um, you omitted some really important details, see above. While many people dislike Thomas Sowell's political commentary, his economic research generally is highly-regarded.
Depending upon the level at which the minimum wage is set, it is often a mechanism deliberately designed to restrict the free market by preventing one group of people from offering to work for less than what another group of people wants for themselves. If one ethnic group would work for less than other ethnic groups, then by definition the minimum wage is discriminatory.
That being said, there is a convenience factor for businesses to have a regional minimum wage.
Frankly, this whole conversation is bass-ackwards.
The fundamental economic issue should not be about the minimum wage at all, but how to re-cast work in the 21st century so that every person who wants a decent job can produce enough value from performing in that job to earn substantially more than the minimum wage. There are a lot of skilled positions going unfilled because too many people went to college who didn't really belong there, and not enough people went to trade schools or entered apprenticeship programs.
Even a two-tiered minimum wage structure might make sense, one for entry-level people, then another for people who have served their apprenticeship so to speak and have graduated to journeyman status.
Ideally, the minimum wage should not be more than a trivial issue; the real focus should be on developing more well-paying jobs that people are willing to fill.
Always wanted to ask what it's like to be a character actor. 