The 600 economists signed that letter supporting a minimum wage of $10.10 that would be enacted over a period of 3 years. That’s different than the proposed $15 dollar an hour minimum wage or the $22 an hour hypothetical minimum wage if it was tied exclusively to productivity. The minimum wage is nothing more than a price floor. If the price of milk set by the market is $2.00 a gallon and the government makes it illegal to sell milk for less than $1.50 the law will have no effect. If workers are getting $10 an hour and the government raises the minimum wage $10.10 over a period of 3 years it won’t make much of a difference. Raising the minimum wage to $15 is much different as Politifact notes. They also found your statement regarding a savings to SNAP from a $15 minimum wage to be mostly false. http://www.politifact.com/truth-o-meter/article/2016/may/09/fact-checking-minimum-wage-debate/