Labour Market
Equilibrium
Reading: Borjas, chapter 4
5-2
Equilibrium in a Single Competitive
Labour Market
• Labour market equilibrium coordinates the desires of
firms and workers, determining the wage and
employment observed in the labour market.
• Competitive equilibrium occurs when supply equals
demand generating a competitive wage and
employment level
• It is unlikely that the labour market is ever in an
equilibrium, since supply and demand are dynamic
• The model suggests that the market is always moving
toward equilibrium
5-3
Labour Market Equilibrium
Dollars
Supply
whigh
w*
wlow
Demand
ED
E*
ES
Employment
In a competitive labour
market, equilibrium is
attained at the point
where supply equals
demand. The “going
wage” is w* and E*
workers are employed.
5-4
Application: The Employment Effects of
Minimum Wages
• The unemployment rate is higher the higher the
minimum wage and the more elasticity the supply and
demand curves
• The benefits of the minimum wage accrue mostly to
workers who are not at the bottom of the distribution
of permanent income
5-5
The Impact of the Minimum Wage on
Employment
Dollars
S
w
w*
D
E
E*
ES
Employment
A minimum wage set at
w forces employers to
cut employment (from E*
to E). The higher wage
also encourages (ES - E*)
additional workers to
enter the market. The
minimum wage,
therefore, creates
unemployment.
5-6
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
(a) Covered Sector
Employment
EU
EU
EU
Employment
(b) Uncovered Sector
If the minimum wage applies only to jobs in the covered sector, the displaced workers might
move to the uncovered sector, shifting the supply curve to the right and reducing the
uncovered sector’s wage. If it is easy to get a minimum wage job, workers in the uncovered
sector might quit their jobs and wait in the covered sector until a job opens up, shifting the
supply curve in the uncovered sector to the left and raising the uncovered sector’s wage.
5-7
Efficiency
• Pareto Efficiency, this is the condition that exists when
all possible gains from trade have been exhausted
• When the state of the world is Pareto Efficient, to
improve one person’s welfare necessarily means
another person’s welfare is decreased
• In policy applications, ask whether a change can make
any one better off without harming anyone else. If the
answer is yes, then a change is said to be “Paretoimproving”
5-8
Equilibrium in a Competitive Labour Market
Dollars
S
P
w*
Q
D0
EL
E*
EH
Employment
The labor market is in
equilibrium when supply equals
demand; E* workers are
employed at a wage of w*. In
equilibrium, all persons who are
looking for work at the going
wage can find a job. The triangle
P gives the producer surplus; the
triangle Q gives the worker
surplus. A competitive market
maximizes the gains from trade,
or the sum P + Q.
5-9
Application: Payroll Taxes and Subsidies
• Payroll taxes assessed on employers lead to a downward
parallel shift in the labor demand curve
- The new demand curve shows a wedge between the amount
the firm must pay to hire a worker and the amount that
workers actually receive
- Payroll taxes increase total costs of employment, so these
taxes reduce employment in the economy
- Firms and workers share the cost of payroll taxes, since the
cost of hiring a worker rises at the same rate the wage
received by workers declines
5 - 10
The Impact of a Payroll Tax Assessed
on Firms
Dollars
S
w1 + 1
A
w0
w1
B
w0  1
D0
D1
E1
E0
Employment
A payroll tax of $1
assessed on employers
shifts down the demand
curve (from D0 to D1).
The payroll tax cuts the
wage that workers
receive from w0 to w1,
and increases the cost
of hiring a worker from
w0 to w1 + 1.
5 - 11
The Impact of a Payroll Tax Assessed on
Workers
S1
Dollars
S0
w0 + 1
A payroll tax assessed on
workers shifts the supply
curve to the left (from S0
to S1).
w1
w0
w1  1
D0
D1
E1
E0
D0
Employment
5 - 12
The Impact of a Payroll Tax Assessed on
Workers
S1
Dollars
S0
w0 + 1
w1
w0
w1  1
D0
D1
E1
E0
D0
Employment
A payroll tax assessed on
workers shifts the supply
curve to the left (from S0
to S1). The payroll tax
has the same impact on
the equilibrium wage
and employment
regardless of who it is
assessed on.
5 - 13
The Impact of a Payroll Tax Assessed on
Firms with Inelastic Supply
Dollars
S
D0
w0
A
B
w0 – 1
D0
D1
E0
Employment
A payroll tax assessed on
the firm is shifted
completely to workers
when the labor supply
curve is perfectly
inelastic. The wage is
initially w0. The $1
payroll tax shifts the
demand curve to D1, and
the wage falls to w0 – 1.
5 - 14
5 - 15
Payroll Subsidies
• An employment subsidy lowers the cost of hiring for
firms
• This means payroll subsidies shift the demand curve
for labor to the right (down)
• Total employment will increase as the cost of hiring
has fallen.
5 - 16
The Impact of an Employment Subsidy
S
w0 + 1
B
w1
w0
A
w1 – 1
D1
D0
E0
E1
Employment
An employment subsidy
of $1 per worker hired
shifts up the demand
curve, increasing
employment. The wage
that workers receive rises
from w0 to w1. The wage
that firms actually pay
falls from w0 to w1 – 1.
5 - 17
Payroll Tax and The tax wedge
• The tax wedge is a measure of the difference between
the total labour cost to an employer and the
corresponding disposable income of an employee
• The tax wedge is the sum of personal income tax,
employee and employer social security contributions
(SSC) and payroll taxes minus any cash benefits from
government welfare programs
• The tax wedge is usually expressed as a percentage of
the total labour costs
• The biggest tax wedges are in continental Europe
5 - 18
Tax wedge
Wage
Labour supply
Wage firms pay
Tax wedge
Wage without tax
Wage workers
receive
Labour demand
0
Quantity
of Labour
Copyright©2003 Southwestern/Thomson Learning
5 - 19
Why
Wage
Labour supply
Wage firms pay
Wage without tax
Wage workers
receive
Labour demand
0
Labour demand
Quantity
of Labour
Copyright©2003 Southwestern/Thomson Learning
5 - 20
Tax wedges in OECD countries
OECD-10 unweighted average
5 - 21
Solving the partial equilibrium:
Household labour supply equation
The representative household decides how much to
work (h) and consume (c) to maximize utility, taking
prices as given (the wage w and the interest rate r).
max U(c, 1 -hs )  ln(c)   ln(1  h)
c,h
s.t c  (1  t w )wh  r k
1
 rk 
h 

(1   ) (1   )(1  t w ) w
s
5 - 22
Solving the partial equilibrium:
Firm labour demand equation
The representative firm decides the amount of output y
to produce and labour h to hire, taking capital k and
prices (w, r) as given.
max   Ah1 k   (1   ) wh  r k
h
1
 (1   ) Ak   
d

h


(
1


)
w


5 - 23
Equilibrium
1
 rk 

 hs
(1   ) (1   )(1  t ) w
1
 (1   ) Ak   
d

h


(
1


)
w


In equilibrium, labour demand is equal to labour supply:
5 - 24
Equilibrium
Solve the two equations system for w and h
1
 rk 

h
(1   ) (1   )(1  t ) w
1
 (1   ) Ak   

 h
 (1   ) w 
5 - 25
Competitive Equilibrium Across Labour
Markets
• If workers were mobile and entry and exit of workers
to the labor market was free, then there would be a
single wage paid to all workers
• The allocation of workers to firms equating the wage
to the value of marginal product is also the allocation
that maximizes national income (this is known as
allocative efficiency)
• The “invisible hand” process self-interested workers
and firms accomplish a social goal that no one had in
mind: allocative efficiency.
5 - 26
Efficiency Revisited
• The “single wage” property of a competitive equilibrium
has important implications for economic efficiency.
- Recall that in a competitive equilibrium the wage
equals the value of marginal product of labor. As
firms and workers move to the region that provides
the best opportunities, they eliminate regional wage
differentials. Therefore, workers of given skills have
the same value of marginal product of labour in all
markets.
• The allocation of workers to firms that equates the value
of marginal product across markets is also the sorting
that leads to an efficient allocation of labour resources.
5 - 27
Wages and International Trade: NAFTA
• NAFTA created a free trade zone in North America
• The effect of free trade in the zone is to reduce the
income differential between the United States and
other countries in the zone, such as Mexico
• Total income of the countries in the trade zone is
maximized as a result of equalized economic
opportunities across the countries in the zone
5 - 28
Competitive Equilibrium in Two Labour Markets
Linked by Migration
Dollars
Dollars
s
SN
SS
SS
A
wN
B
w*
w*
wS
C
DN
Employment
(a) The Northern Labour Market
DS
Employment
(b) The Southern Labour Market
Suppose the wage in the northern region (wN) exceeds the wage in the southern
region (wS). Southern workers want to move North, shifting the southern supply
curve to the left and the northern supply curve to the right. In the end, wages are
equated across regions (at w*).
5 - 29
Wage Convergence Across US States
5.7
LA
Percent Annual Wage Growth
GA
NH
ME
VT
VA
5.5
MS
AR
5.3
MD
MA
IA
FL
NC
SC
KS
MI
CT
DE
TN
AL
NE
5.1
OK
TXMO
RI
MN
PA
WI
NJ
WV
IN
OH
IL CO
UT
WA
NY
KY
AZ
ND
4.9
SD
MT CA
NM
NV
4.7
ID
OR
WY
4.5
.9
1.1
1.3
1.5
Manufacturing Wage in 1950
1.7
1.9
Source: Olivier Jean Blanchard and Lawrence F. Katz, “Regional Evolutions,” Brookings Papers on Economic
Activity 1 (1992): 1-61.
5 - 30
Immigration
• As immigrants enter the labour market, the supply
curve shifts to the right
- Total employment increases
- The equilibrium wage decreases
5 - 31
The Immigration Surplus
Dollars
S
S
A
B
w0
C
w1
F
D
0
N
M
Employment
Prior to immigration, there are N
native workers in the economy
and national income is given by
the trapezoid ABN0.
Immigration increases the labor
supply to M workers and
national income is given by the
trapezoid ACM0. Immigrants
are paid a total of FCMN dollars
as salary. The immigration
surplus gives the increase in
national income that accrues to
natives and is given by the area
in the triangle BCF.
5 - 32
Effect on Native-Born Workers
• Immigration reduces the wages and employment of
similarly-skilled native-born workers, but native-born
workers may be able to increase their productivity by
specializing in tasks better suited to their skills.
• Competing native workers will have lower wages;
complementary native workers will have higher wages
5 - 33
The Short-Run Impact of Immigration When
Immigrants and Natives Are Perfect Substitutes
Dollars
Supply
w0
w1
Demand
N1
N0
E1
Employment
Because immigrants and
natives are perfect substitutes,
the two groups are competing
in the same labor market.
Immigration shifts out the
supply curve. As a result, the
wage falls from w0 to w1, and
total employment increases
from N0 to E1. Note that at the
lower wage, there is a decline
in the number of natives who
work, from N0 to N1.
5 - 34
The Short-Run Impact of Immigration when
Immigrants and Natives are Complements
Dollars
Supply
w1
w0
Demand
N0
N1
Employment
If immigrants and natives are
complements, they are not
competing in the same labour
market. The labour market in
this figure denotes the supply
and demand for native
workers. Immigration makes
natives more productive,
shifting out the demand curve
even though capital is fixed.
This leads to a higher native
wage and to an increase in
native employment.
5 - 35
The Long-Run Impact of Immigration
When Immigrants and Natives Are Perfect Substitutes
Dollars
Supply
w0
w1
Demand
N0
N0 +
Immigrants
Employment
Because immigrants and
natives are perfect
substitutes, the two groups
are competing in the same
labour market. Immigration
initially shifts out the supply
curve. As a result, the wage
falls from w0 to w1. Over
time, capital expands as
firms take advantage of the
cheaper workforce, shifting
out the labour demand
curve.
5 - 36
The Native Labour Market’s Response
to Immigration
Dollars
Dollars
S0
S2
S0
S1
PLA
S3
PPT
w0
w0
w*
w*
wLA
Demand
Demand
Employment
Employment
(a) Los Angeles
(b) Pittsburgh