In the present economy, there are a bunch of folks locally that approach me all the time and ask to work off the books for cash. Their going rate is $10.00 an hour.
And these are older men with skills with farm equipment. They are also willing to do any form of manual labor.
I do the right thing, which in this case I will leave unwritten.
As to the efficacy of a minimum wage, the volumes of opinions on the subject are exhaustive, exhausting.
The real nexus of why we have a minimum wage is political. Wiki actually does a fairly balanced review:
Minimum wage - Wikipedia, the free encyclopedia