(Photo by Scott Olson/Getty Images)

If we want to talk about income inequality, Rand Paul said at Tuesday night's Republican presidential debate, we should start by looking at where in the U.S. the divide between the rich and poor is the widest.

"It seems to be worst," he said, "in cities run by Democrats."

The implication — which scored the Kentucky senator cheers from the audience — is that Democratic policies drive inequality, while Republican ones reduce it. Want less inequality? Move somewhere, Paul added, where Republican politics dominate.

To be fair, he's right on the data here. But Paul gets the lesson all wrong. Big cities in America do have worse income inequality than the national average. And big, dynamic cities like New York, Boston, Washington and San Francisco — which are also, yes, deeply blue — have some of the widest divides, according to data compiled by Alan Berube and Natalie Holmes at the Brookings Institution.

But big cities with vibrant economies should have wider income inequality — it's a feature of cities, not a bug. That's because they're simultaneously home to both the very poor and the very rich. They have the social services to support the poor, as well as the high-paying jobs that attract skilled workers. New York has Wall Street (and Donald Trump), but also the kind of service-sector jobs that promise employment to people without college degrees.

In contrast, what kind of places look really equal? Exclusionary suburbs that keep out the poor and working class appear, on paper, awfully egalitarian (everyone makes $100,000!). Struggling cities without New York's financial district, or San Francisco's tech hub, or Boston's biomed industry, look more equal, too (hardly anyone makes $100,000!).

In the analysis Berube and Holmes did, where they compared incomes at the 20th and 95th percentiles in big cities, San Francisco ranks second-worst in the country. But that's in large part because the high-paying jobs in San Francisco pay really well. Want to go where the high-paying jobs don't pay that much, where — as Rand Paul suggests — you'd find more equality? The bottom of this list includes Detroit, Cleveland, and the host of Tuesday night's debate, Milwaukee: