Why are you confusing private business with the government? The government sets minimum wages not private businesses. It is only in government where you can find an oligarchy, not private businesses. Minimum wages set by the government does not "protect" wages it kills them. Every time the government raises the minimum wage, minimum wages earners get fired. Businesses can no longer afford to have the work force they once had so they eliminate jobs and make those who they keep work harder to cover for the loss of manpower. Small businesses are the ones who employ the vast majority of minimum wage earners and they are the ones who are the hardest hit when the government increases the minimum wage.
And contrary to what the left has indoctrinated the nation into believing, the minimum wage was NEVER meant to be a living wage. You are responsible for your living wage, not the government. If you are earning minimum wages right now then you had better have a plan to improve yourself so that you can offer the kind of value to an employer who will pay you that living wage.
The value of a person is infinite but the value of your labor is not and the two are not the same thing. Too many people confuse the two and that is where the problem begins. An employer/employee relationship is similar a grocery shopper/and grocery store. You might think the prices are too high for the products that are sold and so you might go to another grocery store to shop. The grocery store owner and clerks might think you are a risk to have in your store, perhaps because you stole from them or destroyed their merchandise or what ever.
Neither the shopper or the store is forced to accommodate the other. In the business world the government has stepped in and set a minimum price for which the employer (or shopper) must pay. But either the employee or employer is forced to accommodate the other outside of the minimum wage.
That is why you labor is NOT the same as your value as a human being. Your labor is no different than the relationship between the shopper and the store.