Suppose that the initial rural distribution of income is (1,2, 3, 4) while the initial urban distribution is (3, 4). The poverty line is 2, so the overall poverty rate (headcount index) is 1/3. Now imagine that all of the rural poor move to urban areas and each of them gains 20% in real income. Verify that the overall poverty rate falls to 1/6, yet the urban poverty rate rises from zero to 1/4.