That said, putting the minimum wage to an amount that is surviable at 40 hours a week removes people on the margins that would benefit from a job that paid these than a living wage. Note I am taking as a given that a business will only employe someone if they on average produce more benefit than they cost.
Two examples of people on the margin that would otherwise be priced out.
Frank is retired and draws social security he is old and doesn't move as fast any more. He gets a job with the park service cleaning/resetting campgrounds. He enjoys being outside, interacting with campers, and the extra money is nice. Since the service pays per spot cleaned, Frank will never make a living wage. I think Frank should be able to take this job.
James just got done serving 5 years for felony distribution of crack. Seeing his son only once a month has made James decide to go on the straight and narrow from now on. As an ex-con it is hard for him to find a job. In fact because ex-con tend to be bad employees most business don't bother. If there was no minimum wage a business could hire James at a rate of the average ex-con and he could prove himself a good worker and move to a better paying job. I think such a job should exist for James.
I think these are two examples of productive economic activity that would otherwise be impossible if the minimum wage was set to a living wage.