Labor Demand and Supply

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Labor Demand and Supply
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Overview

• In the previous few chapters we have focused on
  the output decision for firms. Now we want to
  focus on the input decision. How much of an
  input should the firm use? The input and the
  output decision are not independent decisions.

output
inputs
production
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Derived demand

• Resources or inputs are used to make products.
  The desire to use the input is derived from the
  desire to make the output. The input isnt
  desired in and of itself.
• How much of an input a firm wants is influenced
  by profits, but more specifically by
• the productivity of the input
• the selling price of the output made with the
  input
• the price of the input
• other factors not mentioned here.

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Labor

• Initially, we will focus on the demand for labor.
• We will look at the case of labor demand where
  the firm sells output in a competitive
  environment, meaning it is an output price taker.
• The firm buys the input in a competitive
  setting. The firm buys such a small amount of
  labor relative to the market that the firm is a
  input price (the wage) taker.

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• Labor Demand

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Overview
Firms or businesses are profit maximizing
entities (or so assumed in economics). As such,
the only reason labor is demanded is because
labor helps produce the goods and services the
firm wants to sell. Labor demand is a derived
demand derived from the firms desire to sell
output. In this section we study some economic
concepts that influence how much labor the firm
desires.
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The production function
We will assume that firms employ both labor and
capital in the production process, one type of
output is made, the quality of workers is
basically the same, and our emphasis is on the
number of workers demanded. In a shorthand
notation we say q f(E, K) Where q the
amount of output, E the amount of labor
used, K the amount of capital used, and f
means output is a function of, or depends on, the
amount of capital and labor used.
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Marginal Product
The marginal product of labor MP is defined
as the change in output resulting from hiring an
additional worker, holding constant the
quantities of other inputs used. We usually
calculate a number to tell us about MP for each
unit of labor. Take the change in output and
divide by the change in labor, taking labor one
unit at a time.
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Cookie factory
Imagine this room is a cookie factory - like at a
shopping mall. The fixed input, or capital, is
the production facility and it includes a certain
number ( say two of each, for now) of
refrigerators, bowls, mixers, ovens, tables and
other stuff. The variable input will be labor.
We will observe output levels at various levels
of labor used. If the amount of capital were to
change, we would likely have a whole new set of
numbers.
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Numerical example
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Example continued
This is just an example where we have added
labor to a fixed amount of capital. Total output
in this example will be measured in dozens of
cookies per hour.
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MP or marginal product

• MP is the additional output from adding the
  additional worker. Note we go from line to line.
• As more of the variable input is used with a
  fixed input, the marginal product first
  increases, reaches a maximum, then diminishes and
  even becomes negative.

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MP - continued

• MP is a max. at 2 units of labor and begins to
  diminish with the 3rd unit of labor.
• As more labor is added there is less and less
  tools - capital - to use, so additional workers
  can not add as much output as previous workers.

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AP or average product

• At an output level AP (total output)/(amount of
  labor used).

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Law of diminishing returns
You have probably noticed that the marginal
product column first has a rising marginal
product (as you go down the column and use more
labor), then the marginal product reaches its
peak, and then the marginal product declines
you should always use the word diminishes! What
is the reason for this phenomenon? Economists
believe, because of studies of the production
process, when firms have a fixed amount of
capital the first units of labor can specialize
tasks and actually produce increasing returns,
but at some point as more labor is added to the
fixed amount of capital, there will not be as
much capital for the additional workers to use
and thus their contribution to output will
diminish relative to the earlier workers.
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Cookie factory again
Have you ever made cookies without a mixer? If
you have and then made some with a mixer you know
how much nicer it is to use a mixer. Per time
period you could make more cookies with a mixer
than without one. Now, the more workers the more
likely it is there are no mixers to use and thus
additions to output diminish. By the way, here I
am just talking about production possibilities at
this one firm. The firm will end up doing only
one of the possible amounts in a period of time.
(Firms are like some people cant walk and chew
gum at the same time- get it?)
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Perfectly Competitive Firms
For now we will assume that firms are too small
to have the ability to make what price they would
like to sell their output for or what price they
would like to pay for labor or capital. This is
the assumption of perfect competition in both the
input market and the output market. The point
here is some firms simply have to follow what is
going on in the market, or they will not be able
to survive. Lets assume the output can be sold
for 2 per unit.
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Value of the Marginal Product
The price of output times the marginal product is
called the value of the marginal product(VMP).
If you recall the property of diminishing returns
you can see that the VMP follows the same basic
pattern. Lets look at that on the next screen.
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Numerical example
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Value of the marginal product
dollars
The VMP is basically telling us about revenue
changes as we add workers, and hence output.
Notice VMP diminishes just like MP.
VMP
Number of workers
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The cost of more labor
Since the firm is a wage taker, ever time it uses
another worker its cost goes up by the wage. In
a graph similar to previous screen we have
The wage is telling us about how cost changes as
we take on more workers.
dollars
wage
Number of workers
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Employment decision by the firm in the short run
A firm that wants to maximize profit should
always hire another worker if the revenue
generated by that worker is greater than the cost
of that worker and it should never hirer another
worker if the revenue of that worker is less than
the cost of that worker. What should it do in
the case of a tie? We say hire that worker.
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Employment decision by the firm in the short run
dollars
W1 W2
E1 E2
Number of workers
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Employment decision by the firm in the short run
On the previous slide I showed two wages.
Remember the firm is a wage taker and therefore
can not influence the wage. I just show two
possible such wages. Once we have a wage we can
see the firm would hire the amount of labor
indicated on the value of the marginal product
curve at that wage. The demand for labor by a
firm is the downward sloping segment of the VMP
curve.
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The main points we want to get out of this
section are understanding how much labor should
the profit maximizing firm hire and what wage
should it pay? We have just seen the demand for
labor in the context of a firm that sells its
output in a competitive market. If the output
price should rise the value of the marginal
product rises and thus the demand for labor
shifts to the right. Similarly, if firms have
technological change and workers become more
productive the value of the marginal product
rises and the demand shifts right. Now lets
think a little about the supply of labor.
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Labor supply
The supply curve for labor is an upward sloping
curve from right to left. Why is the supply
curve upward sloping? The logic is that people
are willing to supply a greater amount of labor
the higher the wage? Why do they need a higher
wage to supply more labor? Leisure is a good
thing, but it does not pay very much - like
nothing dude and dudettes ). So, if your option
is to work at a low wage or have leisure, you
might take leisure. But if the wage is higher,
you may be willing to give up the leisure to
capture the higher wage. By the way, I am not
saying you are a lazy bum if you do not work at
low wages. You may go to school, retire, work
for the peace corps or volunteer at schools,
parks, churches or even visit the lonely. These
are all great things! Our theory simply says at
low wages we are not willing to give up fun stuff
to work. But at a higher wage we might give up
this stuff for the world of work.
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Wage determination
On the next slide you see that the equilibrium
wage and labor traded in the market is determined
at the intersection of the supply and demand
curves. Why is a higher price not an
equilibrium? There would be an excess supply of
labor and this would drive the wage down. Since
this higher wage would change, we can not say it
is an equilibrium wage. The next screen shows the
market outcome and the decision of as a firm in
the market. Note the market demand for labor is
just the adding up of the demand from many firms.
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Single labor market

In the market we get wage W and amount of labor
traded E.
S
W
D
E
E
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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.
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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.
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Changes in equilibrium The labor market model is
similar to the basic model of supply and demand.
Look at where the curves cross. Now, if demand
rises the wage will rise and the amount of labor
traded will rise. Before we said if the price
of output rises or if the firm gets better
technology the demand for labor will rise. If the
supply rises the wage will fall and the amount
traded will rise. How could the supply rise?
Say many people from others countries move here
immigration. Then with more people living here
the more likely it is that more will supply
labor. So, the supply of labor curve shifts
right the more people there are that want to
work. We see here this pushes the wage down.
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Application Productivity and Wages Remember the
demand for labor is really the VMP curve of
firms. Now say firms adopt better technologies
and thus increase the MP of labor. The firms
would thus have a higher VMP which would mean the
demand for labor would rise. With a given supply
of labor this would mean wages and employment
would rise! So check this out, as firms use
better technologies the wages of workers and the
number of workers working rises. Who gives the
workers the tools that have better technology?
Firms do and thus when firms adopt better
technologies they can pay workers more. Does it
happen overnight? NO, they go home and sleep
first and then later it kicks in!