In the United States we have a minimum wage - sort of...
I remember when I was in my early 20s, just before I started college, I believe the minimum wage was $5.25 where I was living. I applied for a job as a security guard with a small, local security company. I was told I had the job if I wanted it, but that they only paid $5.00 an hour and easy said that it was below minimum wage. I didn't care. I needed income.
In the US we import persons from impoverished nations who are willing to work for below minimum wage or for less than those who are currently doing the work. This is done both legally through work visas or illegally by paying criminal aliens in cash. Then, for those companies who do not wish to deal with the above they simply outsource their work to impoverished nations where persons are willing to work for much, much less then in the United States.
Labor has a value. Minimum wage will not support a person or a family. However, it is not the responsibility of private business to house, clothe, and feed people. Neither is it the responsibility of the government in a free society.