs. unskilled worker?
3-23
Labor Market Equilibrium
Dollars
Supply
whigh
w*
wlow
Demand
ED
E*
ES
Employment
3-24
Minimum Wages in the United States,
1938-2007
Nominal Minimum Wage
Ratio Min. Wage to Avg. Mfg. Wage
7
0.6
6
5
Ratio
0.5
4
0.4
3
2
0.3
Nominal
Wage
1
0
1938
0.2
1944
1950
1956
1962
1968
1974
1980
1986
1992
1998
2004
2010
Year
3-25
The Impact of the Minimum Wage
on Employment
Dollars
S
w
w*
D
E
E*
ES
Employment
3-26
The Impact of Minimum Wages
on the Covered and Uncovered Sectors
Dollars
Dollars
SU
(If workers migrate to
covered sector)
SC
SU
w
SU
(If workers migrate to
uncovered sector)
w*
w*
DU
DC
E
EC
Employment
EU
EU
EU
Employment
(b) Uncovered Sector
(a) Covered Sector
3-27
Asymmetric Variable Adjustment Costs
Variable
Adjustment Costs
C0
-25
0
+50
Change in
Employment
Changing employment quickly is costly, and these costs increase at an
increasing rate. If government policies prevent firms from firing workers,
the costs of trimming the workforce will rise even faster than the costs of
expanding the firm.
3-28
Variable adjustment costs:
Slow Transition to a New Labor Equilibrium
Employment
150
B
100
50
A
C
Time
3-29
Problems with Estimating Labor Demand
S0
Dollars
S1
Z
P
w0
R
w2
Z
Q
w1
D1
D0
E0
E1
E2
Employment
3-30