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I do not think rational is the right word here. One way you can look at it either slave away and make few dollars more or do nothing and get about same outcome.

This is not rationality, this is hopelessness and despair.

I've yet to read the OP, but there is also the question scope, both in geography and in time.

If work produces a small margin of improvement for the worker (e.g. a small amount of disposable income, but nothing substantial nor, under the circumstances, making the difference between life and death). If work does this, but simultaneously produces substantially larger benefit and advantage for the employer.

Well, then you as the worker may be engaging in and facilitating a runaway condition for yourself. The more you work, the more you advantage the "haves" who are employing and holding you in a "have not" position.

I'm reminded of "War Games", which was rerunning the other night: "The only solution is not to play."

Not everyone at the bottom of the economic pile is an undiscovered Will Hunting-esque economist. But there is a lot of "smart" that is conveyed universally through the human and societal dynamics. You don't need an advanced degree to know when you're getting screwed.

And sometimes, it feels paramount to stop the screwing, even if it costs you.

"Rational" is an unfortunate choice of term, but it was the term the field of economics has used for quite some time. It is best to separate in your mind the idea of a rational actor and the colloquial connotations the term carries with it.
> then this means that people who’s labor income will lie between $0 and $20k will have no incentive to work.

This is called begging the question.

Are you referring to the implicit assumption that consumption is the primary incentive for a person to work? That's pretty non-controversial among economists, but if you're a philosopher or something you can certainly argue the point.

Anyway, that assumption about consumption is really only the premise of TFA. The sentence you quote is the implication of that premise and some statistics. Argue with the premise, argue with the statistics, argue with the implication if you want, but I just don't see the circularity here.

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From the original article: "If you exclude children from the numbers..., then 36% of poor people work at least 27 weeks/year" The argument that the poor don't want to work hinges on this number. This number does not take into account the disabled, retired, or otherwise unable to work who disproportionately fall into poverty.

As someone formerly below the poverty line, I take great issue with the statement that the poor do not want to work.

To put this back in terms of the updated graph from the CBO: even a menial job offers the potential to possibly move out of the poverty range with time. Between $20k and $30k the Disposable Income line tracks very closely to the Real Earnings line, meaning that the incentive is high. In a more practical sense, the difference between having $20k in disposable income and $28k is actually very palpable. Living in poverty is a hardship that defies the rationality he suggests.