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Low-wage workers may have received a raise Jan. 1, thanks to the 50-cent increase in the California minimum wage to $11 an hour.

We say “may have” because a lot of those workers were already earning $11 an hour or more, depending on where they live and work.

The Legislative Analyst’s Office estimates there are about 5 million Californians working for minimum wage or less. That’s about 30 percent of the entire work force.

Only a handful of states can match California’s base wage, and there’s a good reason for that — the cost of living in California is high. In fact, if you wanted to choose a place to live and work, California is great on the “live” side, but really tough on the “work” side for those in low-paying jobs.

So, in reality, California bumping its minimum wage to $11 an hour should barely cause a ripple in the state’s economy. Still, even a 50-cent boost could pose problems for small, mostly privately-owned businesses.

Merriam-Webster defines minimum wage as "a wage fixed by legal authority or by contract as the least that may be paid either to employed persons generally or to a particular category of employed persons.”

One group of economists see the minimum wage as an unnecessary, burdensome government regulation of small business. They believe a worker's skill level and market forces should dictate wages. Another group of economists see the minimum wage as a way to elevate unskilled workers out of poverty.

That makes it sound cut-and-dried. It is anything but. There are just too many variables to make a definitive statement on this issue.

But because small shops comprise almost three-quarters of operating businesses in the United States, the overall question of a base wage is huge, both for workers and owners.

The Heritage Foundation published a report in 2016 saying raising the federal minimum wage to $15 an hour would cost the U.S. economy more than 9 million jobs.

A lot of those jobs would be in the hospitality sector, most specifically restaurant operations, in which wages and benefits are about the only controllable costs.

A study by a team from the Harvard Business School indicates the jobs lost would be primarily in businesses on the cusp of failure to begin with. The study focused on several years of restaurant operations in the San Francisco area, during a period when the state was slowly ramping up the minimum wage. A mandated dollar-an-hour wage increase hurt about 14 percent of the mediocre or worse restaurants, but had no impact on more successful operations.

In a way, a required increase in the minimum wage forces borderline operations to step up their game, while at the same time giving their employees some extra cash — which theoretically will be cycled back into the local economy, and in many cases spent at the workers’ place of employment.

The federal base wage has been stuck at $7.25 an hour since 2009, mostly because Republicans and Democrats in Congress can’t find an acceptable middle ground on the issue, even while knowing there are few Americans who could survive on $15,000 a year. The result is minimum-wage workers in 18 states got a raise on New Year’s Day, as states and local jurisdictions try to stay competitive and keep low-wage earners out of poverty.

A poll last year found that more than half of all Americans believe higher minimum wages are good for workers, while only a third thought it’s be a bad idea.