While I agree with your perspective, your argument adds complexity that weakens the case rather than strengthen it.

The government already calculates a “cost of living index” for every part of the country.

A living wage is simply any wage which is at or above the cost of living in that location.

Should we, as a society aim for the higher standard of a “a decent wage”? Absolutely, & I’d define a decent wage as a wage that allows a person to cover the basic costs of living + 10% of their income in discretionary spending & another 10% in savings.

I find it amazing that the idea that corporations have to make a profit from their efforts is considered obvious but the idea that a worker also should profit (profit being income minus expenses) is considered communism.