Respectfully, where we diverge - greatly - is when you say the 'minimum wage doesn't matter.' Of COURSE it matters, and it's hard to take much else seriously on that topic when you discount it.... because local businesses decide how much above the minimum wage they are going to offer workers to be competitive - hence, depressed wages in areas where the minimum wage is already below the poverty line.
It's fundamentally incorrect to say that "local businesses decide how much above the minimum wage they are going to offer workers to be competitive".
Businesses set their wages based entirely on what the local market will naturally support, according to that particular job, with extremely rare exceptions in the most highly impoverished communities.
Take burger flipper jobs, for example. You typically see fast food joints clustered together in an area, which means they're all competing with each other on an almost perfectly level playing field.
Let's say the typical starting wage for these jobs in this small section of town is close to $15.40 per hour. But the economy changes and higher inflation rates have made prices go up for everybody. This puts market pressure on employers to increase wages because employees are much more sensitive to wages.
If Wendy's and Burger King suddenly raise their employees' base pay by $1.00 an hour, then McDonald's, Arby's, Subway, Hardee's, Domino's, and pretty much all of them in the same fast food business have to follow the lead, or else the best (most hard working, reliable, efficient, and compeyent) employees will work for those who pay the most, while the stingiest businesses will be stuck with the slackers and losers.
Meanwhile, the federal minimum wage is what . . . . $8.00 an hour? Totally irrelevant to the situation.
There's an all too common misperception that companies decide where to set prices and wages, while consumers and employees have no choice in the matter.
That's absolutely false. Unless the government interferes with arbitrary mandartes, markets decide prices and wages, with "markets" being defined as the place where businesses and consumers and employees mutually agree to meet.
There's really not much thinking involved. A partucular business might try raising its prices by 5% to try to earn a little bit more profit. If they lose enough customers by doing so that they actually make less profit, despite higher prices, then they've made a mistake and should drop their price back down.
But if they don't lose customers and make the same or higher profit, then they know the market will accommodate the price increase.
Their competitors will immediately see this and will all raise their prices by 5% and everybody's back at parity.
Of course not every business has the exact same prices and wages. There's always a small variation. Probably to most obvious example is gasoline, where you have businesses aelling a virtually identical product (gasoline is gasoline), gas stations tend to be clustered closely together in one place, and their prices are advertised on giant elevated marquis that can be seen blocks away. It doesn't get much more competitive than that.