You think that rises in the minimum wage are always exactly cancelled out by inflation?
OK, that's not even stupid. It's just so counterfactual that it's delusional.
There is a way to raise the minimum wage without inflation, but then that prices a person out of the market. There is a way to raise teh minimum age without pricing a person out of the market, but that involves raising inflation to counter it. Usually, we end up with a compromise between the two.
Using that same logic, nobody should ever get a raise, because it will automatically be cancelled by inflation.
A shortage of supply of people with a particular skill relative to demand will naturally force those who want that skill to raise the offering to attract those workers. That's different from raising the minimum wage on people on whom an employer is not willing to pay that much. See the difference?
Looking at it that way, it would make more sense for the government to send the low-paid back to school so as to increase their value to an employer.
Accurate but unimaginative. Extending the logic in a fun way would be claiming that if we reduce the wage to 10 cents per hour, gasoline will magically cost a penny a litre.
Wrong, because gas is usually at a relatively fixed quantity relative to demand.
Sorry, I'm wrong. It would mean people would have less money to buy gas, so demand would decline, consequently the price would need to adjust a bit at least.