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.
