As a correlary should we have Maximum Wages set?
No, why should we?
The point of the minimum wage is to discourage employers from bidding potential employees against each other in order to artifically drive wages down, not to keep them from moving up.
we have minimum wages... why not maximum? It's perfectly logical.
The problem you have with the FLSA argument is that there are exceptions which prove the point that you can have work that is not worth minimum wage as determined by an uninvolved third party.
So you would be willing to drive wages down for everybody else because of the few in positions worth less than the minimum wage, whose positions are already exempted?
You assume that wages would be driven down for everyone. Let's take the example of say a gas station attendant. It used to be that the person who sat behind the cash register of a gas station was only worth about 5 bucks an hour. It was easy, boring, simple work. Now along comes the minimum wage that boosts it up to 7 an hour. The job isn't worth that much. So the employer has to decide whether or not to fire people and keep on only his best employees and give them overtime to cover the losses, shorten his hours of service to maintain budget or find other revenue streams that make their job worth 7 bucks an hour.
So let's continue with the notion that the owner did manage to get his gas station up to snuff and kept four really good employees when he used to have seven. These four work harder and have been forced to learn new skills to justify his pay. They have experienced growth in their lives, but three others have suffered a real turn of events to the negative. This is another factor in how minimum wage hurts the economy at the lowest end of the spectrum.
But where the fallacy of the need for a minimum wage comes in, let's look at the now unemployed. Assume for instance that there has been a 40% reduction in all gas station staffs in the area. There is now a glut of workers on the market looking for work. This has the potential to depress the market. The problem they have is that they are too unskilled to work at gas stations like they are used to. So they begin tricking through the market finding work wherever they can. Most of it will have to be off the books, or jobs that have been exempted from FLSA because their skills are not worth it. Eventually they will develop the skills worth minimum wage or be driven off or starved out of the market. Mostly this creates a codified underclass of worker that is barred from work that they used to previously have no problem getting.
Next let's look at what's going on with the gas station workers that WERE retained. Thanks to minimum wage, you've forced gas stations to get more creative and work harder for the same amount of profit. They've raised prices on the consumer, cut back hours of operation, given extra duties and maximized their post fill up revenue, but they still aren't making it. So what do you do to increase profits at a single location since you aren't able to expand or do major promotions? You start hunting for better talent that can draw in and keep loyal customers. So instead of paying the new minimum wage, you advertise a higher than minimum wage in the paper for gas station employees with current experience.
Now workers are always looking for their best deal will start looking for better wages. They have current experience and can possibly get the job. So they go for it. Now you start a bidding war between gas stations for qualified employees. Those who can afford to pay the most, due to better revenue streams, location and other factors that have increased their profit will help them aquire the best employees. On the other hand, businesses that cannot keep up will lose the best employees to higher wages. Their business will slowly decline till they go out of business because they have to maintain the same features as the successful gas stations. Suddenly you now have whole gas stations out of business who cannot keep up. So, the damage so far is 40% of all gas station workers are now stuck in below minimum wage work and a few gas station owners bankrupted dumping their staff into the street as well unable to get work because the market for gas station workers is saturated.
Let's then throw a curveball into the mix and congress rescinds the minimum wage law. You have plenty of gas stations for sale, but they don't have all the features to draw in people to make the same revenue as those who had survived the talent price war (who's employees are now making a WHOPPING 7.50 an hour versus 7). But, they could serve if you can survive on a lower profit threshold, which is now possible thanks to the minimum wage being dropped. So a new investor buys an older station and pays his employees the old $5/hr rate. He will quickly get those employees that need work bad, mostly people let go when the minimum wage went into affect, because those who had been working at $7/hr aren't desperate enough for it yet, OR have the skills to be cashiers in other industries if available. Not only that, he can hire more employees for the same money and return a few services that the big stations cannot do and remain profitable like 24 hour or sunday service... or offer a bare bones in and out fill up. This will expand the low end gas station's profitability.
But now a strange thing happens. Do the employees at the big stations wages start going down? No. They are being paid that much because they ARE the best in the area and help generate the bigger profit that the winning stations have gotten used to. Of course, new employees may be brought in at lower wages, but quickly leave because they are being overworked for what they are paid. So service goes down and then sales goes down, decreasing profit. The smart owner looks at where the problem began, and it's when he started hiring cheaper workers and goes back to paying for good employees at the higher wage.
On the other hand, the bad service those little incidents served to bolster sales in the cheap gas stations with cheap employees. The labor market is filling with people who want the higher pay and have some of the skills necessary to make it worth paying them a higher wage. The new customers demand a higher level of service and so the employer, to keep the increased revenue will start paying his employees say $6/hr because their skills are at least that good and they bring in enough extra revenue to manage making it worth paying them that much.
As you can see by this example, creating a minimum wage, or even increasing it after one is in place, harms business ultimately at all levels from the employee to owner to consumer. It destroys choice for all three as well, because it prices options out of reach because of an arbitrary law instead of letting the market find it's own level. You may not think it fair that someone be paid so little, but really, it's none of your business. No. It really isn't. You are doing no one any favors by getting involved. You may not have taken the same deal because your value in your own skills and time are too high. That is your choice. Nobody can force you to work that job... yet. It is also clearly evident in the example that eliminating a minimum wage does not harm those at the top of the game, but does help those who are at the bottom as well as offering new investment opportunities to increase the economic pie for everyone.
I don't know how anyone cannot see how simple this is. A 13 year old girl gets it, and a 38 year old expert who's spent too much time in 'higher education' doesn't.