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PROFESSOR: All right.
Let's get started.
Today we are going to talk
about competition.
Just, once again, I want you
guys to try to have in mind a
flowchart of where the
course is all going.
Where does this fit in?
We talked last time about how
firms decide on the cost
minimizing way to produce a
given level of output through
the tangency of the isoquant and
the isocost. And we talked
about how if we were consumers,
we'd be done then.
Consumers just find the tangency
and indifference
curve in the budget constraint,
and they're done.
But firms aren't done.
Because the level of output,
unlike the budget which is
given to you as a consumer,
the level of output is not
given to the firm.
They get to choose it.
So with firms, we have to
go one step further.
We actually have to choose
the level of
output that we produce.
We don't just choose the way to
produce it but actually how
much to produce.
So, for consumers, it would
be sort of like consumers
choosing what their budget
constraint is.
And the way we do that is we
bring in-- since we now have a
third variable, which is
how much to produce--
we have to bring in
a third equation.
And that equation we bring in
is essentially the market.
Essentially, we say the market
imposes conditions on the firm
which helps them figure out
how much to produce.
So we take all the stuff
we did before.
We then take that and put
that in a market.
And the market interacts
with the firm.
And from that market
setting, the firm
derives how much to produce.
So, basically, the level of
production for a given firm,
little q, will be derived from
how firms behave in different
market settings.
And the market setting we're
going to start with today is
the classic starting point for
economics which is the market
setting of perfect
competition.
We're going to start talking
about perfectly competitive
markets, a benchmark of
perfect competition.
With perfect competition, this
is basically a case where many
firms are selling goods
to many consumers.
We're then going to, in the next
few lectures, talk about
more realistic alternatives like
monopoly which is not a
game but rather a market
structure.
It is basically a case
where one firm
sells to many consumers.
Or oligopoly, my favorite word
in all of economics, not
because I like the
topic so much, I
think it's a cool word.
This is when several firms sell
to a large market, which
is probably the most realistic
setting of all.
And we're going to come
to talk about those.
But, today, we're going to start
with our benchmark of
perfect competition.
Now, what is perfect
competition?
I can give you a technical
definition.
Technically, perfect competition
exists whenever
firms are price takers on both
the output and input markets.
They're price takers on both the
output and input markets.
So perfectly competitive
firms are price takers.
That is no action that they
take can affect either the
price at which they sell their
goods or the price that they
pay for their inputs.
They're price takers.
They're not price makers.
No action they take affects
either the price at which they
sell their good.
No action the individual firm
takes affects either the price
at which they sell their goods
or the price they pay for
their inputs.
Well, when will this be true?
Go back to lecture one.
Technically this would be true
if a firm faced perfectly
elastic demand for their
goods, and if they had
perfectly elastic supply
of inputs.
Under those conditions, firms
will be perfectly competitive
if they face perfectly elastic
demand for their goods and
perfectly elastic supply
of inputs.
OK.
So let's focus on the first of
those which is perfectly
elastic demand.
Let's take a look
at Figure 10-1.
These should be little
q's by the way.
This isn't a market.
This is a firm.
These should be little q's.
So, basically, what you have
here is that you have a firm
facing a perfectly
elastic demand.
What that means is the firm's
quantity is pegged by their
supply curve.
Or, in other words, the point is
the firm cannot change the
price one iota from that level
P. So, in other words, if this
is a supply shift, say the price
of the firm's inputs go
up, the firm doesn't
get to charge any
more for their goods.
They just sell fewer goods.
So the supply shift from S1 to
S2, the firm is going to be--
it should be little
q1 to little q2.
They're going to reduce the
quantity they sell, but they
cannot change the price.
They face perfectly
elastic demand.
So when does this make sense as
a description of the world?
Well, it makes sense as a
description of the world under
four conditions.
So there's four conditions
under which perfect
competition will exist.
The first condition is
identical products.
In a perfectly competitive
market, when the firms in that
market sell identical products,
now let's be clear.
They don't have to literally
be identical.
They have to be perceived by
consumers as identical.
So when I say identical
products, they don't have to
literally be identical.
But consumers have to consider
them identical for purposes of
their demand across firms.
So firms have to sell identical
products for there
to be perfect competition.
Because if products aren't
identical, then firms will be
able to charge different prices
from each other because
they have something
different to sell.
So firms need to be identical.
Second of all, consumers have
to have full information on
all prices.
Well, let me write down the next
two conditions, because
they're related.
And the third is low transaction
or shopping costs.
OK, these two are critical.
Because the way perfect
competition is going to work,
its consumers are going to
shop across firms selling
identical goods.
And they're going to buy
from the cheapest one.
And if there's any failure of
either of these, the consumers
might not know if you're the
cheapest. And, therefore, you
might be able to charge extra.
So perfectly elastic demand,
once again we're getting to
the microfoundation of something
we discussed in the
second lecture.
We discussed perfectly
elastic demand.
Now we're talking about
where that comes from.
What conditions do you need?
Perfectly elastic demand is
going to require that
consumers know all the prices
and can cautiously shop across
all the options.
Otherwise, firms might have
some opportunity to charge
different prices.
And finally-- and we'll come
back to why this is
important--
there needs to be free entry and
exit of firms. This one I
can't really give you
intuition for yet.
Just take my word for it.
We'll come back to why
that's important.
So, basically, what you want for
an example of a perfectly
competitive market, you want a
market where producers are
selling homogeneous goods in
an easily informed, easily
shocked arena.
So I think the best example of a
perfectly competitive market
is those guys selling like
shlocky touristy things around
Port Authority in New York or in
any large open air market.
Basically, in that area, these
guys all sell the same crap.
You can go from one to
one quite easily.
And it's quite easy to find
out what the prices are.
That's not perfectly easy, but
it's quite easy to find out
what the prices are.
That is a condition for a
perfectly competitive market.
It's easy to shop, because
they're all in the same area.
Prices are pretty easy to
observe, and the products are
all, basically, identical.
There are only so many
little Statues of
Liberty you can buy.
So, basically, that's an
example of a perfectly
competitive market.
Now, in reality, no perfectly
competitive market exists.
There's never been a perfectly
competitive market.
But this is sort of as
close as we can get.
Questions about that?
Now that provides a good moment
to pause and talk about
Peter Diamond who just won the
Nobel Prize in Economics.
This is my MIT economics Peter
Diamond, MIT Econ Peter
Diamond shirt.
Peter Diamond just won the
Nobel Prize in Economics.
Peter Diamond is the greatest
economic theorist of his
generation, sort of the heir
of the Paul Samuelson, Bob
Solow generation that founded
this economics department and
made it great.
Peter Diamond was sort of the
next generation that led this
economics department forward
and kept it great.
And Peter has made contributions
throughout
economic theory.
He should have won the
Nobel 10 times over.
What they finally gave it to
him on Monday for was for
search theory.
And search theory is essentially
about what happens
when markets don't work like
these vendors around Port
Authority in New York, when
markets aren't perfectly
competitive.
Where, basically, you have
markets where there is some
mismatch and some search costs
that sellers have to pay to
find the right buyers, and
buyers have to pay to find the
right sellers.
So the best example here, and
the example of which they
really gave him the Nobel Prize,
was the labor market.
It was about search costs
in the labor market.
And what Peter Diamond and his
fellow co-winners talked about
was about how in the
labor market,
your firms have vacancies.
They have jobs they
want to fill.
Individuals have labor supply.
They want to provide themselves
to these jobs.
And so there's unemployment.
There's people out of jobs
looking for jobs.
But there's vacancies.
There's jobs that are empty.
And both exist at
the same time.
And how can that be?
In a perfectly competitive
market, that couldn't be.
You couldn't have both jobs
looking for people and people
looking for jobs.
But what Diamond wrote down,
and these other theorists
developed in their models, is
basically how you get these
frictions in the labor market.
Where since these jobs have
specific characteristics
employers are looking for,
you can't quite match the
vacancies to the unemployed
workers.
There's a sorting process where
some are easy to match.
You can take the high school
dropout and put him in
McDonald's.
That's easy.
But the job which requires some
computer skills, you have
to find the right guy
to take that.
And, basically, it's these
frictions that lead to what we
call the natural rate of
unemployment in our economy,
which is the notion that no
economy would ever get down to
0 unemployment.
That's impossible.
And the reason is because there
will always be some
frictions and some mismatch.
There will always be some
inability of people to find
the right people to fill
their vacancies.
Now, we don't know what
the natural rate is.
When I was in grad school, we
learned that the rate was 7%.
In the 1990s, the natural rate
seemed to fall to about 4%.
That is we got to about a
4% unemployment rate.
Now who the heck knows what the
natural rate is anymore.
And a big debate right now among
economists in macro is
how much of our 9.6% is an
increase in the natural rate,
which is something the
government can't really fix
very well, versus short-term
demand reductions, which the
government could fix by pumping
more resources into
the economy.
And all that is informed,
theoretically, by the work
that Peter Diamond did.
Now, I hope what I just
described sounded pretty
obvious to you.
And that's good, because that's
what great theory does.
Great theory ex-post
sounds obvious.
It's just ex-ante, before Peter
Diamond did this, people
always said, well,
we have these
perfectly competitive markets.
This is how they should
function.
And he's the guy who really
taught us how real markets
should function like this.
And that's why he gets
to go to Stockholm.
So that's very exciting for our
economics department, very
exciting for the profession.
And it's just a great moment,
really, in taking economics--
I saw it described very
well in one article--
these last few Nobel Prizes
are the beginning of
recognizing that economics is
not what we teach in this
course anymore.
You need what we teach in this
course to go on in economics.
But probably the first couple
dozen Nobel Prizes were for
about what we teach
in this course.
And the last few have been about
what you teach in the
subsequent courses.
And that's a real evolution of
Freakonomics, to understand
that we need to mature as a
science and move beyond the
basics that you learn in
14.01 and move beyond
to these other things.
So we're giving you
the basics here.
But the excitement happens
elsewhere.
So it's a very exciting time for
our department and for the
profession as a whole.
Now with that little diatribe
aside, let's go back.
So we have these.
So now, having said all
that, forget it.
Forget Peter Diamond existed.
We're now going back to
perfect competition.
And, once again, as I said
in the first lecture--
and Peter would be the first guy
to say it, this is how he
taught me to do economic
theory-- you've got to make
simplifying assumptions if
you want to get anywhere.
So we're going to make a
simplifying assumption of
perfect competition.
We'll weaken that
as we go along.
But, for now, imagine it's
perfect competition.
And we have the situation of
perfectly competitive firms.
Now a very important distinction
to draw-- and
that's why it's important to
remember that these are little
q's not big Q's--
is the distinction between firm
demand and market demand,
firm versus market.
And this is something
which is confusing.
It confuses me at times.
I may even get it
wrong at times.
I'll need you to correct me.
Even if a given firm faces
perfectly elastic demand, it
doesn't necessarily mean
that market demand
is perfectly elastic.
That is the overall demand for
little, fake Statues of
Liberty around Port Authority
in New York is
not perfectly elastic.
As the price goes up, fewer
people will buy them.
As the prices goes down, more
people will buy them.
But for any given vendor
selling them, it
is perfectly elastic.
Because there's always
someplace next
door you can go.
So it's very important to
distinguish between the demand
facing the firm being perfectly
elastic and the
demand facing the market not
being perfectly elastic.
And the way to think about this
is to think about the
concept of residual demand.
We have a demand function
for market D of p.
We have a demand function for a
market which is that as the
price goes up demand
goes down.
Now the demand function for a
given firm, we'll call the
residual demand D super r
of p, is equal to what?
It's equal to the demand for
the market minus the supply
that all other firms in the
market provide, S super 0 of
p, the supply that all other
firms in the market provide.
So the demand for my
product as a firm
is my residual demand.
It's the market demand minus
what other firms supply.
Well, if you differentiate this
with respect to price,
you'll see that dDr/dp equals
dD/dp minus dS0/dp.
This first one is the
market demand curve.
We know that's a negative
number, because demand curves
slope down.
We're not assuming
Giffen goods.
We know that's a negative
number.
But this is a positive number.
Supply curves slope up.
The amount that other firms in
the market will supply as the
prices goes up is positive.
Supply curves slope up.
So this is a negative number.
But this is a positive number
which means, by definition,
this is a very negative
number.
The firm's residual demand
responds more to price than
the market's demand does.
Because the firm's residual
demand is after all the supply
of other firms.
So we can rewrite this in
terms of elasticities.
So let's assume, for a second,
that all firms are identical.
Assume, for one second, that
we're in a market where all
firms are identical, that little
q equals big Q over N.
Assume that all firms
are identical.
And so, therefore, the amount
produced by other firms, Q
super 0 is (n - 1) x q.
So, basically, the amount that's
produced by other firms
is (n - 1) x q.
So the last is demand facing a
given firm, epsilon sub i is n
times the elasticity of demand
for the entire market minus (n
- 1) times the elasticity of
supply for the market.
So, for example, let's say
you've got a market with 100
firms in it.
It's a big market but not
outrageously big.
We have plenty of markets with
more firms than that.
And let's say that the
elasticity of demand for this
market equals minus 1.
So it's in between elastic and
inelastic, not a crazy number.
And the elasticity
of supply is 1.
Let's just say that's
the example.
Then what you get is that for a
given firm, if you used this
formula, the elasticity of
demand facing a given
firm is minus 199.
It's a huge negative number.
So even though the market demand
is modestly elastic,
minus 1-- it's elastic
but not crazy--
the demand facing the given
firm is crazy elastic.
So, basically, the point is that
even if a market does not
have super elastic demand, a
given firm can face very
elastic demand.
And that's what can lead
to perfect competition.
It's very important to
keep those distinct.
When we talk about demand, think
about demand at the firm
level versus demand at
the market level.
Demand at the market level,
that's about substitutability
with other goods and the things
we've talked about
deriving demand curves.
When we derive demand
curves, we're not
deriving firm demand curves.
We're deriving market
demand curves.
And so the demand curve was a
function of elasticities and
substitutability across goods.
The firm demand curve is a
function of all that but also
how many firms are
in the market.
If there are a lot of firms in
the market, it's going to be
very elastic in a perfectly
competitive market.
Questions about that?
It's an important distinction
to keep in mind.
Now, with that as background,
let's now come to profit
maximization which is what
this is all about.
Remember I said we assume that
every decision consumers make
is driven by utility
maximization.
Every decision producers make
is driven by profit
maximization.
So let's talk about profit
maximization in the short run.
How do firms maximize profits
in the short run?
Now, the first question
we have to
ask is what is profits?
Well, that seems pretty
straightforward.
I defined those already.
I said, the profits were equal
to revenue minus costs.
Profits are equal to revenue
minus costs.
Well, the trick is that there's
two different types of
people who measure costs.
Revenue is revenue.
It's just, basically,
the money you make.
And anybody can measure that.
But there's two different
ways of measuring costs.
There's accounting costs, and
there's economic costs.
And these are different
concepts.
Accounting costs are cash flow
costs what you actually pay.
So your accounting costs are
what you actually pay.
So if you buy something for
x dollars, that's your
accounting costs.
The economic costs are about
opportunity costs, which is
not about what you lay out in
cash, but what you could have
done with that cash.
It's not just about what you
lay out, but what you could
have done with that cash.
So to give you an
example, let's
just do a simple example.
Imagine that you graduate.
You're going to graduate.
I don't mean that.
You're going to graduate.
Imagine that after you graduate,
you decide you're
going to start a website design
firm on the side.
You're going to do this while
you decide what to do with the
rest your life.
You're trying to figure
out where to go to
grad school or whatever.
You'll start a website
design firm.
That seems easy.
Basically, how does the website
design firm work?
Basically, you work full-time,
and you hire some slave
programmer who works for you.
He does all of the grunt work.
And let's say that you have
to pay him $40,000 a year.
So it's going to be you working
full-time plus some
slave programmer you're going
to pay $40,000 a year.
And let's say that you have
a computer that's like six
months old, a year old.
It's still in pretty
good shape.
It's not brand new, but it's
still in pretty good shape.
And you just let the slave
programmer use that.
So you don't have to
buy a new one.
So you've got the programmer,
you're paying him $40,000.
You're letting him use
your computer.
You buy some new computer
you're working on.
So you do your work,
and he does work.
You put it together.
At the end of the year, you
tally up all the receipts
you've had from your
website design,
and you've made $60,000.
So you sit back and say, well,
that's pretty good.
I put in $40,000.
I paid $40,000.
I brought home $60,000.
That's $20,000 in profit.
That's not a bad profit.
If we think about profit
margins, we'll often think
about profit relative
to revenue.
Well that's $20,000 of profit
on $60,000 of revenue.
It's a 33% profit margin.
Most companies would
kill for that.
So you say, that's not bad.
I made a 33% profit margin.
But what opportunity costs did
this calculation miss?
So if you were an accountant,
you'd stop there.
That's why accountants don't
make as much as economists.
Because we're better.
If you're an accountant,
you'd stop there.
But if you were an economist,
what do you recognize?
What did this calculation
miss?
What opportunity costs were
involved in running this firm
that the cash flow calculation
didn't capture?
Yeah?
AUDIENCE: If you plot your
grunt worker and your
computer, you might have been
able to do more work, because
the computer might be
more efficient.
PROFESSOR: Yeah.
OK.
That's sort of a different
issue.
That's sort of about the fact
that you might not have
produced as efficiently
as possible.
I'm not asking that question.
I'm asking, given the numbers I
gave you, why did I misstate
your economic profit?
Yeah, in the back.
AUDIENCE: You could have
gotten another
job that paid more.
PROFESSOR: I could have gotten
another job that paid more.
Here's another thing about it.
I just spent an entire freaking
year, and I made $20,000.
You're hoping you do better than
that with an MIT degree.
At least your parents are hoping
you do better than that
with an MIT degree.
So, basically, the first source
of opportunity cost
that this has missed is the
value of your time.
That doesn't show up as an
accounting cost. But it's a
real opportunity cost,
because you could
have had another job.
So let's say you could
have gone out and
made $60,000 a year.
You could have easily
found a job making
$60,000 as an MIT graduate.
Well, then that's a cost of
running this website.
By spending the year setting
this up, you forgo--
I don't know what the past
tense of forgo is--
forgoed?
$60,000 in income you
could've earned.
You've forgone $60,000 you
could have earned.
That's a real cost. It's not an
accounting cost. It didn't
show up on anybody's books.
But it's an opportunity
cost. What else?
Yeah.
AUDIENCE: Also the $40,000 that
you gave the program, you
could have invested
it somewhere else.
And it could be growing.
PROFESSOR: You could have
invested the $40,000.
You gave him the $40,000.
You paid it.
It's gone.
If you put it in the bank, you
could've earned interest on
that money.
That's an opportunity cost. And
we'll come back and talk
about capital markets
and interest later.
But that's opportunity
cost. What else?
There's one more.
AUDIENCE: You could have
sold the computer.
PROFESSOR: I could have
sold the computer.
I gave it to him, and
he used it for free.
But if I could have sold that
for $1,000, that's an
opportunity cost as well.
So, in fact, if I could have
worked for $60,000.
On the $40,000, I could have
made $2,000 of interest. And I
could have sold the computer
for $1,000.
Then, actually, my opportunity
costs were $63,000 plus the
$40,000 I paid the guy.
So, actually, the entire cost of
the operation was $103,000.
So I actually lost more than
$40,000 running my little
website business.
So opportunity costs represent
the fact that you could have
done other things with
your resources.
It's not just the fact
that your cash flow
said positive $20,000.
Your economic flow said
minus $43,000.
Because while you're plus
$20,000, you were minus
$60,000 that you could
have earned.
Now you're down to
minus $40,000.
You're minus $2,000 that you
could have earned in interest
on the money you paid
the programmer.
Now you're down to
minus $42,000.
And you're down another minus
$1,000 you could have made by
selling that computer.
So you're at minus $43,000.
So you actually lost money.
So when we talk about profit,
we want to think about
economic profit, not
accounting profit.
Now, I'm not going to make that
distinction much now.
But I want you to keep that in
mind as you go out and think
about starting your business or
think about whether firms
are profitable, remember we use
an economic concept which
accounts for opportunity cost,
not just an accounting concept
which follows the dollars.
Question about that?
OK.
Now, armed with this, we now
say, OK, how does a firm
maximize profits?
Well, that's easy.
We say that profits is a
function of quantity produced.
Revenues is a function of
quantity produced minus cost
as a function of quantity
produced.
Remember, what was our goal when
we laid out the start of
this lecture?
It was to figure out what
little q a firm chooses.
Well, what little q a firm
chooses is dictated by
maximizing this equation.
So a firm will choose little q
such that dR/dq equals dC/dq.
That's the profit maximizing
equation.
A firm will choose its quantity
such that dR/dq
equals dC/dq or, to put it in
economic terms, where marginal
revenue equals marginal costs.
The firm will choose to produce
a quantity q where its
marginal revenue, which is the
revenue made from selling the
next unit, equals it's marginal
cost, which is the
cost incurred by making
the next unit.
Well, in a competitive market,
we know what dR/dq is.
Because remember in a
competitive market, dR/dq is
given to the firm
by the market.
In a competitive market, dR/dq,
or marginal revenue,
equals the price.
The price is given
to the firm.
It comes from God in the
competitive market.
We'll talk later about
where it comes from.
But, for now, let's
consider it God.
They're price takers.
They just get some price
handed to them.
So in a competitive market, we
know what marginal revenue is,
it is price.
So what this says is that in a
competitive market, the profit
maximizing equation is price
equals marginal cost. Memorize
it, put it under your pillow.
In a competitive market, price
equals marginal cost is the
profit maximizing condition.
You will produce until the
marginal cost of producing the
next unit is equal to the price
you can sell that unit
for in the market.
So, to see that further, let's
look at an example.
Let's go to the next figure,
Figure 10-2a.
For the next few examples,
I'm going to use a
particular cost function.
The cost function I'm going to
use to make this all concrete
is C equals 10 plus
0.5q squared.
That's the cost function
I'm going to use.
So armed with that cost
function, let's say the price
in the market is 6.
Let's say the price
in the market 6.
I just pulled that
out of my hat.
It's a market for whatever.
We're just doing an example.
Now, what we have on this graph,
we have a cost curve
and a revenue curve.
The cost curve literally
graphs that function.
So, in other words, if you
produce two units, then your
cost is 10 plus half
of 2 squared or 12.
If you produce 2 units, your
costs are 12, and so on.
You've got this cost curve.
You've also got a
revenue curve.
Well, the revenue curve is just
6 times the number of
units produced.
Because the price
per unit is 6.
So it's just a straight line
with a slope of 6.
So each unit you produce,
you make 6.
Now, what you'll see here is
that for this cost curve,
what's marginal cost?
Well, if we differentiate this,
we see that marginal
cost equals q.
I made this an easy example.
If you differentiate that,
you'll see that
marginal cost equals q.
That is just differentiate
this cost equation.
Marginal cost equals q.
So what that says is that the
profit maximizing point is
going to be to set marginal
cost equal to price.
So that says set
q equal with 6.
And you're done.
That's how much the firm
should produce.
The firm should produce six
units, because it's marginal
cost function is q.
It's a linear function.
The price is six.
That's a horizontal line.
So they only intersect in one
point where quantity equals 6.
Now, what you notice in this
graph is that this happens to
be the point where the gap
between the revenue curve and
the cost curve is largest. These
are not marginal curves.
This is revenue and cost. But
notice that at 6 that's
exactly where the revenue curve
and the cost curve have
the largest gap between them.
I think a more intuitive way
to see this is to flip to
Figure 10-2b.
This shows the marginal profit
that you make on
every unit you sell.
So, in other words, if you sell
fewer than 2 units, you
lose money.
Why?
Because if you sell 1 unit, your
costs are 10 plus 10.5.
If you sell 1 unit, your
costs are 10.5.
Your revenues are 6.
You lose money.
You lose 4.5.
If you sell 2 units,
you make 0.
Your costs are 12, your
revenues are 12.
You make 0.
If you sell 3 units, your
costs are 14.5, 10
plus half of 9.
Your revenues are 18.
So you make money.
So each unit, you can calculate
how much you're
making on that next unit.
On the 3rd unit,
you made money.
4th unit, you make
even more money.
5th unit, even more.
6th unit, you make the most
money you can make.
In the 6th unit, your costs
are 10 plus half of
36, or 18, so 28.
Your costs are 28.
Your revenues are 36.
So you make a profit of 8.
You make a profit of
8 on that 6th unit.
Think of yourself as
climbing this hill.
In economics, optimization is
a hill climbing exercise.
Think of yourself as climbing
up this hill and asking
yourself, should I make
the next unit?
Does the hill keep going up?
Yes, it keeps going up.
Make that next unit.
Then you get to the top.
And now you say, well, should
I make the 7th unit?
Well if I make a 7th unit,
my costs are 10 plus
half of 49, so 34.5.
My revenues are 42.
So my profits are only 7.5.
I make less profit
on that 7th unit.
So I shouldn't make it.
Now, you might say,
wait a second.
Why wouldn't you make it?
You still make profits.
Why wouldn't you go ahead and
make all units all the way
down to 10?
You still make profits
on those units.
And the answer is because of
opportunity cost. The answer
is that yes, you make profits.
But given where your marginal
cost curve is, you could do
better by that point going and
producing other goods.
That's why I care about
accounting costs versus
opportunity costs.
Accounting costs says look,
you're going to make money
until you go to 10 units.
But opportunity cost says, no.
At that point, the opportunity
cost has gotten high enough
that you could do
better devoting
your resources elsewhere.
And that's why you want to stop
at the point where you're
at the top of the hill, where
the price equals the marginal
cost.
So what are the profits you make
at the top of this hill?
Well, if you go to the next
diagram, we can see what the
profits you make are.
So this next diagram,
Figure 10-3,
illustrates this example.
So what we have here is an
example with cost curves for
this cost function, once again,
10 plus 0.5q squared.
Average costs is that line
in the middle there.
That's the average costs.
You have an average variable
cost that's a line, that's
linear, an average variable cost
that has a slope of one.
You have an average fixed cost
that's everywhere declining,
because your fixed costs of 10
is everywhere declining.
As you produce more
and more, your
fixed costs are declining.
And, as I said, you have
a marginal cost of q.
So your marginal cost
of 1 unit is 1.
Your marginal cost of 2
units is 2, et cetera.
So this draws out the cost
curves that correspond to that
cost function.
You see them drawn out here.
Now, we also, on this diagram,
have a demand curve.
The demand curve is perfectly
elastic facing this firm.
It's a perfectly competitive
market.
And that perfectly elastic
demand curve is horizontal at
price equals 6.
So what does the firm do?
It chooses to produce where
marginal cost equals price.
When it produces where marginal
cost equals price,
then what profits
does it make?
On each unit, it makes a
difference of the profits
between the price and average
cost. Now it's an important
distinction.
We went over this in lecture
and section.
But let me go through
it again.
Marginal cost is the cost
of the next unit.
Average cost is the average
cost of all the
units you've made.
So if I make 6 units, what
profit do I make?
Well, on that 6th unit, I
make a profit of 1 and
1/8 or 1 and 1/4.
I make profits of 1 and
1/4 on that 6th unit.
But I make those profits
on all 8 units I sell.
So what that means is, in total,
I'm going to make a
profit of 8.
The area of this rectangle
is eight.
Here's the key.
You cannot choose a production
level that produces a bigger
rectangle than this.
So if you produce 7, your
rectangle will be longer.
But the gap between price and
average cost will be smaller.
So your total rectangle
size would fall.
The largest rectangle
is produced at a
production level of 6.
That's the most efficient use of
your resources is when you
produce at a point where
marginal cost equals price.
Because when you produce at
marginal cost equals price,
that causes the maximum gap
between price and average
cost.
Flip back for a second
to the first figure.
Not the first figure,
I'm sorry, 10-2.
This relates back to 10-2.
As I noted, the largest
difference between your
revenue and your cost curve
was that 6 units.
That's where the gap is large
between revenue and cost.
That's where you produce.
Now we flip forward again
to Figure 10-3.
You see that corresponds to the
point of the largest gap
between price and average cost,
I'm sorry, the largest
of the points on the marginal
cost curve between price and
average cost. So if you produce
on the marginal cost
curve, if you produce 7 units,
then you're going to have a
smaller gap between price and
average cost. And, therefore,
even though you produced 1
more unit and are making
profit on it, your total
profits will fall.
The key point is that yes,
climbing back down that hill I
still make money.
But I make less and
less money.
And that, as a result, that
rectangle is being reduced as
I climb down that hill.
That rectangle is maximized
at the top of that hill.
That's the point at which
I make the most money.
So that's why we say profit
maximization occurs at the
point where price equals
marginal cost. Because that is
the point of greatest gap
between revenues and costs.
Where price equals marginal cost
is one of the greatest
gaps between revenues
and costs.
That's the profit maximizing
point where that rectangle is
largest. And you can demonstrate
for yourself, and
you should, that at any other
production level, that
rectangle will be smaller.
Questions about that?
Yeah.
AUDIENCE: What do you
do if you have
a linear cost function.
So that means marginal
cost is a constant.
Then how do you determine
the line?
PROFESSOR: You don't.
It's an indeterminacy.
That's right.
I'll try to avoid giving
you problems like that.
Basically you get a
corner solution.
In a perfectly competitive
market, you'd get an
indeterminate solution.
In a nonperfectly competitive
market, you will have a
determinant solution.
But in a perfectly competitive
market with a linear marginal
cost, you'd have an
indeterminate solution.
Either you produce
0 or infinity.
So you'd have an indeterminate
solution.
Now, just a further drill this
in, imagine, for a second,
there was a cost shock
to the firm.
Imagine there was a cost
shock to the firm.
Imagine that there's a tax on
the firm where the firm has to
pay a tax of an amount t.
Let's say t is $1.
The firm has to pay a tax of $1
on every unit they produce.
Well, what is their
new cost curve?
Somebody tell me what the
new cost curve is.
If you have a tax of $1 on
every unit you produce,
someone tell me the equation
for the cost curve.
I didn't write it down
here, did I?
No.
OK, what's the equation
for the cost curve.
Yeah.
AUDIENCE: Just add plus
tq to the top thing.
PROFESSOR: Exactly C equals 10
plus 0.5q squared plus tq.
Because for every unit you
produce q you pay a tax t.
And since t is $1, it would
just be plus q.
If t is $1, it would
just be plus q.
So the cost function
has now shifted.
So what we see is that it has
shifted average cost and
marginal cost both upwards.
Average cost has shifted
upwards by that amount.
And average cost has
shifted upwards.
And marginal cost has shifted
upwards by precisely $1.
It's just a linear shift of
marginal cost. Because
marginal cost is now q plus 1.
If you differentiate this with
respect to q assuming t is 1--
t is now $1--
if you differentiate this with
respect to q, marginal
cost is q plus 1.
So your marginal cost curve has
shifted up by $1 or by t,
in this case, in the
more general case.
Well, what does that do to the
first production decision.
Well, now it doesn't change
their maximization formula.
They still want to set marginal
cost equal to price.
So now they say, set q plus
1 equal to price.
Well, the price is 6.
So it says set q equal to 5.
Now the profit maximizing
level is 5 units.
The profit maximizing
level is 5 units.
What this is saying is because
the tax increases your
marginal cost, you are
now producing less.
And what we can see now, if we
flip to Figure 10-4, we can
see what that's done
to your profits.
Your profits have now fallen to
the dotted rectangle, the
much smaller dotted rectangle.
Your profits used to be
that entire slashed
rectangle plus the dots.
Now your profits are just
where the price exceeds
average cost which is just that
smaller dotted rectangle.
Your profits have fallen
dramatically.
So by imposing a tax on this
firm, we've dramatically
reduced their profits.
Now, this is the economics
behind why taxes can lower
production.
Now, you might say,
wait a second.
In reality, if we tax a
firm, the don't have
to lower their profits.
They just pass it on and charge
consumers higher prices
but not in a competitive
market.
In a competitive market,
they can't do that.
If you tax a firm in a
competitive market, it comes
out of their profits.
Because they face a perfectly
elastic demand, so they can't
raise the price.
All they can do is just say,
well, the price is the same.
My marginal cost has gone up.
I'm going to produce less, and
I'm going to make less profit.
And that's life.
So a tax in a market like this
is just going to lower the
firm's profits, and it's going
to lower their level of
production from 6 to 5.
In noncompetitive markets,
different things can happen.
We'll talk about that.
But in a competitive market,
this is what
happens with the tax.
You basically set the new
marginal cost equal to price,
and you get that they produce
5 units instead of 6 at a
lower profit level.
Yeah?
AUDIENCE: Would that
be a good cause for
entering the market--
PROFESSOR: You're right.
That's an excellent point that
I should have pointed out.
What do I mean by short run?
What I mean by short run is
remember, labor is variable.
Capital is fixed.
What do I mean in
this context?
Think about the short run as
being the period over time
over which firms cannot
enter and exit.
When we talk about competitive
markets in the short run, we
talked about short run
being the time in
which capital is fixed.
Now we're going to add
another condition.
We're going to say the short run
is the period of time in
which there's no firm
entry or exit.
That's the short run.
We'll come back and talk about
what entry and exit does.
And that's going to have
some funky effects.
We'll talk about
that next time.
But what we mean by short
run here is no
firm entry and exit.
Whichever firms are in the
market at the beginning of the
short run people are in the
market at the end of the short
run period.
Yeah.
AUDIENCE: But in your
conditions, you had like free
and fluid entry and
exit of firms.
PROFESSOR: Right, exactly.
And that's why I said, don't
pay attention to that yet.
In some sense, those are the
conditions of perfect
competition.
I didn't say if that was
short run or long run.
Those are the full long
run set of conditions.
That's why I said we're going
to ignore four for now and
just focus on the first three.
In the short run, only the
first three are relevant.
Because in the short run there's
no firm entry or exit.
In the long run, which we'll
talk about next time, that
fourth one will be relevant.
Good question.
That's a good point.
Thank you for pointing
that out.
Other questions or comments?
One other thing I want to cover
before we stop which
relates to the long run, is that
in the long run, this is
sort of the transition,
the bridge to talking
about the long run.
We also have to decide,
ultimately, whether or not we
want to shut the firm down.
So, in other words, we want to
set price equal to marginal
cost. That's one condition.
But, actually, short run profit
maximization has a
second condition.
Short run profit maximization
has two conditions.
The first is to set price equal
to marginal cost. The
second condition of short run
profit maximization is to
check whether the firm
wants to shut down.
Why would a firm want
to shut down?
It might want to shut down if
it actually loses money by
continuing to produce.
And that's because firms may
lose money but not shut down.
Firms may lose money
but not shut down.
Or firms may lose so much
money they shut down.
And we need to consider that.
Let's get rid of the tax.
Let's go back to the marginal
cost with the tax.
Imagine the price in this
market suddenly
fell from 6 to 3.
The price of the market is
now $3 per unit you sell.
Well what would the
firm's profits be?
Well, if the price fell to 3,
the firm would choose to
produce 3 units.
You would still have this
condition, marginal cost
equals price.
Price is 3, and marginal
cost is q.
So q is 3.
You still produce 3 units.
If you produce 3 units,
its costs are 10 plus
4.5 which is 14.5.
At a price of 3, it makes 9.
So its profits are
negative 5.5.
It would lose money from
this production.
Remember marginal cost
equals price.
That doesn't vary with what
the price is or anything.
This is a maximizing
condition.
If a price changed, it's not
like you change which equation
you follow.
You always follow
this equation.
The efficient production level
is always marginal cost equals
price regardless of
what the price is.
So if the price is 3, the
efficient thing to do would be
to produce 3 units
and lose money.
Now, you might say, well,
then that's stupid.
If that goes negative, wouldn't
they just shut down?
And the answer, is in
the short run, no.
And the reason you wouldn't shut
down in the short run is
what I talked about last time
which is about the notion of
sunk costs.
In the short run, the fixed
costs that you paid
to produce are sunk.
They're unchangeable
in the short run.
In the long run, they're
changeable.
You can just leave.
But in the short run, you've
invested fixed costs of 10 in
being in this market.
You've paid a fixed cost of 10
to produce in this market.
Given you're in this market, and
you've paid 10 to produce,
you will not exit unless
you lose more than $10.
You will not shut down unless
you lose more than $10.
You will not shut down unless
you're losing so much money
that you can't cover
your fixed costs.
Because you've paid those fixed
cost. In the short run,
they're sunk.
So unless you're actually losing
more than your fixed
costs, you will not shut
down your firm.
OK.
This is actually pretty
confusing, and
we're out of time.
So what I'm going to do is we'll
pick it up on Monday
exactly at this point.
And I'll go through some more
of the intuition for this.
And that will be our segue for
talking long run profit
maximization which we'll
talk about on Monday.
