T O HER CREDIT , Elizabeth Warren is the kind of politician who likes to show her maths. The Massachusetts senator has climbed near the summit of the Democratic presidential primary carrying amply footnoted and thoroughly costed plans on matters both prominent and obscure. She has plans for a wealth tax on the rich, for universal child care and cancelling student debt, yes, but also plans to promote competition among farmers, improve the funding of Native American reservations and relieve Puerto Rico’s debt. Yet on health care, perhaps the most consequential policy area, Ms Warren was hazy for months.

The senator had yoked herself to Medicare for All—a single-payer system free at the point of service proposed by her competitor, Bernie Sanders. Unlike Mr Sanders, though, she dodged questions on whether taxes on the middle class would rise to pay the $3.4trn in added annual costs. On November 1st she released a detailed financing plan “without increasing middle-class taxes one penny.” Other candidates, she declared, should put forward similarly detailed plans or “concede that they think it’s more important to protect the eye-popping profits of private insurers and drug companies and the immense fortunes of the top 1% and giant corporations.”

The details explain both the initial reticence and the subsequent defensiveness. The underlying sums strain credulity, requiring heroic assumptions on cost reductions and budgetary gymnastics on revenue-raising. This mars Ms Warren’s wonkish reputation. It may placate voters for the primary, but would surely damage her in a general election against President Donald Trump, if she gets that far.

Start with the spending. Over the next ten years Americans are expected to spend $52trn on health care. Under a generous single-payer system, spending would increase by $7trn, according to a recent study by the Urban Institute, a left-leaning think-tank, which serves as the starting point of the campaign’s calculations. Through a number of steps, Ms Warren whittles this difference down to zero. She argues that national health spending would remain constant, even though more people would be covered (eg, the 28m citizens and undocumented migrants without insurance) and the use of medical services would increase were they free.

Among her modifications of the Urban Institute’s numbers are lower administrative costs (2.3% of overall spending, compared with Urban’s 6%). Ms Warren’s plan assumes a slower rate of growth in health costs (3.9% versus Urban’s 4.5%) and less generous payments to hospitals for services (110% of current Medicare reimbursement rates versus Urban’s 115%). Added to this are targets for reducing spending on drugs—by 30% on generics and 70% on branded medicines—enforced by the threat of large excise taxes, the possibility of overriding patents and the option of having the government produce drugs itself. Given the resistance to such a plan from doctors, insurers, drug companies and hospitals, this would be hard to pull off.

Even with these steps, and the redirection of all existing public spending on health care, Ms Warren has a $20.5trn budgetary hole. Filling it is made harder by her insistence that taxes on the middle class will not increase. Currently employers shoulder a significant portion of health-care costs. Under Ms Warren’s plan, the same cheques would be redirected to the federal government. In practice this would be a tax on employment, which seems likely to hurt middle-class Americans. It would also increase the relative cost of hiring low-wage workers, hurting the people Ms Warren most wants to help.

She finds some money from the kind of conjuring promised by less rigorous campaigns, like better tax enforcement (which provides $2.3trn), comprehensive immigration reform (providing $400bn) and the elimination of the fund that pays for the defence department’s Middle East operations (another $800bn). After all that, she is still short by $6.8trn.

To make up the shortfall, Ms Warren plans to add levies on large firms and rich Americans—beyond those she has already proposed. On top of the repeal of Mr Trump’s tax cuts and a new 7% charge on corporate profits, she would eliminate the ability of businesses to immediately write down depreciating capital; she would also impose a minimum tax of 35% on their foreign earnings. A new financial transactions tax of 0.1% would be placed on sales of shares and bonds, wrecking the business of high-frequency traders (perhaps a plus from Ms Warren’s point of view). The country’s 40 biggest banks would pay an annual fee of 0.15% on “covered liabilities” (liabilities minus federally insured deposits). The wealth tax has been revised upwards too. Fortunes above $1bn would be charged a 6% annual levy. A Warren presidency could cost Jeff Bezos, the boss of Amazon, $26bn over a single term. Nor could he escape by shedding his American citizenship. Ms Warren has proposed an “exit tax” of 40% on the net worth of billionaires to head off that threat.

These contortions are all the result of past decisions. Despite her earlier, more pragmatic instincts on health care, Ms Warren adopted two nearly incompatible pledges: to deliver Mr Sanders’ version of single-payer health care—more generous than that of Britain or Canada—but without any premiums or deductibles and without raising taxes on the vast majority of Americans. Because her evasiveness on funding was attracting criticism from her more moderate competitors, like Pete Buttigieg and Joe Biden, Ms Warren released this plan, which seems to assume that anyone outside the top 1% of earners counts as middle class. During the primary election, the strategy could work. She can credibly answer her opponents’ claims by repeating her quasi-official catchphrase, “I have a plan for that”. Primary voters may shrug off the entire episode.

A general-election contest with Mr Trump would be a different matter. There was reasonable speculation that Ms Warren’s woolliness on health care was a tactical move, enabling her to strike a more centrist pose on securing the Democratic nomination. That option now looks closed off. The new plan opens her up to all manner of attack from Mr Trump, even though his own health plan is ill-defined, beyond a so-far unsuccessful drive to repeal Obamacare, and his record on health—2m more Americans are uninsured than when he came to office—is dreadful.

Going into an election promising to discontinue the health insurance of the 178m Americans who have private plans through their employers seems mad. “Democrats now have a 30-point advantage over Donald Trump on health care,” says Jim Kessler of Third Way, a centre-left think-tank. “If that gap narrows—and it will narrow if Democrats are for Medicare for All: it could narrow to zero—he gets re-elected.” According to the Kaiser Family Foundation, a health-policy think-tank, 51% of Americans support Medicare for All while 47% oppose it. But when various objections to the programme are made—such as the elimination of private health insurance, and the possibility of increased taxes and queues for treatment—support drops to below 40%. As a policy, Warrencare might be described as negligent. Politically it looks more like malpractice.■