What wage system will dominate?
The federal government's minimum wage dominates all states' minimum wage laws.
A state's minimum wage law will dominate the federal government's wage law if the state's minimum wage is higher.
A state's minimum wage law will dominate the federal government's wage law since the Constitution specifies that any provisions not specified in the Constitution are delegated to the states.
The federal government will challenge a state's minimum wage if the state's minimum wage is higher and the federal government wishes to force the state to comply.
Poor states can make their own minimum wages lower than the federal government wishes.