That might work, in theory, as long as the incremental % in wage costs resulting from the hike doesn't result in a commensurate % reduction in hours/jobs.  

I am surprised that the proponents of $15/hr minimum wage are the same people who favour carbon taxes, yet fail to see the corollary.  The whole idea behind a carbon tax is that, if carbon usage becomes more expensive, people will make different decisions to reduce their carbon footprint.  Makes sense.  But if the cost of unskilled labour becomes more expensive, don't be surprised if business owners make different decisions to reduce their "employment footprint".