The European Union is responding to President Trump’s sweeping trade war with a handshake and a punch: It is promising the administration potential wins while also preparing its own retaliatory tariffs on American products starting next week.

The questions are whether the enticements are enough, and whether a show of strength could backfire.

“Europe can hurt America, and retaliating seems like a good strategy if you believe that Trump cares about the political fallout from economic pain here at home,” said Michael Strain, director of economic policy studies at the conservative think tank American Enterprise Institute, in Washington. “The worry is that he doesn’t care.”

Mr. Trump has threatened to impose huge additional tariffs on Chinese goods to punish the nation for retaliating against his previous tariffs, and his team appears to be giving some nations that did not retaliate and have close economic ties to the U.S. — notably Japan — priority in negotiations.

At the same time, Mr. Trump has yet to grab the carrots that Europe has dangled in front of him. Ursula von der Leyen, the president of the European Commission, offered on Monday to drop tariffs on imported American cars and other industrial products to zero if the U.S. does the same, a “zero-for-zero” strategy. Asked about that possibility, Mr. Trump said “it’s not” enough to make him back down.

Instead, the administration appears to be standing by its spate of recently-announced tariffs, at least for now. The Trump administration has announced 20 percent across-the-board levies on the E.U., in addition to even higher ones on steel, aluminum and cars.

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