Much higher tax rates on the highest earners can generate revenue to pay for new programs, and they can encourage a more equal distribution of pretax income. But these two objectives are in tension with each other — the more Mr. Saez is right that high rates will discourage ultrahigh incomes, the less revenue Mr. Sanders will get from his new taxes on ultrahigh earners.

Like much research about the interaction between taxes and the economy, theories about the revenue-maximizing tax rate are subject to high levels of both controversy and uncertainty. Some claims can be identified as clearly wrong — see, for example, the Tax Foundation’s claim that large across-the-board tax cuts proposed by Marco Rubio would cause revenues to be higher within a decade — but the range of possibly correct answers about what tax changes will do to pretax incomes remains large.

Mr. Saez and Mr. Diamond report a range of uncertainty around their own estimate of 73 percent as the revenue-maximizing top rate, which depends on the open question of how elastic taxable income is — that is, how much it declines when you tax people more. Other economists choose different ways to characterize the best estimate for the revenue-maximizing rate, even before applying a range of uncertainty. Joel Slemrod, a collaborator of Mr. Saez’s, told The Washington Post in 2010 that the revenue-maximizing rate was “60 percent or higher.” Some conservative economists argue for lower rates by expressing concern that the revenue-maximizing rate will decline over time.

Michael Strain, a labor economist at the conservative American Enterprise Institute, noted that most existing research on revenue-maximizing tax rates looks at the years immediately after a tax change, and therefore could miss long-run effects on taxpayer behavior. What if a high tax rate not only encourages people to work less, but also discourages them from going into certain high-paying fields in the first place? A result could be that revenues would first go up, and then down as new workers enter the work force and fewer specialize in fields that make ultrahigh incomes possible.

The problem with this theory is that it is very difficult to test. Lots of factors besides tax rates affect incomes and economic growth, so looking over a long time range and figuring out which changes to incomes were caused by tax changes is very hard. Plus, in a 2012 paper with Seth Giertz, Mr. Saez and Mr. Slemrod pointed out there is a reason to suppose tax increases might do less to reduce taxable income in the long run than the short run: A taxpayer can react to a tax increase by shifting income into a year when he thinks tax rates might be lower, but that strategy won’t work if rates stay high for a long time.

“There are no truly convincing estimates of the long-run elasticity,” they wrote in that paper. Still, they settled on one that became the basis of the 73 percent estimate, and they offered a good reason not to worry too much about the uncertainty: You could move the estimate quite a bit in either direction and still find that the maximizing rate would be much higher than the then-existing top rate, which was just 42.5 percent before tax increases on high earners that took effect in 2013.