How and why do the elasticities of supply and demand affect the deadweight loss of a tax policy?

Video transcript

Voiceover: Let's look a little bit at the market for hamburgers. This is the supply and the demand curve for the price and the quantity of hamburgers sold per day. If we have a completely unfettered market, no intervention, no taxes, nothing like that, then we see we have an equilibrium price and an equilibrium quantity. The equilibrium price looks like it's about $3.75 per hamburger. The equilibrium quantity looks like it's about a little bit more ... Maybe if I draw that line a little bit differently, the equilibrium quantity looks like it's about $3 - Sorry, it's about 3.5 million hamburgers per day. Just to review what we've talked about before, up here, below the demand curve and above the price. The price equals $3.75 line, right over here. This is how much value, this is how much benefit the consumers are getting above and beyond what they have to pay. That is the consumer surplus. Then, between this price equals $3.75 line and the supply curve, you have your producer surplus. This is how much more the producers are getting for each hamburger, relative to what their opportunity cost of producing that incremental hamburger was. This right over here is the producer surplus. Now, let's say ... Actually these numbers are quasi-realistic. I have a 3.5 million hamburgers per day. I actually looked it up before this video. It looks like McDonalds, at least based on the information I got, sells a little bit over 4 million hamburgers per day in the United States. I didn't clarify whether this is just hamburgers from one vendor or multiple vendors, but it's not a crazy number of hamburgers to sell in a fairly large country. For the sake of this, it's not necessarily McDonalds hamburgers, we're just talking about this is the total market for hamburgers in a country. We're making the simplifying assumption that all hamburgers are created equal, which we know is not true. Now, the government in this hypothetical civilization says, "Wow, a lot of hamburgers are being sold. "We need more revenue for the government "to do other things," or maybe to pay off their debt or whatever they need to do. So they decide to tax hamburgers. They want to tax hamburgers. They're going to make it very simple. They're not even going to do a percentage. Most sales taxes tend to be a percentage of the price, but instead they're just going to do a tax of $1 per hamburger. Let's think about what this does to the surplus, to the price at which transactions will go on and what people will have to pay versus what they will have to get. At any given point, if we look at the supply curve right over here, in order to get someone to produce that very first hamburger, they have to get at least $2 for it, because that's their opportunity cost. They could use those exact same resources, that land, the labor, whatever else, to produce something else that has $2 of value, so you have pay them at least $2 in order for them to produce hamburgers. The more hamburgers you want the suppliers to produce you have to pay them more and more for those incremental hamburgers, because they're going to start using resources that might have better used for other things and that are not as efficiently used for hamburgers. You have to pay them more and more and more. This is what the supply curve that I originally drew in magenta is what the suppliers need to see in order to produce a certain quantity. If you want them to produce 3 million hamburgers, you have to be willing to pay $3 per hamburger, because that's their opportunity cost of those incremental hamburgers up here. Now, let's think about what happens when you add the tax. This is what the suppliers are going to get or the producers are going to get, but when you put a tax, the consumers are going to have to pay a dollar more. Over here, in order to produce this much, the suppliers are going to have to get $3 per hamburger, but then the consumers are going to have to pay a dollar more, so they're going to have to pay $1 more. In order to get the suppliers to produce 2 million hamburgers, you're going to have to pay them this much, you're going to have to pay them about $2.50, but then the consumers are going to have to pay a dollar more than that. They're going to have to pay that much. In order to get them to produce it all, you're going to have to pay at least $2, but then if the suppliers or producers are getting $2, the consumers are going to have to pay a dollar more for the tax. One way to think about it is the supply curve, from the consumer's point of view, is going to be shifted a dollar more than the supply curve from the producer's point of view. It's going to be shifted up $1, so it's going to look something ... I can do a better job than that. It's going to look something like that. At every point, because this is a fixed dollar, it's not a percentage, at every point, this distance right over here is going to be $1. What happens there? From the consumer's point of view, what we have is now a new price that they're willing to consume at, because now this reality is not possible anymore. There's no way for the consumers to pay $3.50 and for the producers to see $3.50, as well. So we get to a new equilibrium price and equilibrium quantity now, because now, since this is from the consumer's point of view, the point at which they intersect is right over there, which is about a little bit over $4 per burger and it's a slightly lower quantity. It's about, let's just say just for round numbers, that's about 3 million burgers per day. What happened there? Before this whole area was a total surplus. Below this green line was the producer surplus, above the green line and below this curve right here was the consumer surplus. Now we've lost part of it. We've lost this part right over here, so this is our dead weight loss. This is no longer part of the total consumer and producer surplus. That is dead weight loss. The taxation got us from an efficient situation, where we had that maximum consumer and producer surplus. This is our dead weight loss over here. How much revenue is the government going to get now? Well, if we assume that this is 3 million, they're going to have 3 million burgers. This is 3 million right over here. They're going to have 3 million burgers times a dollar per burger. Let me do it this way. This length right over here is going to be the area of this rectangle that I'm doing in orange. This length right over here is 3. That length right over there is 3 million and then height is that dollar. Let me shade it in. The height is that dollar right over there. This is going to be $1 height. The tax revenue that the government is going to get is 3 million times $1. 3 million burgers times $1, which is going to be $3 million per day, which is interesting, because maybe the government officials thought they were going to get more, because they look at the projections and they say, "Wait. "There's going to be 3.5 million burgers sold per day, "so I'm going to get $3.5 million." What they didn't realize is that they're making the burgers more expensive, so there's going to be a lower quantity demanded. The actual clearing quantity or the actual equilibrium quantity now is only going to be 3 million. The way we see it, it removed this surplus here, from both the consumer surplus and the producer surplus and no one's getting that, not even the government's getting that. No one's getting that white part right over there and this orange part right over here is eating into the consumer surplus, so now they're paying more than ... Another way to think about it is the difference between the benefit they're getting and what they're paying at any given point, for any given incremental consumer, is now less and the producer surplus is less. The excess of what they're getting for each hamburger versus their opportunity cost is now less. The producer surplus has now been shrunken back to this area right over here and these are curves here, so we can't just do simple geometry to figure out the area of triangles. We would actually have to do a little calculus to figure out the area of these curves. Then the consumer surplus has been pushed back to this area above the orange right over here. You see, governments, for the most part, have to do some type of taxation in order to get revenue and it could be income tax or it could be a sales tax, like this right over here, but when they do it, it gets us into a non-efficient state and it does cause some, depending on how these curves are shaped, it does cause some dead weight loss. Some benefit in excess of what had to be paid, some of that disappears, but it allows, at least, the government to get revenue, depending on whether you think that's a good thing or not.

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