You are a planner in Ping, a poor land, where poverty line is set at 1000 pah a year. It turns out that in Ping there are two equal sized groups both below the poverty line. This is the entire population of Ping. One group consists of 100 individuals: they have equal earnings of 500 pay a year each. The second group also has 100 people: they earn 900 pah a year each. You have been allocated a budget of 20,000 pah a year. You must allocate this among the 200 poor people.
a. Suppose you were to forget the poverty line. How would you distribute the money?
b. Calculate the following prior to any redistribution
i. The Headcount Ratio
ii. The Total Poverty Gap
iii. The Average Poverty Gap
iv. The Normalized Poverty Gap
v. The Squared Poverty Gap.
c. What are the strengths and weaknesses of each of these measures of poverty? (Explain for each measure).
d. Now suppose that you are firmly told by the President of Ping to use this money to minimize, as far as possible the head count. Who would you give money to?
e. Now imagine that you are told to minimize (as far as possible) the Squared Poverty Gap (SGP). Does the way you now spend your money necessarily contrast with the intuitive reactions you noted earlier?