Are we subsidizing fast food restaurants?

Clearly, fast food workers are trying to change their circumstances.  They've been striking for most of the summer and into the fall.  They think that $7.25/hour is not a sum that enables them to live and feed their families.  Many survive largely because of food stamps, which you and I pay for.  You could say that we are subsidizing McDonald's and similar companies who are able to pay their employees minimum wage.  Would our subsidy be greater if McDonald's etc. paid a living wage?  I doubt it, as there would be fewer people on food stamps while we would pay a little more for a Big Mac.