Question

1. If the distribution of income in country "C"is (1, 2, 2, 3, 5), and in country "D" it's (1, 1, 2, 3, 5). The poverty line in both countries is 2.5 a) By the average income shortfall (AIS) measure which country has more poverty? b) By the headcount index measure which country has more poverty? C) By the average poverty gap (APG) which country has more poverty? d) Calculate the FGT index for each country using p-alpha = 2

Answer 1

ans a) AIS = TPG/ H

where TPG is total poverty gap

H is head count( no of people below poverty line

Yp is poverty line income

Y is obsevations of income

for C,

TPG= = (2.5-1)+(2.5-2) +( 2.5-2)= 2.5

Y<Yp

H= 3

AIS=TPG/H = 2.5/3 =0.83

for D

TPG= = (2.5-1)+(2.5-1) +( 2.5-2) = 3.5

Y<Yp

H= 3

AIS = 3.5/3 = 1.17

according to AIS, country "D" is more poor

b) head count index= H/N

where H= head count

N= total population = population size

for C,

head count index= 3/5

for D,

head count index= 3/5

according to head count index , both are equally poor

c)

APG= TPG/ N

for C,

APG=2.5 /5= 0.5

for D

APG =3.5/5 =0.7

according to APG, D is more poor

d) FGT= $1/N \sum_{i=1}^{H}(\frac{Yp-Y}{Yp})^{a}$

here a= 2( given) here all Y with Y<Yp will be used

for C,

FGT = 1/ 5 ( (( 2.5 -1)/2.5)2+(( 2.5 -2)/2.5)2+(( 2.5 -2)/2.5)2​​​​​​​) =1/5 (0.36 + 0.04 +0.04) = 0.44/5= 0.088

for D,

FGT =1/ 5 ( (( 2.5 -1)/2.5)2+(( 2.5 -1)/2.5)2​​​​​​​+(( 2.5 -2)/2.5)2​​​​​​​) = 1/5 ( 0.36+ 0.36+ 0.04) =0.76/5 = 0.155