Labor Market Equilibrium
1
Overview
In this chapter we want to explore what happens in a competitive
labor market. After that we will explore other labor market
structures. Plus we will look at applications of these types of
labor markets.
2
Single competitive labor market
If the whole economy comprises a single competitive labor
market, then the wage and amount of labor employed is
determined by the interaction of supply and demand.
Then any one firm, or worker, is a wage taker. This means the
worker or the firm can not determine the wage alone. Again, the
wage is set by the interaction of all parties concerned.
Recall from our earlier work that a profit maximizing firm hires
labor up to the point where the value of the marginal product is
equal to the wage.
3
Single labor market
$
S
W*
D
E
E*
In the market
we get W* and
E*. Each firm
takes W* and
hires what they
want and when
you add that
across firms
you get E*,
which is just
the total
supplied . 4
Equilibrium
W* is the equilibrium wage because at this wage both
suppliers and demanders obtain the desired amount.
At wages higher than W* an equilibrium would not exist
because at those wages the quantity supplied is much higher
than the quantity demanded – an excess supply. All those
willing to supply do not get to trade because there are too few
buyers. Since this excess supply will encourage suppliers to
change by lowering the wage at which many will work, the
initial high wage (relative to the equilibrium) will not last and
will change to the equilibrium wage.
5
More equilibrium
At wages lower than W* an equilibrium would not exist
because at those wages the quantity supplied is much lower
than the quantity demanded – an excess demand. All those
demanding do not get to trade because there are too few
sellers. Since this excess demand will encourage demanders to
change by raising the wage which they will pay for work, the
initial low wage (relative to the equilibrium) will not last and
will change to the equilibrium wage.
6
Firms in this environment
$
$
W*
VMP1
E1
VMP2
E2
7
Firms in this environment
Firms in a competitive market are wage takers and in order to
maximize profit they hire labor up to the point where the wage
is equal to the value of the marginal product.
On the previous slide we see two such firms accept the wage as
W*. Each has a slightly different VMP curve but each takes
labor until W = VMP. So, for the last worker taken by each
firm the VMP is the same.
Recall that VMP = output price times marginal product and this
concept is telling us about the value of output made by a
worker.
8
Invisible hand
The invisible hand concept in economics says that individuals
and firms acting in their own self interest achieve something
none had even thought or worried about. That something
achieved is the greatest value of output for the resources
expended.
Another way of saying this is that the allocation of resources is
efficient. Let’s see how that can be here.
Say the firm on the right on screen 5 has to take one more unit of
labor and the firm of the left is forced to take one unit less of
labor. The total amount of labor used would be the same as
before, so we would have the same amount of labor used.
9
Invisible hand
Now the firm on the right would add output but the value of
the output would be less than the wage (how do I know this?).
The firm of the left would lose output and the value of the
output would equal the wage.
Thus the value of the output lost is greater than the value of the
output gained from the switch and the total value of output
must fall from this reallocation of resources. In other words,
the original value of output was higher than we could achieve
by switching workers to different places.
Adam Smith noted this type of result way back in 1776, but he
was in England (which really doesn’t matter, but was fun to
10
type).
Efficiency of Competitive
Labor Market Equilibrium
11
Single labor market
$
S
A
W*
B
D
C
E
E*
In the market
we get W* and
E*. Each firm
takes W* and
hires what they
want and when
you add that
across firms
you get E*,
which is just
the total
supplied . 12
Single labor market
$
S
A
W*
B
D
C
1
E
E*
13
Producer surplus in the labor market
On slide 3 if you focus on the demand curve in the upper left I put
a different supply curve and in the market we would have supply
and demand equal where there is 1 unit of labor employed. Since
the demand is really the value of the marginal product the area of
the rectangle from the origin out to an E = 1 and up to the demand
is really the value of the marginal product of the first unit. Almost
all the area under the demand curve out to E = 1 is the value of the
marginal product. So, we just say all the area is the VMP. In the
real market outcome with E* the areas A, B and C represent the
sum of value of the marginal product for each E out to E*.
The areas B and C add up to what the firms pay the labor. So,
area A represents revenue labor has helped generate but has not
been paid back to labor. It is called the producer surplus and is
the profit of the firms if labor is the only input, or it is used by the
14
firms to pay for other inputs and then what is left is profit.
What is producer surplus all about? Well, you see that firms
hire labor to help make output. Not only does the labor
contribute to revenue that can be used to pay the labor, it pays
for other stuff for the firms. This producer surplus is a gain
from having trade in the labor market.
Worker surplus in the labor market
Back on slide 3 if you focus your attention on the lower left of
the graph you see I have a different demand with the supply so
that only unit of labor is supplied. The rectangle made by the
origin out to an E = 1 and up to the supply is a measure of what
the supplier would have if they were doing something else and
not giving their time here. The rectangle is a little over the
supply curve, but we just focus on that part under the supply
curve.
15
Worker surplus
If we go all the way out to the equilibrium the area C is a
measure of the suppliers’ use of time in some other area instead
of supplying labor.
The area B + C is what the suppliers earn in the labor market.
SO, B is worker surplus and is a measure of what they get over
and above what they would get in their next best use. It is a
gain from trade in the labor market.
16
Efficiency
In the competitive labor market we see
Producer surplus of A
Worker surplus of B.
These surplus values represent gains from trade. No other
amount of labor generates as much gain from trade. In that sense
the competitive labor market is said to be efficient.
17
The law of one wage
Before we had one labor market. But, in reality we have many
labor markets – perhaps different by geography. On the next
slide we show the case of two labor markets and initially we
have different wages.
In the north the wage is much higher than in the south. Note:
we are using perfectly inelastic supply curves to simplify the
analysis. This essentially means the worker surplus is the
whole area below the wage.
If workers are mobile and can freely move to another region
we would see folks leave the south and go to the north. The
wage will fall in the north and rise in the south. The graphical
analysis is shown on the next slide.
18
Competitive Equilibrium in Two Labor
Markets Linked by Migration
Dollars
Dollars
s
SN
SS
SS
A
wN
B
w*
w*
wS
C
DN
Employment
(a) The Northern Labor Market
DS
Employment
(b) The Southern Labor 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*.
Efficiency again
As workers leave the south and the wage rises, both producer
and worker surplus is lost. But in the north as those workers
are added, the wage is lowered and there are additions to both
producer and worker surplus.
As the wage rises in the south as workers leave the VMP of
labor is rising, while in the north the wage is falling and the
VMP is falling.
But, in the south the workers are leaving low VMP for high
VMP in the north. SO, on the net workers are moving to
higher valued uses. This is efficient.
20