You realize that’s got the direction wrong? “Given the affordability of housing somewhere within a pretty huge circle, what must the local minimum wage be?”
The federal government already tallies prevailing rent for every US city/county.
If the policy goal was to set minimum wage to a 40% of full time gross income, and the prevailing rent for basic housing is $1000/mo, 1000/40%=$2500, or $15/hr. You can rent an apartment for $450 in the small town I grew up in. Same calculation would be $6.75/hr.
Most employers use a similar methodology to set travel expense thresholds, etc.
A system like this could be subsidized by tax credits on the payroll side.
