Econ 30041
Workshop 2
1. Consider a society Y with the following distribution: Y = (10, 20, 30, 40) which is divided into following two groups,
(i) A = (10, 40) and B = (20, 30). Using the Mean Log Deviation Inequality measure find the between group and within group inequality.
(ii) A = (10, 30) and B = (20, 40). Using the Mean Log Deviation Inequality measure find the between group and within group inequality.
2. Consider the following income distribution
|
Income
|
Frequency
|
|
10
|
10
|
|
20
|
20
|
|
50
|
20
|
|
70
|
10
|
|
100
|
5
|
(i) Find the relative poverty line based on 60 percent of the median income.
(ii) Calculate the head count ratio and poverty gap.
3. Find an income distribution and poverty line such that head count ratio reduces but poverty gap increases.
4. 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.
(i) Show that for both Head count and Poverty Gap, the weighted sum of poverty of group A and B is the same as the overall poverty in S.
(ii) Now suppose the poverty line is given by 60 percent of the median income for each group, then can we still claim that the weighted sum of poverty of group A and B is the same as the overall poverty in S?