Trump did two things yesterday. He went to Mexico, and gave a speech to try to undo the damage of his deportation flip-flop, which, as I said, wasn't really damage anyway. What I found fascinating was the disagreement over whether or not the wall came up during his Mexico trip. Even if Trump does pull out a victory (23% chance in the markets this morning), I haven't seen anyone go through the deal-making mechanics of "making Mexico pay" in this way, so here's some basic microeconomics.
If I have A, and you offer me B, I won't take the trade unless the value of B to me, in utility terms, is greater than the value of A. Ume(B)>Ume(A). But, you won't offer B unless A is more valuable to you than B. Uyou(B)<Uyou(A). This is the old Adam Smith thing. The baker prefers the money to the bread, the customer prefers the bread to the money, so everyone is happier after the transaction, and yay capitalism.
Without some external enforcement mechanism, then, the only way to get Mexico to pay for the wall is to offer them something that they want more than the money. But, we're not the country with the stuff, we're the country with the money. That's why we run trade deficits.
Which brings us to option b. If you don't keep up on mortgage payments, the bank can repossess your house. Why? Because an external enforcement agency-- the government-- recognizes the legitimacy of the debt. That's because you signed a contract, and even the most hardcore libertarian will say that the government's job is contract enforcement. Mexico never signed a contract (treaty) agreeing to pay for the wall, and never will, and even if they had, there is no supranational enforcement agency that will take the money out of their banks.
There is supranational enforcement of debt, though. When a country, like Greece, fails to pay its debt, nobody will lend it money at low rates anymore. In principle, if other countries recognized the legitimacy of Mexico's responsibility to pay for the wall and they didn't, their interest rates would go up like Greece's, but that ain't gonna happen because Mexico never agreed to pay for the wall and never will, and nobody outside the U.S. thinks they should.
That leaves only one mechanism. When there is no legal or general social enforcement of debt, there is force. Loan sharks can't go to the government and repossess your property through legal means because they didn't loan you the money through legal means. So, how do you like your kneecaps? The problem, of course, is if they get caught. It isn't clear what the international analogy to that would be, short of actual force, which, well...
Will Donald Trump become president? Probably not. 3-1 against in the markets, as of this morning. Would the wall get built? No. No contractor would start construction on spec, Congress won't appropriate that level of money even as seed money, Mexico won't cough up the dough, and Trump won't really have the tools. But, it is still worth going through the economics of it.