Example breaking down tax incidence

- [Instructor] We are asked, which of the following correctly identifies the areas of consumer surplus, producer surplus, tax revenue, and deadweight loss in this market after the tax? So pause this video, have a go at it. Even if you struggle with it it will make your brain more attuned to when we work through it together. All right, now let's work through this together. And I just want to sort of understand what's going on here before I even try to answer their questions. So let's first take a look at what's going on before the tax. So before the tax, I have this supply curve right over here in blue. And I have this demand curve. Where they intersect gives us our equilibrium price. Right over here. And our equilibrium quantity right over there. And if we wanted to look at the consumer surplus it would be the area above this horizontal line. And, below the demand curve. So that is our original consumer surplus. And our original producer surplus is above the supply curve and below this price horizontal line. And so, the total surplus would be this entire triangle right over here. All before the tax. But they're not asking us before the tax they want us to figure out everything after the tax. So what happens to the tax? Well, if we assume it's a tax on each unit that is being supplied. The effect it has, and we see it here, they've drew it for us. Is it shifts the effective supply curve up. And I say the effective one because that's the one that's going to affect the equilibrium price, or the new equilibrium price. But as we'll see there's some nuances in terms of considering the surplus. So first, let's think about the consumer. Well, actually let me label the now price with the taxes. So, this is now the R equilibrium price where we have the taxes. It's where our demand curve hasn't shifted. That's where the existing demand curve intersects with this new shifted supply with tax curve. And similarly, that point of intersection also tells us our quantity with the taxes. Now, now that we've understood everything, or hopefully we have, let's think about the various surpluses and the deadly weight losses and the tax revenues. So first, let's think about the consumer surplus. Well, the consumer surplus is going to be the region above our new horizontal price. And below the demand curve. So that is this region R right over here. That still, you have this consumer right over here who was willing to pay a lot but still has to pay less than that even with the taxes. So they're getting this benefit more than they would have needed in order, it would have been willing to pay more than the tax, and so they're getting this surplus. And so if you look at the entire market right now the total consumer surplus after the tax is R. R is equal to consumer surplus. And this is all after the taxes. Consumer surplus. Now, what about the producer surplus? Well, if we weren't dealing with the tax we would just look above the supply curve and below this equilibrium price line and say hey, maybe it's that area. But remember what's happening from the producers point of view. The producer does not see this new increased price at this quantity. The producer, remember, they don't get to keep the tax revenue. That, they have to give to the government. So the producer actually this is the price that the producer sees. So you can see this is this is what what producers what producers get after taxes. After taxes, or I say net of taxes. May be a better way to think about it. Net of taxes. And so the producer surplus is going to be the area below what they're getting from the market, net of taxes. And above what they the price is at which they were willing to produce various quantities. And so the producer surplus is this area of V over here. So, V is equal to the producer. Producer surplus. And now, what about the tax revenue? Well, the tax revenue is, is essentially going to be all of this other part of the total surplus. This is what goes to the government. The difference between these two. If the producers did not have to give that tax to the government then they wouldn't have been able to keep all of this. But this, right over here. Let me do this in a different color. So this region, right over here, is what the government is able to keep. Notice, it's this quantity and they get this much tax per unit quantity. And so this area is the government, is the revenue to the government. So, S plus U is equal to tax revenue. Tax revenue. And then last but not least, what about the deadweight loss? Well remember, the deadweight loss is the difference between the original the total surplus. When we just let things naturally go to equilibrium. The difference between that and now our new total surplus, which is now lower because we have not allowed the market to function in a very natural way because of this tax on it. Well, as we said before, the original total surplus was this entire triangle. Now the total surplus is this trapezoid that's the sum of all of these areas. And so what we lost is this area right over here. So that is the deadweight loss. So T plus W is equal to the deadweight loss. And we're done.