Low-wage workers can benefit from the minimum wage even if the minimum wage reduces employment.

The simple textbook theory says minimum wage laws reduce employment because they make jobs more expensive for employers, and the extra expense either drives some employers out of business, encourages them to produce with less low-wage labor or some combination thereof.

Federal and state minimum wage laws are more complicated than the textbook illustrations because federal and state laws have many exemptions (e.g., tipped employees) and only restrict cash compensation rather than total compensation. Employers could respond to these laws by changing the terms of jobs in order to have more cash pay and fewer fringe benefits, such as medical benefits, flexible work schedules or opportunities for training.

But because employers would be making the job changes to satisfy a regulation rather than for business reasons, the net result would still be fewer jobs for low-wage workers.

Much of the debate about the minimum wage therefore focuses on whether these employment effects of minimum wages are actually observed empirically. Supporters of a higher minimum wage sometimes say that higher minimum wages have historically created jobs. Opponents say that a higher minimum wage would reduce employment and sometimes add that, for this reason, minimum wages harm the poor.

A related argument is that raising the minimum wage to, say, $10 per hour is bad for the same reasons that raising it to $100 would be: They both harm economic growth, albeit in different amounts.

But, in theory, low-wage workers could benefit from a higher minimum even if jobs were lost. Suppose, for example, that by doubling the minimum wage, low-wage workers who found themselves continuously employed before the increase now find that the higher minimum makes them unemployed half of the year. That is quite a bit of unemployment, but nonetheless their annual income would be the same (or even greater if we count unemployment benefits) because they earn twice as much during the half of the year that they are at work.

I doubt that it’s all that harmful to the affected workers to allow them to earn their salary in half the time and have the rest of the year off.

The real harm accrues to the businesses and other workers who would indirectly pay for the minimum wage increase in terms of less productivity, lower profits and higher consumer prices. On the whole, I believe that the harm outweighs the benefits, but that’s different than saying that low-wage workers are necessarily harmed. For the low-wage-worker perspective, what really matters is the effect on their total income (see also Chapter 4 of “Minimum Wages”), not whether the minimum wage creates or destroys jobs.

Admittedly, my example is oversimplified because the unemployment created by a higher minimum wage need not be equally shared. Instead of all low-wage workers being unemployed half the time, it could be that half of the low-wage workers are unemployed practically all of the time and the other half remains continuously employed.

It might seem that half of low-wage workers benefit from earning double, while the other half are harmed by earning nothing. But even this case is not so simple, once we recognize that workers live in families.

Low-wage workers typically live with a partner, parent or sibling. If two low-wage workers live together and one has his wage doubled by a minimum wage increase while the other finds herself unemployed, household income is the same and is earned with half the effort.

Low-wage workers can reasonably support a higher minimum wage, even though regulations like this reduce employment, for the same reason that, say, the plumbers’ union might support higher wages for plumbers or medical doctors might support higher fees for physicians: these changes may increase total group income, and the reduced employment of group members is a tolerable side effect.

Casey B. Mulligan is an economics professor at the University of Chicago. He is the author of “The Redistribution Recession: How Labor Market Distortions Contracted the Economy.”