The math is easy: raising the minimum wage leaves minimum wage workers better off than before, although with slightly different work patterns and higher quality of work.
Let's work through the math.
We're gonna use some numbers which you may or may not agree with, but it doesn't matter. Change the numbers to anything you want; it works the same unless you use really strange numbers (like $0/hour or $100/hour).
ASSUME: an increase in minimum wage means employers will cut back somewhat on the amount of minimum wage hours employed. (The actual cut is typically small since the labor cost of most goods is only a fraction of the total cost of goods produced.)
An economy with one million hours of minimum wage work at $5/hour.
An 10% increase in minimum wage means a 5% cut in minimum wage hours worked.
The pool of minimum wage workers get $5 million and work 1 million hours.
RUN THE MODEL:
* Minimum wage goes up 10% to $5.50/her
* Employers cut hours employed 5%, to 950,000 hrs
* The pool of minimum wage workers get $5 225 000 and work 950,000 hours.
The workers have more money
The workers have a little more free time
NOTE ALSO: since the workers are paid higher wages, it is more economical for the employer to use technology to improve their productivity.
EDITTED: for support, see http://www.uvm.edu/~vlrs/doc/min_wage.htm