The benefits of a $15 minimum would greatly outweigh the costs.
The “common sense” fears, such as “low paid workers losing their jobs” with a hike in the minimum wage turn out to not actually happen in real life. A raise in the minimum wage turns out to not be the death knell for small businesses, and in fact the benefits end up being experienced all around when implemented.
Source: The Counterintuitive Workings of the Minimum Wage – The Atlantic