I live in Santa Fe, and we have a pretty high minimum wage in this city. People, meaning businesses, keep on trying to blame the high cost of living here on the high minimum wage. I earn somewhat more than that, so I don't pay careful attention to what it actually is.
I moved here from Overland Park, Kansas, four and a half years ago, and I'm constantly open-mouthed in surprise at the claims that Santa Fe is so expensive. I can only conclude that no one here has ever visited, much less lived in any other part of the country. I initially rented a two bedroom apartment for exactly as much as a comparable place would have cost me in Overland Park. Should I mention that OP is considered a low cost of living part of the country?
The small two bedroom (but perfectly adequate for me) home I bought on the unpopular south side of this city is less than half of the median home price in this city. In OP, my perfectly adequate home for a family of four was about double the local median price of homes.
Probably the real issue about cost of living is the schools. I am saddened by how bad the schools are here, how low the standards. Oh, did I mention that my property taxes are low? Do you think there might be a connection?
I first entered the job market when the minimum wage was $1.25 per hour. I was actually able to live on my own (in Tucson, AZ) on that money. A few months later the federal minimum went up to $1.65 per hour, which made my life much nicer. I doubt I could currently live as well on the current federal minimum as I could nearly 50 years ago. And I'm someone without any health issues, so that's not even a factor. Just paying rent and buying food and gas for my car are the only things that would come into play. When I was last earning the minimum wage I didn't even own a car, but walked to work and to the grocery store and on occasion took the bus. I am fortunate that Santa Fe is a small town, so I only buy gas every other week or so, but it's still a larger part of my budget than it used to be.
A living wage is what everyone should be paid.