PRESIDENT DONALD TRUMP is about to find out how easy trade wars are to win. In the name of America’s national security, on May 31st he announced tariffs on steel and aluminium from Canada, Mexico and the European Union. From midnight that same day, trade flows worth $23bn in 2017 faced duties of up to 25%.

Tariffs are a tax. These ones are supposed to hand market power to American metal producers, allowing them to raise prices. In that respect, so far they seem to be succeeding. Over recent months, premiums for American steel and aluminium over metal bought in Europe or Asia have surged. But in this case, help for one industry harms others. Business lobby-groups from the American Beer Institute to the American Petroleum Institute, whose members use aluminium and steel, respectively, have lined up to denounce the tariffs. Even the United Steelworkers Union (USW), previously supportive of trade restrictions, has criticised the action. (In North America some unions as well as many supply chains are integrated; the USW has members in both Canada and the United States.)

Although the tariffs will be a blow to steel- and aluminium-consuming industries, their direct effect on America’s economy will not be large. Goldman Sachs, a bank, estimates that the latest round of tariffs could boost one measure of inflation by 0.01 percentage points. But the retaliation is likely to sting. The EU has been preparing for retaliation for months. And on the day of the Trump administration’s announcement, Canada and Mexico each published tariff lists detailing plans to hit American exports of steel, aluminium, sausages, pizza and whiskey, among other things. Chrystia Freeland, Canada’s minister for foreign affairs, pointed out that proposed duties on C$16.6bn ($12.8bn) of American exports (4.5% of the bilateral total) would constitute the largest trade measure the Canadians had undertaken since the second world war.

The indirect effects of the tariffs are likely to have a bigger impact. Under Mr Trump, American trade policy has become highly uncertain, as he demonstrates to the world that he is willing to inflict harm on his own supporters to get his way. The American market is big, perhaps big enough for a policy of intimidation to work in persuading companies to make things closer to their consumers. But though this might seem to serve the president’s agenda of protecting and repatriating manufacturing jobs, scaring companies away from global supply chains will leave America poorer in the long run.

Beyond steel, the bigger question is what the metal tariffs mean for the North American Free-Trade Agreement (NAFTA), which links America, Canada and Mexico together for production of many goods, and which Mr Trump is seeking to renegotiate. Neither Canada nor Mexico has walked away yet, at least. (Indeed, the Canadians are boldly planning to use the original deal to launch an official dispute.) But talks are in a hiatus. On May 31st Justin Trudeau, Canada’s prime minister, spoke of his offer to meet Mr Trump to resolve their differences and finalise a NAFTA deal. But after he was told that a precondition for the meeting was that the Canadians accept a five-year sunset clause for NAFTA, he refused. Then came the tariffs.

Mr Trump may think tariffs on steel and aluminium will make his trade counterparts more likely to agree a new NAFTA deal. If so, he is playing a dangerous game. Mr Trudeau must think of his own political standing. And Mexico is in the middle of an election campaign, where looking tough against the yanquis plays well. In frustration, Mr Trump may decide to escalate the situation. On May 31st he said, “The United States will agree to a fair deal, or there will be no deal at all.” But if he were to pull America out of NAFTA he would face a huge domestic backlash, opening up yet another front in his war on free trade.

So far, it looks as though America’s trading partners are at least trying to preserve the rules-based trading order. Both the EU and Canada are planning tariff retaliation on the basis that America’s actions are a “safeguard” action; in such cases the rules allow for near-immediate compensation. America, however, claims its tariffs are in the name of national security and that retaliation is therefore unjustified. So there is a risk that it may retaliate in turn.

As talk of tariffs on America’s imports escalated over the past few months—from $50bn of steel and aluminium, to $150bn on goods from China, to $350bn of American car and car parts imports—observers could be forgiven for assuming that calmer heads would eventually prevail. Some became inured to the Trump administration’s repeated threats and reversals, and therefore complacent. This latest action on steel and aluminium could be a gambit to show that Mr Trump is not bluffing when he threatens to erect trade barriers. His opponents will be hoping that this is the action that convinces him of the high cost of doing so.