Sometimes misconceptions really matter. A failure to understand, and an intransigence on misguided beliefs lead to disaster both public and private. It’s the spirit of a vandal.
Trump misunderstands accounting identities. He views a trade surplus as a win and a trade deficit as a loss. By his logic, the British Raj must have been the pinnacle of human achievement. Trump’s failure to understand the relationships in trade will impoverish Americans and the world over. For a country founded on a tax revolt, it’s strange to see the inheritors rejoicing in new taxes, declaring them a saviour.
A trade deficit simply means that you buy more from someone than you sell to them. As an example, nearly everyone has a trade deficit with the grocery store. You buy food, but you sell nothing to the grocer. On the other hand, you have a large trade surplus with your employer. You sell your labour and buy nothing in return. This is what a trade surplus and deficit means between nations. Canadians sell more stuff to Americans than Canadians buy from Americans. It’s tempting to talk as though Canada sells and the US buys, but it’s really millions of people and businesses making market decisions. Individual freedom is at the heart of trade. Perhaps Trump should take a careful read of the last stanza of his nation’s anthem and make sure to answer the question in the affirmative.
International trade is a large field of economics but we don’t need advanced training to understand the basics. Here are the essentials:
Imagine that a country generates 
output in a year. That’s everything made – cars, agriculture products, accounting services, everything. That output has to go somewhere. We can consume it (
), the government can consume it (
), we can invest it (
), or we can export it (
). That’s it; that covers where the output has to go. So:
(1) 
If exports are positive we have a trade surplus, if negative we have a trade deficit. The difference between what we produce and everything we consume is our savings (
):
(2) 
Rearranging, we get,
(3) 
A trade deficit or surplus is determined by the difference between savings and investment. THIS IS AN IDENTITY. This is not a theory, this is the Piaget test of pouring water into different containers. The identity makes intuitive sense: If our savings equals our investment there is nothing left to (net) export.
In the case of the United States, is large; Americans run a large fiscal deficit. American consumers like to consume. They have a low savings rate; is high. The US has high production, , but investment, , is also high. As a result is negative for the US, yielding a trade deficit. To make positive the American consumer will have to consume less, the government will have to spend less, or the US must invest less. Unless some combination of those things happen, no matter what Trump does with tariffs, the trade deficit will remain. One way for Trump to get rid of the trade deficit would be to so damage American consumers that they have little opportunity to consume – drive C way down. Not fun in a democracy.
There is no sense trying to argue identities with a vandal. The optimal response is unilateral free trade. Allow Canadians to buy and sell from anyone, anywhere. Unfortunately, our political class is just as bad at arithmetic as Trump. Maybe we need to re-read our national anthem, too…
Not being a mathematician, I wonder if you have neglected to consider that the intent of tariffs is not to punish the foreign producer but to move X (which, I think should be net exports) from a negative to a positive or, at least, less negative and stimulating domestic production to fill the gap.
Yes, free trade is the ideal, but we are not actually in a global free trade environment. Many countries, not just the US, have their own set of tariffs, or impediments to importation. China does, Canada certainly does. The EU does, as well. So, simply saying that Trump is making a mistake falls far short of addressing the global problem with free trade. It is much like the climate accords; the greater burden always seems to be placed on the US.
Free trade is far different from climate change accords. It doesn’t matter what the other country does when it comes to trade. If they want to prevent imports, that’s their own business. It’s their citizens who will suffer. Ultimately tariffs (taxes) on imports end up taxing exports. Remember, exports are what we use to pay for imports. Trade is indistinguishable from a technology – we put stuff into the machine (the other country) and stuff we like more comes out. If a country want to subsidize exports – that is take less stuff to pump out more stuff we want – I say back the truck up and dump your below cost stuff on my front porch. In the end, it’s the other country’s problem if their citizens go to work to make stuff below cost for me. There is no “problem” with global trade.
The burden the US has is that the US has a giant fiscal deficit. If the US doesn’t get that very real problem under control, their will be a reckoning like never before experienced.