The Bidens’ income increased sharply after he left office. On their 2016 tax return, the Bidens reported an adjusted gross income of $396,456. At the time, their income included Mr. Biden’s annual salary as vice president and his government pension, Dr. Biden’s income as a community college professor, and social security benefits.

Mr. Biden’s newfound wealth has not changed his message. In his first remarks during last month’s Democratic debate, Mr. Biden spoke of “enormous income inequality” and promised to eliminate Mr. Trump’s “tax cuts for the wealthy.”

“Ordinary middle-class Americans built America,” Mr. Biden said. “My dad used to have an expression — he said, ‘Joe, a job is about a lot more than a paycheck; it’s about your dignity, it’s about respect, it’s being able to look your kid in the eye and say everything’s going to be O.K.’”

But in contrast to some of his more progressive rivals, who have sought distance from wealthy donors — or have at least played down their reliance on them — Mr. Biden is open about his frequent high-dollar fund-raising events, which are covered by the news media. He raised $21.5 million since entering the race at the end of April, his campaign said last week — less than Mayor Pete Buttigieg of South Bend, Ind., raised in the second quarter of the year, but still outpacing other top rivals.

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According to the campaign, which sought to emphasize Mr. Biden’s appeal to small-dollar donors, the average donation was $49.

As Mr. Biden grew his personal wealth during his time away from elective office, he saw how Hillary Clinton’s 2016 presidential bid faced withering attacks over claims that she and her husband had cashed in on their public service as they made tens of millions of dollars giving speeches, consulting and writing books.

Mr. Biden tried to toe the line of making money off his celebrity while also not damaging a future presidential bid.