[btilly]

The answers are unclear, no, and no.

Also your conclusion about "rational decision" is clearly wrong. Taking risks is not necessarily rational. Doubly not when you are a single mother with 3 kids and a deadbeat ex.

Taking the job guaranteed losing her money. If she kept the job for a couple of years, she would have started to break even, but it would be quite a few years until she was ahead of where she was. Instead she continued to look for a job that either paid just little enough to keep food stamps, or offered a prospect of paying enough to offset losing food stamps.

Your reasoning is based on the theory that your best way up is to take the best job you can and then work your way up. That was how things worked when I was a kid. But today people tend to improve their job by switching jobs, not by being promoted in their current one. Therefore staying underpaid is often a better route up than switching to a job you don't want in the hope of maybe being promoted some day.