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- [Alex] We learned last time
that a firm

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in a competitive market
doesn't have much control

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over it's price.

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It must accept the market price.

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So its decision about profit
maximization turns into a decision

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about what quantity to choose,

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and that's what we're going
to be focusing on now.

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So what is profit?

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Profit is total revenue
minus total cost.

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Total revenue is just price
times the quantity sold.

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Total cost has two parts.

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First are the fixed costs.

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These are costs
that do not vary with output.

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So, for example, suppose you
are the owner

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of this small oil well
and you have to pay rent

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for the land
on which the oil well sits.

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Those rental costs --
you have to pay them

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regardless of how much
the oil well is producing.

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Every month you have to pay
some rental cost

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whether you're producing
one barrel of oil per month,

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10 barrels of oil per month,
11 barrels of oil per month.

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It doesn't matter.

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You still have to pay
the same rental cost.

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Indeed, even if you don't produce
any oil that month,

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if your oil well breaks down,
you still have to pay

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those rental costs.

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So the rental costs
are fixed costs.

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They don't vary
with the quantity produced.

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By the way, notice
that even if you owned the land,

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if you could have rented it
to someone else,

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then that would be
an opportunity cost.

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So your calculation of profit
should also include

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opportunity costs.

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That's what makes the economic
calculation of profit, by the way,

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differ from the accounting
definition of profit.

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The economic notion of profit
includes opportunity costs.

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Okay, what else?

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Well, variable costs --
these are the cost

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that do vary with output.

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So for example, the electricity cost
for pumping oil --

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the more oil you pump,
the faster you get your rig to go,

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the more electricity
you're going to use up.

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If you run it 24 hours a day,
you're going to use

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more electricity
than if you only run the pump

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12 hours a day.

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Transportation cost --
you got to go and get the oil,

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truck it out of there,
move it and so forth.

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So these costs are all costs
which vary with output,

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which typically will increase
the more output that you produce.

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Those are your variable costs.

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So just to summarize on cost,
total cost is equal

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to your fixed costs
plus your variable costs

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and these depend upon output.

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Okay, so how do we maximize profit?

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Well, we're not going
to use calculus in this class,

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but for those of you
who do know calculus,

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I want to do a quick aside --
show you actually how useful

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calculus is and show you
an easy way

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of answering this problem.

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So we know the profit
is total revenue minus total cost

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and both of these are functions
of the quantity produced.

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Now in calculus
how do we maximize a function?

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Think back to your calculus class.

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You take the derivative
of that function

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and you set it equal to zero.

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So in this case,
we want to take the derivative

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of profit with respect
to quantity and set that

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equal to zero.

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So derivative of profit 
with respect to quantity --

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that's just the derivative
of total revenue

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with respect to quantity
minus the derivative of total cost

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with respect to quantity.

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Now in economics,
we have special names

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for these two derivatives.

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The derivative of total revenue
with respect to quantity

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is simply called marginal revenue.

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And the derivative of total cost
with respect to quantity

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is called marginal cost.

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So we want to find the quantity
such that marginal revenue

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minus marginal cost is zero,
or in other words,

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we want to find the quantity
such that marginal revenue

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is equal to marginal cost.

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In other words, the quantity,
which maximizes profit,

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is the one where marginal revenue 
is equal to marginal cost.

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Now I'm about to give you
a more intuitive explanation,

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especially for those of you
who don't get no calculus,

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but for those of you who do,
this is just exactly

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what you were to do in calculus --
you take the derivative,

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set it equal to zero.

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Okay let's get to more intuition.

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When the firm produces
an additional unit of output,

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there are additional revenues
and additional costs.

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Profit maximization
is all about comparing

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these additional
revenues and costs,

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and we have names for these.

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Marginal revenue is the addition
to total revenue

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from selling an additional
unit of output.

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Marginal cost is the addition
to total cost from producing

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an additional unit of output.

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Profits are maximized at the level
of output where marginal revenue

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is equal to marginal cost.

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Now why is this?

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Well, let's suppose
that marginal revenue

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is not equal to marginal cost
and let’s show

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that you can't be profit maximizing
if that's the case.

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For example, if marginal revenue
is bigger than marginal cost,

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you're not profit maximizing --
producing more

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will add to your profit.

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Why? Well, remember marginal
revenue is the addition

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to revenue from producing
another unit.

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Marginal cost
is the addition to cost

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from producing another unit.

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If marginal revenue is bigger
than marginal cost,

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that says producing that unit
adds more to your revenues

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than it does to your costs.

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In other words,
you could increase profit

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by producing more.

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So if marginal revenue
is ever bigger

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than marginal cost,
you want to produce more.

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On the other hand,
suppose marginal revenue

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is less than marginal cost,
or to put it the other way,

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suppose marginal cost is bigger
than marginal revenue.

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Well then, you're not
profit maximizing

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because producing less
will add to your profit.

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Why is this?

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Well, think about marginal cost.

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If you were to produce
one unit less your costs would fall

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by marginal cost,
your revenues would also fall

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by marginal revenue,
but since marginal cost is bigger

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than marginal revenue,
your costs by producing

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one unit less fall by more
than your revenues fall.

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So if your costs are going down
by more than your revenues

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are going down,
you're again increasing profit.

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So if marginal revenue
is ever less than marginal cost,

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you want to produce less --
you'll be increasing your profit

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by producing less.

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So, if marginal revenue
is bigger than marginal cost,

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you're not profit maximizing.

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If marginal revenue is less
than marginal cost

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you're not profit maximizing.

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You can only profit maximize
if marginal revenue

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is equal to marginal cost.

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Now let's put all this in a diagram
beginning with marginal revenue.

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Now for a competitive firm,
this is going to be easy

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because remember,
that a competitive firm

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is small relative
to the total market.

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That means it can double
its production easily

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and not push down the market price.

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As a result,
for a competitive firm,

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marginal revenue is equal
to the market price.

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So for example, suppose the firm
is producing two units of output

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and it decides to produce
a third unit,

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what's the additional revenue
from that third unit?

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It's the price.

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It's the price it gets
for that barrel of oil.

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What about if it produces
a fourth barrel of oil?

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What does it get?
What's the addition to revenue?

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It's the price of a barrel of oil.

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What about the fifth unit?

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Again, the price is the addition
to revenue, is marginal revenue.

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So, marginal revenue
for a competitive firm

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is equal to the price
and it's flat --

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it doesn't change when the firm
changes its output

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because the firm is small
relative to the market.

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Now what about marginal cost?

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Well, a typical shape
of a marginal cost curve

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would be upward sloping like this.

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Again, think about
our stripper oil well.

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We can produce more
from that oil well,

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but there's a limit.

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We can only run it so quickly.

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We have to push it really hard
when we start to produce more.

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So we can easily produce,
you know, three, or four units,

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but in order to produce six,
seven, eight, or nine barrels of oil

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from that oil well,
we're going to have to run it

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really quickly, we're going
to have to put in

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a lot of electricity,
we're going to have to do

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a lot of maintenance and so forth.

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So our costs will tend to increase.

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We can't produce
an unlimited amount of oil

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at the same cost
from this oil well.

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Our costs are going to go up,
are going to rise,

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our additional costs
are going to rise

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the more we want to produce
from that oil well.

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So this is a typical shape
of a marginal cost curve.

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Now, where's profit maximization?

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Well, profit is maximized
where marginal revenue

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is equal to marginal cost.

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In this case,
for a competitive firm,

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marginal revenue is equal to price.

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So profit is maximized
where price is equal

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to marginal cost
or at this point right here.

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Now let's think
about that intuitively.

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On the left hand side,
this is the additional revenues

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from selling a barrel of oil.

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These are the additional costs
from selling a barrel of oil.

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So you want to compare --
revenues bigger than costs,

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therefore sell more.

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Revenues bigger than costs,
therefore sell more.

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Revenues bigger than costs.

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You keep selling more
until you reach this point.

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Do you want to go further? No.

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Here, costs are bigger
than revenues.

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So by selling less,
you can reduce your costs

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by more than you'd reduce
your revenues

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and therefore profit goes up
going this way

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and that's why this point,
where marginal revenue

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is equal to marginal cost,
or price is equal to marginal cost,

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that's the point where profit
is maximized.

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Now remember way back
in the first talk,

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we wanted to explain
a firm’s behavior.

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So let's look how maximizing profit
explains the firm’s behavior.

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Suppose the market price
is $50 per barrel.

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Well, then in order
to maximize profit,

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the firm chooses the quantity --
in this case,

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about eight barrels of oil --
such that marginal revenue

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is equal to marginal cost,
bearing in mind

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that for the competitive firm,
marginal revenue is equal to price.

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So to profit maximize
the firm produces a quantity

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of about eight barrels of oil.

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Now suppose that the market price
goes up to $100.

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Now in order to profit maximize,
the firm increases its production

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along its marginal cost curve
keeping this relationship the same

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so price is still equal
to marginal cost.

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Price has gone up to 100,
but because the firm has expanded

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along its marginal cost curve,
marginal cost has gone up as well.

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So this again is the profit
maximizing point

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when the price is equal to 100.

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When the price is equal to 100,
the profit maximizing quantity

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is just under 10 barrels of oil.

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So profit maximization explains
what the firm does when the price,

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when the market price, changes.

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We now know how to find
the profit maximizing quantity --

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look for the quantity
where marginal revenue

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is equal to marginal cost,
which is the same

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for the competitive firm
where price is equal

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to marginal cost.

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Now we want to ask,
what is the size of the profit?

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This raises a subtle point.

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You can be maximizing profits
and actually have a loss.

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That is, the best that you can do
might be a loss.

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So we want to show on the diagram
how large your profits

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or how large your losses are
when you are maximizing profits.

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In order to do that,
we need to introduce

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another concept
and another curve --

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average cost.

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Average cost is simply
the cost per unit of output.

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That is the total cost
divided by Q,

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the quantity of the output.

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So average cost again --
total cost divided by Q.

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Adding the average cost curve
to our graph

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will let us show profit
on the graph.

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And that's what we want to do,
and that's what we'll do

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in the next talk.

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Thanks.

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- [Narrator] If you want
to test yourself,

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click, "Practice Questions,"

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or if you're ready to move on,
just click, "Next Video."

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♪ [music] ♪