In this case, I think the causation is in the other direction. Over time, people with less intellectual capacity will be less successful, and therefore poorer. That is rational. The other direction is irrational.
If intellectual capacity was purely genetic, this would make some sense. You can't buy better genes for yourself or your children. [1] However, intellectual capacity is demonstrably affected by a variety of environmental factors, including early nutrition, that themselves are strongly influenced by wealth, so we've got pretty good ideas of some of the mechanisms by which wealth influences intellectual capacity.
> In this case, I think the causation is in the other direction. Over time, people with less intellectual capacity will be less successful, and therefore poorer. That is rational. The other direction is irrational.
I think you are confusing "rationality" with fit to your preferred, non-evidence-based, model of the way the world should work.
[1] Well, except that wealth affects mate selection opportunities, so, even with purely genetic intellectual capacity, wealth could plausibly have some influence.
Good nutrition, stimulation, and education are all important during development. This things are all much easier to access when you have more money.
But not so important that they would have a 40 point IQ difference. If it is, show me the studies confirming that.
No.
But it does make sense to say that a 4 year old is both poor and has a low IQ because his parents do. And this applies whether you believe that his low IQ is due to heredity or a poor environment caused by his parents.