The New York Times told readers that Mayor Bloomberg is right, the data show that the poor have benefited by having more billionaires in the city. The basis for this assessment is that rich people pay a disproportionate share of the city's tax revenues. Therefore by having more rich people, the city has more tax revenue to help out poor people.
The article even gives readers some basis for quantifying this gain. It tells readers that households with incomes of more than $10 million a year accounted for almost 20 percent of the city's income tax revenue last year. Since the city raised just under $8 billion in income taxes, this means that the rich paid a bit less than $1.6 billion to the city in income taxes.
By comparison, the article tells us that 46 percent of the people in the city have an income of less than 1.5 times the poverty level. With a population of 8.25 million, this implies that roughly 3.8 million people live near or below the poverty line. This means that if all the tax revenue from the wealthy was used to benefit the poor, as opposed to benefiting the wealthy by providing them services or general support for the city infrastructure and services, it would come to $420 per poor person per year.
However tax payments are not the only way that the rich would affect the well-being of the poor. Their demand for housing and other resources (e.g. building space devoted to restaurants, gyms, art galleries, etc) drives up the cost of real estate in New York City. As a result, rent costs the poor more than it would if there were fewer rich people in the city.
It's not easy to calculate what rents would be in the city if the number of rich people had not increased so much under Bloomberg, but they would almost certainly be considerably lower. According to the Bureau of Labor Statistics (BLS), since 2000 rents in the New York have risen by 40.7 percent in the New York metropolitan area compared to 36.2 percent in the country as a whole. The increase in rents in the city itself is almost certainly more than this number, since the BLS figure is for the whole metropolitan area.
The Census Bureau reports that the median rent for the city is $1,125 a month or $13,500 a year. If the presence of such a large number of rich people raised this figure by 10 percent, then rich people cost low and moderate income people $1,350 in higher rents. With an average of 2.7 people per housing unit, this is considerably more than the $1,130 they would get if all the income taxes raised from the rich were redistributed to the poor.
Of course the rich would impose costs on the poor in other ways as well. Because the price of real estate in general is higher due to their demand, all the stores in the city must pay higher rents because of the presence of so many rich people. These higher rents are passed on to low-income people in the price of their food and clothes and everything else they buy.
If the NYT wanted to do a serious analysis of whether the poor in New York City benefit from having so many rich people in the city, then it would have to examine all the ways in which their presence has an impact on the well-being of the poor. Just looking at tax revenue collected from the rich is an incomplete and obviously biased way to make this assessment.
Note: typos corrected.