Fortunately, there is neither a necessary connection nor correlation. A country could have absolutely no poverty at all and have extremely high-income inequality. The reason is because income inequality (measured by the Gini coefficient), measures relative, not absolute, income.
But you don’t have to take my word for it. Harry Frankfurt, a philosopher who has written a book on inequality, has a guest post at Forbes in which he makes the same point: income inequality and poverty aren’t the same thing.
What is bad is not inequality; it is poverty. We should want each person to have enough—that is, enough to support the pursuit of a life in which his or her own reasonable ambitions and needs may be comfortably satisfied. This individually measured sufficiency, which by definition precludes the burdens and deprivations of poverty, is clearly a more sensible goal than the achievement of an impersonally calibrated equality.
It is not inequality itself that is to be decried; nor is it equality itself that is to be applauded. We must try to eliminate poverty, not because the poor have less than others but because being poor is full of hardship and suffering. We must control inequality, not because the rich have much more than the poor but because of the tendency of inequality to generate unacceptable discrepancies in social and political influence. Inequality is not in itself objectionable—and neither is equality in itself a morally required ideal.