Identifying tax incidence in a graph | APⓇ Microeconomics | Khan Academy

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'll make your brain more attuned to when we work through it together.

All right, now let's work through this together, and I just really want to understand what's going on here before I even try to answer the questions. So, let's first think about what's going on before the tax. 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.

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. 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 due 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 drew it for us—is that it shifts the effective supply curve up. 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 are some nuances in terms of considering the surplus. So first, let's think about the consumer. Actually, let me label the new price with the taxes. This is now our equilibrium price when we have the taxes. It's where our demand curve hasn't shifted, but where the existing demand curve intersects with this new shifted supply with tax curve. 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 deadweight losses and the tax revenues. 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. You still 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—they would have been willing to pay more than the tax—and so they're getting this surplus. 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 the equilibrium price line and say, "Hey, maybe it's that area." But remember what's happening from the producer's 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; they have to give it to the government. So the producer actually sees this price; this is what producers get after taxes—or I'd say net of taxes. Maybe a better way to think about it is net of taxes. This producer surplus is going to be the area below what they're getting from the market net of taxes and above the prices at which they were willing to produce various quantities. So, the producer surplus is this area V right over here. V is equal to the producer surplus.

Now, what about the tax revenue? Well, the tax revenue 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 would have been able to keep all of this.

This right over here—let me do this in a new color—is what the government is able to keep. Notice it's this quantity, and they get this much tax per unit quantity. This area is the government revenue to the government. So, S plus U is equal to tax revenue.

Last but not least, what about the deadweight loss? Well, remember the deadweight loss is the difference between the original total surplus when we just let things naturally go to equilibrium and the difference between that and now our new total surplus, which is now lower because we have not allowed the market to just function in a very natural way because of this tax on quantity.

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. So what we lost is this area right over here. So that is the deadweight loss. T plus W is equal to the deadweight loss, and we're done.