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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- 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.

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