I recall a study I saw last year that was similar both here and in parts of the US where businesses are having a hard time filling low skilled jobs (waiters + factory workers, etc) and that was effectively due to the fact that no one wanted to do these jobs so perhaps you could use that argument to proclaim that wages should be higher on the low skilled jobs (but my argument would be to let undocumented workers have them). That being said I don't necessarily have a problem with minimum wage as much as I have an issue with regulations. I think the latter has a much higher cost per worker impact than boosting the minimum wage but I have no actual empirical evidence.