But this hardly means setting minimum wage at some arbitrary high level would make everybody middle class -- it would just cause mass unemployment.
Or cause inflation.
Another way to look at it is to realize that setting a minimum wage sets a maximum value on the unit of currency in which that wage is defined.
If you set the minimum wage at $10 per hour, then you are defining the dollar as having a maximum value equal to that of six minutes of labor from the very lowest-value worker who you are going to allow to be employed. In the mean time, those who were at the bottom of the employability scale at $10 or $20 per hour, now cannot buy that candy bar at all, because no one will hire them.
If, from there, you raise the minimum wage to $20 per hour, you devalue the dollar, so now it is worth no more than three minutes of labor from the lowest worker.
Raise the minimum wage to $100/hour, and you devalue the dollar to the point that it is only worth 36 seconds worth of labor from the lowest worker.
This really doesn't make anyone wealthier at all. The worker who had to work six minutes at $10/hour to earn the money to buy a candy bar that costs a $1, will find that he still needs to work six minutes at $20 to buy that same candy bar that now costs $2, or six minutes at $100/hour to buy that same candy bar that now costs $10. The value of his labor, relative to the value of the things he would buy, doesn't really change; only the value of the unit (the dollar) used to measure and exchange this value.
This is somewhat oversimplified, or course. There are some factors that won't flex completely with the minimum wage. At the higher minimum wage, the very lowest worker will be someone who, at a lower minimum wage, will have been a few steps above the lowest worker, with those below him now having been rendered unemployable. The new bottom-level worker at $100/hour will probably find himself slightly better off, at the expense of those below him who are now unemployable. Perhaps that candy bar will cost $8.33 instead of $10, so now he only has to work five minutes rather than six minutes to earn enough to buy it.