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Now suppose a law gets passed to expand coverage. Paul gets insurance, but Mary remains uninsured. Now Peter and Paul are spending $1,000 apiece. Paul spends more than when he was uninsured, so total national health spending goes up to $2,500.

But because more people are covered, spending per insured person goes down to $1,250.

It’s a simplistic comparison, but would you call that a savings?

Mr. Paulos said it would make more sense to first figure out the share of total national health care spending by people with health insurance, and then divide that result by the number of insured people - before and after the health care law.

The government hasn’t run that calculation.

Richard Kronick, a senior Health and Human Services official, said the Obama administration disagrees that its number is misleading.

“There are a number of ways to evaluate health care spending and the new law,” Mr. Kronick said. “Examining spending on each individual with health insurance is one useful data point.”

National health care spending is a kitchen-sink statistic that includes personal health costs of the insured as well as the uninsured, and such categories as research and development and medical infrastructure. In 2019, when the overhaul is fully phased in, the tab will be $4.6 trillion.

Mr. Foster says it’s acceptable to divide the number by the total U.S. population. In that case, per capita spending would $13,652 as a result of the law, and $13,387 without it.

The difference: just $265 per person more.

Mr. Paulos, the mathematician, said that sounds like a bargain to him. “It’s a relatively small cost given that 30 million more people will be covered,” he said. “You don’t really need this kind of apples-to-oranges miscomparison.”