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Two hundred and forty years after his country ostentatiously tore up its membership card in the British Empire, the American president is traveling to London to warn the British not to do the same with theirs for Europe. It's a bit rich, as some Brits would put it, but Barack Obama has not merely the right but the obligation to make his case.

He's smart enough, no doubt, to be subtle about it. Like most people, the British don't take well to being bossed around by foreign leaders. He should keep his message simple, too, and along the following lines: A British exit from the European Union, which will be decided by a referendum on June 23, would be a major disruption for the U.K. and all its trading partners, at a time when the world economy is far from strong. The U.K. needs to think about what's at stake — not just for itself, but for its friends.

Last week the U.K. Treasury published a detailed report on the potential economic costs of separation. It isn't an evenhanded document — the government, after all, is campaigning for Britain to stay — but its estimates of costs are credible. In what the Treasury deems the most plausible scenario, the annual cost of diminished trade (and, with that, slower productivity growth) would be around 6 percent of GDP by 2030.

The true cost could easily be much higher or lower, depending on how events unfold, which is impossible to predict. Yet there's no denying the risk. Adding to the danger, the exit campaigners are divided among themselves about what should come next.

Granted, the U.S. interest in Britain's decision might be a little more complicated than Obama allows. His view that Britain would be a more useful ally as part of the EU than as an independent nation, for instance, is debatable.

But the economic calculation is clearer. The global economy is already sagging, and the normal remedies aren't working well. A British exit would be a serious economic shock to the U.K., Europe, the U.S. and the rest of the world. That's the last thing the U.S. or any other friend should want — and Obama ought to say so.