Question

Consider the following distribution of income in a 12-person economy, with the modern urban
wage =3, the traditional rural income =1, and the informal urban wage =2: (1,1,1,1,2,2,2,2,3,3,3,3). The poverty line =1.25.

(a) Calculate the number of poor, headcount index, TPG, APG and AIS.

(b) Suppose rural incomes are raised to 1.5 through expanded agricultural exports.What happens to relative inequality? Absolute poverty?

Answer 1

a).

Consider the given problem here there are “N=12” peoples having income “Yi = (1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3)”. Now, the poverty line is given by, “Yp=1.25”, => numbers of poor are those whose income is less than “Yp”, => here there are 4 people having income less than “Yp”, => H=4. Now, the “head count index” is given by, “H/N = 4/12 = 1/3”.

TPG (total poverty gap) measure the total income require to raise all the poor people up to the poverty line. So, here “H=4”, “Yp=1.25”, => TPG = 4*(1.25-1) = 1, => TPG = 1. The “APG (average poverty gap)” measure the total poverty gap per person, => APG = TPG/N = 1/12. Similarly, “AIS (average income shortfall)” is given by the ratio of “TPG” and “H”, => “AIS = TPG/H = 1/4.

b).

Now, as the income of the poor increases from “1” to “1.5 > Yp”, => all people are above the “Yp”, => the gap between the maximum and the minimum income decreases, => the inequality decreases. Absolute poverty also decreases because “H” reduces from “4” to “0”.