But by what standards do you define someone as poor? If the rich have enormous assets and those 'on the bottom' have TV sets and VCRs, are they really poor?
If we define "poor" in relative terms, then the definition of "poor" will continually shift upward as a society grows wealthier overall. If we define "poor" in absolute terms, then there is little question that the poor of today enjoy a standard of living that is much higher than the poor of a hundred years ago, or the "wealthy" of a thousand years ago.
In any case, the point I wanted to make is that a person being wealthy, whether in absolute or relative terms, is not the cause of someone else being "poor". Like I said, economics is not a zero-sum game.