But isn't raising the minimum wage along with productivity increases sustainable? Why would that mean companies immediately start automating, when more people have more money to spend on their goods? Raising it to $1000 is unrealistic, but not $10 - $15.
No; if you are worth $15 dollars an hour, you will already be paid $15 an hour. What if you're not worth $15 an hour and minimum wage is raised so that you have to take at least that much? In other words, what if you cost a company more than you produce? You don't get a pay increase, you get fired. It has nothing to do with productivity, it has to do with efficiency.
Let's say a machine costs $12 an hour to produce $20 worth of goods or service an hour. 20 - 12 = $8 profit/hr.
Let's say a person is paid $10 an hour to produce $20 worth of goods or service an hour. 20 - 10 = $10 profit/hr.
The better option is the person.
Let's say the person has to work for $15 minimum an hour to produce $20 worth of goods or service an hour. 20 - 15 = $5 profit/hr.
The machine is the better option, but the person is still doable depending on the job.
However, consider this:
A machine costs $20 an hour to produce $10 worth of goods or service. 10 - 20 = $10 deficit/hr.
A person has to work for $15 minimum an hour to produce $10 worth of goods or service. 10 - 15 = $5 deficit/hr.
Clearly the better option, between the two, is the person; however, this doesn't mean the person will have a job, it means he will cost the company $5 an hour to work there. Nobody can work that job anymore, because it's not profitable. The job goes away, or gets consolidated into another job at that company, increasing the work load of the people still there and keeping the guy who doesn't have work unemployed.
In other words, a $15 minimum wage means anyone worth <$15 an hour now makes $0 an hour. Their lives now must be paid by the people who do make more than $15 minimum wage, whether directly e.g. friends or parents, or indirectly i.e. welfare. When is this ever sustainable?