How did Mexico manifest itself in your brain? Did you think of a sort of vague outline of the country? Did you imagine Trump, standing at a rally, basking in the applause of his supporters? Regardless, you made the connection instantly: From even before he announced his candidacy, Trump was insisting that the costs of the wall would be borne by our neighbors to the South.

At least until he became president. Then, faced with the reality that Mexico was not going to pay for the wall and there was no real way to force Mexico to pay for the wall, Trump mostly stopped making the claim.

The last time he did so publicly was in May, when, standing in front of signs saying “Promises Made” and “Promises Kept,” he again claimed he would get Mexico to cover the costs.

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That was the most recent time he'd made the assertion — until Thursday morning. In a tweet, Trump claimed not only that Mexico would pay for the wall but that, in essence, it already was.

This doesn’t make sense, though it’s not exactly clear what Trump is referring to here. What is “the money we save” in the context of the new trade agreement with Mexico and Canada?

The most likely candidate is that Trump is referring to the trade deficit between the United States and Mexico. In a campaign rally in Mississippi last month, Trump touted the trade deal as a way to reduce the deficit in trade the United States sees with Mexico. In 2017, that figure was $63.6 billion. Assuming the wall costs $18 billion, dropping the trade deficit to $45.6 billion would, under this framework, pay for the wall’s cost.

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But, of course, that isn’t at all how this works. The trade deficit is not a measure of how much cash the U.S. government sends to Mexico and how much the Mexican government sends back. It is a measure of how much the United States spends on goods and services from Mexico compared to the amount Mexico — that is, Mexicans — spend on American goods and services.

If the only trade that occurred between the United States and Mexico was my buying 10 Mexican avocados for $30 and someone there buying a T-shirt from me for $10, the trade deficit would be $20. But if I only bought five avocados, dropping the trade deficit from $20 to $5 ($15 for the avocados minus $10 for the shirt), it is not the case that the U.S. government is suddenly $15 richer. The feds don’t suddenly have $15 more to spend on wall building; the $15 is in my pocket.

Now, look: I'm not going to complain about having $15 more in my pocket. Trump's argument for revamping NAFTA during the 2016 campaign was precisely that consumers would see the benefit. But it's not the case that a reduction in the trade deficit is something that's going to power construction of a wall.

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What’s more, Trump already starts at a disadvantage. In 2016, the trade deficit with Mexico was $55.6 billion, meaning that it increased by $8 billion during Trump’s first year in office. Presumably then, we need the trade deficit to drop by $26 billion — that $8 billion increase plus the $18 billion cost for the wall — to come out ahead on this thing.

I’ll need to sell a lot of T-shirts.

There's another theory for how this new trade deal will pay for the wall — a circuitous one. Our Heather Long (who knows this world well) speculates that perhaps the increased government funding is a function of the creation of additional jobs after companies reintroduce additional manufacturing in the United States.

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So let’s assume that this is the argument Trump is making, to the extent that he’s making an argument. Let’s assume that the USMCA, as the trade deal is known, leads to new manufacturing or farming jobs in the United States and that an additional 10,000 people get jobs who otherwise wouldn’t be working. Let’s assume, too, that each of those jobs pays $100,000 a year. A lot of assumptions, but let’s go with it.

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Let’s use this estimate and assume that each of those new employees would be paying about $18,000 to the federal government each year. That $18 billion for the wall would be paid off in only ... 100 years.

But, of course, that money just goes into the Treasury, where it is allocated by Congress. There's no special Wall Fund into which the taxes paid by new jobs is partitioned. So we're basically back at square one: The government needs to fund the wall.

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Particularly since — minor detail — the new trade agreement hasn’t been ratified by Congress, meaning that literally nothing has changed yet anyway.

Senate Minority Leader Charles E. Schumer (D-N.Y.) scored a point in his response to Trump on Twitter. This week, in a meeting with Democratic leaders in the Oval Office, Trump insisted that money for the wall needed to be included in a government funding bill or he wouldn’t sign it.

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"If you say Mexico is going to pay for the wall (which I don’t believe), then I guess we don’t have to!” Schumer wrote. It’s very Schumer-y to include that parenthetical, weakening the joke, but the point is fair: If Mexico paid, why does the United States need to?