ECON 448: Week 9-
1. Poverty and Undernutrition
(1) A poverty line is a critical threshold of income, consumption, or, more generally, access to goods and services below which individuals are declared to be poor. It represents a minimum level of "acceptable" economic participation in a given society at a given point in time, as an approximation.
(2) In Ping, a poor land, there are two equal sized groups below the poverty line, which is set at 1000 pah a year. One group consists of 100 individuals: they have equal earnings of 500 pah a year each. The second group also has 100 people: they earn 900 pah a year each. Of course, there are also people who are above the poverty line. The third group has 800 people and they earn 2000 pah a year each.
a. Compute the HCR, PGR, and IGR. If you want to minimize each poverty measure within a given budget (say 20,000 pah), what would you do?
b. (relative deprivation among the poor) Suppose that each person who earns 500 pah gave 50 pah to each person who earns 900 pah. Compute the HCR, PGR, and IGR again. What if the transfer was 110 pah instead of 50 pah?
Head-Count Ratio (HCR):
HCR = HC/n, HC = i=1∑n 1(yi < p)
Poverty Gap Ratio (PGR):
P GR = ∑y_i(p - yi)/mn
Income Gap Ratio (IGR):
IGR = ∑y_i(p - yi)/pHC
Foster-Greer-Thorbecke index (FGT index):
Pα = 1/n ∑yi(p - yi/p)α
2. Population Growth and Economic Development
(1) Why does a young age distribution make it more difficult for a country to slow its rate of population growth? If a country suddenly drops its total fertility rate to two (which makes for a stationary long-run population), describe the path that population will take before settling at this long-run level.
(2) In this chapter, we studied a model where a family wants one surviving child to provide old-age security. Let us say that the probability of any one child living to look after its parents in old age is 1/2. However, the family wants this security level to be higher, say a probability of q > 1/2.
(a) Describe the family's fertility choices for different values of q, by first writing down a model that captures this story, and then examining the results for different values of q.
(b) Calculate the expected number of surviving children for this family, under various values of q.
(c) Suppose the family relies on sons only for old-age security. Assume that the family has equal probability of having a son or daughter. What are the fertility choices and the expected numbers of surviving sons and daughters respectively?
(d) If all families rely on sons for old-age security and make sequential fertility decisions after observing the fate of their earlier children, how would you predict the aggregate sex-ratio of the society?