A man in New York protests for a minimum wage increase there. (Mike Segar/Reuters)

CORRECTION: An earlier version of this post incorrectly cited the range of hourly earnings affected by a federal minimum wage hike to $10.10. It would affect anyone with earnings within a range of $4.25  in states that currently match the federal level.

Expect to hear a lot from both sides of the aisle about the new minimum wage report out Tuesday from the nonpartisan Congressional Budget Office. On one hand, it found that a federal minimum wage hike would bump up earnings for 16.5 million people. On the other hand, 500,000 people will lose their jobs. It’s not exactly the most stunning conclusion—a minimum wage hike will help a lot and hurt a few.

But embedded in the nearly 40-page report are two other takeaways — both of which show why states matter so much to federal policy. There’s the obvious: State policies serve as laboratories of policy. And CBO compared them to one another to suss out what effect a national wage hike might have. The other may not be so clear, but it’s an important one: the population affected by a new federal policy can vary widely by state thanks to how state and federal policies interact. Here’s how:

The nation is a patchwork of minimum wage laws. About half of America’s workers live in the 29 states where the minimum wage matches the federal minimum of $7.25. A fourth live in states where it’s $8.01 or higher. (Washington state’s is highest, at $9.32.) And a fourth of workers live in states where it’s somewhere in the middle.

As with almost all economic policies, there would be ripple effects from a federal hike. Obviously, anyone earning below the new proposed federal minimum of $10.10 would be affected. But so, too, would some workers who are just above that level. If you’re earning four dollars above the current minimum wage and suddenly that rises by nearly three dollars, your pay might get bumped by market forces even if it’s still technically above minimum wage.

But the size of that ripple effect, it turns out, is directly related to a state’s minimum wage. In fact, it’s kind of easy to calculate, according to CBO, and it can have a big impact on what slice of a state’s residents is affected. The size of the ripple effect above and beyond the proposed federal $10.10 level is about half of the difference between that and the state’s current minimum. Here are some examples from CBO that show how the math works out:

Thus, in states where the current minimum wage is $7.25, CBO anticipates that workers earning up to about $11.50 per hour would probably be affected by the $10.10 option. In states with a higher minimum wage, the ripple effect would be much smaller. For instance, under current California law, the minimum wage is scheduled to increase to $10.00 in 2016, and in that state, only workers earning up to $10.15 per hour would probably be affected by an increase to $10.10 in the federal minimum, by CBO’s estimate.

Some 29 states currently match the federal minimum of $7.25. If they do nothing and Congress passes a federal hike to $10.10, then the hike would affect the lives of anyone whose hourly earnings fall within a $4.25 range — a wide swath of people. In California, however, the range of workers affected by 2016 falls within a $0.15 range — a narrow slice of earners.

State policies on their own have direct effects on the lives of residents, but they also interact with federal policy. A worker earning $10.25 in California might not be affected by a $10.10 federal minimum wage — perhaps because the ripple effect would already be absorbed by hikes to the state minimum wage. But someone earning the same amount in neighboring Arizona might see pay bumped up thanks to the interactive effect of state and federal policies.