Trade allows people and firms to specialize in what they produce. This enables them to be more productive. This raises the income (standard of living) of both the seller and the buyer (who must also sell something in order to buy something)—i.e. both the exporter and importer. https://wcoats.blog/2017/09/15/a-basic-human-right/ https://wcoats.blog/2016/12/22/save-trade/
So what does Trump’s steel and aluminum tariff do?
The American economy is now fully employed (ok, maybe some of those who left the labor market in recent years, not all of whom are old, can be coaxed to return). Thus if high tariffs on steel and aluminum make previously non competitive and inefficient American steel and aluminum producers competitive again, where will the workers come from to do that work? They must be attracted away from what ever they are producing now—lets call it good A. So we will produce less of good A, which was competitive without taxpayer subsidies or regulatory favoritism, in order to produce more steel and aluminum, which was not competitive before given tariff protection. Add it up and our overall income goes down. The economy over all will be less efficient, less productive, and our overall incomes and standard of living will be reduced.
This reallocation of our resources from more productive to less productive products will make owners of steel and aluminum companies and property owners around closed foundries happy. Trump-may-prosper-from-tariffs-even-if-this-faded-port-town-doesnt/2018/03/02/. But what about those who buy steel and aluminum made more expensive by the tariffs? What about Boeing and other aircraft manufacturers who are the fourth largest American exporters, whose products will now be more expensive and less competitive with Airbus, etc.? When steel tariffs were imposed in the year 2002, 200,000 Americans in steel using industries lost their jobs. That is more than the total of around 150,000 workers in the steel industry! “If-the-US-steel-industry-employs-150000-people-then-how-can-imports-threaten-500,000-jobs?”
Subsidizing inefficient industries with tariffs hurts consumers, who will have to pay the higher prices of aluminum beer cans, etc., as well as exporters like Boeing. We will all (except steel and aluminum producers) pay the cost of this increased inefficiency. Commerce secretary Wilbur Ross thinks we should just get over these modest increases in the costs of our purchase of goods that include steel and aluminum for the greater good of American steel and aluminum producers and the 150,000 people who work for them. In case there are children listening I am withholding what I would like to say to Mr. Ross.
Only 2.2% of our steel and aluminum imports come from China while Canada (hardly a security threat to the U.S.) provides 16.1% of our imports of these products: https://www.washingtonpost.com/world/the_americas/canada-top-exporter-of-steel-and-aluminum-to-us-flabbergasted-by-trumps-tariff-proposals/2018/03/02/7c906c2a-1e22-11e8-98f5-ceecfa8741b6_story.html?undefined=&utm_term=.294884487749&wpisrc=nl_headlines&wpmm=1. The rest of the world will not roll over and play dead. The EU is already preparing counter measures to punish American exporters to Europe. “EU-vows-to-hit-back-against-trump-in-trade-war”
Following the end of WWII the world, lead by the U.S., has built up mechanisms for promoting fair trade (first the General Agreement on Trade and Tariffs—GATT—now called the World Trade Organization—WTO). Where countries violate these rules, and China frequently does, they should be addressed via the WTO. American interests, and the world’s interests more generally, are served by strengthening the WTO not weakening it. Trump’s unilateral tariffs do not serve our interests. Not only has he persistently undermined free markets with his misplaced attack on bilateral trade deficits https://wcoats.blog/2017/07/23/the-balance-of-trade/ but he has systematically undermined the WTO and the international rule of law. Please, Mr. President, stop this nonsense before it gets even worse.
Trade wars are never good, and no one wins in the end. Instead we should be enforcing and improving the rules of trade via the WTO, which has helped lift millions of people out of poverty and raised the standard of living of the average person.
Warren's space 
The redistribution effects of the steel and aluminum tariffs are clear, but what I wonder is why Trump and his supporters favor thos guys? Tariffs and quotas reward fixed capital and labor, but it is seen as temporary also. No growth; no recalling of laid off labor. This is just a payoff for something they have done, or expect to do for the Presidency.
Of course, it smells “nationalistic” and “defense,” which sounds like Navarro. But Lightheizer and Ross came out of the community of such industries. This is simple Public Choice evaluation of the process.
Or as Dan Vencill used to say, “if you mess with the market, the market will mess w/ you.”