Price discrimination for a monopoly | Microeconomics | Khan Academy

Let's say that you own the only hotel that is in a city. For a wide variety of reasons, maybe all of the city council members are your friends or whatever else, no one else can build a hotel in the city. So there are insurmountable barriers to entry. In that situation, you would have a monopoly; you are the only player in the market, and there are very, very high barriers to entry.

Now, this is a typical cost structure and demand curve for a monopoly. We've already talked about your marginal cost; it might dip down a little initially, but then it might go up. We could debate whether that would be true for a hotel or not, but this is the typical model we see. While your marginal cost is below average total cost, average total cost trends down and then hits a minimum point where marginal cost intersects it. Then it starts to trend up as marginal cost is higher than that.

The demand curve for monopoly looks familiar. When the prices are high, if the prices on the hotel rooms per night are high, very few people will demand them. Conversely, if the prices are low, a lot of folks would demand them.

Now, something that we've talked about in a lot of detail in other videos is how the marginal revenue curve is different than the demand curve for a monopoly. That's because if you were to charge a price of, let's say, 500 dollars per room, you might be able to get one room rented out for the night but no other rooms. If you wanted to get two rooms rented out, you would have to charge four hundred dollars, not just for that room.

So now we get a little bit further down this demand curve. When you charge four hundred dollars, maybe for that second room—because someone's willingness to pay is four hundred dollars—you might have to also charge 400 for that first room. In many monopoly industries, whatever you charge to one consumer, you have to charge to other consumers.

Now, I know what some of you are thinking: "Hey, that doesn't always happen in a hotel." That's why I picked this example, because we're going to look at the situation where you do have to charge the same to everyone. Then, we'll look at another situation known as price discrimination where you don't have to charge the same to everyone.

Let's just go with the model where you do have to charge the same to everyone. So when you go from one room at 500 to two rooms at 400, your marginal revenue isn't the incremental 400. That's because this 500 is now 400 as well. You go from 500 to 800, so your marginal revenue is an incremental 300 as you go from 500 total to 400 plus 400, or 800 total.

That's why we go into significant detail on this in other videos. We do it with tables of numbers, and I encourage you to do that. This is why your marginal revenue curve for a monopoly has twice the negative slope than your demand curve would have.

So your marginal revenue curve would look something like this. We've already talked about in multiple videos that for any firm, it's rational to produce the quantity where marginal cost is equal to marginal revenue. This monopoly would produce this quantity, and the price they would get—well, that quantity we go to look at on the demand curve—the price would be right over there.

So this monopoly firm would be able to get that price, and we can think about what its economic profit would be on every room. In this case, it charges that price, and its average total cost is this blue line right over here. Its average total costs are there. So the difference is how much economic profit per room, and then you multiply that times the total number of rooms. This area is the firm's economic profit.

Now there's still some consumer surplus here. This is the benefit that consumers are getting above and beyond what they're paying for it. So the consumer surplus in this situation would be all of this. That first person who's willing to pay maybe 500 dollars per room is now able to get this market price that everyone is able to get, which is maybe 300 per room. This benefit for that one unit goes to the consumer.

We've also seen that there is deadweight loss here. You're allocatively efficient when marginal cost is equal to the demand curve, and so we studied that in other videos. This right over here is our deadweight loss.

But now let's imagine the other scenario. Let's say that we are a hotel where we try to capture as much of someone's willingness to pay as possible. I'll give a little bit of an idealistic scenario that doesn't really exist in the real world, but just to look at an extreme case.

Let's say that you were able to get a computer that can read people's minds. Every time they call for a quote on a room, you know exactly what their willingness to pay is. So if I call, the computer says, "Hey, Sal's willingness to pay for that room is 375 dollars." So you quote me, "Alright, 375 dollars." I say, "Okay, sure."

When that first person who has a high willingness to pay calls, it says, "Okay, why don't we quote them 500?" So we quote them 500, and they get that room. In that situation, every incremental room—you don't have to change the prices on all the other ones. This causes this marginal revenue curve to slope down faster. Instead, for every incremental room, you get those dollars.

So in that situation, your demand curve is equal to your marginal revenue curve. You're able to discriminate on prices. Let me write this: this is price discrimination. You're able to charge—and price discrimination is a general term for charging different customers, different consumers different rates ideally based on their willingness to pay.

It might sound bad; in normal life, we don't like discriminating against others. But price discrimination is a very legitimate thing, and actually, you will see it happen in things like the hotel industry where they're going to try to charge different prices to different people based on their willingness to pay for essentially the same room.

If you go stay in a hotel, it's very likely that the person in an identical room next to you is paying a different rate. Airlines will also do it. Now, they're not going to be able to do it as perfectly as I just described with this magical computer, but they'll do it, where depending on how far ahead or whether you can return the ticket or cancel your reservation, you could get a different price.

The prices change over time, so they're trying to capture as much of consumers' willingness to pay as possible. If we took this extreme situation where you're able to charge exactly everyone their willingness to pay, well then, what is going to be the rational quantity for this profit-maximizing monopoly to produce?

Once again, it would be where marginal cost intersects marginal revenue, but the marginal revenue curve is now the demand curve. So it'd be right over there. That's the quantity that this monopoly would produce. Then what's the price it would get? Pause this video and think about that.

You might be tempted to just go horizontally here and say, "Okay, this is the price it would get," like we did here. But remember, it’s able to get a different price for every consumer. So there isn't just one price, like in this first example that everyone is paying.

We can see the quantity it is producing. You can see the average total cost at that quantity, but the profit per room is going to be dependent on what people are willing to pay. This first person is going to pay a lot, so they're not going to get much of—or they're not going to get any consumer surplus in this extreme example.

All of this is going to accrue to the firm, and that's going to be the case for all of these consumers in this extreme circumstance. Now you have a fascinating situation. Notice when this monopoly firm is able to do price discrimination, its economic profit is far larger.

Economic profit, the consumer surplus, shrunk through price discrimination. The extreme example disappeared. But you also see that this is actually allocatively efficient, that we are actually producing at a quantity where marginal cost is equal to marginal revenue.