You can't motivate someone by underpaying him.

If this means that you can't entice someone to take a job while offering less than they are willing to accept, then this problem solves itself.

If it means something else, then the question is "underpaying, compared to what?"

As far as paying the elderly and crippled starvation wages...

Yikes. I'm just trying to make some widgets.

But it is good news that the EEOC exists, so discrimination against these people doesn't, so they already have jobs elsewhere and don't belong in this thought experiment.

But there is still the guy with the drug conviction. U.S. federal law does not protect him from discrimination, and state law varies.

He is willing to take $25,000 per year. That suggests that he doesn't have a better option. You can hire him at $50K, but you have equally qualified applicants at that price without the additional worry that this guy's past might bring you. If you do not offer him the "starvation wage" of $25,000, he will necessarily take the next best option, which will perforce be worse.

you have to pay at least a living wage

I see the advantage of preferring long-term workers and providing compensation that is good for retention. But there is a cost too -- additional salary and benefits aren't free. I have to recover that cost from my customers. If I lose market share to the competition because I give richer compensation, I might end up having to lay people off.

If your workplace has a budget for management training, it may be a high-skill, established operation in which churn is inefficient and wasteful. But this won't be true if you're running a car wash or Burger King or some other business that operates on very narrow margins with low-skilled staff. It may make sense to save on salary and put up with more churn.

The motivation of this thought experiment is to answer the question "is it inherently unethical to pay an employee less ... ?" Less than what, I'm not sure. There is always some variety in the salaries of my coworkers; that's no big deal.

There seems to be a line, though, beyond which people start talking about "starvation wage" and prefer to condemn job hunters to their next best option rather than seeing them paid at that level. I would like to understand that line.