Imagine a world in which every man, woman and child had their income increased 10-fold overnight. You'd think that while the rich would be even richer, the poor would also become quite well-off - having ten times their current income would let them pay off their debts, buy a new car, send their kids to college, and so on... But you'd be wrong. The poor would still be poor, and they'd be just as many poor people as there are now.
Don't believe me? Well, just consider this quote from an article today regarding a study by the United Nations Children's Fund on wellbeing in more than 20 countries :
"Nearly 12 per cent of Australian children fell below what the UNICEF report considered the poverty line - a household where the total income is less than half of the country's median."
The way UNICEF (and social welfare lobby groups) measure "poverty" is in purely relative terms. So it doesn't matter how high a household's income becomes, if their income is less than half the median household income then they're classed as "poor".
While I agree that poverty is relative to some degree (ie. a family in a developed country may have enough income for all the basics of life, yet still be considered "poor" if they cannot afford expenses that are normal for the society they live in, such as a colour TV), logic dictates that there must be some absolute level of income above which a family living in an affluent society is no longer really "poor" just because their income is considerably lower than the typical (median) income.
Otherwise there is no relationship between GDP, incomes and poverty - and the only way to "reduce" poverty is to have everyone on nearly the same income levels.