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Taxes and perfectly inelastic demand

Who bears the burden for the taxes when demand is inelastic. Created by Sal Khan.
Video transcript
Let's think about who bears the burden of attacks in different situations. In this video, we're going to focus on insulin. Insulin is interesting. It's what's needed by Diabetes in order to maintain their blood sugar level so for them, you can almost imagine they need this just to survive. It almost has an infinite marginal benefit for them. So they're willing, no matter what the price, they're essentially willing to take the insulin that they need to take. So, for example, even if the price of insulin were a dollar, if the doctors in this town say collectively all the diabetics need 3,000 vials a year, they will take 3,000 vials a year. If the price is $80 a vial, they'll still take 3,000 vials a year. So within reason, within a reasonable price range, you have no change in quantity demanded. So, in this case, at least in a reasonable price range, the demand curve for insulin is vertical. Obviously, if we went up to prices like $9 million per vial, then all of a sudden, some of the diabetics just won't be able to afford it, and all of a sudden, the curve wouldn't be able to be vertical anymore. But at least in a reasonable price range, you have a vertical curve. So this right over here is our demand curve. That is our demand curve. You might remember when we talked about elasticity, this is perfectly inelastic demand. It's perfectly inelastic ... perfectly inelastic. The way you can think about it, I kind of think of a brick as perfectly inelastic. No matter how much you push or pull on the brick within reason, at least with my level of strength, you're not going to be able to deform the brick. That's the opposite of a rubber band, which is very elastic, or you can think about the definition of elasticity, the one that we've been using, elasticity is equal to percent, change in quantity over percent, change in price. Over here, no matter how much we change price within reason, at least in this range of price along this curve, people are still going to demand a quantity of 3,000 vials per year. Let's just draw a supply curve here, so let's do a supply curve, looks something like that, So if you have ... this is supply, so if you have no taxes, no regulation of this market, based on the way I've drawn it right over here, the equilibrium price lands us right around $75. I did a little research before this video, it actually turns out that is about the market price for a vial of insulin. The equilibrium quantity, because that is the exact quantity that people need is 3,000 vials. A slightly interesting thing to think about in this situation where you have perfectly inelastic demand, is what is the producer's surplus and the consumer's surplus? The producer's surplus is how much more money they're getting relative to their, you can view them as their opportunity cost or their incremental marginal cost, and here we will [unintelligible] multiple times, this is the producer's surplus right over here. It's the area between the prices equal to the clearing price and our supply curve. So, that's our producer surplus. Producer surplus. Our consumer surplus is where things get a little bit interesting. Consumer surplus is how much more marginal benefit people are getting than what they are paying. We've traditionally said that's the area between the demand curve and the price. But now, all of a sudden, this area is infinite. This area is infinite. One way to think about it is that these diabetics get, you could almost say close to infinite marginal benefit from that insulin. It allows them to have a healthy life. It allows them to stay alive. For them, it's essentially priceless. It's kind of an interesting idea that you have infinite consumer surplus. It's not necessarily saying that this is like a great deal for the diabetics, it's really just saying that their benefit is something that they need to survive. If this was just slightly more elastic, so if we were to get, maybe to a slghtly more real world scenario. In a real world, if things got a little bit more expensive, there might be a few diabetics who would all of a sudden try to lower their dose or something like that. The curve, in a real world, actually might have some very slight elasticity. It would still be a very steep slope, but it would actually have some slight elasticity. You could imagine if I kept taking this up and up and up, and at some point, it actually would bound the area, but it would, so maybe it goes up here. Maybe if this was like $2 million up here, then the demand would go down dramatically, but it would be bounded. But it is a very, very, very large consumer surplus. Now with that out of the way, let's think about what happens if some misguided politician decides to tax insulin. Obviously a very bad idea, and nothing that I would ever advocate, but let's think about who would bear the burden? I think you could probably guess who would bear the burden if you had to put a tax, but we'll actually see it. We'll think it through with our supply and our perfectly inelastic demand curve. What ends up getting passed is a tax of $10 per vial. I'm just making it, instead of a percentage, I'm just doing it as a fixed amount so that we get kind of a fixed shift in terms of the perceived supply price. For the producers, this is what they need to get. If you want them to produce 3,000 vials, they need to get $75. If you [unintelligible] that first vial, they need to get $60. What the producers need to get, plus the tax, we can draw a new curve. We've done this multiple times. For the very first vial, the producer needs $60, but then you add the tax there, it's going to be $70. For 1,000 vials, it looks like it's going to be I don't know, 60 something ... you add the tax, it's going to move up to here. For 3,000 vials, the producers need around $75, $76, you add $10 to it, it gets to $85, $86 like that. What you get is this new curve, you could use the price from the consumer's point of view, or you could view it as the supply plus tax curve. I'll call this supply plus tax curve and that's hard to read, but that says tax over there. This is the supply plus tax curve. Where does that intersect our perfectly inelastic demand curve? Well, you can imagine people, even though the prices are higher, people still have to get exactly 3,000 vials per year. They intersect right at that quantity, but now we have a new equilibrium price. Our new equilibrium price is exactly $10 higher. If this was $75 or $76, this is $85 or $86. This distance right over here is $10. Let's think about a few things. Let's think about the total revenue that the government is going to get in this situation. The total revenue is going to be that $10 times the 3,000 vials per year ... times 3,000. So they're going to get $30,000 per year. Let's think about whose surplus that came out of. The tax revenue, this right over here is the tax revenue. That right over there is the tax revenue. The producers are still going to have the exact same producer surplus, so all of that tax revenue came directly out of the consumer surplus. Another interesting thing to note here is, because we had this perfectly inelastic demand, that even when you raise the price, it didn't lower the quantity demanded that we actually don't have a dead weight loss here because this was perfectly inelastic. We're actually having the same quantity produced so you have a transfer of surplus from essentially the diabetics to the government in this situation, but you don't have any lost surplus here because there's no lost area, I guess you could say, between where the supply curve and the demand curves intersect. Another way to think about it is the quantity demand did not go down because the price went up.