People seem to think that minimum wages are some left wing idea. They're not. People not earning enough to live cost the state money. They cost it in terms of benefits (believe it or not, the cheaper option) or in terms of law-enforcement and the corrosive effects it has on your society. Paying people below a certain level is tantamount to taking government subsidies.
Where exactly that level is is a matter for debate, but everyone should stop pretending like it's a choice between "tough" and "kind".