### SR Demand

```More Chapter 3
Labor Demand in the market in the
short run.
The firm’s short run labor
demand curve
A demand curve is designed to show how the quantity demanded
changes or responds when there is a change in the price of the
item – here the price is called the wage.
The firm is a wage taker here, taken as the market value. The
downward sloping portion of the VMP curve below the value of
the average product curve is the demand for labor curve because
it shows what demand curves are designed to show.
Change in labor demand due to
output price change
Look back at table 3-1 page 90. In the table the VMP was
determined with the understanding that the price of output was
\$2 per unit. Say the output prices rises to \$4 per unit. How
does the VMP change?
The VMP increases at all levels of labor used and thus at a given
wage more units of labor will have a VMP greater than the wage
and thus the firm would experience an increase in the demand
for labor.
In this case the demand for labor would shift to the right. How
would the curve shift if the output price fell?
Short run industry demand curve
An industry is a group of firms that make the same type of
output. We have assumed the industry is perfectly competitive in
that there are so many firms that any one firm has to accept the
market price of output.
But in a perfectly competitive market if all firms try to increase
their supply of output the market price will fall. As a group all
firms can influence the market price.
This idea has an impact on the short run demand curve for labor
in an industry.
Short run industry labor demand
Wage
Wage
Curve T is the
industry labor
demand curve.
W1
W2
D2
E1
E2’
Employment
Firm
D1
E2
T
E1
E2’
D
E2
Employment
Industry
Short run industry labor demand
On the previous screen say the existing wage is W1. Then the
quantity demanded by the firm is E1 and when we add the demand
by other firms at this wage we get the total market demand for
labor as E1 in that graph.
Now say the wage is W2. The firm would initially increase the
quantity demanded to E2 and other firms would as well and the
market quantity demanded would be E2. BUT, if all firms hire
more labor they will expand out and the market price will FALL.
This shifts in the firm’s labor demand and thus at W2 the firm only
wants E2’. This is true for other firms and so the real increase in
the quantity of labor demanded is less than what we might think
initially. In other words the industry labor demand in the short run
is NOT the horizontal sum of the demand by each firm.
Labor Demand and Elasticities
7
In general, the idea of an elasticity is about how much does one
variable change, in percentage terms, when another variable
changes, and is measured in percentage terms.
Why should we care about elasticities? Well, we have theory
about how variables are related. Often with a theory we will say
if this changes, then that changes. As an example, we say if the
wage changes the quantity of labor demanded will change. The
concept of elasticity is adding to this idea because we get an
amount of the change.
Formula
In general, an elasticity is a ratio of percentage changes. If A
changing causes B to change the elasticity is
percentage change in B divided by the percentage change in A.
8
Elasticity of Labor Demand in short run
The elasticity of labor demand is
The percentage change in the quantity of labor demanded divided
by the percentage change in the wage.
How do you calculate a percentage change? Normally you take
the later value minus the earlier value and divide the result by the
earlier value.
Let’s do an example on the following screen where we are looking
at wage declines.
9
W E % change in E
% change in W
elasticity
11 0 no change yet
no change yet
can’t do yet
10 1 (1-0)/0 =undefined
(10-11)//11 =-1/11
undefined
9
2 (2-1)/1=1/1
(9-10)/10=-1/10
(1/1)/(-1/10)=-10
8
3 (3-2)/2=1/2
(8-9)/9=-1/9
(1/2)/(-1/9)=-9/2
7
4
1/3
-1/8
-8/3
6
5
1/4
-1/7
-7/4
5 6
1/5
-1/6
-6/5
4
7
1/6
-1/5
-5/6
3
8
1/7
-1/4
-4/7
2
9
1/8
-1/3
-3/8
10
1
10
1/9
-1/2
-2/9
So, on the previous slide you note
1) Since we are looking at wage declines the % change in the
wage is negative and the % change in the quantity of labor
demanded is positive.
2) The elasticity value is negative.
3) I just wrote the answers in fractional form.
So the elasticity of demand is a negative number.
Typically we say if the elasticity is:
From 0 to, but not including, -1 demand is inelastic;
-1 demand is unit elastic; and
Less than -1 demand is elastic.
11
Note in our example demand was elastic down to a price of 5 and
was inelastic from there on down.
The total expenditure on labor equals the wage times the amount
of labor demanded.
Go back to slide 10 and add the total expenditure on labor for
each wage. You will have the values 0, 10, 18, 24, 28, 30, 30, 28,
24, 18, and 10.
Note that when the wage falls and demand is elastic the total
expenditure rises, or at least never falls, while if the demand is
inelastic when the wage falls the total expenditure falls.
So, does the total expenditure on labor always fall when the wage
falls? No.
12
One more idea
In our short run story of marginal productivity theory we said
the competitive firm will hire workers up to the point where the
VMP = w. This is a statement about taking workers.
We could make a statement about taking units of output. Then
we would be in the same neighborhood of ideas from a
different point of view. It would be kind of like looking at the
opposite side of the same coin.
Note VMP = price output time p times marginal product MP. So
VMP = w means p times MP = w or
p = w/MP.
One more idea
If a unit of labor is added to the firm, additional output
results. The labor cost of the worker is the wage and the