A supporter of raising the minimum wage listened as the Kansas City City Council debated the issue, Thursday, July 16, 2015, at City Hall. After more than three months of furious debate, the Kansas City Council voted 12-1 Thursday for a minimum wage increase that calls for $13 per hour by 2020. (Rich Sugg/The Kansas City Star via AP) MANDATORY CREDIT

Last night, the Kansas City Council voted overwhelmingly to raise the city's minimum wage to $13 an hour by 2020. But these policies aren't as simple as they seem -- they also involve choices about who the new wage floor applies to, what the penalties are for noncompliance and whether small businesses should get a break.

In this instance, perhaps the biggest argument was over age: Should everybody be entitled to the higher minimum wage, or should teenagers be left out?

The fight goes to the heart of the debate over the impact of the minimum wage, and whether it might hurt the very people it's supposed to help.

Proponents of excluding teens from the new ordinance argued that they want to make sure young people -- for whom getting a job can be both very difficult, and very helpful in the future -- have a shot at that first rung on the employment ladder.

"What we would be doing, as a practical matter, is eliminating seniors in high school from jobs at Worlds of Fun, at the zoo, Bright Futures, and other seasonable employment," Councilmember Ed Ford said during the debate. Plus, he said, it's not like they're trying to support a family. "The vast majority are kids that trying to cover a cellphone bill, an auto payment. This is not the age of social justice. This is the age where kids learn to get a job, learn work ethic, and all that."

There's some evidence to support the assertion that boosting a minimum wage out of proportion with median wages might keep teens out of jobs. Economists David Neumark and William Wascher, in a comparison of many countries, found that youth employment was depressed in those with a higher minimum wage. The effect was particularly pronounced in Puerto Rico, where the New York Fed recommended allowing people under age 25 to be paid a lower rate. The federal government even acknowledges the risk, by allowing that workers under 20 years old be paid less than the minimum wage for a few months, theoretically while they're being trained.

But some councilmembers -- in addition to nearly all of the groups that fought for the minimum wage hike -- strongly opposed the exemption. One city councilmember argued that it discriminated against older workers, who might be passed up in favor of the cheaper youngster. Others pointed out that even teenagers sometimes need to provide for their families.

"There’s this myth that young workers are teens just looking for extra pocket money, when really they’re contributing to their family’s income," says Tsedeye Gebreselassie, who analyzed the issue for the National Employment Law Project. "It makes no sense to lock them into the pay structure where they’ll always be paid less than their older counterparts."

Plus this exemption would be permanent, not just for the duration of a training program.

"The youth exemption provision wasn’t a carve out for internship or externship programs where youth are getting professional career and trade training," says Missouri Jobs with Justice director Lara Granich. "These exemptions only help the corporate CEOs who want to pay people less."

Ultimately, the city council kept the exemption for workers under age 18, which takes some of the sheen off the minimum wage hike for those who fought for it. But the effort represents an attempt by a second-tier city to protect itself from some of the potential negative effects of following the lead of big cities with relatively hot labor markets -- like Los Angeles, San Francisco, and Seattle -- that are going all the way up to $15.

Because even though raising minimum wages is tremendously popular, there's an emerging recognition that the same policy might not work in every place. Yesterday Hillary Clinton declined to support the $15 minimum everywhere, even after telling fast-food workers that she supported their fight for exactly that. Even L.A. mayor Eric Garcetti -- who strongly backed a $15 minimum in his own city -- said that some cities should probably aim lower.

So as minimum wage initiatives roll through cities across the country, once in a while, teens might be left out.