- [Instructor] We are
now going to continue
our discussion of factor markets.
And we're going to go beyond
just thinking about labor as a factor.
In fact, in this video,
we're going to start
thinking about capital as well,
which we know is another one
of the factors of production.
But just as a little bit of review,
we've already thought about
it from a firms perspective
on what is the rational
amount of labor to hire
based on the marginal
revenue product of labor
and based on the marginal
factor cost of labor.
So, in the horizontal axis,
we have the quantity of labor
hired by the firm.
And in the vertical axis,
you have the wage rate,
wage rate, which you could
view as the price of labor.
And we've seen this multiple times.
You are likely to have a downward sloping
marginal revenue product curve, MRP.
And I'm going to be very specific
that this one is the marginal
revenue product of labor.
And then we have the
marginal factor cost curve.
And if we're assuming that this firm
is in a competitive, perfectly
competitive labor market,
well, they're just going to have to pay
whatever the wage is in the market.
And so, that's why we have
a horizontal line there,
so that's the marginal
factor cost of labor.
And we've talked about multiple times
that it's rational for
the firm to keep hiring
as long as the marginal
revenue product of labor,
as long as the incremental revenue
that the firm gets for
each of those people
or each of those units
of labor that they hire
is higher than the incremental cost
of each of those units of labor.
And so, it'll keep hiring until
these two lines intersect.
And so, it would be rational for it
to hire that quantity of labor.
I'll do this is the labor for the firm,
and I'll put a little star over here,
so that quantity of labor.
And we can draw an
analogous thing for capital.
So, this is how a firm
thinks about that input,
how it thinks about labor.
But we could also do
something similar for capital.
Or we could do it for land as well.
But hopefully, so this
is going to be the firm,
the firm as you think about capital.
And we'll see that they
have analogous axes.
The horizontal axis right over here
is going to be the quantity not of labor,
but the quantity of capital.
And then the vertical
axis, the price of capital,
you could view that as the rent rate,
rent rate, if you're thinking about maybe
you're renting some type of machinery.
And so, you will have your
marginal revenue product of capital.
We could still imagine that
you have diminishing returns,
so that's why it's downward sloping,
so marginal revenue product.
And we typically use a K for capital,
just so we don't get the C
confused with other things.
And then we have our marginal factor cost,
which is really just, and
we'll assume, once again,
that this is a perfectly
competitive capital market,
so you just have to pay
whatever the market rate
for renting that capital is.
And so, that would be the marginal
factor cost of the capital.
And so, once again, it makes sense
to keep bringing on more
and more and more capital
as long as the incremental
revenue that you get
from each of those extra units of capital
is higher than the cost of each
of those extra units of capital.
And so, here, it would
be rational for the firm,
if we're just looking at the dimension
of capital to product this much.
So, this would be, actually, let me,
this would be the capital,
the quantity of capital
for the firm to employ.
Now, an interesting question that might've
already crossed your minds are,
is that firms have a
certain amount of resources
that they are going to think about,
well, how much do I put in labor
versus how much do I put into capital.
So, they don't just think
about these dimensions
of how much inputs of
these factors they want,
they have to think about
them relative to each other.
And to help us think through this,
let's say that we are at
a certain level of output.
So, let's say that our output right now,
I don't know, our current output,
our current
output
is, I'm just going to make up something,
1,000 units per day.
And at our current output,
we know what the marginal product of labor
and the marginal product of capital is.
Let's say that we know that
our marginal product of labor
at this output, remember it changes,
as we have different output
and we bring on more
labor or more capital,
so our marginal product of
labor at that level is 90 units.
So, another way to think about it,
for every incremental
unit of labor we bring on,
we're going to be able to
produce 90 more units of output,
so this is, and then let's
say that the price of labor,
which is the wage rate, is equal to $10,
$10 per unit of labor.
So, let me call this output units,
output units.
And let's say that the
marginal product of capital,
let me do this in a different color,
the marginal product of capital right now
is 80 output units,
output
units.
So, every unit of this factor of capital,
we are able to produce an
incremental 80 output units.
And let's say that the price of capital,
which would be the rent, is equal to $5,
$5 per input unit of the factor.
So, right at this moment, if
I have an incremental dollar,
would it be more rational
for me to add more labor,
or would it be more rational
for me to add more capital?
Pause this video and see
if you can figure that out.
Well, to think about which
one is more rational,
you just have to think about which one
do I get more of a bang for my buck.
So, per dollar, how many
output units do I get
when I put a dollar into labor
versus, per dollar, how
many output units do I get
when I put that dollar into capital?
So, let's do it first for labor.
So, if you want your bang
for the buck, so to speak,
you would just take your marginal,
let me do this in a different color,
if you want your bang for buck,
you would just take your
marginal product of labor,
so your output, and
divide it by the price.
So, this is gonna tell
you output per dollar.
And so, in this situation,
it's 90 output units,
we could say widgets for a
general term for output units,
output units, over $10,
over $10.
And so, this is going to be equal
to nine output units per dollar.
So, this is equal to nine output units
per dollar.
So, that's our measure
of our bang for our buck
when we put an incremental
buck into labor.
Now, what about for capital?
Well, our marginal product of capital
divided by the price of capital,
right at this moment, remember it changes
depending on our output level
and different combinations,
is going to be equal to 80 output units
divided by $5,
which is equal to 16 output units
per dollar.
So, which one would I get
a better bang for my buck?
Well, right at this moment,
I'm getting a better bang for my buck
from investing in capital.
Every extra dollar I put,
I get 16 output units.
So, it'd be rational for this firm
that wants to maximize its
profit and reduce its cost,
if it has an extra dollar to invest,
it would put it into capital.
And so, maybe it puts it into capital,
and then it gets a little bit more output.
And then the marginal product of capital
is likely to go down.
And so, you could imagine, at some point,
these things might be equal,
and then the firm might be
indifferent between the two.
And then maybe, at some point,
if they kept adding capital,
then maybe you get a better bang
for your buck from the labor.
In general, a firm would wanna keep
investing in one or the other
until these two things
are equal to each other.
So, big picture, you would
look at the marginal product
of the factor divided by
the price of the factor,
and then you'd compare that
to the marginal product
of the other factors divided by the price
of those other factors.
And whichever one has the
best bang for the buck,
that's where it would be
rational to invest in.
And then you have, in some ways, your,
one way is a very efficient combination,
is if you get to that point
that you're indifferent,
when the marginal product
divided by the prices
of the various factors
are equal to each other.
So, for example, if I were to tell you
that we are at a different
point of production,
let me cordon this off,
so if we're at a different
level of production,
where our marginal product of labor
is equal to, I'll call it 10 widgets,
this saves time,
and let's say that the price
of labor is equal to $5,
and let's say that the price
of capital is equal to $10,
what would have to be the
marginal product of capital
for me to be indifferent
between labor and capital?
Pause this video and
try to figure that out.
Well, in order for me to be
indifferent right over here,
that means that my
marginal product of labor
divided by price of labor
needs to be equal to my
marginal product of capital
divided by my price of capital.
And so, I would have 10 over five
would have to be equal to my
marginal product of capital over 10.
So, 10 over five, this is
two widgets per dollar.
And so, if I want two
widgets per dollar over here,
this has got to be equal to 20.
So, at this point, I'm
indifferent between producing,
between bringing on more
capital versus labor,
because in either case,
every dollar I bring on,
if the marginal product of capital is 20,
then I'm able to get
two widgets per dollar
of investing in either factor.
