What Nathan and Doug said, with only one small addition: the presumption of 'different populations' is a premise that requires more than repetition. Without that premise, nothing of what Brett insists on 'asking' makes any sense. That is, without that basic demographers' premise, the assertion would look like a tautology (poverty = poverty) instead of the discovery of a cause (immigrants = poverty). Someone should have changed the thread title to 'migrants import income disparities'.
Demography is such bullshite. It doesn't matter whether you drain it of more explicitly xenophobic points of reference by transposing births/deaths for migrants, nor even if you depict an economy and labour market in the cartoonish terms of a deposit box of monies that come from some other imaginary place, as Nathan suggests. The relationship between population numbers and income disparity is a fiction that can only ever amount to, and is implicitly geared toward, 'solving' income disparities by 'solving' the 'population problem', because it takes 'populations' to be _the_ significant and explanatory variable in the first place. Here, everything remotely troublesome -- environmental degradation, income disparity, whatever else might emerge as a problem on the horizon of the policy wonk looking for an historically-intuited, apparently untroubling solution -- is reducible to 'populations'. Of course, by rendering something in the terms of 'populations', you get to create that crucial device of a policy-speak-for-troublesome-times: 'us' and 'them' in which even beginning to think about 'them' as those who own our skins sounds illogical by virtue of the fact that there are so few of them, how could they possibly be significant.
Angela