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Taxes and perfectly inelastic demand

The burden of a tax falls most heavily on someone who can't adjust to a price change. That means buyers bear a bigger burden when demand is more inelastic, and sellers bear a bigger burden when supply is more inelastic.  Created by Sal Khan.

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  • blobby green style avatar for user mlicarvalho
    Maybe I'm wrong, but I think the producer's surplus does diminish here, though Sal says at that it remains the same. Am I wrong?
    (11 votes)
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    • male robot hal style avatar for user BrentWassell
      Look at the graph, the yellow "supplier surplus" doesn't change at all. They produce the exact same; there is no deadweight loss. It is a tax completely on the consumers and doesn't affect the suppliers at all because demand doesn't change (due to the perfect in-elasticity of the curve).
      (37 votes)
  • male robot hal style avatar for user Cameron Brannock
    In a situation where there is a monopoly on insulin, what keeps the producer from taking advantage of this state of almost perfect in-elasticity by raising prices to the point of maximum profit ?
    (13 votes)
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    • leafers ultimate style avatar for user Andris
      I think, in the real world, public outrage would prevent any firm from raising prices. A monopolistic firm could charge really high prices for insulin and explain it by some hoghwas about R&D costs, but not without limit. Actually, this is what we see today, insulin prices are much higher than they would be in a competitive market.

      In an economic model, the monopolistic would maximize profit, but it would not mean that it charges the full income of every single consumer, because the demand curve is never perfectly inelastic (even if your life depends on it, you may not want to buy insulin if it means your family will have to live in extreme poverty). But the fact still holds true, in an economic model consumers would be willing to pay much money for the medicine which they depend on.
      So the moral of the question is this: competition really matters.
      (16 votes)
  • female robot grace style avatar for user Natalie
    Where may Sal have been able to do "market research" in order to get the correct insulin prices? I don't know where to get prices for things.
    (3 votes)
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    • blobby green style avatar for user Tom Ottaviano
      Typically you'd look at a "Market Research Report." These are produced by a number of different companies and can be quite expensive. (If you "google" Insulin Market Research Report you can get an idea of the suppliers and prices) Some libraries (particularly at research institutions with a Business School) will subscribe to Mintel and/or IBISWorld, two databases with a large number of Market Research Reports available. My hunch is that this is what Sal used.

      For something like Insulin, you would likely have not-for-profit organizations conducting research and making this information available. Here is an example: http://www.haiweb.org/medicineprices/07072010/Global_briefing_note_FINAL.pdf
      (15 votes)
  • boggle green style avatar for user Thomas Wood
    I'm confused. If there's no dead weight loss, and the consumer surplus doesn't technically change (infinity minus any number is "theoretically" infinity) then why was it a bad idea? Or was he joking when he said it was, because I really couldn't tell.
    (3 votes)
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    • ohnoes default style avatar for user Tejas
      It is not a bad idea economically. However, it would be political suicide for the said misguided politician. Voters would be extremely angry that diabetics, who are already facing life-threatening problems, are being additionally burdened by this tax.
      (12 votes)
  • blobby green style avatar for user Bills_Engel
    So if there isn't a DWL can will still say that the tax makes this to an inefficient situation ?
    (3 votes)
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    • piceratops tree style avatar for user Jayden Tan
      It depends how you define "inefficient". In economics the equilibrium point is reached when supply equals demand and more importantly: Consumer and Producer surplus is maximized. i.e maximizing consumer and producer happiness. Dead weight loss is usually created when consumer and producer surplus is reduced.

      In this example producer surplus is unchanged, consumer surplus is reduced and the government receives the lost consumer surplus. There is no dead weight loss technically speaking, but I would argue that the tax causes an inefficient situation because consumer and producer surplus is not maximized due to an unnecessary tax.

      Think of it this way: If overall happiness (consumer + producer surplus) is not being maximized then the market is in an inefficient situation, regardless of dead weight loss.

      Hope that helped! :)
      (7 votes)
  • leaf green style avatar for user yoro
    Fuel federal and state taxes seem to be inelastic...am I right?
    (0 votes)
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    • blobby green style avatar for user Rafael Nahapetian
      @ Sam Allon - that is only true in the long run, in the short run, people can't change their habits that quickly so demand for oil is relatively inelastic (and so is supply, really, because oil producers can't increase or decrease production instantly - usually takes years)

      If you're taking this class in school, teachers/professors like to ask this question on exams (at least in my experience), be sure you know what "time horizon" they're talking about. In other words, in what period of time it's taking place - a couple of weeks? a year? decade?
      (7 votes)
  • blobby green style avatar for user bakejustin13
    i know this is hypothetical, but wouldn't the doctors buy a surplus of insulin if the price was lower then the equilibrium assuming that it could be stored for a decent amount of time?
    (2 votes)
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    • leafers ultimate style avatar for user Andris
      Yes, this may be the case in real life. Please keep in mind that the model in the video has only one period, meaning there is no future, so there is no point in storing anything. It may seem unrealistic, but these simple models are really good for explaining the basics.
      And, to really satisfy your curiosity, there are more complex economic models, where there are more periods, but I'm afraid you will not find any videos on those (yet).
      If you are really interested in the matter, try looking up for example the Real Business Cycle model, and look for intertemporal substitution.
      (1 vote)
  • male robot hal style avatar for user Sarfaraz
    Assuming the same idea of perfect inelastic demand of alcohols, cigarettes etc. the govt. can make higher revenues by putting higher tax percentage on such things and all @ the cost of consumers surplus... right?
    (1 vote)
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    • piceratops ultimate style avatar for user saywachavez
      But alcohol, cigarettes, etc are not in perfect in-elasticity, if the prices were to rise less people would want to buy it and the supply would go down too, thus creating a dead weight loss. Usually when governments put taxes on such tings is due to health reasons. I hoped it helped you. :)
      (2 votes)
  • leaf orange style avatar for user ThioLiting
    If supply is perfectly price inelastic, is the tax burden placed entirely on the the producers only?
    (1 vote)
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  • starky sapling style avatar for user Schuitema, Aaron
    why wouldn't the amount of Insulin in-take rise or lower depending on the price of Insulin?
    (1 vote)
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    • aqualine ultimate style avatar for user Martin
      Because some things people need to survive.
      Insulin is a medicine that diabetics need, so they can't just say that it's too expensive and wait until it gets cheaper again. It's the same way you can't just stop eating, because you think food is too expensive.
      On the other hand cheap insulin won't increase the amount of diabetics and people with diabetes won't start injecting themselves with more insulin just because it got cheaper.
      The same way you wouldn't start visiting the doctor twice a day every day just because you can go to the doctor for free.
      (2 votes)

Video transcript

Let's think about who bears the burden of a tax 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.