Some bad news and then some good news and then some bad news.
Bad News
On January 21, on his first full day in office, President Trump threatened to impose a 10% tariff rate on imports from China. His beef is that “China,” whatever that means (cue co-blogger Pierre Lemieux), is sending to Mexico chemical ingredients (precursor chemicals) that are used to make fentanyl.
I was a little surprised by this—not that Trump did it, but that the tariff rate he proposes is “only” 10 percent. Why was I surprised? During the campaign, he threatened to impose a 60% tariff on Chinese imports. Ten percent is only one sixth of 60%. Moreover, he threatens 10% on Chinese imports at the same time he threatens a whopping 25% tariff rate on imports from Mexico and Canada.
Good News
There is good news here. The damage done by a 10% tariff is not 1/6 of the damage done by a 60% tariff. It’s only 1/36.
How do I get that? There’s a basic theorem in economics, one that I taught my students with simple algebra, that says the deadweight loss from a tax is proportional, not to the tax rate, but to the square of the tax rate. If Trump were to impose a 60% tax rate, therefore, the deadweight loss (DWL) from that would be 36 times the DWL from a 10% tax rate.
The deadweight loss is the loss in consumer surplus and producer surplus from a tax.
Bad news
It’s also important to note that imports of goods from China were about $440 billion. Imports of goods from Canada and Mexico together were about $410 billion (Canada) plus about $500 billion (Mexico) for a total of over $900 billion. In other words, imports of goods from Canada and Mexico were about double imports of goods from China.
The deadweight loss from a tax is proportional to the quantity of the item taxed. The value of imports equals the quantity times the price. But in running the DWL formula we can approximately cancel out price from China on the one hand and Mexico and Canada on the other.
So here’s the bottom line. If Trump goes ahead with the 10% tariff on China and the 25% tariff on Canada and Mexico, the DWL from the tariffs on Canada and Mexico will be 6.25 times 2 times the DWL on tariffs on China. I get 6.25 by squaring 2.5 (25% divided by 10%) and 2 from $900 billion divided by $440 billion. 6.25 * 2 and = 12.5. So the deadweight loss from Trump’s proposal tariffs on Canada and Mexico is approximately 12.5 times the DWL from the proposed 10% tariff on China.
Notes: For simplicity, I’m assuming that the baseline tariff rate before these proposed tariffs is 0. That’s not quite true and the results would change a little if I made it more accurate. Also, the triangle in the picture is the deadweight loss from a tax.
READER COMMENTS
Rachel Edenfield
Jan 27 2025 at 7:45am
This was helpful – thanks for taking the time!
David Henderson
Jan 27 2025 at 12:19pm
You’re welcome, Rachel.
Bryan B
Jan 27 2025 at 9:33am
Interesting points. Do you think that the relatively low rate on China will cause trade to flow from Mexico to China then to the US rather than the China to Mexico to the US route?
David Henderson
Jan 27 2025 at 12:20pm
Possibly, for high-value per weight goods. Not for things like tomatoes, though.
Craig
Jan 27 2025 at 9:58am
“The deadweight loss from a tax is proportional to the quantity of the item taxed.”
Makes sense, but isn’t it the result of having to pay higher prices for the non-tariffed substitutes as well. I mean the tariff on BYD/EVs is designed, I think, to make sure BYD doesn’t sell cars here AT ALL. And I can say I want two of them. Flat out, I’d buy 2 (based on what I’ve read)…..
David Henderson
Jan 27 2025 at 12:22pm
That’s already wrapped into the demand curve, because the demand curve is already based on the closeness and availability of substitutes. Indeed, a big part of the deadweight loss is due to people seeking substitutes that, at the no-tariff price, are inferior for the money spent.
Richard A.
Jan 27 2025 at 2:59pm
From what I have found on the internet, it appears that Japan, UK, and Australia have no special tariff on Chinese EVs. We and the Canadians are outliers.
Here are the BYDs you can buy in Australia. The prices are given in Australian dollars. To change to American dollars, multiply by 0.63. Australia does have a tariff of about 5% on imported cars in general from those countries that they have no trade agreement with.
David Henderson
Jan 28 2025 at 6:25am
Thanks, Richard A.
Sierra
Jan 27 2025 at 2:00pm
If the DWL acronym were to come into common use from here on out, it might almost be worth it. As I recall, the OMB has (or perhaps used to have) a baked-in rule of thumb that any budgeted line item automatically had a DWL of 25% from taxation. Inaccurate, but at least it’s a gesture.
Scott Sumner
Jan 27 2025 at 2:05pm
Very good post. I’d add that some of the damage from China tariffs was mitigated by their exports being rerouted through places like Vietnam. That’s less likely to occur with imports from Canada and Mexico, and hence the damage would be even greater.
steve
Jan 27 2025 at 8:08pm
Michael Strain has a fairly recent paper looking at how protectionism is failing. By his measurements if you use “value-added” as your metric as a way to look at how much we get from China is indirect, then our protectionist policies haven’t accomplished anything.
https://www.economicstrategygroup.org/wp-content/uploads/2024/10/Strain-AESG-2024.pdf
Steve
David Henderson
Jan 28 2025 at 6:27am
Thanks, Scott.
And good point about transshipping.
Jose Pablo
Jan 27 2025 at 6:35pm
The deadweight loss is the loss in consumer surplus and producer surplus from a tax.
But then, the loss in producer surplus wouldn’t necessarily be “felt” within the U.S. The actual loss to the U.S. economy would depend on retaliatory tariffs from China, Canada, and Mexico.
And also on the reduction in the amount of dollars available to invest in dollar-denominated assets. Which could be not a minor issue.
What happens in your “model” if part of the impact is absorbed (or caused) by a change in the dollar exchange rate?
And what if, as Trump argues, tariffs increase the disposable income of U.S. consumers through a reduction in income taxes?
Sometimes, I wish I could understand economics—if only a little.
David Henderson
Jan 28 2025 at 9:00am
Dear Jose,
Good questions. They’ll take a lot of time to answer and I’m in Miami now visiting a friend, so working less. Maybe I’ll try to do it bit by bit over the next few weeks.
Jose Pablo
Jan 28 2025 at 2:00pm
You’ve been lucky with the weather! It was freezing cold (by Miami standards) just a few days ago. Enjoy it!
Thank you for trying later. Your clear and easy-to-follow explanations are greatly appreciated at any time.
Richard W. Fulmer
Jan 28 2025 at 11:39am
Jose,
Your questions are a great example of why economists tend to qualify their opinions with the caveat, “all else being equal.” In the real world, of course, all else rarely remains equal. Every move engenders a response, and every response its own set of consequences.
Jose Pablo
Jan 28 2025 at 4:35pm
I understand, Richard.
However, the “ceteris paribus” caveat should apply only to exogenous changes. For the sake of argument, we can assume that “tariffs + retaliatory tariffs” are the only exogenous change.
My point is that David’s model seems overly simplistic (though that’s not a criticism—it’s always the best place to start). In a coherent and complete economic model, endogenous changes—such as those in interest rates, exchange rates, taxes (assuming no changes in government spending or the tax code), and so on—would likely be also triggered by the tariff changes and were not included in the original S-D curves.
These adjustments would, in turn, influence the ultimate impact of the exogenous change in tariffs and retaliatory tariffs on economic activity. I would expect those endogenous adjustments to have a mitigating effect on the “initial” impact estimated by David. It would be interesting to know the direction and relative size of this potentitally mitigating effects.