1 Supply of Labor
1
14.01 Principles of Microeconomics, Fall 2007
Chia-Hui Chen
December 3, 2007
Lecture 31
Factor Market
Outline
1. Chap 14: Supply of Labor
2. Chap 14: Demand of Labor
1
Supply of Labor
We derive the supply of labor by solving consumers’ utility maximization prob­
lems.
Two variables determining the utility are leisure (L), which is measured by
hours, and income (Y ); the prices are w and 1 respectively.
To maximize u(L, Y ), we have
∂u
∂L
∂u
∂Y
= w.
If w increases, on one hand, higher wages encourage people to work more (point
A to point B), which is a substitution effect; on the other hand, higher wages
allow the worker to purchase more goods, including leisure, which reduces work
hours (point B to point C), which is an income effect (see Figure 1).
When the wage is higher, if the substitution effect exceeds the income effect,
labor supply increases, and leisure decreases; if the income effect exceeds the
substitution effect, labor supply decreases, and leisure increases (see Figure 2).
Like product markets, competitive, monopolistic, and monopsonistic mar­
kets are types of factor markets.
In a competitive factor market, if the product market is also competitive,
M RPL = P × M PL .
If the product market is monopolistic,
M RPL = M R × M PL = P (1 −
1
) × M PL .
|ed |
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1 Supply of Labor
2
10
9
8
7
C
Y
6
B
5
4
A
Income Effect
3
2
1
Substitution Effect
0
2
3
4
5
6
7
L
8
9
10
11
12
Figure 1: Substitution Effect and Income Effect of Labor Supply.
10
9
8
7
Wage
6
Supply of Labor
Income Effect
> Substitution Effect
5
Income Effect
< Substitution Effect
4
3
2
1
0
3
3.5
4
4.5
5
5.5
6
Hours of Work per Day
6.5
7
7.5
8
Figure 2: Backward-Bending Supply of Labor.
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1.1
Factor Competitive
3
10
9
8
SL
7
w
6
w*
5
4
3
DL=P× MPL
2
1
0
L*
0
1
2
3
4
5
L
6
7
8
9
10
Figure 3: Competitive Factor Market.
1.1
Factor Competitive
Competitive market is most efficient, and there is no deadweight loss (see Fig­
ure 3).
When M R < P , both w and L decrease; the market is then not as efficient
as competitive market, and has deadweight loss (see Figure 4).
1.2
Factor Monopsony
Marginal Value equals the demand. Marginal Expenditure
ME =
∂PS (Q)Q
∂PS
=
Q + PS > PS .
∂Q
∂Q
Because L is determined by
M E = M V,
we can see that
′
w < w∗ ,
and
′
L < L∗
(see Figure 5).
One example of factor monopsonist is the government hiring soldiers.
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1.2
Factor Monopsony
4
10
9
8
SL
7
w
6
w*
5
P× MPL
w,
4
3
2
1
0
L, L*
0
1
2
3
4
DL=MR× MPL
5
L
6
7
8
9
10
9
10
Figure 4: Noncompetitive Factor Market.
10
9
ME
8
S=AE
7
w
6
w*
5
4
w,
3
D=MV
2
1
0
L,
0
1
2
3
L*
4
5
L
6
7
8
Figure 5: Monopsonistic Factor Market.
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1.3
1.3
Factor Monopoly
5
Factor Monopoly
An example of monopoly power in factor markets involves labor unions.
Economic rent is the difference between payments to a factor of production
and the minimum payment that must be spent to obtain the factor; it is like
producer surplus in a product market (see Figure 6).
10
9
8
SL
7
6
w
w
5
Economic Rent
4
3
2
1
0
0
0.5
1
1.5
2
L
2.5
3
3.5
4
Figure 6: Economic Rent.
When some workers lose their jobs, remaining workers have higher wages.
If the union tries to maximize the number of workers hired, it should set the
wage and labor employed w∗ and L∗ ; if the union tries to maximize economic
rent, it should set the wage and labor employed w1 and L1 .
w1 > w∗ ,
and
L1 < L∗
(see Figure 7).
It is hard to say which one is better for the workers.
Now consider a model of union workers and non-union workers. Assume
the demand for union workers is DU , and the demand for non-union workers is
DN U . The total market demand
DL = DU + DN U
is fixed.
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1.3
Factor Monopoly
6
10
9
8
SL
w,
7
w
6
w*Economic
5
Rent
4
3
DL
MR
2
1
0
L,
0
1
2
3
L*
4
5
L
6
7
8
9
10
Figure 7: Monopoly Power of Sellers of Labor.
When a monopolistic union raises the wage rate in the unionized sector of
the economy from w∗ to wU , employment in that sector falls; for the total supply
of labor to remain unchanged, the number of non-union workers increases and
the wage in the non-unionized sector must fall from w∗ to wN U (see Figure 8).
Assume the total supply of workers is 60; the demands for nonunion and
union workers are
1
wN U = 30 − LN U ,
2
wU = 30 − LU .
• When the union does not intervene,
wN U = wU = w.
Thus
LN U = 60 − 2w,
and
LU = 30 − w.
Then
L = 90 − 3w = 60,
which gives
w = 10,
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1.3
Factor Monopoly
7
10
9
wU
8
SL
7
DU
w
6
DNU
w*
5
4
3
wNU
2
DL
1
0
0
1
2
3
4
5
6
Number of Workers
7
8
9
10
Figure 8: Wage Discrimination in Labor Market.
and therefore
LU = 20,
LN U = 40.
• When the union maximizes the total wage of union workers as a monop­
olist, the first order condition is
d
d
(wU × LU ) =
(30 − LU ) × LU = 0.
dLU
dLU
Then
30 − 2LU = 0,
LU = 15;
thus
wU = 15.
For the nonunion workers,
LN U = 45,
wN U = 7.5.
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2 Demand of Supply
2
8
Demand of Supply
In competitive factor market, assume
Q = 10L − L2 ,
and
P = 1.
M RPL = M PL × M R = 10 − 2L.
w is marginal cost of hiring labor, thus
w = 10 − 2L,
then
LD =
10 − w
.
2
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OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month
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