McDonald's labor costs are well over $1B and a $15 minimum wage would probably increase those costs by hundreds of millions. Corporate executives make far too much money but the excess is taken from stockholders, not the workers
I think we all agree there's a wage level that optimizes the earnings of those subject to the minimum wage. I just don't think we know what that is, or that we should be looking at the minimum wage as an anti-poverty policy
there are better ways at attempting to increase the well-being of those at the bottom end of the income distribution. direct cash assistance is better, the earned income tax credit (basically the same thing as direct cash assistance) is better, wage supports are better
with that said i haven't seen anything to suggest that $15 is the wrong number; it's certainly closer to the right number than $7