The minimum wage is raised, but the costs of everything else rises proportionally, if not more than the minimum wage itself. I mean you can increase the minimum wage, but it doesn't mean you are increasing the purchasing power.
Furthermore I will give an example: if I'm a business owner and have to raise my employees' wages I will raise my services costs to customers so I can dilute this *loss* and keep my profit intact. In the end the customers (who are also earning 15$ hourly) will have to pay more for the same services they were paying cheaper before.
The purchasing power changes from state to state. There are already states with 15 bucks an hour, some of them very expensive places and some of them are not so much, there are also places with under 10 dollar minimum wage, some of them again expensive while others not so much.
Basically it all comes down to public situation, could a $15 per hour increase the prices? It definitely can for some places, but doesn't have to do that in every single state, some states will just continue like nothing happened.
But this is about basically preventing starvation wages, because let's be honest 7.25 per hour is starvation, people work 39 hours a week in most cases so that companies doe not have to give full benefits, that means 1131 dollars per month, there are no states, no cities, no towns that you can live with 1131 dollars and survive, that is barely enough for food and I am not even talking about other expenses. So to justify 7.25 is not enough, because you can't justify starvation.
Well, it may depend from state to state, but from my own experience raising minimum wage never solved or even reduced financial problems in my country. It has only political marketing effect instead of practical effect in citizens lives. Actually a minimum wage isn't enough to live anywhere I suppose. A minimum wage here is about 200$ dollars and someone can't afford home, food and another basic expenses with such amount of fiat, but the minimum wage keeps increasing every new year...
In my opinion instead of increasing wages the living costs should decrease and that is possible through technology advancement and adoption, like alternative sources of energy, for an example. But the government doesn't look very interested in this kind of political platform.