The studies, published jointly by the nonpartisan Tax Policy Center and the Urban Institute in Washington, conclude that Sanders's plans are short a total of more than $18 trillion over a decade. His programs would cost the federal government about $33 trillion over that period, almost all of which would go toward Sanders's proposed system of national health insurance. Yet the Democratic presidential candidate has put forward just $15 trillion in new taxes, the authors concluded.

In principle, national health insurance could make many families better off overall, without imposing unsustainable burdens on the federal budget. For the system to work in terms of dollars and cents, though, the benefits would have to be less generous than they are in the system Sanders has proposed, or the taxes would have to be more onerous for the middle class, as they are in many European countries.

In the short term, at least, almost every household would be better off, as Sanders's proposals for health care, secondary education and more would save ordinary Americans money and provide other valuable benefits. The typical middle-class household, for example, would receive benefits worth $13,000 a year, almost all of it for health care, while paying just $4,500 more in taxes.

Those benefits would be especially meaningful for poor households. The poorest 1 in 5 households would receive benefits worth about $10,000 a year on average, while paying just $209 in additional taxes. Among this group, there are many households with people who need long-term care — for example, elderly women who have outlived their husbands and who are surviving on Social Security, and those who are disabled and cannot work.

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They would benefit enormously from Sanders's proposal to include pay for long-term care through the federal government, which accounts for about 13 percent of the benefits the poorest 1 in 5 households would receive. In total, Sanders's proposals would effectively quadruple the incomes of this group on average.

The benefits would exceed the increased taxes for all but the richest 1 in 20 families. Even for the next richest 20th of the population, the new benefits would exceed their increased taxes by about $1,700 on average, or 0.9 percent of their average income.

Over time, though, the government would have to borrow money to fund the programs, potentially increasing interest rates with uncertain consequences for households and businesses.

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The new estimate of the cost of Sanders's health-care plan is even more pessimistic than a previous estimate produced by Kenneth Thorpe, a former health official in the Clinton administration. Sanders's staff criticized Thorpe for predicting their plan would cost $25 trillion over a decade, about twice what they had projected. The Urban Institute puts the cost to the federal government at $32 trillion.

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That is $17 trillion more than Sanders has proposed in new taxes. When his other programs besides health care are included, the shortfall is more than $18 trillion, money the government would have to borrow.

Warren Gunnels, Sanders's policy director, disputed the findings in a statement, saying a national health insurance system would be more efficient.

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"This study significantly underestimates the savings in administration, paperwork, and prescription drug prices that every major country on earth has successfully achieved by adopting a universal health care program," he wrote.

"The fact of the matter is that the U.S. spends far more per capita on health care with worse health outcomes than any major country on earth. And unlike every major country on earth over 28 million of our people are still uninsured," Gunnels added. "If every other major country can spend less on health care and insure all of their people, so can the U.S."

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Economists would generally view Sanders's proposals "as basically hurting the economy, potentially significantly," Leonard Burman, director of the Tax Policy Center, told reporters. "It pushes up the cost of borrowing for businesses. It makes it harder for people to buy their own homes."

Burman added that it might be impossible to get the money for Sanders's plans by further increasing taxes on the rich, who would already pay steep rates under the plans the senator from Vermont has advocated.

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These households have substantial wealth that supporters of Sanders's ideas might want to use toward funding his ideas. Yet they might respond to additional increases in taxes beyond what Sanders has proposed by, say, investing less or retiring early, producing less income for the government to tax.

Households with more than $10 million a year would pay a marginal rate of 54.2 percent on additional income under Sanders's proposals. Among the richest 1 in 100 households, the marginal tax rates on capital gains would reach nearly 60 percent, the Tax Policy Center previously concluded, depending on the type of investment.

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"Those rates have to be close to the highest levels they could be assessed without starting to lose revenue," Burman said.

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Sanders propose raising more in taxes from the middle class. Given the value of the benefits they would be receiving, doing so could still leave them in the black on paper.

"It's likely, given how large the benefits are for many people, that they would still be better off on net," Burman said.

On the whole, Sanders's plan would require more in new taxes than Americans currently spend on health care. Sanders's goal is to offer national health insurance that is more generous than many Americans' current policies, and to extend insurance include the roughly 28 million people who are still uninsured, according to the Urban Institute.