Review of revenue and cost graphs for a monopoly | Microeconomics | Khan Academy

What I want to do in this video is review a little bit of what we've learned about monopolies and in the process get a better understanding for some of the graphical representations which we have talked about in the past.

But I want to put it all together in this video here. So let's say that the industry that we are in, the demand curve looks something like that. So that is demand, and I'm going to assume that it is a linear demand curve. This axis right over here is dollars per unit; in the context of demand, that's price, and this is quantity over here.

This little graph here, we still have quantity in the horizontal axis, but the vertical axis isn't just dollars per unit; it's absolute level of dollars. So over here we can actually plot total revenue as a function of quantity, total revenue. So obviously, if— and we're remember we're assuming we're the only producer here—we have a monopoly.

We have a monopoly in this market. So if we pick a quantity, if we pick—if we don't produce anything, we're not going to generate any revenue. So our total revenue will be zero. And if we produce a bunch but we don't charge anything for it, and that's this point right over here, our total revenue will also be zero.

And we've done this in other videos, but then as we increase quantity from this point, our total revenue will keep going up and up and up. There'll be some maximum point, and then it'll start going down again. So our total revenue would look something like this; total revenue would look something like that.

Total revenue, and from the total revenue we can think about what the marginal revenue would look like. Remember, the marginal revenue just says if I increase my quantity by a little bit, how much am I increasing my total revenue? And so that's essentially the slope—the slope of the total revenue curve at any given point.

Or you could think of it as the slope of the tangent line, and we've seen before when you start here you have a very high positive slope. We've seen in other videos it actually ends up being the exact same value as where the demand curve intersects the vertical axis right over there. But then it keeps going lower; the slope becomes a little less deep, less deep, less deep—it's still positive—less deep, less deep, and then becomes zero right over there.

And then it starts going negative. So it becomes zero right at that quantity. So it becomes—the marginal—the slope of this keeps going down and down and down; it's positive, then it becomes zero, and then it actually becomes negative. And you see that here now; it starts downward opening even more steep, even more steep, and even more steep.

So that's the revenue side of things, and let me label this—this is our marginal revenue curve, slope of the total revenue. If we're going to maximize profit, we need to think about what our costs look like. So let me draw our total cost curve and I will do it in magenta.

So let's say our total costs look something like this. Total cost looks something like that. Out here, when we have very few units—when we have zero units—all of our costs are fixed costs. And then we—as we have produced more and more units, with the variable costs start piling on over there.

And even from this diagram you can actually start to visually see economic profit. Economic profit—and when we talk about cost and profit in an economics class like this, is kind of one, I guess, remember you should view it in terms of economic profit.

And when we're talking about total cost, we're talking about opportunity cost. So this is total total opportunity costs—both the implicit, the ones that—or both the explicit, the ones that you're actually paying money for explicitly, and the implicit opportunity cost. Total opportunity cost—that's total opportunity cost.

And the difference between your total revenue—so for a given quantity, for a given quantity, the distance, the difference between your total revenue and your total opportunity cost, that gives you your economic profit. So for this quantity right over here, your economic profit would be represented by the height of this little bar between these two curves.

But what we see going on is as we increase the quantity over here, these curves are getting further and further apart. That's because the green curve, the total revenue, has—its slope is larger than this purple curve, which is total total opportunity cost—or you could say total cost.

And so we could even go even further along; the distance between the two curves gets bigger, bigger—looks like it maxes out right about right around here someplace. And then the two things start getting closer and closer together. Now this purple curve's slope is now larger than the orange curve's slope, so then they start getting closer and closer together.

And so if you were to just look at this graph, whatever the maximum distance between these two things are, it looks like it's about there, right over here, that would be your maximum economic profit. But we know we can also visualize it on this curve over here, and we can do that by plotting our marginal cost.

And remember, marginal cost, just as marginal revenue is the slope of your total revenue curve, marginal cost is the slope—the instantaneous slope at any point of your total cost curve. So I will do that—let's do that in yellow.

So right over here you have a zero slope, or pretty close to zero at least the way I drew it over there, so your marginal cost is going to be pretty close to zero right over there. And then we see that the slope keeps increasing and increasing, and increasing, and so our marginal cost will keep increasing, increasing, and increasing.

So it will look something like that—that is our marginal cost curve. So if we pick a quantity, and if we find that the marginal cost over here, I don't know, let's say it's $5 per unit—that literally means that the slope at that same quantity, the slope of our total cost curve, that the slope over there would have to be five.

That's what that is telling us; this is plotting the slope of this curve right over here. And if we want to maximize profit—we already talked about how we would do it visually on this curve, we can do it over here.

Well, right over here as we produce, if we start from producing nothing to producing something, for each incremental unit, our marginal—the incremental revenue we get on that is much higher than the incremental cost. So hey, we should produce it because we're going to get profit there.

We could keep producing because we're going to get profit on each of these incremental units. So we'll keep doing it, we'll keep doing it, we'll keep doing it until the marginal revenue is equal to the marginal cost. At that point it doesn't make sense for us to produce anymore.

If we produce an extra unit past that point, on that unit our cost will be higher than our revenue, so it will eat into our economic profit. So this right over here is where we maximize—the quantity at which we maximize profit. And we see it—we see it right over there, the way I drew it, luckily, it looks like that is the maximum point between those two curves as well.

And it makes sense before this point when marginal revenue is higher than marginal cost, that means that the slope of the total revenue curve is larger than the slope of the total cost curve, so they're getting further and further apart. After this point—right at that point, their slopes are the same, so the slopes are going to be the same right over there.

And then after that point, the slope of the marginal cost curve, or sorry, the marginal cost is higher, which tells it the slope of the total cost curve is higher than the slope of the total revenue curve. And so they're going to get closer and closer together, and this distance gets quenched apart.

So that is where you maximize profit. And if you wanted to visualize the actual profit on this graph over here, we can obviously visualize it here as the distance between these two curves. If you want to visualize it over here, we would have to find—we would have to plot our average total cost curve.

And essentially what you're doing, you're just taking this total cost curve and you're not just taking the slope at any point—that's the marginal cost. Instead, you're just dividing it by the quantity.

So if you take this total cost curve, if you take this value and divide it by a very, very low quantity, you're going to get a very, very, very, very large number. You could imagine as you're spreading your fixed costs amongst a very small quantity, so you're going to get a very large number.

Then as you produce more and more and more, your average total costs go down, but then your variable costs start picking up and your average total cost might look something like that—average total costs.

And so if you want to know your profit, that which you have maximized from this graph right over here, you say, well this is the—that maximizes my profit, marginal revenue is equal to marginal cost, the price that I can get in the market for that quantity.

Well then you go back up to your demand curve, and it gives you this is the price that you will get for that quantity. And so that is on a per unit basis. That is the revenue that you will get; you could view price as equal to price. It's the same thing as revenue, revenue per unit.

So on a per unit basis, this is the revenue you're getting, and on a per unit basis, this is your average cost; this is average total cost. This is taking all your costs and dividing it by units.

So on an average per unit basis, this is going to be your economic profit on a per unit basis. And if you wanted to find your actual economic profit, you would have to multiply it by the total number of units. So you would essentially have the area of this rectangle right over here.

This is your per unit average economic profit, and your total economic profit is going to be quantity times profit per unit. So this right over here is economic economic profit, or maybe I should call it total economic profit. Let me write it out—total total economic economic profit.

And the area of that rectangle should be the same thing as the height of this right over here. And the only reason—and we can maintain this as a sustainable scenario because we have a monopoly; no one else can enter.

If this was not a monopoly, if there were no barriers to entry, then other people would say, hey, there's economic profit there. That means there's an incentive for me to put those same resources together and try to compete because I'm going to get better returns than my alternatives; that's a good way to think about it.