I think we are disagreeing on terms. People support a living wage normally mean legally mandating that the minimum amount of money that is exchanged for an hour

I think we are disagreeing on terms. People support a living wage normally mean legally mandating that the minimum amount of money that is exchanged for an hour of labor is set to $X where X is higher than today's rate. I gave two examples where increasing the hourly rate would make it so that the business would not hire the worker because it would provide negative value to the company. Working half the hours does change the fact that each hour loses money for the company.