- [Narrator] We're told that Epic Eats
is a perfectly competitive,
profit-maximizing producer
of stuffed sandwiches, and hires workers
in a perfectly competitive labor market.
Part A says, draw side-by-side
graphs for the labor market
and for Epic Eats and show
each of the following.
So pause this video and see
if you could have a go at it
before we do it together.
All right, now let's do it together.
So we're gonna do side-by-side graphs,
one for the market, and
one for the firm Epic Eats.
So let me do that.
So, this will be my market.
This is my market graph.
And so this is going to
be quantity of labor.
Quantity of labor.
And then on the vertical
axis, I have my wages,
which you could view as the
price of labor, the wage rate.
And so this is the market.
And then over here, I
wanted it side-by-side.
This is going to be the firm.
This is going to be Epic Eats.
Once again, I have
quantity, quantity of labor.
And I'm going to have the wage rate.
And this is Epic Eats.
That's the firm level.
Now, they want us to show the market wage
and the quantity of workers
hired in the market.
Well, to do that, we're
going to have to think about
the demand for workers in the market.
Well, at a high wage
rate, there's not gonna be
a lot of labor demanded.
And then as the wage goes
down, more, more people
are going to wanna hire people.
This is the market labor demand curve.
Demand curve.
And then then supply curve
is gonna be upward sloping.
At a low wage rate, not a lot
of people are going to wanna
give their labor.
But then as wages go up, people will,
more and more people are likely do enter,
want to be part of the labor force.
So this is going to be the
market labor supply curve.
And then we have our equilibrium wage,
which they want us to label W sub M.
So that is going to be right over here.
W, sub lowercase M.
And then the quantity of
workers hired in the market
is going to be capital L, sub lowercase M.
Capital L, sub lowercase M.
So we did this first part, the fact part
that focuses on the market.
Then they want us to focus on
the marginal factor cost curve
labeled MFC.
Well that's what it's
going to cost Epic Eats
to hire folks.
And we're dealing with a,
it hires in a perfectly
competitive labor market.
So which is gonna pay the market wages.
So let me do that.
So this is going to be the
price it pays for labor
which is its marginal factor cost curve,
MFC, just like that.
So I did the second part.
The marginal revenue product, labeled MRP.
Well the way you typically look at it,
it is for Epic Eats that it has some
marginal revenue product
at a certain quantity.
And then as it hires more and more people,
intends to have diminishing returns.
So typical marginal revenue product curve
looks something like this.
So it's MRP, did that part.
The wage paid by the
firm, labeled W sub F,
and the quantity of
workers hired by the firm,
labeled L sub F.
Well the wage paid by the firm,
that's dictated by the market wage.
So we can say that this is
equal to the market wage,
which is equal to the
wage paid by the firm.
And you could put this over here.
The wage paid by the
firm is right over there.
So I did this first part,
and the quantity of
workers hired by the firm.
Well what would be rational is,
is that they would keep hiring people
until the marginal revenue
product is no longer higher
than that marginal cost of
hiring that extra unit of labor.
So it's right at that
point of intersection.
And so that is the quantity
of workers hired by the firm,
so L.
Now let's do the next part.
It says, assume that there is an increase
in the price of Epic
Eats' stuffed sandwiches.
In the short run, will
the wage paid by Epic Eats
be higher than, lower
than, or equal to W, sub F?
Explain.
So pause this video and
see if you can answer that.
Well in the short run, Epic Eats,
no matter how much it
hires or doesn't hire,
it's just going to pay the same wage.
So we could say, it is
going to be equal to.
Equal, equal.
So pay equal to WF
because operating
in perfectly competitive
labor market.
Labor market.
In the short run, what will
happen to the number of workers
hired by Epic Eats?
Explain.
So in the short run, if
the wage is being the same,
but hey had a price increase.
So that means that the MRP is
going to shift to the right
because per unit, they're
going to be able to sell it
for more, you're gonna a have a situation
where the MRP switches
shifts to the right,
or right and up.
And so you're gonna have MRP to,
this is after the price increase.
And notice, now we intersect
the MFC line at a higher point.
And so what will happen to
the number of workers hired?
So number of workers goes up
because
MRP shifts up
due to price increase
which causes it
to intersect
your marginal factor
cost curve, MFC at higher
quantity of labor hired.
All right, now let's do part C.
Epic Eats uses capital and labor
in the production of sandwiches.
The marginal product of the
last unit of capital used
is 4,000 units and the marginal
product of the last unit
of labor used is 3,000.
If Epic Eats minimizes costs
and the rental rate of capital
is $400, what is the wage rate?
So pause this video and see
if you could answer that.
All right, so they give us a few things.
So the marginal product of
the last unit of capital.
So you say, marginal product
of the last unit of capital.
I used K for capital even
though I know it's...
Not to confuse ourselves
with something else.
Although, you could argue
to use C, but we'll use K
to ease confusion.
So the marginal product
of the unit of capital
is equal to 4,000 units.
We know that the marginal
product of the last unit of labor
is equal to 3,000 units.
And we could view this right of here.
The rental rate of
capital, you can view this
as the price of capital.
You could also view this
as the marginal factor
cost of capital, but I'll just call this
the price of capital is equal to $400.
And they want us to get the wage rate..
So you could view this
as the price of labor
is equal to what?
And they tell us that
it's minimizing cost.
And what we can think about
it is, the number of units
per dollar that the firm
gets it on the margin,
if they're able to get
more units per dollar
by switching, by putting
that extra dollar into labor
versus capital, or capital versus labor,
they're going to do it.
So what we would assume is,
is that the number of units
per dollar that they're
getting at this point
are going to be the
same whether they invest
in labor or capital.
And so the number of units per
dollar that they're getting
from the capital is the
marginal product of the capital
divided by the price of the capital
this is the number of units per dollar.
And this needs to be equal to
the number of units per dollar
that they're getting from
that last unit of labor.
So that's the marginal product of labor.
So the units they're getting
from labor on the margin
divided by the price
of labor on the margin,
and then we just solve for this.
So this will get us to,
we're gonna have 4,000,
this is 4,000 units divided by $400.
It's going to be equal
to 3,000 units divided by
the price of labor.
So you can manipulate this a little bit,
you could divide both sides by 400.
So this is going to be
10 units per dollar.
So let me scroll down a
little bit right over here.
So we could, this is, let's see...
Yup, this is going to
be 10 units per dollar
is going to be equal to
3,000 units divided by
the price of labor.
And so, you just do a
little bit of manipulation,
multiply both sides by the price of labor,
divide both sides by 10.
You do a little bit of Algebra.
This gets you to $300 per,
for the incremental cost of labor.
So this is going to get
us to the price of labor
is equal to $300.
And you can verify that,
you could plug it back in
if you like.
And we're done!
