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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.