This week, the Los Angeles City Council voted to increase its minimum wage to $15 an hour, from the current $9, by 2020, joining the ranks of other liberal cities like Seattle and San Francisco who are acting despite federal inaction on the issue. But L.A. is the largest city to have raised the minimum wage so far, and the increase is much higher than the proposed federal hike to a little more than $10 from the current $7.25. Not only that, but as much as 50 percent of L.A.’s workforce may be affected, which is many more people than in any city that has raised its minimum wage so high to date.

Can a minimum wage be too high? Conservative economists have long warned that minimum wage hikes will increase unemployment or push businesses out of cities with such requirements. Most economic research hasn’t found such warnings to be true. But the federal minimum wage is at a historic low, and the increase in L.A. is so big, that the truth is it could have a small effect on factors like unemployment, how long it takes workers to find a new job after they lose one, and how many hours they receive at work. Still, most observers agree the benefits of the higher wages far outweigh the risks of these problems.

But there’s another potential problem. The finances of those at the bottom are delicately balanced and intertwined with so many safety net programs, like food stamps and rental assistance, that the question of whether workers are better off must be weighed against whether and how they lose the support they receive from those programs. And the truth is it’s not clear how much better off people who make the minimum wage will be.

In L.A., a worker who currently makes $9 an hour and works 40 hours a week (which is not a given, but that would be a full-time workload) will earn $360 a week, or about $1,440 a month and $18,720 a year, before taxes. If that worker is a mom with two children, she is below the poverty line. She qualifies for a bevy of federal and state programs like food stamps, rental assistance, child care subsidies, health care for her children, and Medicaid because she is lucky enough to live in a state that agreed to expand that program under Obamacare.

To take just one example, this mom could qualify for about $500 in food stamps every month. If her wages go up, her food stamp benefits are reduced by 30 cents for every dollar she makes, until they end completely when her income passes $2,116 a month, which it would more than pass under the new minimum wage. Access to other programs, like child care subsidies, drop off completely as soon as a family earns one dollar too much to qualify.

If the new minimum wage went into effect today, without any changes to any of the safety net programs, this mom might lose all of her benefits except access to medical care for her and her children and the tax credits she gets as a working mom, including those meant for poor workers like the Earned Income Tax Credit. (The limits will probably be higher in five years’ time, but not that much higher.) Technically, she might have more money overall. At a $15 minimum wage, this mom would make $600 a week working full time, or more than $31,000 a year, and would no longer be in poverty.

But it’s hard to say whether she would really be that much better off. Food stamps have another benefit, and that’s that they come regularly and predictably, and must always be used for food. What happens if this worker’s income proves even more volatile because her hours change week-to-week and each hour of work lost means more money lost?

What happens if all of the extra money she’s making gets eaten up by an unexpected car repair, or a surprise finance charge from her bank, or the interest she has to pay on a payday loan because her income was so hard to predict, or the extra rent she has to pay because she no longer qualifies for Section 8 vouchers to help? How will she pay for child care without subsidies, or free Head Start if her kids were young enough? She probably won’t, and will seek care in an unregulated workplace that is worse for her children than a quality day care center would be.

Some of the support for higher minimum wages is coming from people who don’t believe anyone who works should have to depend on the government, and are outraged that profit-making corporations like WalMart and fast-food restaurants are raking in the dough while depending on taxpayers to support their workers. Some of the advocates fighting for higher minimum wages are touting the money taxpayers would save as a benefit.

A Center for American Progress study found that if the federal minimum wage were raised to $10.10 an hour and then continued to rise according to inflation every year after, as a current bill pending in Congress would do, then savings in federal safety net spending over the next 10 years would be $46 billion. It probably makes workers happy, too, to think they might get off food stamps and other types of assistance. “Workers are looking to be able to rely on themselves, to take care of themselves. Certainly I think this is a step in the right direction, great step forward, not the end of the road,” says Rusty Hicks, the Secretary-Treasurer of the AFL-CIO in L.A., who was a champion of the minimum wage increase.

That’s not a bad impulse. I think companies should have to pay employees for the work they do, and I think the minimum wage should be higher than it currently is. But I’m worried that too many people think a higher minimum wage will solve the problem, and that people won’t still need help from government programs. The truth is, these workers probably need more pay and more help from government programs, not less.

I spoke to a young woman named Angie Govoy as she was coming back from a rally in L.A., after the minimum wage was raised. Angie is 19 and just graduated from high school this month. She’s worked at McDonald’s for about a year, and her income, which ranges between $150 and $350 a week, pays her phone bill, her little brother’s phone bills, and helps chip in with rent by giving her mother, who works three jobs cleaning houses, between $80 and $100 a month. She rarely has money left over. “Sometimes I don’t have anything at all,” she told me. “Sometimes I have to pay the bank, because I pass what I have in the bank.”

Angie would like to go to college, and if she made extra money, she told me, that’s what she would spend it on. She once wanted to be a radiologist, but being involved in the Fight for $15 has sparked a new interest in political science, and she’s thinking about studying it. But community college is still beyond her reach. A $6-per-hour raise is unlikely to help her pay tuition anywhere, and she’ll have expenses even if she gets help for tuition like a Pell Grant, and in an ideal world she’d be able to finish college before it even takes effect, anyway. I asked her why she got involved in the Fight for $15, and it was about more than money. “I deserve better, I deserve respect,” she told me. “I deserve a way where I can live off doing my best.”