The External Revenue Service, Continued
Some more context
Note: This post looks A LOT better on desktop than it does on mobile. I’m not really sure why, but it’s my first time using LaTeX on Substack. Also, the LaTeX environment on mobile doesn’t like the plus sign for some reason. I promise you that they’re there!
I got bumped from NewsMax this week in favor of their covering the Trump cabinet nomination hearings. C’est la vie, I suppose. So instead of listing talking points, I thought I’d use this space to cover something somewhat wonky that I think is worth covering, even if no editor would ever agree to publish it.
In case you haven’t seen, Trump recently announced that on Monday, he’ll create the External Revenue Service as a means of collecting revenue from foreign countries/companies who benefit from “trade” with us. In reality, I think he just means “collecting tariff revenue,” but I guess time will tell. I wrote about this in today’s The Daily Economy, which you should absolutely check out for more actual discussion of what this all means.
In the article, I made a number of claims. These are intuitively true to someone who has an economics background. However, for someone who does not have a firm grasp of Econ 101, they might be less obvious, and so I want to spend some space here explaining them. It’s also a chance for me to let out some of my vestigial “professor” habits and explain something that I’m passionate about, even if just to a relatively small audience. I am going to presume at least a little familiarity with supply and demand, though, and then I’ll use that to bridge into discussing the economic incidence of taxation.
Claim #1: The Price of a Good Does Not Rise by the Full Tax Amount
In the article, I used the example of a candy bar which sold for $2.00 before any taxes were applied. I then imagined a $1.00 tax being imposed on each and every candy bar and asserted that the final price to the consumer would not rise to $3.00 despite the truism that 2+1=3. I then said that this was because “demand curves slope down and supply curves slope up.” Let’s unpack all of this real quick:
Here, we have a simple supply and demand graph that I whipped up real quick. Nothing fancy, no algebra (yet), just a simple “demand slopes down, supply slopes up, and X marks the spot” kind of picture. Let’s add in that $1.00 tax that the seller has to pay:
This one has a LOT going on in it. Notice that the supply curve shifts up by the amount of the tax, in this case, by $1.00. I tried to indicate that with the green arrows to show that it’s a parallel shift of the entire supply curve. I also labeled that curve St so as to differentiate it from the normal Supply curve.
The new equilibrium point between St and D would be the red point. Coming straight over to the Y-axis gives us the amount that the consumer will pay, which I’ve labeled P+ for simplicity.
Coming straight down from the red dot all the way to the x-axis, we have the quantity of candy bars that will be sold as a result of this tax (Qt). Notice that it is less than the quantity originally sold (Q). This makes intuitive sense; we know that taxes make things more expensive, not less, and that people will buy less of something if it is now more expensive.
If we come straight down from the red point by the amount of the tax ($1.00), we hit the original Supply curve (blue point). Coming straight over from the blue point to the y-axis will give us the amount of money that the seller will actually get to keep after the tax, which I’ve labeled P- for simplicity.
The incidence of the tax for the buyer would be calculated as P+ - $2.00. For the sellers, it would be $2.00 - P-. In this example, I’ve deliberately constructed the figure such that the incidence was equal for both — it just looks prettier if I do it that way (and the math in LaTeX/TikZ was a LOT easier!).
But notice that, while the supply curve did move up by the full amount of the tax ($1.00), the price that consumers pay does not increase by the full amount of the tax. Even without assigning numbers or equations to these functions, we can know that this is true since the green line connecting the red and blue dots (which shows the shift of the Supply curve due to the tax) has some portion that is below the dotted black line! This means that P+ - $2.00 must be less than $1.00!
Claim #2: It Doesn’t Matter Whether We Tax Buyers or Sellers, The Result Is The Same
I made a second claim in my piece that it doesn’t matter whether we place the tax on the buyers or the sellers; the economic result will be exactly the same. In the previous figure, I placed the tax on the sellers. But what would it look like if I placed it on the buyers instead? Since it’s on the buyers, we know that it will affect the demand curve. Let’s add a $1.00 tax to the buyers and see what that does:
Again, there’s a lot going on here, but it should look familiar if you saw the last graph. The only difference is that in this figure, the entire Demand curve moved down by the amount of the tax. Everything else about this picture is exactly the same. I’ll spare the copy/paste job from above and instead address the claim that the economic incidence is exactly the same.
I could post the LaTeX code that I used to generate these images, point out that all I did was add/subtract the same constant from the original supply/demand curves (in black) and that the points for the red, black, and blue circles are all the same, but that would be ridiculous. Besides, wouldn’t algebra be more fun? I think so!
Let’s give ourselves some simple supply and demand equations to work with:
First, we set Supply equal to Demand and solve to find our equilibrium point. Since at equilibrium, P = P, we can say that:
Solving this for Q gives us Q = 2. Plugging that back in and solving for P gives us P = 2 as well.
Let’s add a $1.00 tax to the producer. The producer knows that, whatever price they charge, they’re actually going to get to keep $1.00 less than that. So from their perspective, we need to replace “P” with “P - 1.” This gives us:
Which is the same thing as:
Thus, all we have done is moved the Supply curve up by the amount of the tax, 1. From here, we can simply solve, setting this new Supply curve equal to the original Demand curve:
Solving for Qt gives us 1.5. Taking that 1.5 and plugging it back into our original supply and demand curves, without any taxes, will then give us the values for P+ and P-, which are 2.5 and 1.5 respectively.
So here’s what we’ve established. If we put the tax on the seller, then:
Qt = 1.5
P+ = 2.5
P- = 1.5
Let’s do the same exercise again, but this time we’ll put the tax on the buyers instead. Since we’re putting the tax on the buyer, we know that whatever the price of the good is, they’re going to have to pay the tax on top of that. Thus, from their perspective, the Price that they’ll pay is whatever the price of the good is plus $1.00. Thus, we can rewrite the demand equation as:
Which is the same thing as:
Thus, all we have done is moved the Demand curve down by the amount of the tax, 1. From here, we can simply solve, setting this new Demand curve equal to the original Supply curve:
Which, solving for Qt gives us 1.5 once again. And from here, we can repeat the above to solve for P+ and P- just as we did before and we’ll get the same values, 2.5 and 1.5 respectively.
So if the buyer pays the tax, then:
Qt = 1.5
P+ = 2.5
P- = 1.5
Thus, we can say that the economic incidence of the tax is the same whether we place the tax on the seller or the buyer. The final outcome of either of these is that the buyer will pay $2.50 and the seller will keep $1.50. Incidentally, this is also why most economists will scoff whenever policymakers say something to the effect of, “we’re going to raise income taxes on employers, not on the employees. That way YOU keep more money in your pocket while your employer will pay their fair share!” We scoff because, despite the bluster and rhetoric, it doesn’t actually make a difference whatsoever.
Applying This To Tariffs
I’ll be honest, this post has gotten long enough as it is and has taken me long enough to write (those graphs took me about an hour to do). I’ve also got a kid home sick at the moment and I’m still trying to decide if I want to go the simple, Econ 101 explanation of how tariffs work graphically and algebraically or if I want to do the full, in-depth discussion of how they actually work. The difference is minute, which has me inclined to do the former, but it also matters which has me inclined to do the latter. I might need some time to figure this one out. Regardless, I’ll write a follow-up, possibly on Monday, that will address this one.
Conclusion
Anyway, if you’ve made it this far in reading my post, thank you! It means a lot to me. This topic was, ironically enough, the topic that made me fall in love with economics in the first place when I was an undergraduate student. I had gotten Cs in my Microeconomic Principles and Macroeconomic Principles classes (technically a C and a C+, but whatever) and I failed my first exam in Intermediate Microeconomics. I failed it so badly that I had to meet with my professor one-on-one every week for extra tutoring!
After a few weeks, we covered the incidence of taxation in class and he was going over exactly what I went over above and suddenly… everything just clicked for me. I actually understood economics to a point where supply and demand became tools that I could use to understand the world around me, not just a simple abstraction that I could answer questions about on an exam, to be forgotten at the end of the semester. I started thinking about everything in terms of supply and demand and, well, I haven’t stopped, even after almost 20 years.
Post-Script
Also. Before anyone brings this up: yes, I’m aware of AC/DC Econ’s video on taxes where he says that taxes cause the supply curve to shift to the left. I’m just going to put it simply: he’s wrong. Taxes shift supply/demand curves up/down because they affect the price of all units.
When we say the phrase, for example, “demand has increased,” what we typically mean is “at any given price, the quantity-demanded has increased.” Thus, we would shift the demand curve right to reflect this. If we said instead something like “supply has decreased,” then what we’re really saying is “at any given price, the quantity-supplied has decreased.” Thus, the supply curve would move left to reflect this.
I will fully admit that this is a nuanced and, at some level, pedantic point. I’ll also admit that the rest of his video is excellent. But math matters and being clear in math is incredibly important. He’s wrong, but his video is otherwise just so good.