"Oddly, this does not end up true for dieting, as I've found out."

I don't think yours is a proper analogy for the parents ...

In your case, the analog to income expansion would be exercise and "banked exercise" in the form of muscle added that has a baseline caloric upkeep just to keep it around.

I have no idea if that analogy works ... it's more complicated than his simple income behaviors ... this is just to say that your analogy is probably not a great one.