[sershe]

They don't really create this externality, though. A person taking this job apparently cannot get a better paying job. With a higher minimum wage in otherwise free market, no jobs for that person would exist, so the social burden would exist just the same.

The situation is diametrically opposite - minimum wage forces businesses to engage in welfare. Those who have enough margins to engage in welfare might do it; the others may disappear with the jobs, or cut the jobs by reducing service/automating/outsourcing (again leading to the same "social burden" existing).