It is no secret that US President Donald Trump wants to build a border wall that is intended to separate the US-Mexican border. While it is largely accepted that Trump's bid to get Mexico to pay for the wall is always going to be a long shot, given the tens of billions of dollars the project is likely to cost, it is his idea of imposing tariffs on Mexico to finance the border wall that deserves a shot-down. It is not just bad economics, but also highly misleading to the American public who believes that this idea would work.
For us to understand how tariffs work, it is intuitive to see it as a tax on foreign goods and services intended to shelter domestic firms from foreign competition. It is often used for a variety of reasons: to protect infant industries to allow them to reap economies of scale, as a countervailing measure against dumping, or as a measure to reduce structural unemployment for sunset industries, or to protect jobs in a recession.
No one has ever suggested imposing tariffs on foreign goods and services as a way to earn revenue from foreign firms. This doesn't imply the idea is original, rather, the idea of using tariff to raise revenue from foreign firms, without harming domestic consumers, is purely wrong.
To prove this, I would refer to the tariff diagram (pardon the technicalities) below.
Suppose US is imposing tariffs (t) on imports of cars from Mexico. Further suppose US is a price taker in the market for cars, which is a reasonable assumption since there is a large global market for cars, and no country can influence the world price of cars. At the original world price (Pw), the quantity demanded (Qd) of cars exceed quantity supplied (Qs), implying that US is importing Qd - Qs units of cars. With the imposition of the tariff, the price of cars increases from Pw to Pw + t, resulting in a decrease in imports to Q2 - Q1.
While US government earns the revenue area of C (per unit tariff x number of imports) from Mexican firms, it is noteworthy that this comes from the pockets of American consumers who have to pay a higher price for their cars. In other words, although the tax is imposed on Mexican firms, these firms would just simply pass on the tariff increase to US consumers in the form of a price increase.
Put simply, if I am selling kaya toast to US at $1 per unit, and US decides to impose a tariff of 50 cents, I would just simply sell it in the US market for $1.50. Although I am still effectively earning $1 per unit, I have successfully passed on the full tariff hike to the US consumers.
To conclude, it should be plain obvious that Trump will not build the border wall, and it is merely rhetoric to get US voters to side with him, as he denigrates the Mexican immigrants as murderers and rapists.