The US ramped up trade friction last week with key allies Canada, Mexico and the European Union, by implementing proposed metal tariffs, underscoring the Trump administration's effort to rewrite trade rules, and the risk that wide-scale tariff increases could dull global commerce.

The duties - of 25% on steel and 10% on aluminum - went into effect on March 23, but the EU, Canada and Mexico had been exempted pending negotiations. The US was unable to get the concessions it wanted out of its partners, and did not renew the exemptions.

Although these latest duties don't even enjoy broad support among US leaders - some Republican lawmakers have used words such as "dumb" and "tax hike" to describe them - the Trump administration says they're necessary to rebuild the US's industrial base, protect jobs, and improve national security.

In response, trade authorities in Brussels, Mexico City and Ottawa decried the move as protectionist and promised retaliation.

The Trump administration is engaged in a "dangerous game," said EU trade commissioner Cecilia Malmstrom. The tariffs would hurt recovery in the EU and US, she said, adding that EU would challenge the US at the World Trade Organization.

Both sides have something to lose. Total trade - and both imports and exports -- between the EU and US rose during the first three months of this year.

EU-US total trade, first three months of year

• 2018: $198.2 billion
• 2017: $173.1 billion
• 2016: $165.3 billion

And the US shouldn't be too concerned about EU steel. Shipments to the US from Europe declined during the first quarter of 2018.

EU Steel exports to US, first three months of year

• 2018: 979,363 tons
• 2017: 1.24 million tons
• 2016: 962,050 tons

Justin Trudeau, the prime minister of Canada, said Ottawa would respond by imposing tariffs on US food, agriculture and other goods. Those duties would go into effect July 1, after consultation. In a tweet, President Trump said Canada had "treated our Agricultural business and Farmers very poorly".

However, the US trade deficit with Canada declined during the first quarter, thanks to an increase in US exports of aircraft parts, electrical machinery and other industrial goods.

US-Canada trade deficit, first three months of year

• 2018: $3.7 billion
• 2017: $7.1 billion
• 2016: $3.4 billion

Although imports of both steel and aluminum were down during the first quarter of 2018, shipments from Canada and Mexico increased.

Top US steel importers, first three months of 2018

• Canada 1.3 million tons (+5.4%)
• Brazil 951,541 tons (-9.8%)
• Mexico 649,515 (+13.2%)
• Russia 525,341 (-14%)
• South Korea 390,716 (+8.4%)j
• Japan 309,605 (-16%)
• Turkey 269,164 (-60%)
• Germany 216,596 (+25%)
• South Africa 170,537 (-7.6%)
• Taiwan 170,175 (-27%)

The US trade deficit with Mexico increased 9% to $18.3 billion in the first quarter of 2018 from $16.7 billion during the first quarter of 2017.

US-Mexico trade deficit, first three months of year

• 2018: $18.3 billion
• 2017: $16.7 billion
• 2016: $14.9 billion

In the first quarter of 2018, Mexico passed Japan as the owner of the second biggest trade surplus with the US.

Top US trade deficits, first three months of 2018

• China $91.1 billion
• Mexico $18.3 billion
• Japan $17.5 billion
• Germany $15.9 billion
• Ireland $11.2 billion
• Vietnam $9.3 billion
• Italy $7.3 billion
• Malaysia $6.1 billion
• India $5.4 billion
• Thailand $4.5 billion

Mexico said it would retaliate against the metal duties with tariffs on US goods, including steel and pipe products, fruit including apples and grapes, and cheese.

China still has, by far, the biggest surplus with the US. Washington has said it might impose additional tariffs on tens of billions of dollars worth of Chinese industrial goods.

Washington is now engaged in trade spats with almost all its key economic partners. It's been in regular talks with the EU, China and South Korea, and renegotiating the North American Free Trade Agreement.

Meanwhile, the tariffs don't appear to be having much impact on the behavior of the world's main disrupter of industrial markets, China. With prices rising this year, Chinese aluminum exports increased for the third year in a row, quarter on quarter.

Chinese aluminum exports, first three months of year

• 2018: 1.78 million tons
• 2017: 1.53 million tons
• 2016: 1.49 million tons
• 2015: 1.67 million tons
• 2014: 1.2 million tons
• 2013: 1.1 million tons

The situation is much different for Chinese steel. Exports declined to 67.5 million tons in 2017 from 97.4 million tons in 2016, and in the first quarter of 2018, they fell 29% compared to the year before.

Chinese steel exports, first three months of year

• 2018: 13.1 million tons
• 2017: 18.4 million tons
• 2016: 25.2 million tons
• 2015: 22.7 million tons
• 2014: 15.8 million tons
• 2013: 12.1 million tons

However, in neither case was the variation directly triggered by tariffs.

In the case of steel, construction firms and makers of cars, ship and refrigerators are sucking up more steel, and capacity is being cut in order to reduce pollution, according to Chinese steel and government officials.

And in the case of aluminum, what changed was simple: Prices went up.