[1] Consider an income distribution S: (10, 20, 30, 50, 100). Suppose it is divided into two groups, group A: (10, 30, 50) and group B: (20, 100). Let the poverty line be 30. (a) Show that for both Headcount and Poverty Gap, the weighted sum of poverty for group A and group B is the same as the overall poverty in S. (b) Now consider a relative poverty line which is 60 percent of the median income for each group. Will the decomposition rule still hold? Explain
[1] Consider an income distribution S: (10, 20, 30, 50, 100). Suppose it is divided into two groups, group A: (10, 30, 50) and group B: (20, 100). Let the poverty line be 30. (a) Show that for both Headcount and Poverty Gap, the weighted sum of poverty for group A and group B is the same as the overall poverty in S. (b) Now consider a relative poverty line which is 60 percent of the median income for each group. Will the decomposition rule still hold? Explain
Chapter12: Income Distribution, Poverty, And Discrimination
Section: Chapter Questions
Problem 6SQ
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[1] Consider an income distribution S: (10, 20, 30, 50, 100). Suppose it is divided into two groups, group A: (10, 30, 50) and group B: (20, 100). Let the poverty line be 30.
(a) Show that for both Headcount and Poverty Gap, the weighted sum of poverty for group A and group B is the same as the overall poverty in S.
(b) Now consider a relative poverty line which is 60 percent of the median income for each group. Will the decomposition rule still hold? Explain.
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