Maximizing Profit under Competition

A company in a competitive environment does not control prices. So the key to maximizing profit is choosing how much to produce. To do that, we need to factor in the costs involved in production. So what exactly are the costs? How do these costs influence how you maximize profit? And, remember, if you want to think like an economist, you must factor in opportunity cost!
In this video, we define profit, including how to calculate total revenue and total cost. We also go over fixed costs, variable costs, marginal revenue, and marginal cost
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- [Alex] We learned last time
that a firm

in a competitive market
doesn't have much control

over it's price.

It must accept the market price.

So its decision about profit
maximization turns into a decision

about what quantity to choose,

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

So what is profit?

Profit is total revenue
minus total cost.

Total revenue is just price
times the quantity sold.

Total cost has two parts.

First are the fixed costs.

These are costs
that do not vary with output.

So, for example, suppose you
are the owner

of this small oil well
and you have to pay rent

for the land
on which the oil well sits.

Those rental costs --
you have to pay them

regardless of how much
the oil well is producing.

Every month you have to pay
some rental cost

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

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

It doesn't matter.

You still have to pay
the same rental cost.

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

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

those rental costs.

So the rental costs
are fixed costs.

They don't vary
with the quantity produced.

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

if you could have rented it
to someone else,

then that would be
an opportunity cost.

So your calculation of profit
should also include

opportunity costs.

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

differ by the accounting
definition of profit.

The economic notion of profit
includes opportunity costs.

Okay, what else?

Well, variable costs --
these are the cost

that do vary with output.

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

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

the more electricity
you're going to use up.

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

more electricity
than if you only run the pump

12 hours a day.

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

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

So these costs are all costs
which vary with output,

which typically will increase
the more output that you produce.

Those are your variable costs.

So just to summarize on cost,
total cost is equal

to your fixed costs
plus your variable costs

and these depend upon output.

Okay, so how do we maximize profit?

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

but for those of you
who do know calculus,

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

calculus is and show you
an easy way

of answering this problem.

So we know the profit
is total revenue minus total cost

and both of these are functions
of the quantity produced.

Now in calculus
how do we maximize a function?

Think back to your calculus class.

You take the derivative
of that function

and you set it equal to zero.

So in this case,
we want to take the derivative

of profit with respect
to quantity and set that

equal to zero.

So derivative of profit
respect to quantity --

that's just the derivative
of total revenue

with respect to quantity
minus the derivative of total cost

with respect to quantity.

Now in economics,
we have special names

for these two derivatives.

The derivative of total revenue
with respect to quantity

is simply called marginal revenue.

And the derivative of total cost
with respect to quantity

is called marginal cost.

So we want to find the quantity
such that marginal revenue

minus marginal cost is zero,
or in other words,

we want to find the quantity
such that marginal revenue

is equal to marginal cost.

In other words, the quantity,
which maximizes profit,

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

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

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

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

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

set it equal to zero.

Okay let's get some more intuition.

When the firm produces
an additional unit of output,

there are additional revenues
and additional costs.

Profit maximization
is all about comparing

these additional
revenues and costs,

and we have names for these.

Marginal revenue is the addition
to total revenue

from selling an additional
unit of output.

Marginal cost is the addition
to total cost from producing

an additional unit of output.

Profits are maximized at the level
of output where marginal revenue

is equal to marginal cost.

Now why is this?

Well, let's suppose
that marginal revenue

is not equal to marginal cost
and let’s show

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

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

you're not profit maximizing --
producing more

will add to your profit.

Why? Well, remember marginal
revenue is the addition

to revenue from producing
another unit.

Marginal cost
is the addition to cost

from producing another unit.

If marginal revenue is bigger
than marginal cost,

that says producing that unit
adds more to your revenues

than it does to your costs.

In other words,
you could increase profit

by producing more.

So if marginal revenue
is ever bigger

than marginal cost,
you want to produce more.

On the other hand,
suppose marginal revenue

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

suppose marginal cost is bigger
than marginal revenue.

Well then, you're not
profit maximizing

because producing less
will add to your profit.

Why is this?

Well, think about marginal cost.

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

by marginal cost,
your revenues would also fall

by marginal revenue,
but since marginal cost is bigger

than marginal revenue,
your costs by producing

one unit less fall by more
than your revenues fall.

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

are going down,
you're again increasing profit.

So if marginal revenue
is ever less than marginal cost,

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

by producing less.

So, if marginal revenue
is bigger than marginal cost,

you're not profit maximizing.

If marginal revenue is less
than marginal cost

you're not profit maximizing.

You can only profit maximize
if marginal revenue

is equal to marginal cost.

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

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

because remember,
that a competitive firm

is small relative
to the total market.

That means it can double
its production easily

and not push down the market price.

As a result,
for a competitive firm,

marginal revenue is equal
to the market price.

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

and it decides to produce
a third unit,

what's the additional revenue
from that third unit?

It's the price.

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

What about if it produces
a fourth barrel of oil?

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

It's the price of a barrel of oil.

What about the fifth unit?

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

So, marginal revenue
for a competitive firm

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

it doesn't change when the firm
changes its output

because the firm is small
relative to the market.

Now what about marginal cost?

Well, a typical shape
of a marginal cost curve

would be upward sloping like this.

Again, think about
our stripper oil well.

We can produce more
from that oil well,

but there's a limit.

We can only run it so quickly.

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

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

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

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

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

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

a lot of maintenance and so forth.

So our costs will tend to increase.

We can't produce
an unlimited amount of oil

at the same cost
from this oil well.

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

our additional costs
are going to rise

the more we want to produce
from that oil well.

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

Now, where's profit maximization?

Well, profit is maximized
where marginal revenue

is equal to marginal cost.

In this case,
for a competitive firm,

marginal revenue is equal to price.

So profit is maximized
where price is equal

to marginal cost
or at this point right here.

Now let's think
about that intuitively.

On the left hand side
this is the additional revenues

from selling a barrel of oil.

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

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

therefore sell more.

Revenues bigger than costs,
therefore sell more.

Revenues bigger than costs.

You keep selling more
until you reach this point.

Do you want to go further? No.

Here, costs are bigger
than revenues.

So by selling less,
you can reduce your costs

by more than you'd reduce
your revenues

and therefore profit goes up
going this way

and that's why this point,
where marginal revenue

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

that's the point where profit
is maximized.

Now remember way back
in the first talk,

we wanted to explain
a firm’s behavior.

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

Suppose the market price
is $50 per barrel.

Well, then in order
to maximize profit,

the firm chooses the quantity --
in this case,

about eight barrels of oil --
such that marginal revenue

is equal to marginal cost,
bearing in mind

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

So to profit maximize
the firm produces a quantity

of about eight barrels of oil.

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

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

along its marginal cost curve
keeping this relationship the same

so price is still equal
to marginal cost.

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

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

So this again is the profit
maximizing point

when the price is equal to 100.

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

is just under 10 barrels of oil.

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

when the market price, changes.

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

look for the quantity
where marginal revenue

is equal to marginal cost,
which is the same

for the competitive firm
where price is equal

to marginal cost.

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

This raises a subtle point.

You can be maximizing profits
and actually have a loss.

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

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

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

In order to do that,
we need to introduce

another concept
and another curve --

average cost.

Average cost is simply
the cost per unit of output.

That is the total cost
divided by Q,

the quantity of the output.

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

Adding the average cost curve
to our graph

will let us show profit
on the graph.

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

in the next talk.

Thanks.

- [Narrator] If you want
to test yourself,

click, "Practice Questions,"

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

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