Ultimately, the employer determines the price of wages and salaries for their employees, in accordance with applicable laws, while employees have a certain level of bargaining power of course. Employee costs rise in large part due to low populations and environmental hazards involved, such as extreme weather, working with explosives, working in war zones, long hours or constant travel is involved, etc.
Well, it has to do with both as it’s reciprocal, if the cost of making each product is reduced, profits are then increased, so prices can then be decreased, as the profit margin is able to be maintained (contrary to the mantra of Wall Street, capitalism is not simply a what is best for the shareholders equation), but this is never the case, not even under slave labor (as is so often the case nowadays), not even while receiving governmentally sanctioned tax breaks/exemptions, tax shelters/avoidance, bailouts, and/or subsidies.
Minimum wage statutes are within a state’s policing powers, as a sovereign entity, see: Bill of Rights, Amends. IX and X. The federal government (as is so often the case) is entirely overstepping its authority on the matter.