Comment by llamaimperative

It's self-evidently the case: go to any city in the world and you will find people in poverty regardless of the city's productivity and, as nradov points out, countless more who fled as the baseline cost of living overtook their own productivity potential.

An extreme example is Palo Alto where local productivity is so high that a family income of ~$200k/yr qualifies for public housing assistance. These are people who are outputting massive amounts of productivity but in dire need of public assistance.

Why? Rent.

There is an equilibrium between rent prices, people's willingness to live in a region, and the productivity of that region.