Review of revenue and cost graphs for a monopoly

- [Instructor] 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 wanna 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. That is demand and I'm going to assume that it is a linear demand curve. This axis right 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. Over here we can actually plot total revenue as a function of quantity, total revenue. 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 don't produce anything, we're not going to generate any revenue, so our total revenue will be zero. 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. 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? So that's essentially the slope, the slope of the total revenue curve at any given point, or you can think of it as the slope of the tangent line. We've seen before, when you start here, you have a very high, positive slope and 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 it becomes zero right over there and then it starts going negative. It becomes zero right at that quantity. 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 sloping even more steep, even more steep, and even more steep. That's the revenue side of things. Let me label this, this is our marginal revenue curve, slope of the total revenue. If we're gonna 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. Let's say our total costs look something like this. Total cost looks something like that. Out here, where we have very few units, where we have zero units, all of our costs are fixed costs. And then as we produce more and more units, the variable costs start piling on over there. Even from this diagram, you can actually start to visually see economic profit. Economic profit, and when we're talking costs 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 opportunity cost, both the implicit, both the explicit, the ones that you're actually paying money for explicitly and the implicit opportunity costs. Total opportunity costs, that's total opportunity cost and the difference between your total revenue, so for a given quantity, the difference between your total revenue and your total opportunity cost, that gives you your economic profit. 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 what's 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, it's slope is larger than this purple curve, which is total opportunity cost, or you could say it total cost. So we could go even further along, just the distance between the two curves gets bigger, bigger, looks like it maxes out right around here someplace and then the two things start getting closer and closer together. This purple curve's slope is now larger than the orange curve's slope, so then they start getting closer and closer together. 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 costs, this is 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. 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 this 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. If we pick a quantity and if we find that the marginal cost over here, I don't know, let's say that it's five dollars per unit, that literally means that the slope, that 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 you 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, the incremental revenue we get on that is much higher than the incremental cost. So, hey, we should produce it because we're gonna get profit there. We could keep producing because we're gonna 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 what will eat into our economic profit. So this right over here is where we max the quantity, which we maximize profit. When 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, and 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, sorry, the marginal cost is high, which tells us the slope of the total cost curve is higher, than the slope of the total revenue curve. And so they're gonna get closer and closer together and this distance gets squinched apart. That is where you maximize profit. And if you wanted to visualize the actual profit, on this graph over here, we cannot obviously visualize it here as the distance between these two curves. If you want to visualize it over here, we would have to plot our average total cost curve. And essentially, what you're doing is 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 quantities. So if you take this total cost curve, you take this value and you divide it by very, very, very low quantity, you're going to get a very, very, very, very large number. You can imagine, as you're spreading your fixed costs amongst a very small quantity, so you're gonna 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 costs might look something like that. Average total costs. And so, if you wanna know your profit that you have maximized from this graph right over here, you say this is the quantity that maximizes my profit, marginal revenue is equal to marginal costs, the price that I can get in the market for that quantity, you go 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 can view price is equal to, price is 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 costs. This is taking all your costs and dividing it by units. 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 so your total economic profit is going to be quantity times profit per unit and so this right over here is economic profit, or maybe I should call it the total economic profit. Let me write it out, total economic profit. And the area of that rectangle should be the same thing as the height of this right over here. The only reason, and we can maintain this is 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 say hey, there's economic profit there, that means that 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 opportunity costs than my alternatives is a good way to think about it.