The Laffer Curve

so the government needs to collect more tax revenue, what do they do? They raise taxes? Right, But that doesn't necessarily lead to more tax revenue. We can actually find a pretty interesting conclusion when we use what's called the laffer curve to show us how higher taxes do not necessarily mean more tax revenue. Let's check it out. So like I said, this larger tax does not necessarily lead to higher tax revenue. Why is that the case? Well, remember as the size of a tax increases, how do taxes affect our quantity exchanged as we have more tax? Well, that's more cost here. Right? So it's going to keep decreasing the quantity exchange, right? The quantity exchange is going to decrease as uh the tax increases. So as we learned here with taxes in our other videos, um let's go through three examples here where we'll have a small tax, a medium sized tax and a large tax. And let's see how that affects tax revenue. So as you remember, we can represent the size of the tax by the space between the demand curve and the supply curve. So if this is our demand or downward demand, upward supply. And let's say this green line right here, let's start with a well do extremes will have a very small tax here. So if we have a very small tax here, right? And this would be the size of the tax. So, if we were at this point, this would be the quantity exchanged if we had that size size tax. So I'll put Q. T with the tax, right where we would originally be at this equilibrium over here. But the tax, it moves us away from equilibrium because the the price that the suppliers receive and the price that the buyers pay is now different because of the tax, right? So what's gonna happen in this case? Remember how we calculate our tax revenue? Well, it's it's the amount of tax times the quantity exchange, right? We're dealing with per unit taxes here. So if we're gonna exchange this quantity and there's a certain amount of tax, say $1, let's say this is a $1 tax. Well, the amount of tax revenue would be represented by this box here, right? Because if we go to the the demand curve here, this is the price that the buyers pay and this down here is the price the sellers receive, right? And everything in the middle goes to the government. So what we'll see here is that this space here, just like we saw when we studied taxes originally, this is the amount of tax revenue. So this is our tax Revenue in this little box here. Right? So notice there's a small tax revenue here because we have a small tax. Now let's go to the other extreme, let's go to where we have a really large tax. Okay, let's start here on this bottom one where we have a really large tax, let's do the same thing, right? And now let's say the taxes this big, big amount over here, way over here, there's this huge tax, maybe $15 per item where before it was just $1. Right? So now we've got this $15 tax per item. And notice what's happened to the quantity exchanged in this case. The quantity exchange is gonna be way down here with the quantity with the tax. Um Yeah, our Quantum exchange has decreased a lot because there's a big tax here. So now the price the buyers pay is way over here. So notice there's not so many people that want to pay this high price. So there's not gonna be that much exchanged. This is our demand curve, our supply curve. And this is the quantity uh supply down here because this is the price that the sellers received. And there's not that many sellers that want to supply at such a low price received. Right? So notice what our tax revenue here is, even though there's this big amount of tax right there, getting a lot per exchange. Well, there's not so many exchanges happening now. So what happens to our tax revenue? Well, it's this space again, the space of the tax, the amount of the tax times the uh the quantity exchanged. So again, notice what our box looks like. So the area of the box hasn't increased very much or is pretty much the same as when we had the small tax up here, right? In this case, notice we had a very long box, but not very tall. In this case we have a very tall box, but it's not very long. So the area of the box has not changed very much. So even though this is our kind of example here, you can kind of see where I'm getting at. So our tax revenue there is still not much different than when we had a small tax. Now, let's go to the situation where we have maybe a more ideal tax somewhere in the middle. So let's see what happens if we have maybe this tax right here, maybe this is a better tax for the government right here. So something in the middle again, we have a quantity exchanged. That's gonna be right here with the tax and what's gonna happen with the price the buyers pay and the price the sellers receive. We're gonna have this as our demand curve, our supply curve here. So this is the price the buyers pay price the sellers receive. And notice what's happened to the area of the box. There's a lot more area here, Right? And that's the idea with the, with a medium sized tax, the correct sized tax. Now, in every market, this could be a different amount, right? We can't say what the correct taxes. That's gonna maximize tax revenue uh, in any market just like this. But this is the idea where there's more tax revenue when there's the correct tax because notice what's happened in this case, there's still quite a lot of quantity being exchanged because we're not in those extremes, but there's also a sizable tax revenue, so the length of the box and the width of the box is greater and that leads to a higher area which leads to higher tax revenue here. Okay, so the tax revenue we're gonna say is the biggest when we have that medium sized tax. So what is the laffer curve? How do we translate this all onto a graph to let us know what the proper tax revenue or what the proper size of the taxes. So the laffer curve, what it shows us, let me get out of the way a little more, what it shows us is that we've got. If we put the the size of the tax so the size of the tax on the X axis here, and we put the tax revenue, the amount of tax revenue received by the government on the Y axis. Well, when we as we increase the tax, right, we're getting more and more revenue up to a point where the tax has gotten too big and the revenue is gonna start decreasing again, Right? So if we start with the small tax up here, we're gonna have a small amount of revenue and it's gonna start increasing and increasing as we reach the perfect amount of tax for the maximum tax revenue. And then it's gonna start and that's here in the medium graph. And then it's gonna start decreasing again as we get to the large graph, the area of the box gets smaller and smaller again. Right? So notice our laffer curve is gonna look something like this then as the size of the tax increases what we're gonna have an increase in tax revenue until it reaches some sort of maximum like that at that ideal maximizing tax revenue tax and then it's gonna start decreasing again. Right So we're gonna have this kind of parabolic shape where we're gonna have the tax revenue increasing to a point and then it starts decreasing again. So what does this tell us that higher tax higher taxes does not necessarily lead to more tax revenue because the quantity exchange is gonna keep decreasing as those taxes increase. Okay so that's what this laffer curve is depicting its depicting the relationship between that size of the tax and the amount of tax revenue. And it's named after Arthur Laffer, that's the guy who created this idea, creator of the Laffer curve and he suggested that the USA was already on the downward slope of the curve. So he's saying that the U. S. A. Was already somewhere, let's say here on the curve maybe the USA is right here. So any increase to taxes was actually going to decrease tax revenue. Okay, now we don't know if he's right or wrong but the idea is that he was proposing that as we increase taxes, it's actually gonna hurt our tax revenue because it's gonna hurt the quantity exchange. So in this situation, what it's saying is that larger taxes are gonna have multiple negative effects First, we're gonna have less quantity exchanged. Let's quantity exchanged, which is also going to lead to less tax revenue. Right? Just as we saw in our examples, there were already at that large tax. So if we were to increase the tax even more that tax revenue, would the total tax revenue would decrease? Cool. So that's about it for the laffer curve. That's what you have to remember here, that it's a relationship of larger taxes and the amount of tax revenue. Cool. Let's go ahead and move on to the next video.