Main content

## Microeconomics

### Course: Microeconomics > Unit 7

Lesson 2: Monopoly- Perfect and imperfect competition
- Types of competition and marginal revenue
- Marginal revenue and marginal cost in imperfect competition
- Imperfect competition
- Monopolies vs. perfect competition
- Economic profit for a monopoly
- Monopolist optimizing price: Total revenue
- Monopolist optimizing price: Marginal revenue
- Monopolist optimizing price: Dead weight loss
- Review of revenue and cost graphs for a monopoly
- Optional calculus proof to show that MR has twice slope of demand
- Monopoly
- Efficiency and monopolies

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Monopolist optimizing price: Total revenue

AP.MICRO:

PRD‑3 (EU)

, PRD‑3.B (LO)

, PRD‑3.B.6 (EK)

In this video we explore how a monopolist decides on the best quantity to produce and the price to charge for that quantity. Created by Sal Khan.

## Want to join the conversation?

- If you integrate P = -Q + 6, you get -.5Q^2 + 6Q, but Sal got -Q^2 +6Q when he multiplied P x Q. Which is correct?(14 votes)
- Sal is. Integrating the price curve will get you the total area underneath the triangle: but realize that on sal's graph when he is determing revenue, he is multiplying price by quantity to get the area of rectangles (or squares in the case of 3 x 3). Total revenue is not the area of triangles under the graph, but rectangles instead. Try drawing it out to help yourself visualize it. I hope this helps.(27 votes)

- At around3:30, when the producer is producing 6000 oranges and selling them for $0 (free), wouldn't that result in a negative profit, which would be plotted on the negative price axis of the graph?(3 votes)
- It would be plotted on a graph showing Profit vs Q of oranges sold. But Sal never draws that graph in the video.

In the two graphs he plots Revenue vs Q and Price vs Q. But remember revenue is different to profit because Profit = Total Revenue - Total Cost.

Revenue is how much cash is coming in from sales regardless of expenditures. if you sold say 5999 oranges at $0.01 then profit would be negative but the revenue would be positive. In fact the farm would be generating $59.99 of revenue.

Only at the point where you make the price so high that not one orange sells or you give oranges away for free will revenue equal 0.(5 votes)

- As a company, how would you find out about the demand curve?(3 votes)
- There are two ways to get an idea of what the demand curve looks like.

The first one is trial and error. Let's say that on day one you sell your oranges for $2.80 per lb. you sell 3,200 lb oranges that day. At day 2 you sell them for $2.90 per lb and you sell 3,100 lb. On day three you sell them for $3 per lb and you sell 3,000 lb. By connecting these three points you can figure out the demand curve.

The second one is through market research. Try to survey all of your customers for one day by asking them questions like: 'How many pounds of oranges would you buy if I would sell them for $2.50 per lb?' After looking at the results it's possible to draw the demand curve.

Note that both explanations are simplified. If you'd want to execute them in real life you'd have to take other things into account. For example, if you'd sell your oranges for $3 per lb it would be unlikely you'd sell exactly 3,000 lb every day. It would change a little bit from day to day.(4 votes)

- How did Sal come to the conclusion that P= 6-Q?(2 votes)
- It is derived from the equation of a straight line y = mx +c (or y = mx + b if you're from America), where c is the y-intercept, m is the gradient, y is the y-axis and x is the x-axis. In this case the y-intercept is 6, the gradient is -1, the y-axis is P, and the x axis is Q. Substitute these back into the formula and you get P = -1Q + 6, which can also be written as P = 6 - Q.(5 votes)

- what would be the intutive explaination for the revenue curve to be an inverse parabola,i.e., why does the revnue increase with slight increase in units sold and decrease as the number of units sold keeps on increasing(2 votes)
- A literal example could be explained as such: Lets say you're buying oranges from farmers and creating orange juice with them, it follows that the higher quantity you produce the higher your revenue you would make. But only to a certain extent. Perhaps your delivery trucks have to drive further and further every day to get more oranges since you bought up all the local ones. Or perhaps you were buying the least expensive oranges and now, since those have already been consumed by your Orange Juice Factory, you have to buy the slightly more expensive oranges. Perhaps you have to hire even more employees, or rent a larger Factory building. At this point, your revenue would turn from continuing to go up with volume, and start going back down while volume continues to increase.(4 votes)

- which video helps with price of dollares to revenue?(3 votes)
- At the beginning of the video, why does the demand curve intersect with the y-axis? Why bother plotting a point when 0 quantity is present?(1 vote)
- In the video, it is showing a supply and demand chart. One of the reasons why zero is present, is because if the price was 6 dollars per pound, no body would buy oranges. They would most likely buy a substitute, like apples or grapes. Thus, the quantity sold would be 0. Hope that helps!(3 votes)

- If we were break up monopoles into smaller firms we would be guaranteed to get more output at a lower price(1 vote)
- Depending on the industry, it would either become more or less efficient. In most cases, breaking up the monopoly would create competition, which drives down prices, ultimately reaching equilibrium. This is a socially optimal result. However, in the case of a natural monopoly, it is most efficient for the industry to be a monopoly. An example of this is power generation. If there were many small power generation companies, there would be much redundancy and waste of resources. Most of the time, breaking up monopolies will result in more output at a lower price.(2 votes)

- I still don't understand what the term "revenue" exactly means. What is the difference between total revenue and profit?(0 votes)
- Total revenue is the total amount of money customers pay for your products.

Profit is the total revenue minus the costs.

For example, I sell 3000 pounds of oranges for $3 per pound. That means my total revenue is 3000 * $3 = $9000.

But oranges don't magically appear. It's required to water the orange trees, pay somebody to harvest the oranges, transport them to the customer, etc. All of those things cost money. Let's say it costs $6000 to cultivate and sell those 3000 pounds of oranges.

Then the profit is the total revenue of $9000 minus the total cost of $6000, which is $3000.

I hope this cleared things up.(4 votes)

- aw could someone show us the quadratic equation for that parabola. that is just a tease.(1 vote)
- He provided it as TR = -Q^2 + 6Q. This can be rewritten as Y = -X^2 + 6X(1 vote)

## Video transcript

What I want to start thinking
about in this video is, given that we do have a
monopoly on something, and in this example,
in this video, we're going to have a
monopoly on oranges. Given that we have a
monopoly on oranges and a demand curve for
oranges in the market, how do we maximize our profit? And to answer that
question, we're going to think about
our total revenue for different quantities. And from that we'll get
the marginal revenue for different quantities. And then we can compare that
to our marginal cost curve. And that should give
us a pretty good sense of what quantity we should
produce to optimize things. So let's just figure
out total revenue first. So obviously, if
we produce nothing, if we produces 0 quantity,
we'll have nothing to sell. Total revenue is
price times quantity. Your price is 6 but
your quantity is 0. So your total revenue is going
to be 0 if you produce nothing. If you produce 1 unit--
and this over here is actually 1,000
pounds per day. And we'll call a unit
1,000 pounds per day. If you produce 1 unit,
then your total revenue is 1 unit times $5 per pound. So it'll be $5 times, actually
1,000, so it'll be $5,000. And you can also view it as
the area right over here. You have the height is price
and the width is quantity. But we can plot that, 5 times 1. If you produce 1 unit,
you're going to get $5,000. So this right over here
is in thousands of dollars and this right over here
is in thousands of pounds. Just to make sure that we're
consistent with this right over here. Let's keep going. So that was this point, or
when we produce 1,000 pounds, we get $5,000. If we produce 2,000
pounds, now we're talking about our price
is going to be $4. Or if we could say
our price is $4 we can sell 2,000 pounds,
given this demand curve. And our total revenue
is going to be the area of this
rectangle right over here. Height is price,
width is quantity. 4 times 2 is 8. So if I produce
2,000 pounds then I will get a total
revenue of $8,000. So this is 7 and 1/2,
8 is going to put us something right about there. And then we can keep going. If I produce, or if the
price is $3 per pound, I can sell 3,000 pounds. My total revenue is this
rectangle right over here, $3 times 3 is $9,000. So if I produce
3,000 pounds, I can get a total revenue of $9,000. So right about there. And let's keep going. If I produce, or if the
price, is $2 per pound, I can sell 4,000 pounds. My total revenue is $2
times 4, which is $8,000. So if I produce
4,000 pounds I can get a total revenue of $8,000. It should be even with that
one right over there, just like that. And then if the price is $1 per
pound I can sell 5,000 pounds. My total revenue is going
to be $1 times 5, or $5,000. So it's going to be
even with this here. So if I produce 5,000 units
I can get $5,000 of revenue. And if the price
is 0, the market will demand 6,000 pounds
per day if it's free. But I'm not going to generate
any revenue because I'm going to be giving
it away for free. So I will not be generating
any revenue in this situation. So our total revenue curve,
it looks like-- and if you've taken algebra you
would recognize this as a downward facing
parabola-- our total revenue looks like this. It's easier for me to draw
a curve with a dotted line. Our total revenue looks
something like that. And you can even
solve it algebraically to show that it is this
downward facing parabola. The formula right over
here of the demand curve, its y-intercept is 6. So if I wanted to write price
as a function of quantity we have price is equal
to 6 minus quantity. Or if you wanted to write in
the traditional slope intercept form, or mx plus b form-- and
if that doesn't make any sense you might want to review some
of our algebra playlist-- you could write it as p is
equal to negative q plus 6. Obviously these are
the same exact thing. You have a y-intercept of
six and you have a negative 1 slope. If you increase quantity by
1, you decrease price by 1. Or another way to think about
it, if you decrease price by 1 you increase quantity by 1. So that's why you have
a negative 1 slope. So this is price is a
function of quantity. What is total revenue? Well, total revenue is equal
to price times quantity. But we can write price as
a function of quantity. We did it just now. This is what it is. So we can rewrite it, or we
could even write it like this, we can rewrite the
price part as-- so this is going to be equal to negative
q plus 6 times quantity. And this is equal
to total revenue. And then if you
multiply this out, you get total
revenue is equal to q times q is negative q
squared plus 6 plus 6q. So you might recognize this. This is clearly a quadratic. Since you have a negative out
front before the second degree term right over here,
before the q squared, it is a downward
opening parabola. So it makes complete sense. Now, I'm going to leave
you there in this video. Because I'm trying
to make an effort not to make my videos too long. But in the next video
what we're going to think about is, what
is the marginal revenue we get for each of
these quantities? And just as a review,
marginal revenue is equal to change in
total revenue divided by change in quantity. Or another way to think about
it, the marginal revenue at any one of these
quantities is the slope of the line tangent
to that point. And you really have to do
a little bit of calculus in order to actually calculate
slopes of tangent lines. But we'll approximate it
with a little bit of algebra. But what we essentially want
to do is figure out the slope. So if we wanted to figure out
the marginal revenue when we're selling 1,000 pounds--
so exactly how much more total revenue do we get if
we just barely increase, if we just started selling
another millionth of a pound of oranges-- what's
going to happen? And so what we do
is we're essentially trying to figure out the
slope of the tangent line at any point. And you can see that. Because the change
in total revenue is this and change in
quantity is that there. So we're trying to find
the instantaneous slope at that point, or
you could think of it as the slope of
the tangent line. And we'll continue doing
that in the next video.