Even if a netional minimum wage was set, there'd still be differences in weight of dollars accross the state. Less developed places have less income inequality, so higher price differences on products is less feasible. Businesses would either leave that state, or lower their prices. Then someone who came from a richer state would have much more money to spend. They'll flood that place and the prices will jump and you now have more income inequality, and spreading inflation of prices.
Even if a netional minimum wage was set, there'd still be differences in weight of dollars accross the state. Less developed places have less income inequality, so higher price differences on products is less feasible. Businesses would either leave that state, or lower their prices. Then someone who came from a richer state would have much more money to spend. They'll flood that place and the prices will jump and you now have more income inequality, and spreading inflation of prices.