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JON GRUBER: At the beginning of
the lecture, we're going to
actually talk about
productivity, one of the most
important topics in economics.
And really one of the most
famous applications--
or, more generally,
misapplications--
of the principles of diminishing
marginal product
in the history of economics.
Many of you may have heard of
a guy named Thomas Malthus.
He was a famous philosopher
who, in 1798, posited the
theory that we're all
in big trouble.
And he did so following the
basic tenets that I've taught
you so far.
Malthus pointed out
look, we've got--
he said, think about
production of food.
He said, with the production
of food you've got, as with
any other production process--
he didn't put it in these
terms, but basically he was
appealing to what we
learned last time.
He said, like any other
production process you've got
two inputs, labor and capital.
But with food, the
capital is land.
And unlike other kinds of
capital, it's fixed even in
the long-run.
That is, we talked about the
long-run being defined as the
period of time over which
all inputs are variable.
Well, land is never variable.
There's a certain amount
of land on
earth, that's not variable.
And at the end of the day,
production of food is
essentially just short-run,
there is no long-run.
At the end of the day,
production of food, capital's
fixed, it's only labor.
Moreover, in that situation
labor has diminishing marginal
product with a given
amount of land.
It doesn't matter how many
workers you have, there's only
so much you can grow on it.
Obviously, as you increase
workers you can grow more
originally.
But eventually, you'll run out
of useful use for those
workers, yet the demand for food
will not stop growing.
So basically, the demand for
food is going to continue to
grow unabated over time
as population grows.
Demand for food [? it fuels ?]
proportional to population, so
it's growing over time.
Yet the production of food
eventually has to slow down,
because there's a diminishing
marginal product of labor
without an increasing capital.
So basically what you've got is
a forever growing demand,
but a gradually slowing
production, because the
marginal product of labor's
diminishing with this fixed
capital or land.
The result is mass starvation.
So Malthus predicted that by
about where we are now, if not
before, the world would
be suffering from mass
starvation.
Through the basic principles--
not because he's a
crazy nutcase--
but the basic principles
we've studied so far.
Which you've got ever-increasing
demand, but
diminishing marginal product
of producing food.
And in the end you get
mass starvation.
Well, as we all know
Malthus was wrong.
World population has risen about
800% since he wrote his
article at the end of the
18th century, and yet
we're fatter than ever.
Our problem is we eat too
much, not enough.
Now that's not true
around the world,
there's starvation elsewhere.
But there's clearly no more
starvation worldwide than
there was at his time despite
the fact that the world
population has grown
eight-fold.
So what did Malthus get wrong?
What Malthus got wrong is what
I haven't taught you yet.
Which is that aggregate
production is not just about k
and l, but also about
productivity.
It's also about productivity.
That the production function
really looks like-- the form
of the production function,
which we wrote last time as q
equals f of k and l.
Really more generally, can be
written as q equals A, times f
of k and l, where A is aggregate
productivity.
Really, let's say that this is
big Q. If we think about the
big Q for society, now let's
think of aggregate quantity
for society or else
we wouldn't talk
about a specific firm.
But if we think about aggregate
product, aggregate
quantity produced in society,
it's a function of the
aggregate capital and labor
of the society, but also a
function of productivity.
It's also a function of the fact
that we use our inputs
more effectively over time.
So for example, one thing
Malthus missed is that the
acreage of land-- it's an
empirical fact, the number of
acres of land on Earth
are fixed.
Earth is not growing--
but the arability of that
land is not fixed.
We get better and better at
figuring out how to grow more
and more stuff on the
same amount of land.
That's the factor A, that's a
productivity improvement.
Likewise, agricultural
technology has improved.
We have disease-resistant seeds,
we have better land
management.
The bottom line is we are making
more and more of a
given plot of land compared to
what Malthus saw in his time.
So while k if it's defined as
land may be fixed, and l
therefore there's diminishing
marginal product of a given
production function, the
production function itself is
improving over time because of
productivity improvements.
Productivity, the arability of
land, disease-resistant seeds,
and other things are making that
given quantity of land
more productive over time.
So effectively, in the long-run
if A goes up faster
than the marginal product of
labor diminishes, then overall
quantity can increase even
though k, the underlying level
of land, is fixed.
That's what Malthus missed, is
that there's two factors going
on over time.
The marginal product of labor's
falling, it's true,
for a given plot of land.
But we're making each plot of
land so much more productive,
it's overcoming that.
And as a result, food production
is actually rising
per capita.
So since 1950, world food
consumption per capita has
gone up 40%.
Despite the fact that the
Earth's not gotten any bigger,
and despite the fact the
population's grown a
lot over that time.
And basically this huge increase
of agricultural
productivity has overcome
the diminishing
marginal product of labor.
There's actually a great little
box in the Perloff Text
about a single individual and
his contributions to that.
A scientist who led what's
called the Green Revolution.
He experimented in Mexico with
different methods of improving
agricultural productivity, and
then essentially brought those
to Southeast Asia--
India, Pakistan and
other places.
And they estimate, saved about
a billion lives through the
increase in agriculture
productivity he made possible
for this Green Revolution
in Southeast Asia.
Really, just changed the entire
trajectory of that part
of the world through the
agricultural productivity
improvements that
he put in place.
So it's very interesting putting
a personal face on
this impersonal letter A, how
one scientist can really make
a difference in that case.
This also leads to the larger
question which this course
doesn't spent a lot of time
on, but which is more of a
macro question, which is what
determines the overall
standard of living
in our country?
The standard of living in our
country, that is basically for
a given level of labor we
supply, what determines the
level of our utility, of our
social welfare, given how much
labor we can supply?
Well, ultimately, what's going
to determine-- or another way
to think of it is what
determines the amount of stuff
we can have for a given amount
of labor effort we put in?
Well, that's society's
productivity.
Society's productivity is how
much more we can have for each
given level of labor input.
So what determines how much
stuff we can have?
Well, it's k and A. Given a
fixed amount of labor input,
given how much we work, what
determines how much stuff we
can have, with how much capital
we have, and how
productively we make
use of it?
Now, productivity in the
US has followed a very
interesting trend.
So productivity, which is how
much we produce for a given
amount of inputs, has followed
an interesting trend.
From World War II until about
1973, productivity grew
rapidly in the US.
Productivity grew at about
2.3% per year--
2.4% per year--
from the end of World
War II through 1973.
That is, working no harder and
having no more machines, we
can consume 2.4% more stuff
every single year.
That's pretty impressive.
That means we can just sit
around, work no harder than we
were, and have no more machines,
and produce 2.4%
more per year.
Now, of course, over time we
worked harder and had more
machines, so overall output in
US economy grew much faster
than 2.4% a year.
It grew more like 7-10% a
year over that period.
Yet, the point is that a lot of
that we can get for free,
essentially, without any harder
work or any more capital.
However, starting in 1973
until the early 1990s,
productivity growth fell
dramatically to 1% per year.
That is literally we lost 1 1/2%
per year of stuff we were
getting before.
We were getting 2 1/2% a year
up to '73, all of a sudden
it's down to 1%.
That's 1 1/2% a year less stuff
we can get unless we
work harder to make up for it.
Why did this happen?
Well, we don't exactly know,
but there's two good
candidates.
We know the two candidates, we
just don't know the right
proportions.
One is that we have less capital
in our society because
savings fell.
The amount of savings US
households do fell
dramatically.
And the US has a very
low savings rate.
The US savings rate over this
period averaged about 3%.
That is, every dollar
we earned we saved
about 3% as a society.
Compared to countries
like Japan, where
it's more like 20%.
Every dollar they earn
they save about 20%.
Now why does that matter?
Well, we'll talk about this
later in the course, but
essentially the amount we save
determines the amount of
capital we have in society.
Because essentially, where
do firms get the
money to build machines?
They get it by borrowing from
households who save. And the
less we save, the less money
there is that firms could
invest in building machines.
And we'll talk about that at
length later in the semester.
But the bottom line is, the more
we save as a country, the
more money we have available,
the more firms can take that
money and build machines
that improve
our standard of living.
And that saving fell a lot,
and that's one reason.
And the other reason is that
productivity fell for reasons
we don't quite understand.
We know that productivity slowed
down, but we don't
quite understand why that is.
But then in the 1990s,
productivity shot up again.
So productivity went back up
towards our historic levels,
from 1% back up to
over 2% a year.
Why is that?
Well, it's unclear, but we think
it's basically the IT
revolution.
Essentially, we think that the
slow diffusion of computers,
which people were predicting
should increase productivity
as way back as the 1980s,
suddenly in the 1990s it
really happened.
And this IT revolution led to
a big productivity increase.
It's not clear if that's dying
down now again, or if it's
going to continue.
It'll be interesting
to see what happens
over the next 15 years.
So we have this period of high
productivity growth, slowed
down from '73 to the early '90s
and then picked up again.
We're not quite clear if that
year's coming to an end or
not, but that's sort of where we
are now in that time path.
What's very interesting--
so that's what happens to
productivity, that's all I'll
talk about it for this course,
it's more of a macro topic.
But I will mention
an interesting
micro spin on that.
Which is, if society's more
productive, that's like found
money for society.
That's like saying with all our
resources we suddenly get
extra money.
Society then has to decide
what to do with that.
The US and Europe have followed
very different paths
in what to do with that money.
In the US, we've taken
that money and
bought a lot more stuff.
We have the highest standard
of living in the world.
We buy the most stuff per capita
of anyone the world.
In Europe, they took a lot of
that money and took more
leisure with it.
They decided we're not going to
quite have as much stuff,
but we're going to have six
weeks a year of vacation
instead of two weeks
a year of vacation.
So if we go back to our
discussion of what determines
labor supply is the choice
between leisure and
consumption, and you think of
the wage as the opportunity
cost of leisure, well, what
they've decided in Europe is
to choose more along the leisure
axis, and less along
the consumption axis.
In the US, we've chosen less
among the leisure axis-- we
work way harder than Europe--
but we have more stuff.
And the question is, how do
we feel about that choice?
Has that been ultimately a
welfare maximizing choice?
Now an economist will say of
course it's been, because it's
a choice we made.
Of course, it's been
welfare maximizing.
We talk about revealed
preference, and people's
choices reveal what
they prefer.
So our revealed preference, we
just prefer stuff more and
leisure less than Europe.
But in fact, it's not clear that
that is each individual's
optimal choice.
If a given individual says,
look, I'd rather have less
stuff and more time off, it may
be hard to find the job
that lets them do that.
So while that may be the choice
we've made as a society
with our social institutions,
that may not serve the
interests of every individual
in society.
And that's the kind
of trade-off we
need to think about.
So anyway, that's sort of
what I wanted to say on
productivity.
Yeah, question?
AUDIENCE: Does higher
productivity translate into
more income, or more income for
individuals who will buy
stuff [INAUDIBLE] taking
more leisure?
JON GRUBER: Because basically
the point is think of our
economy as a pie.
That basically the idea is
let's think of you have a
start up, and your start up is
such that you can make this
product, and you could
make $1 million a
year with 10 workers.
You could make $1
million worth of
stuff with 10 workers.
So each of your workers
takes home $100,000.
Now imagine that you discover
new technology which lets you,
with the same amount
of workers, make
$2 million a year.
Well, some of that you'll keep,
but some of it you'll
pay your workers more.
So suddenly they have more
money, because you've suddenly
managed to make twice as
valuable stuff with the same
amount of resources.
So that's the situation
which improves
our standard of living.
Other questions about that?
Comments?
OK, so the bottom line, coming
back to sort of micro-theory
we're talking about, is we have
to think about production
functions as having a
productivity adjustment.
Macro raises these big issues
about sort of ultimately what
determines our standard of
living in this country, and
how do we want to spend
that money?
So, with that as background,
we're now going to stop
talking about production
and move on
to cost. Cost is--
quite frankly this is perhaps my
least favorite thing in the
whole course.
It's a little bit boring, but
you need to understand how
cost structure in a firm works
to understand how firms make
the decisions that ultimately
get to be a lot more
interesting again, so just
sort of bear with me.
Now, so we talked about costs,
let's start with a couple of
definitions.
Basically, let's back up, where
are we coming from?
I talked about what the firm's
decision is, the firm has to
maximize profits, which is
revenues minus cost. So we
have to ask what are costs if
we're going to make this
profit maximizing decision.
Well, costs are going to
have a few components.
The first component, costs are
going to have really two major
components--
fixed costs, and
variable costs.
Fixed costs and variable
costs.
Fixed costs are the costs of
inputs that cannot be varied
in the short-run.
Remember, I said that the
short-run is defined as a
period over time which only
some inputs can vary.
Well, fixed costs are the costs
of those inputs that
can't vary in the short-run.
Variable costs--
so that's like capital
in the short-run--
variable costs are the cost of
goods that can vary in the
short run, that's like labor.
So total costs is the sum of
these two, so total costs
equals fixed cost plus
variable cost.
Finally, another definition
that's important is marginal
cost, which is the change in
cost with a change in output.
So the marginal cost
is just like--
remember, we want to think in
terms of marginal decision
making in this course.
So the marginal cost is the
change in cost with the change
in-- actually, that should
be a little q.
The change in a firm's cost with
the change in the firm's
output is marginal cost.
And then finally, average cost
is just what it sounds like.
Average cost is just c over
q, it's just the average.
So the difference between
marginal and average cost, is
basically average costs is the
average over the whole set of
goods produced.
Marginal cost is the cost of
that next unit of production.
So those are our key
definitions.
Now with those in mind, let's
ask how do we get costs?
And the answer is we get them
from the production function.
Once we do a production
function, we can derive costs.
So if we have some production
function, q equals f of l and
k, then we can say the cost of
producing q is equal to f of
wl plus rk.
Where w is the wage rate, or the
rate you pay per unit of
labor, and r is the rental rate,
or the rate you pay per
unit of capital.
Now, let me just pause here
for a second to talk about
pricing capital.
It's easy to think the cost of
an hour of labor, it's the
wage you pay for an hour.
It's harder to think about the
cost of a unit of capital.
Because we buy the
machines, right?
So how do we think
about the cost?
I'm going to cover this later in
the course, for now imagine
all machines are rented.
Imagine you rent every
machine you use.
And think of r as the rental
price of that unit of capital.
So with buildings it make sense,
firms often rent the
buildings they're in.
Think of r as the rental price
of that unit of building, or
that unit of machine.
We'll come back later to see why
that's a sensible way to
think about it.
The key point is, the reason we
have to do this is the wage
is a flow measure, every hour
I pay you a new wage.
If I use the cost of buying the
machine, that be a stock
measure, so you couldn't really
compare it to wages.
So we want to use
a flow measure.
The flow measures is what we
have to pay every period to
rent the machine.
Yeah?
AUDIENCE: [INAUDIBLE]
just take the cost of the
machine and estimate the
amount of time we want,
and then divide it?
JON GRUBER: Sure.
No, and I'll cover that later.
You could think of
the rental--
if I bought the machine today
and sold it tomorrow, that'd
be like I rented it.
And this would be the cost
difference between what I paid
for it and what I'd
sell it for.
But it's just easier to think
of it as the rental, because
the flow measure-- like the
wage-- is a flow measure.
Now, in the short-run,
capital is fixed.
So in the short-run, our
fixed costs are rk bar.
That's our fixed cost, the
rental rate times the fixed
amount of capital in
the short-run.
And our variable costs are
w times l, which is
a function of q.
That is, the more you produce
the more labor
you use in the short-run.
So total costs in the short-run,
short-run total
costs, are rk bar
plus wL of q.
k is not a function of q because
k's fixed in the
short-run, but the amount of
labor used is a function of
how much you produce.
This implies that the marginal
cost, the key concept we want
to work with, marginal cost,
which is the derivative of
total costs with respect
to quantity.
So dc dq is going to
be equal to w--
or, let's do it in deltas,
because we're not doing
calculus here.
Delta c delta q is going to be
w times delta l over delta q.
That's going to be the
marginal cost.
The marginal cost-- so I'm just
differentiating the total
cost function--
is going to be the wage
times delta l delta q.
So the marginal cost of
producing the next unit is
going to be how much labor I
have to produce to produce the
next unit, times the wage
I pay per unit of labor.
Now, does anyone remember
what we call this?
I know this wasn't on the exam
last night, so you may not--
cast your mind back to the
lecture on Monday.
Do you remember what we call
delta l over delta q?
Anyone?
Bueller?
No?
It's the marginal product
of labor.
Remember from Monday?
So this is the wage times the
marginal product of labor.
So what we say is that the
marginal cost is equal to the
wage times the marginal--
I'm sorry the wage over.
I'm sorry, it's one over.
That delta q does-- l was
the marginal product.
The wage over the marginal
product of labor.
So marginal cost is
the wage over the
marginal product of labor.
Marginal product of labor was
delta q delta l, so wage over
the marginal product of labor
is the marginal cost.
So think about this
intuitively.
What we're saying is the cost of
the next unit of production
is declining with the marginal
product of labor, it sort of
makes sense.
The more productive is a worker,
the less expensive is
producing the next unit.
The less productive is the
next worker, the more
expensive is producing
the next unit.
So it's an inverse relationship
between the
marginal cost and the marginal
product where the wage is the
constant that scales
that relationship.
So basically, when workers are
very, very high marginal
product, then it's going
to be cheap to
produce the next unit.
When workers have a low marginal
product, it's going
to be expensive to produce the
next unit, and that's going to
depend on what you actually
have to pay the worker.
Questions about that?
So basically, the first key
thing we want to derive here
is that the marginal cost is
directly related to the
marginal product of labor, and
the marginal product of labor
we saw last time comes out
of production function.
So if you're given a wage, and
given a production function,
you should be able to derive the
short-run marginal cost.
You might someday be
asked to do that.
Now what about the long-run?
The short-run's no fun, what
about the long-run?
In the long-run, firms
can choose their mix
of labor and capital.
Remember, in the short-run the
capital is fixed, so fixed
costs rk bar.
The only thing they could
change was the amount of
labor, so we could derive
their marginal costs.
What about in the long-run?
Well, the long-run's a little
more interesting because in
the long-run firms get to choose
their input mix to
maximize their production
efficiency.
So input mix is chosen to
maximize production efficiency
which equates to minimizing
costs.
Maximizing production efficiency
equates to
minimizing costs.
So we talked last time about
isoquants, and the notion that
isoquants were combinations
of labor and capital that
delivered the same output.
Just like indifference curves
are combinations of pizza and
movies that deliver the same
utility, isoquants are a
combination of labor
and capital that
deliver the same output.
The key point is that,
technologically, any choice of
labor and capital produces the
same q, so there's nothing
that tells you technologically
which of those to use.
We just know, technologically,
there's a set of choices which
deliver the same q.
Well, how do we tell
which to use?
Well, we want to choose the one
which is minimizing costs.
So to do that, we're going to
have to bring in the cost of
those inputs.
Just like we said there's a set
of pizza and movies, all
of which leave you
indifferent.
How do you decide which pizza
and movies to choose?
Well, you bring in the
relative price
of pizza and movies.
Here, we're going to bring in
the relative price of capital
and labor to determine
how we choose
between capital and labor.
So to do that, we're going to
draw isocost lines which are
going to be just like our
old budget constraints.
Isocost lines which represent
the cost of different
combinations of inputs, just
like our old budget constraint
represented the cost of
different consumption goods.
So if you look at figure 9-1,
here we're going to have
isocost curves which are
going to represent--
and we're going to assume here
that the wage is $5 an hour,
and the rental rate is $10
per unit of capital.
So, in other words, the $50
isocost line in figure 9-1
shows all combinations
of labor and
capital that cost $50.
So you could spend $50 in
production if you had 10 units
of labor, and no units
of capital.
Or five units of capital, and
no units of labor, or any
combination in between.
These are all the combinations
of labor and
capital that cost $50.
Likewise, the $100 isocost is
all combinations of labor and
capital that cost $100.
So each of these isocosts give
you the combination of inputs
that cost a certain amount.
Just like a budget constraint
gave you the combination of
pizza and movies on which
you spent your income.
Now, you may have said well,
wait a second, the difference
with consumers is we knew their
income so we knew what
their budget constraint is.
Here we don't know whether to
choose the $50 cost, the $100
cost, $150.
We don't know what the
total amount is.
That's what makes firms
hard, that's why we
have an extra step.
So hold that thought,
we'll come back
to that next lecture.
For now, let's just say there's
a set of trade-offs
that the firm can choose from,
and a set of isoquants that
they have.
And what's the slope of
this isocost line?
It's the negative of the
wage rental ratio.
The slope of the isocost
is minus w over r.
The slope is minus w over r.
It's basically the trade-off
between labor and capital's
going to be determined by the
relative prices of those
inputs, so slope is going
to be minus w over r.
So basically, how many units of
capital do you have to give
up to get the next
unit of labor?
Well, what this isocost tells
you is you have to give up 1/2
a unit of capital to get
a unit of labor.
So the slope is minus 1/2.
Likewise, you could say you have
to give up two units of
labor to get one unit
of capital.
So that's why the slope is minus
1/2, that's what it's
telling us.
Once again, budget constraints
are about opportunity costs.
How much labor do you have
to give up to get
another unit of capital?
Or how much capital do you have
to give up to get another
unit of labor?
Now, armed with isoquants, which
are like indifference
curves, and these isocosts
which are like budget
constraints, we can then
figure out what is the
economically efficient
combination of inputs for the
firm to use.
The economically efficient
combination of inputs for a
given level of output.
So the economically efficient
input combination for a given
level of output is going to be
determined by the tangency of
the isoquant with the isocost,
as you see in figure 9-2.
Here we're going to use our same
isoquant we had before,
which is we're going to assume
that q equals square
root of k times l.
So same production function we
had before, which gave a
series of isoquants
last lecture.
So basically, what we see
is that the efficient--
if you want to produce a given
amount of q, then basically
what you're going to do is
you're going to look for the
tangency of that isoquant with
the isocost. And you're going
to say that the efficient way to
produce that is going to be
to use 2 1/2 units of capital
and 5 units of labor.
It's going to say look, given
the relative prices that are
given to us by this budget
constraint, the production
technology is given to us by
this production function from
which we derived isoquants
last time.
So the optimal combination of
inputs to get this level of
output is going to be 2
1/2 units of capital
and 5 units of labor.
And that will produce basically
square root of 12 1/2.
So basically the quantity will
be equal to the square root of
5 times 2 1/2, or the square
root of 12 1/2 units of
production.
So basically, that is
going to give us the
efficient way to do that.
Now, once again as always, we
want to think about things
intuitively, graphically,
and mathematically.
Let's think about for a second
the mathematics.
We know that the slope
of the isoquant--
we talked last time--
the slope of the isoquant
at any given point.
The isoquant slope was the
marginal rate of technical
substitution.
We defined that last time.
The slope of the isoquant was
the marginal rate of technical
substitution which is the
marginal product of labor over
the marginal product
of capital.
And what we're saying is we want
to set that marginal rate
of technical substitution
equal to the input costs
ratio w over r.
That's what we're saying, the
efficient thing to do is to
set the marginal rate of
technical substitution equal
to the price ratio.
That's what happens when
the slopes are equal.
Now, once again, I
find it easier to
rewrite this equation--
once you've developed the
intuition, I find it easier to
think of it this way.
Rewrite this as the marginal
product of labor over the
wage, equals the marginal
product of capital over the
rental rate.
What this is telling us is the
efficient place is where
essentially for every dollar you
spent on workers, you're
getting the same return as a
dollar spent on machines.
The marginal product of labor
over the wage is sort of the
bang for buck of workers.
What are you getting for your
next dollar of wage?
The marginal product of capital
over r is the bang for
the buck of machines.
What are you getting for your
next dollar of rent?
And the efficient point is
where these are equal.
If they're not equal, then you
have too much of one and not
enough of the other.
So basically, what we
can do is we can
solve in this example--
in this example, we could say
the marginal product of labor
is 1/2 k over the square
root of k times l.
The marginal product of capital
from this production
function is--
once again I'm using this
production function q equals
square root of k times l.
Marginal project of capital
is 1/2 l over square
root of k times l.
So the ratio of the marginal
products is simply k over l.
The marginal rate of technical
substitution, given this
production function,
is k over l.
That's the marginal rate of
technical substitution.
So this says that given this
production function and these
prices, at the optimum you
should set k over l equal to w
over r, which equals 1/2.
So what this says is given
this production function,
these price ratios, the optimal
thing to do is to use
half as much capital as labor.
Half as much capital as labor
is the optimal thing to do,
and that's what we see in figure
9-2, is the optimal
thing to do is use half as
much capital as labor.
Now, in other words,
let's say, to
now develop the intuition.
Imagine you told me no, I should
use as much capital as
I should use labor.
As much capital as I
should use labor.
Imagine I told you that.
Imagine I said no, in fact, the
efficient thing to use is
why not have one machine
for every worker?
How would you tell me
intuitively why that's wrong?
Why would I be wrong
to say use one
machine for every worker?
Why would that be wrong,
given the prices
prevailing in the market?
Someone can tell me this.
Yeah?
AUDIENCE: Well, renting
machines is a lot more
expensive than paying
more workers.
JON GRUBER: Twice as
expensive to rent a
machine as get a worker.
AUDIENCE: So it would be more
cost-effective to have the
workers share machines rather
than get a whole new machine.
JON GRUBER: The key point is
the machine costs twice as
much, but the machine doesn't
do twice as much.
The machine and the worker
do the same thing.
The marginal rate of technical
substitution is one.
You're indifferent between one
more machine and one more
worker, but the machine cost
twice as much as the worker.
So you want more workers and
fewer machines, right?
Given the machines and workers,
this is a perfectly
substitutable production
function.
The marginal rate of technical
substitution is k over l.
You're perfectly indifferent
between these two, given
that-- not perfectly
substitutable, but at this
point you're indifferent
between the two.
So given that you're indifferent
and the machines
cost twice as much, why not
buy half as many machines?
Yeah?
AUDIENCE: But then, if the
machines cost twice as much,
why buy any machines?
JON GRUBER: Oh, that's
very good point.
Because it's not a perfectly
substitutable function.
My bad.
If it was, if the production
function--
great question.
Let's say the production
function was of the form q
equals k plus l.
That's perfectly substitutable
production.
Then you're right, in that
situation you should only buy
workers because they do exactly
the same thing.
But that's not the case here.
This exhibits diminishing
marginal product.
So if you only bought workers,
eventually each worker would
do so much less that you'd be
better off getting a machine.
It's not perfectly
substitutable, I misspoke before.
At the margin they have
an equal effect.
But as you get more and more
laborers, they'll be less and
less productive, so eventually
you're going to
want to buy a machine.
But you're only going
to buy half as
many machines as workers.
You never want to buy one
machine per worker.
But you also don't want no
machines per workers, because
the workers won't have
anything to do then.
Here you'd want no machines
per worker, right?
The optimal thing to do,
if you have a perfectly
substitutable production
function, you'd only just buy
the cheaper input.
But that's not the case when you
have diminishing marginal
products, then you're going to
use a combination of inputs.
But the combination used will be
determined by the prices in
the market.
Other questions about that?
So now we can ask, just as we
asked in consumer theory, how
does a price change in the price
of goods affect your
consumption decisions, we can
ask how does a change in the
price of inputs affect your
production decisions?
You could see that in the
next page, figure 9-3.
Imagine that wages went up.
So imagine now wages, instead
of being $5 an hour,
are $7.50 an hour.
They pass a new minimum
wage, and wages go
up to $7.50 an hour.
What does that do?
Well, that steepens the isocost.
Your trade-off is now
you're going to get fewer
workers for every machine you
give up, or more machines for
every worker you give up.
And so at the same isoquant,
that's going to shift you to
using less labor and
more capital.
By the same logic as before,
you're going to use less labor
and more capital, because you're
going to see this shift
in relative prices.
This figure shows why the
minimum wage leads to
unemployment.
We talked about it last time.
We did in a graph, we just said
supply and demand and
showed you.
But actually this is the
underlying mechanics of how
minimum wage leads
to unemployment.
Because the minimum wage,
by change, is
relative input prices.
If the only way you could
produce things was with labor,
there wouldn't be much
unemployment for a minimum
wage because basically you
wouldn't have anything else
you could do.
You'd still have to
hire the workers.
But, in fact, that's not the
only way to produce things.
You can substitute to capital.
As a minimum wage goes up, firms
will substitute towards
capital, and that's why the
minimum wage will lead to
unemployment.
So this is sort of the
underlying mechanics of how
that happens.
All right, now armed
with that--
so basically when we
did consumer theory
we were done here.
We basically said, look, we
now know you have a budget
constraint, you have
indifference curves, you're
fine with their tangent,
you're done.
The reason firms are one step
harder is you don't have a
budget constraint.
q is not given to you, q is
ultimately decided by you.
You the firm are going to
decide on little q.
With our example for consumers,
your parents gave
you $96, you had no choice.
Well here the firm isn't given
little q, it's going to
decide little q.
What that means is we're
not done yet.
There's one extra step we need
to do with firms, which is
figure out where little
q comes from.
So to do that, we're going to
have to then say well, how
does a firm think about the set
of choices of little q?
And how does it think about how
it changes production as
little q changes?
So to see that, go
to figure 9-4a.
This shows the long-run
expansion path for a firm.
This shows how, as it produces
different amounts of goods, it
will choose different
units of inputs.
So for the first level of
production, it chooses five
machines and 10 workers.
Then if it wants to double
production, it chooses 10
machines and 20 workers.
So if it wants to increase
production by another 50%, it
chooses 15 machines and
30 workers, and so on.
This is a linear
expansion path.
This says this firm is a
production function, and
prices are such that basically
they always want these inputs
in fixed proportions.
So it would be a fixed
proportional expansion path.
No matter how much you choose to
produce, you always want to
use twice as much labor
as capital.
However, that doesn't
have to be the case.
So this long-run expansion
path is going to be what
becomes our underlying
cost curve.
This is where underlying cost
curves are going to come from,
and hopefully where supply is
going to come from, is this
long-run expansion path.
This long-run expansion path is
going to show us how much
more we have to spend
to produce
different amounts of quantity.
Now in this case, what you see
here is that you have these
fixed proportions.
That as you increase quantity,
that the input portion stays
the same, but that doesn't
have to be.
For instance, figure 9b, you can
imagine a world where, as
you produce more units,
capital becomes less
productive.
So you want more and
more labor, but not
that much more capital.
So this might be the example
of like McDonald's.
If McDonald's wants to produce
more burgers, ultimately
there's only so many fryolators
it can use.
Ultimately, it needs more
people to package up the
burgers and sell them.
So you might think that capital
becomes less and less
productive.
And as a given McDonald's
franchise expands its sales,
it might want to increase the
ratio of labor to capital.
So this is a case where
capital's becoming less
productive.
And as you see, as you expand
production you're going to
more labor and less capital.
In other words, the marginal
product of labor is still
steep, and the marginal
product of capital is
flattening.
So you want more
and more labor,
and not as much capital.
That's one kind of
expansion path.
Figure 9c shows a different
kind of expansion path.
Here's one where labor becomes
less productive.
So this might be, for example,
something which is a mass
production process, like
producing automobiles.
Where basically as you produce
more and more automobiles, you
need more and more machines
to produce them.
The people just run
the machines.
So it's much more efficient to
have to do it through more
machines and less through more
workers in automobile
production.
So in that case you could have
a steeper expansion path,
where basically the marginal
product of labor is falling
relative to the marginal product
of capital, so you
want to increase the ratio of
capital to labor over time.
The bottom line is as firms
produce more, they may hold
constant or may change the ratio
of their inputs, but
they'll clearly use
more inputs.
They're going to use more
inputs, but the mix of the
inputs they'll use will change
with their production levels.
So the question we have to ask
is, well, what's going to
determine their production
level?
Where does q come from?
I'll have to leave that as
a teaser for next time.
Let me just say where q comes
from, is q is going to come
from market competition.
We're going to get q--
I'm not done, I have one
more thing to cover.
But we're going to get q from
market competition.
Now there is one other
thing I want to cover
though related to costs.
Which is an important concept
that we have to have in the
back of our mind, which when we
come back, we think about
competition.
Which is fixed versus
sunk cost. Fixed--
my wife always thought I was
saying some costs, I'm not.
I'm saying sunk costs.
Fixed versus sunk costs.
Fixed versus sunk costs.
Sunk costs are costs which are
fixed even in the long-run.
Fixed costs are costs which are
fixed in the short-run,
and variable in the long-run,
so capital.
Sunk costs are costs which are
fixed in the long-run.
That is, they're foregone
once you produce.
The minute you produce one unit,
those sunk costs are
gone forever, and
they cannot be
changed even in the long-run.
In other words, importantly,
they cannot be changed by how
much you produce.
So in the long-run, you can
change the cost of capital by
building bigger or
smaller plants,
producing more or less.
But some costs cannot
be changed.
So what's a classic example?
Well, the classic example for
example would be medical
education, or any professional
education.
Once you've gone to med school
and done all your grueling
years of staying up all night,
you've paid those costs.
They're now paid for, and it
doesn't matter if you see
three patients the rest of your
life or three million
patients the rest of your life,
you've already paid
those costs.
Think of that as the capital
of a doctor's office.
Now when you take your office
as a doctor, if you want to
see more patients in the
short-run, they might be
crammed into your office, and
in the long-run you might
build a bigger office.
So in the short-run, how hard
you work is variable.
In the long-run, how big your
office is is variable-- how
many secretaries you
hire, et cetera.
But your medical school
spending is gone.
That's not variable in the
long-run, that's sunk.
And that's a very important
distinction is between
basically these fixed costs,
what we call fixed costs.
Which are costs where, like the
costs of the office and
the machinery the physician
uses, which can be changed
over a 10-year period, versus
sunk costs which once paid are
gone forever.
And the key reason, just to
give you a hint about why
these will matter, is because
when firms set up this--
we may see firms in the
market losing money.
You may see firms in the
market losing money.
In fact, in any point in time
we see lots of firms in the
market losing money.
You might say, why don't they
go out of business?
The reason they don't go out of
business is because they've
already pay huge sunk costs.
It's not efficient to
go out of business.
They've already invested
a certain amount.
It's not going to be efficient
to go out of business, because
then they'll give up the
cost they've invested.
So if you're a doctor, and
you've spent all this money on
med school, and you're not
making money as a doctor in
the first couple of years.
If you quit and go do something
else, you've just
given up all the investment
you made in med school.
So if there's any prospect that
eventually you'll make
money, you might want to hang
on and keep being a doctor.
So that's the difference between
a fixed cost and a
sunk cost.
So I'm going to come back to
that, but it's important to
remember that distinction when
we talk about competition.
So let me stop there, and
we'll come back on
Wednesday, I guess.
Have a good three-day weekend.
We'll come back on Wednesday
and we'll talk about
competition.
