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The first lady “is so supportive of so many American designers,” Mr. Browne noted.

But Mr. Collins said he was a bit surprised the public doesn’t pay much attention to the president’s wardrobe. He joked that Mr. Obama should perhaps try one of Mr. Browne’s signature shrunken suits — the ones that show a man’s ankles.

At the end of the inaugural festivities, Mrs. Obama’s outfit and accompanying accessories will go to the National Archives.