If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

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?

  • male robot hal style avatar for user burnsofflora
    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)
    Default Khan Academy avatar avatar for user
    • mr pants teal style avatar for user jakewirfel
      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)
  • leaf red style avatar for user Jack McClelland
    At around , 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)
    Default Khan Academy avatar avatar for user
    • piceratops tree style avatar for user Jayden Tan
      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)
  • aqualine ultimate style avatar for user David Ray
    As a company, how would you find out about the demand curve?
    (3 votes)
    Default Khan Academy avatar avatar for user
    • aqualine ultimate style avatar for user Stefan van der Waal
      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)
  • duskpin ultimate style avatar for user Lezzlly Real
    How did Sal come to the conclusion that P= 6-Q?
    (2 votes)
    Default Khan Academy avatar avatar for user
    • leaf green style avatar for user mdmetallica01
      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)
  • blobby green style avatar for user harshinder kaur chawla
    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)
    Default Khan Academy avatar avatar for user
    • male robot donald style avatar for user jordanpirch
      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.
      (3 votes)
  • blobby green style avatar for user Jeffrey Sepulveda
    which video helps with price of dollares to revenue?
    (3 votes)
    Default Khan Academy avatar avatar for user
  • orange juice squid orange style avatar for user freya hanley
    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)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Mum Gotbi
    If we were break up monopoles into smaller firms we would be guaranteed to get more output at a lower price
    (1 vote)
    Default Khan Academy avatar avatar for user
    • aqualine ultimate style avatar for user CPU
      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)
  • leaf green style avatar for user Sena
    I still don't understand what the term "revenue" exactly means. What is the difference between total revenue and profit?
    (0 votes)
    Default Khan Academy avatar avatar for user
    • aqualine ultimate style avatar for user Stefan van der Waal
      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)
  • leaf green style avatar for user Hayley  Bourgault
    aw could someone show us the quadratic equation for that parabola. that is just a tease.
    (1 vote)
    Default Khan Academy avatar avatar for user

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.