This whole discussion is a little strange to me.
Why would we tie minimum wage to worker productivity OR inflation?
What is the minimum wage trying to accomplish in the first place?
It seems obvious to me that we have to index it to the living wage instead.
A full-time job needs to cover: one half of a 2-bedroom apartment in the outskirts of town, plus food, bills, and basic medical expenses. If it doesn't cover this, then this person is going to rely on government programs.
And if the government programs aren't there, they'll be coming home each night after a full day of work and watching their kid get skinnier, seeing their CEO collect multimillion dollar bonuses in the news, and you can be damn sure they won't stand for it. They'd unionize, protest, and demand higher compensation.
Our social safety nets are an important part of our society, but when they're required and used by full-time employees, it's something of a taxpayer subsidy for the corporations who can now pay their employees less than what's required to live.
And if a job can't be done profitably for a living wage, we need to let that job go. Automate it, outsource it, let the companies that depend on this exploitative labor pivot to new business models, or let them wither and die. The jobs are going to leave eventually anyway - we might as well accelerate the push toward a modern labor economy that's already underway. We can funnel the productivity gains from automation into education, to allow the displaced a chance to retool and learn a new skill, and to bulk up our social safety nets for those who are too old to do so.