As I see it, a "living wage" would start at the point where one goes from merely being able to pay bills and buy groceries to having "disposable income". Around here, that would be slightly lower than where you are. A rat trap apartment around here is about $600-$700 a month. Decent apartments start around $900 a month.
So, for a single parent with one child to acheive "disposable income"------I know women who've managed it on about $18/an hour. ($36-38,000/ year.) Less than that and you have to have "roomies". I date a woman who worked in day care and only made $9 an hour. She had two roomies in a one bedroom apartment. She slept on the couch. Really, she spent most of her nights at my house.
Dave