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PROFESSOR: Now what I'm going
to do is, I'm going to turn
and start producer theory, OK,
which will not be in the exam,
but be the next subject
to the course.
OK, and we're going to spend a
little bit longer on this.
So what we've been doing so
far is saying, look, we
introduced the course with
supply and demand curves,
elasticities, all that.
Hint, all that's on
the exam too.
OK, and all that.
Then we say, well gee,
where do supply and
demand curves come from?
Well, demand curves come from
utility maximization.
And we talked about how where
indifference curves come from,
how the tangency with the budget
constraints leads to
the demand curve.
That's where demand
curves come from.
We talked about what underlies
demand curves is income and
substitution effects.
OK, now let's come
to supply curves.
What underlies supply curves?
Now on the one hand, this will
be much easier than demand
curves, because a lot of
the logic is the same.
So we can march more quickly
through the analysis, because
it's basically the same kind
of tangency of curves with
straight lines that yield supply
curves that we've seen
with consumer theory.
On the other hand, supply
curves are a ton harder,
because now we don't
just have the
price as given to consumers.
The suppliers actually
make up the price.
With consumers, we said the
price -- you just went to the
store. you're given a price.
And you choose what to
buy at those prices.
Well, who set those prices?
Producers do.
And that's what determines the
underlying supply curve.
So life gets a little bit more
difficult with producers.
And that's why I'll probably
spend about twice as many
lectures talking about producer
theory as we've spent
talking about consumer theory.
Now, let's go to the basics.
The basics are, just as we had
consumers making decisions, we
thought of a consumer as
somebody choosing across a
bundle of goods, pizza versus
movies, now we're going to
think of a producer very simply
as a black box, where
inputs go in and outputs
come out.
So think of the firm.
Let's think of a firm,
a producer, as
just some black box.
We're literally thinking
a flow chart.
You've got inputs that go in
and outputs that come out.
And that black box, that firm,
just as individuals have a
simple goal which is to maximize
their utility,
producers have a simple
goal which is to
maximize their profits.
And profits are defined as
revenue minus cost. OK?
Producers are these black boxes,
where their goal is to
maximize their profits, which is
revenue minus cost. And the
key to maximizing profits
is efficient production.
The key to maximizing profits
is going to be to produce
goods as efficiently
as possible.
OK, so profit maximization
requires production
efficiency.
To maximize your profits, you
need to produce as efficiently
as possible.
Now, you might ask yourself,
gee, I can read about all
these companies that have
executive corporate jets, and
the guys in these lavish
lifestyles, and that doesn't
seem very efficient
production.
I'll come back to that.
OK, in a couple of lectures,
we'll talk about do firms
actually maximize profits, and
whether they do or not.
But for now, let's take as
a given that they do.
OK, just as it is a given that
consumers maximize utility,
let's take as a given that firms
maximize their profits.
OK?
Now, to decide how to
efficiently produce goods,
we're going to turn
and today discuss
firm production functions.
OK, today, we'll focus on
production functions.
That's essentially the
technology by which a firm
takes inputs, or what we call
factors of production, and
turns them into outputs,
is through
this production function.
So just like your utility
function is a tool for which
we take bundles of goods and
turn them into happiness, a
production function is a tool
for which we take bundles of
inputs and turn them
into outputs.
OK, but something that's a
little easier to understand
this, you could think of a
factory where stuff comes in,
and think of a belt, a
mechanical belt, going through
and stuff goes in and other
stuff comes out.
You could think of that
production function.
We're going to think about two
different kinds of inputs that
firms are going to use.
Once again, to make life easy,
we're going to assume firms
only use two kinds of inputs.
Later, we'll expand this, but
from mostly intuition you can
get from thinking about
this-- two kinds of
inputs, labor and capital.
Labor and capital are the two
kinds of inputs firms use.
Labor is clear.
It's just hours of labor,
hours of work.
OK?
It's just hours of work
in production.
Capital is a lot trickier.
And we'll spend a lot of time
this semester struggling with
what capital really means.
Basically for now, think of
capital as everything else
that goes into production, the
machines, the buildings, the
land, everything.
Think of capital as everything
else that goes into
production.
So basically, when you produce
stuff, you produce it with
workers working with stuff.
Capital's the stuff.
Now, this capital is sort of a
composite of everything else
that goes into production.
And once again, we'll add some
more detail on this later.
OK, and the output is
some output, q.
That's the units
of production.
That's the output that is
produced by the firm.
So basically, we can think of a
production function is q is
some function of l and k.
That's a production function,
that the output you produce as
your firm--
and by the way, we're going to
use little q to represent a
firm's output, and big Q to
represent market output.
OK, so little q, and if I slip
in this, yell at me, OK?
But we're going to try to
consistently use little q to
represent a given firm's output,
and big Q to be the
market's output--
So little q is some function of
the amount of workers you
have and the amount of
capital you use.
Now, the important distinction
we're going to make here is
between variable versus
fixed inputs.
Variable versus fixed inputs
is an important distinction
we're going to draw.
Variable inputs are inputs that
are easily changed, like
how many hours somebody works.
In principle, you could just
have some work five hours one
day, one hour the next day, 10
hours the day after that.
It's easy to change
hours of work.
So that's a variable input.
Fixed inputs are things which
are harder to change quickly,
like the size of the building
that the workers
are building in.
Once that building's built, it's
pretty hard to change it.
You can't like lop off 2/3 of it
on one day and add it back
the next day.
OK, that's more of
the fixed inputs.
And this will lead to a critical
distinction for
production theory, which
is the short run
versus the long run.
The short run versus
the long run.
The long run is the
period over which
all inputs are variable.
The short run is a period over
which some inputs are fixed.
Let me say it again, it's
very important.
The short run is the
period over which
some inputs are fixed.
The long run is the
period over which
all inputs are variable.
Now, what does that mean?
I can't tell you.
OK?
I can tell you that, clearly,
tomorrow is the short run.
Clearly, you can't vary all
your inputs over one day.
And probably next month
is the short run.
And probably even next year
is the short run.
There's a lot of inputs that it
takes more than a month to
change, or a year to change.
On the other hand, 10 years from
now is almost certainly
the long run.
There's very few inputs to
production you can't change
over a 10-year period.
So we know a day are
the short run.
And we know 10 years
is the long run.
We don't really know where
the transition is, but in
substance that doesn't
matter for you guys.
What matters is the definition
of short run, long run.
When someone asks you what the
long run is, you say it's the
period of time over which
all inputs are variable.
That's what matters.
So it doesn't matter if
you define it in days
or months or years.
It's a theoretical concept,
which the break from the short
run to the long run is the break
between when some inputs
are fixed and all inputs
are variable.
OK?
Now of course, once again
this is tricky.
And economists recognize
this subtlety.
A lot of times, economists will
talk about quasi-fixed
factors of production, which are
things which could change
in between the short run
and the long run.
So for instance, take labor.
OK, we'll talk about labor as a
variable unit of production
you can change in
the short run.
But in fact, we know in
practice you can't.
Most jobs, you can't ask the
guys to come for an hour one
day, and 10 hours the next day,
five hours the day after
that, maybe some jobs like
hourly construction.
But most jobs you guys will
have, OK, your labor isn't
that variable.
We're typically on some kind of
reasonably set work schedule.
Now that work schedule
can evolve.
OK, but it can't change
day by day.
None of us are going to have
jobs where they're going to
say, look, work two hours
today, 12 hours the
next day, et cetera.
OK, we're all going to have
jobs with a fairly smooth
distribution.
There'll be peaks and valleys,
but a fairly smooth
distribution of our
labor effort.
So really, truly, there's very
few inputs which are truly
perfectly variable.
OK?
Just like there are no inputs
which are truly perfectly
fixed, but for the purposes of
this model, let's think about
labor as a variable input.
Let's think about labor as being
like hourly labor, like
hourly construction, OK?
And let's think about capital as
being a fixed input, like a
building that you can't pare
down or rebuild overnight, but
over a 10-year period you can.
OK?
Questions about that?
Once again, we talked about
simplifying assumptions at the
beginning of the semester.
This is our set of simplifying
assumptions.
Simplifying assumptions are that
firms produce goods with
two inputs, labor and capital,
that labor is variable, which
means you can change it minute
to minute or day to day, and
capital is fixed, which means
you can only change
it in the long run.
OK?
All right, so armed with that,
let's now talk about how firms
make short-run production
decisions.
And once again, these are
a lot of assumptions.
But at the end of the day, I'm
going to be able to teach you
in a couple of lectures how
firms make decisions.
And I'm going to be
about 80% right.
So that's pretty good.
OK, so there are some
assumptions, but we're going
to go a long way with
these assumptions.
So let's start by considering
the short run, and considering
that period of time over
which labor is variable
but capital is fixed.
Labor is variable but
capital is fixed.
That is, you have a given plant,
but you can adjust how
many workers you use every
day in that plant.
And now the firm has to decide,
given that that plant
exists, how many workers
should I hire
to produce my good?
How many workers should I
hire to produce my good?
And the key concept that's going
to determine that is
something we'll call the
marginal product of labor,
which is the change in total
output resulting from the next
unit of labor used--
that is, delta q, delta l--
is the marginal product
of labor.
It's going to be the change in
total output from another unit
of labor, once again holding
capital constant because
that's fixed.
So really, it's really at a
given k bar, but that's
implicit in the fact
it's the short run.
So the given level of capital,
what is the change in output
for another unit of labor?
And once we get to the short
run, I shouldn't
have to write this.
If I tell you short run, you
should know this is true.
But technically, we would
write that out.
Now, what we're going to do here
is we're typically going
to assume this--
hint, hint--
if you're comfortable with
consumer theory, this is like
marginal utility.
Marginal product is like
marginal utility.
Just as the marginal utility was
your utility from another
unit of one good, holding the
other good fixed, marginal
product is the marginal
production from another unit
of an input, holding the
other input fixed.
So just sort of a parallel
to keep in mind.
And just as we've assumed and
discussed the intuition for
diminishing marginal utility,
we're going to typically
assume diminishing
marginal product.
So we're going to assume
diminishing marginal product.
That is, from a given level of
labor, the next worker you add
increases your total product by
less than the previous one.
Now once again, just like we
have a non- satiation rule in
utility, we're not going
to say the next
worker doesn't help.
Every worker helps.
But every worker helps less and
less and less, just like
every pizza means less and
less and less to you.
Now, the trick here, once again,
this is like consumer
theory, only more subtle.
With consumer theory, it's
pretty clear that once you had
one pizza, clearly, the second
pizza means less.
And once you've seen one movie,
your first-place prize,
the movie you most want to see,
clearly the next movie
you want to see means
a little bit less.
Producer theory is a
little more subtle.
And you can imagine ranges over
which more workers help.
They can work together.
So that actually two workers
can do more than twice what
one worker can do.
And we'll talk about that.
But we're going to focus in the
main on ranges over which
each additional worker does
less and less and less.
And the reason is because,
to remember, this
is less than two--
Yeah?
AUDIENCE: Is there going to
be a point where actually
additional workers won't do
anything, because of like
constrain to the amounts
of other inputs?
PROFESSOR: Once again, we're not
going to get-- just like
there's a point at which extra
pizza will make you barf--
OK, we're assuming we don't
get to that point.
But yes, technically of course,
at some point more is
not better.
At some point, extra workers
just sit around.
And so I agree.
So basically, it's
a little tricky.
You could imagine an initial
range where more
workers would help.
Then there's the main range
we'll focus on each additional
worker does less and
less and less.
And you could imagine that
running out, which is a worker
does nothing.
But let's just now assume
we don't get there.
So basically, what's
the intuition?
Now the intuition for in
utility theory, for
diminishing marginal utility,
I thought was pretty easy,
which is each pizza
means less.
The intuition for why each
worker does less, I find a
little bit harder.
You could say, well, gee, why
should one worker do less than
the next worker?
Why shouldn't the next worker
do less than the first?
And the key is this
part, that we're
holding capital constant.
The reason each worker does less
is because they only have
the same amount of stuff
to work with.
And the classic example we
use here is the example
of digging a hole.
You go to dig a hole and your
capital's a shovel.
And let's say for some reason
the shovels are out, so you
can't get another shovel
for a while.
OK, so there's one shovel.
So you have one worker digging
a hole, then the next worker
comes along and that's where
he can help because he can
spell the first worker.
And maybe the next worker's just
as good because he can
work more hours, but probably
it's a little bit less good.
But certainly by the time you
add a fourth and a fifth and a
sixth person, with one shovel,
they probably each help
because they can rotate
and rest each other.
But certainly the sixth person
is not going to help dig the
hole as much as that second
person did, or the third, or
fourth, or fifth person, because
only one shovel.
So they can share a little
bit and share the
burden a little bit.
But at some point each
additional worker helps less
because they have to share
the same shovel.
So that's what diminishing
marginal product is, because
capital's fixed.
With a certain amount of capital
to work with, each
additional worker just
can't help as
much as the one before.
Now eventually, you can
add more shovels.
And you could have
wheelbarrows.
So some people could run the
wheelbarrows, some people
could run the shovels.
But that's the long run.
In the short run, there's the
one shovel, so each additional
worker does less good.
And that's the intuition.
Once again, not as clean as with
consumption, where it's
easy to see each additional
pizza is worth less, because
you could imagine the second
worker might actually help.
They could rest, et cetera,
and you could imagine
eventually the ninth worker does
nothing because there's
nothing left to do.
But let's focus on that range
where it's intuitive.
We're staying between the second
and sixth worker, which
is when a worker would help,
but they help less
and less and less.
OK, and that's the diminishing
marginal product.
Questions about that?
That's short-run production.
And we're going to come
back to this.
But I just want to introduce
these concepts.
Now let's talk about long-run
production.
Now in the long run, all
inputs are variable.
That's how we defined
the long run.
So now a firm doesn't just
choose how many workers to
hire, or how many hours
of labor to buy.
It chooses both l and k, and
has to trade them off, just
like you chose both pizzas
and movies and had
to trade them off.
So the long-run production
theory is the same, basically
the same mechanics,
as utility theory.
There's a production function.
You have two inputs.
You trade them off.
Just like you're a consumer.
You have two goods to consume.
You trade them off.
The difference is going to be
that ultimately production is
going to self--
the difference is, when you
decide how to trade them off
as a consumer, you're given
a budget constraint.
The difference with production
is the budget constraint is
going to be itself determined
by the same system.
So you're not only going to
develop your production
function, but you're going to
develop your budget constraint
and, you're going
to decide both.
It's a little bit funky
but we'll get to it.
But for now, let's just think
about the parallels to
consumer theory, and think about
a production function
which is q--
little q--
is the square root
of k times l.
That same functional form I used
with pizza and movies,
where utility is the square root
of pizza times movies.
Now I'm going to say what you
produce of your good is the
square root of k times l.
Now let's go to figure 8-3.
And what we see here is, if
you're trading off k and l and
deciding to produce, then you
get what's called isoquants.
Isoquants are the parallel
to indifference curves.
Once again, this is all
the same mechanics.
Just as there were sets of goods
across which you were
indifferent, two pizzas and one
movie versus one pizza and
two movies.
Isoquants are sets of
inputs along which
production is the same.
So along a given isoquant,
q is fixed.
Each of those isoquants is a
different level of q, but they
show how you can vary k and l
to get the same amount of q.
So producing q equals
square root of 2.
I can use two units of capital
and one unit of labor, or one
unit of capital and
two of labor.
So I can choose lots of
combinations of k and l along
that isoquant to produce a
given amount of output.
And isoquants have all the
same features as in
indifference curves.
The further out the better
because you're producing more.
They can't cross.
All the same set of things we
have in the indifference
curves are true with
isoquants as well.
And they slope downwards because
there's a trade off
between capital and labor.
Now, what's going to determine
the slope of an isoquant?
Can someone tell me
what determines
the slope of an isoquant?
What determines if isoquants
are steep or shallow?
Well, what determines the slope
of a indifference curve?
Yes, go ahead.
AUDIENCE: It's based on the
ratio of how much labor is
worth versus capital?
PROFESSOR: Right, and what
do we call that?
What determines how much they're
worth from each other?
What determines the slope
of a indifference curve?
The marginal rate of
substitution, it was the
substitutability
between goods.
Likewise, the substitutability
between labor and capital will
determine the slope of
these isoquants.
So to see an example, let's do
an extreme example here.
Let's consider goods that are
perfectly substitutable.
So like, I don't know, just like
a Harvard undergraduate
and a beanie baby.
OK, perfectly substitutable.
Figure 8-4a shows the
case of perfectly
substitutable inputs.
In that case, you would have a
linear isoquant, because what
that would mean is you don't
care if you have three capital
and one labor, or three
labor and one capital.
You don't care.
You don't care if you have two
labor and two capital, or
three labor and one capital,
as long as you
get a total of four.
That's all that matters.
They're perfectly substitutable
inputs, which
would say that it would be
something like q equals k plus
l would be the case
of perfectly
substitutable inputs.
You don't care if it's k or l,
you just care about the total.
That'd be perfectly
substitutable inputs.
That would be a linear
isoquant.
OK, on the other hand, let's
think about goods which are
not at all substitutable like
cereal and cereal boxes.
The cereal wouldn't be any
good unless you have a
box to put it in.
The box doesn't do anything
unless you have
cereal to put in it.
That would be like in 8-4b.
8-4b would show you
non-substitutable inputs where
basically, given the amount of
one input, it doesn't matter
how much you have
of the other.
So for example, if you take
these-- these we often call
non-substitutable isoquants--
Leontief production functions.
Leontief production function,
for Wassily Leontief, some old
economist.
And basically, the Leontief
production function is that
your production, q equals the
Min of k and l, is the
Leontief production function.
So given how much k you have,
given you have 10 cereal
boxes, once you have 10 chunks
of cereal, it doesn't matter
if you have 10, 11,
12, 1 million.
You only have 10 cereal boxes.
So given an amount of k, then
it doesn't matter how much l
you have. Once you get to the
amount of l you need to fill
the cereal boxes, it doesn't
matter, and vice versa.
So basically, they're perfectly
non-substitutable.
So all that determines your
output is which you
have the least of.
OK, so substitutabilities
determine the slope of the
isoquants and of this
production function.
Now in general, we'll be
in between these cases.
There'll be some
substitutability.
Goods won't be perfectly
substitutable, but they'll be
somewhat substitutable.
So in general, we'll be in
between these cases.
And more generally, just as the
slope of the indifference
curve is the marginal rate of
substitution, the slope of the
isoquant we will call the
marginal rate of technical
substitution.
The marginal rate of technical
substitution-- the rate at
which you can substitute one
input for another in a
production function is the
marginal rate of technical
substitution--
which we'll define as delta k,
delta l for a given q bar, the
rate at which you can
trade off k for l
to hold q bar fixed.
Now, as with marginal rate of
substitution, the marginal
rate of technical substitution
will
change along the isoquant.
So if you go to figure 8-5,
here we've drawn a typical
isoquant for the production
function q equals square root
of k times l.
So the production function
is q equals the square
root of k times l.
And here's a isoquant.
This is the isoquant
of all combinations
which produce two units.
This is the q equals
2 isoquant.
Now, unlike utility--
remember utility?--
we said where u equals
2 was meaningless.
Utility was an ordinal concept,
not a cardinal concept.
Here, quantity is meaningful.
If you produce four, you would
have only produced twice as
much as if you produced two.
We can care about both the
ordinality and the cardinality
of these outcomes.
So we can say, what are the
combinations of inputs which
lead you to produce two units?
What's all these combinations
of inputs?
So whereas you can have one unit
of labor and four units
of capital, two of each, or four
units of labor and one
unit of capital, all
will produce two
units of the output.
And what you can see is that the
marginal rate of technical
substitution varies.
So for instance, when we start
with four units of capital and
one unit of labor, and we think
about adding a second
unit of labor, then the marginal
rate of technical
substitution is minus 2.
That is, one unit of labor is
worth two units of capital.
In other words, we can produce
the same amount of widgets of
q, but if we replace two units
of capital with one unit of
labor, so at that point we're
very capital-intensive, and
that unit of labor
is very valuable.
On the other hand, now if you
imagine we're down at 4-1, at
the third point--
we are probably using
a, b, c--
now we're at the third point,
where you have we have four
units of labor and one
unit of capital.
Now, if you'd be willing to
give up two units of labor
just to get one unit of capital,
that's the marginal
rate of technical substitution
is now minus 1/2.
When you're very
labor-intensive, you'd be
happy to give up a lot of labor
to get a little capital.
Once again, the principle of
diminishing marginal product,
just like the principle of
diminishing marginal utility,
implies that the marginal rate
of technical substitution is
going to be falling as you
go down the isoquant.
Just like the marginal rate of
substitution fell as you went
down the indifference curve, the
marginal rate of technical
substitution is going to fall
as you go down the isoquant.
And why is this?
Once again it's because of
this diminishing marginal
productivity.
That is, as you add more and
more labor, given capital,
each unit of labor can
do less and less.
And likewise, as you add more
and more capital, given an
amount of workers to use it,
each unit of capital can do
less and less.
So it's a very different
approach, but gets you the
same answer, which is with
consumption, each piece does
less and less for you, but we
can see that as consumers.
Here's the notions of labor,
each worker does less and less
for you, holding
capital fixed.
And each machine by the same
logic, if you have one guy in
the hole, it doesn't
matter how many
shovels you throw there.
He still is only one guy.
So each machines is doing less
and less by the same logic.
And those diminishing marginal
products lead to this
decreasing marginal rate of
technical substitution as you
move along the isoquant.
That's about the most technical
statement I'll make
all semester.
OK, questions about that, about
what's going on here?
That's production theory.
That's what you need to know
to know basically how firms
produce things.
Now, what we're going to do
is, now take this basic
production theory, and turn it
into actually understanding
how firms make decisions
on how much to produce.
But before we do that, I want
to talk about one other
concept, which is very important
for thinking about
production theory.
And it comes back to these
assumptions that we make which
might be a little bit
unrealistic, which is the
concept of returns to scale.
The concept of returns
to scale.
So here the question is, what
happens if we increase all
inputs proportionally?
Return to scale.
By scale, I mean, what if we
just double everything, twice
as much labor and twice
as much capital.
That's an increase in scale,
increasing all inputs
proportionally, twice as much
labor, twice as much capital,
half as much labor, half
as much capital.
So a change in scale is an equal
increase or decrease in
all inputs?
Equal proportional.
So what happens if we increase
all inputs, increase or
decrease proportionally?
And this is an interesting case,
because it's like, OK,
what if we just make the
firm half as big?
What happens?
Well, the answer is,
it depends on
the production process.
Some production processes will
exhibit what we call constant
returns to scale.
This is a convenient form.
It's convenient because the way
constant returns to scale
works is, it says that f of
2l, 2k, is equal to 2
times f of l, k.
That is, if it's constant, you
can just pull the 2 out.
Doubling the inputs leads to
doubling the outputs, which
equals to 2q, I'll write here.
Doubling the inputs equals
doubling the outputs.
So if I have twice as much labor
and capital, that's the
same as twice producing what I
had with the original labor
and capital which will get me
twice the original production.
That's the constant
returns to scale.
So every time I double my firm,
I get exactly twice as
much stuff out.
We can contrast that with
increasing returns to scale,
IRS, which says that f of 2l,
2k, is greater than 2
times f of l, k.
Or it's greater than 2q.
That is, when I double my firm,
I produce more than
twice as much stuff.
That'd be increasing
returns to scale.
On the other hand, we could also
have decreasing returns
to scale, which not surprisingly
means that f of
2l, 2k, is less than 2 times
f of l, k, or less than 2q.
That would be decreasing returns
to scale, which is
when I double my firm I get less
than twice as much stuff.
Can anyone give me an example or
some reason why returns to
scale is going to be increasing
or decreasing?
Think about firms out there.
Give me some that, by returns to
scale, would be increasing
or decreasing, any examples
you can think of.
There's no right answer here.
Yeah.
Go ahead, on the end.
AUDIENCE: Oh, if you're mining
something, you can only get to
stuff at one time, so having
more equipment and more people
doesn't mean you can
get more out of it?
PROFESSOR: Right, so if there's
a limited resource,
you could imagine decreasing
returns to scale.
Good.
What else?
Yeah.
AUDIENCE: If the company gets
harder to manage, that could
be decreasing returns
to scale?
PROFESSOR: Right, exactly.
If you're an entrepreneur,
you've got a great idea, but
it turns out that idea only
works if you really are
hands-on about it.
You're not Mark Zuckerberg, who
can just farm the thing
out, it's really your idea.
And you've got to be there.
Then after it expands and
you lose control of the
production, it might not be as
effective because you're not
there making it happen.
Any ideas why return--
Yeah.
AUDIENCE: If you or
[UNINTELLIGIBLE]
PROFESSOR: So that's
an example of
increasing returns to scale.
Increasing returns to scale
would be, gee, maybe if I'm
bigger, I can get a better
deal on the inputs.
But that's not quite right,
because we haven't really got
into prices yet.
I'm looking-- that's really
a market response--
I'm looking for a more
technological story, a
technological story of
increasing returns.
Go ahead.
AUDIENCE: If you're bigger, you
can hire a specialist to
do work, like a manager
who can [INAUDIBLE]
PROFESSOR: Exactly.
So it's the opposite, which is,
let's say you have an idea
which is pretty good, but
in fact it's replicable.
And right now, you're trying
to manage some guys.
And then all of a sudden, when
you get twice as big, you
bring other people in who can
effectively replicate your
idea, and really expand it
in a very effective way.
You can have increasing
returns to scale.
Now, so an example of what that
looks like, if you go to
the last page in the handout,
figure 8-6a shows constant
returns to scale.
So let's start with
8-6a, that's
constant returns to scale.
So here-- and these are
from the textbook--
for example, when we doubled the
inputs from 100 labor, 100
capital, to 200 labor, 200
capital, you doubled output.
Those are constant returns
to scale isoquants.
The last page shows
decreasing and
increasing returns to scale.
So for instance, tobacco is an
example of decreasing returns
to scale, because there's only
so much leaf that you have
that you can produce.
So here, when you double the
inputs from 100 to 200, your
output only goes from
100 to 142.
OK, and if you want to double
the 200 units, you've got to
go way the heck up
there on inputs.
On the other hand, primary metal
production is something
where you can have increasing
returns to scale, because
there's such high costs of
building a plant that once
it's built, so just like I said,
gee, in fact that second
digger of the hole might
actually make it more
productive.
Once that plant's built, there's
one worker banging
around the plant, a second
worker adds a huge amount to
productivity because they
can specialize.
Basically, increasing returns to
scale is going to come from
specialization.
So if you build this big plant
to build primary, to build
steel, one worker in that plant
is no good, because he's
got to pour the steel,
then run over and
cool it down, et cetera.
Once you have two, they can
specialize, and three, they
can specialize more.
You might think of something
like that would have
increasing returns to scale
through specialization.
And that's illustrated here,
where doubling the inputs
actually leads to more than
doubling the output.
Now we're going to talk
about all these cases.
Typically, economists are
suspicious of increasing
returns to scale.
Anybody, anybody who ever has an
IPO, whoever starts a firm
will always tell you
that they have
increasing returns to scale.
Well, we say, I've got a great
idea and the bigger, the more,
the better it's going to be.
And they're generally wrong.
Generally, we think of
increasing returns to scale as
being like a free lunch.
And we don't like free lunches,
we economists.
We think, gee, if it's really
increasing returns to scale,
you would have already
expanded there.
OK, if it's really such a good
idea to get bigger, why aren't
you bigger already?
Now, it doesn't mean you can--
Yeah.
AUDIENCE: Well, they
need capital.
PROFESSOR: Well, they need
capital, and so that would be
their argument.
And that's great.
And typically, they're wrong.
But that would be why you would
argue that they need
capital to get bigger.
So typically, we like decreasing
returns to scale.
That's going to be our
sort of default
assumption of the world.
In other words, here's a way to
think about it, think about
we're dealing with mature firms.
We're modeling, for
instance, mature firms.
We think that for mature firms,
at least, there's not
increasing returns to scale,
because in a mature firm they
would have hit that
point already.
Now they're on the
decreasing part.
So that's where we're
going to focus for
the rest of the semester.
OK, let me stop there.
And good luck tomorrow night.
And we'll come back
to talk more about
production on Wednesday.
