One of the greatest myths of capitalism is that businesses want cheaper labor. While trying to keep costs low is a good business practice in general, cheaper labor isn't necessarily a good business practice.
In the private sector, businesses don't operate based on "cheap" but rather "profitable". In fact, it might be more profitable to hire someone at a higher wage, depending on what value that worker brings to the business.
A good example of an employee's return on investment (ROI) would be in the area of movie production. An unknown actor might offer their services for free while a famous actor could cost millions of dollars and yet high paid actors seem to get work all the time. Again, the good business practice in capitalism is profit and sometimes hiring a famous actor at a much higher wage is more profitable. George Clooney recently earned $239 million last calendar year followed closely by Dwayne "The Rock" Johnson at $124 million. These actors are employed under capitalism and they're not cheap.
Alright, enough with the movie industry. What about regular jobs? Sales is a great example. A car salesman with better people-skills would be better suited to selling more cars. A commission-based wage would obviously be higher, but an hourly-based wage should also be higher. Companies want to keep profitable employees even at the expense of paying higher wages, if the value returned on the dollars spent is greater.
If a worker's value drops below minimum wage, a company can't afford to keep that employee. The minimum wage is the government regulation set to determine whether a job can legally function. Raising the minimum wage either raises a worker's wage that the worker could have negotiated themselves or the employment could be deemed unprofitable and the worker will be terminated.
When it comes to a worker getting a self-requested pay raise, keep in mind that most workers become more efficient over time. Also training new workers is costly so a company is incentivized to keep experienced and efficient workers from leaving. It's sometimes within employers’ best interest to accept pay raise requests, within reason.
Lastly, Imagine the job of a dishwasher. If a machine could wash dishes for $2 an hour and an employee requested $10 an hour, what should the business do? The value of the work being performed is determined by the fact that the business can obtain the service for $2 an hour. This brings up the idea of exploitation. If a business was forced to hire a person to perform this service, the business is being exploited. In a free society, it's difficult to label a worker as being exploited as the worker is always able to ask for more money or quit. If a business can obtain services for work at a lower price than your bid, whether it's a machine or another person, the idea that you're being exploited is false. Only under slavery or some method of force would exploitation be legitimate. A free-market defies exploitation.