The big thing -- and it is a very big thing -- that progressive economists (I could understand if it were CATO) perpetually leave out of minimum wage/employment discussions is any acknowledgement of the tradeoff between the proportion of the wage gain and the proportion of the possible job losses. Simply, if we double the min wage and some of the jobs are automated out (in Australia the customer may operate her own order on the key pad) the workers are way (way!) ahead. This should be at the center of every discussion or we are leaving out what could be -- literally -- the most important factor.
Another huge factor -- which I don't expect individual store owners to grok (they might)-- but which should be the alpha and omega of progressive economists' thinking, is how the income shift of, say, 45% of employees getting an $8,000 average raise ($15 min) will affect the demand at the businesses those employees work in (and don't forget the businesses/employees whose wages get pushed up as a secondary result).
Toughest case: fast-food? Doubt it. The 25% increase in prices (33% labor costs) may not even be noticed by the 65% of customers coming through Ronald's drive-thrus if they don't listen hard before they pop the plastic -- what are they going to do, bring peanut butter sandwiches? When Illinois raised its min wage pretty quickly from $5.15 to $8, I and retired teacher who were regulars in the Ronald's across the street from me noticed a pickup in what we might call the third-world end of the business, mostly Mexican. Now the new owners across the street have just raised prices on many items 20-25% seemly because they think they can get away with it -- didn't seem to worry them.
The 35% coming through the doors will have more money to spend -- which wont cost the consumers of businesses they work in very much -- SORT OF A "MAKE-BELIEVE" MULTIPLIER. Un-toughest example: Walmart. $15 min wage raises Walmart prices 4% (7% labor costs). Wonder how many jobs lost at Walmart -- unless their newly flush low income buyers decide to move upscale -- Walmart can always move their merch upscale.
When people argue whether the economics profession knows what it is doing on macro-micro theory -- way above my (NY-Chi-SF cab driver) pay grade. But when economists perpetually leave out the most important labor market factors (to people actually in the labor market!) I wish they would plant their feet more solidly on terra firma.