## The Human Poverty Index (HCR), Poverty Gap Ratio (PGR), and Income Gap Ratio (IGR)

A region has 20 people and three income groups A,B,C. Group A has population 10, group B has population 6 and group C has population 4. Each person in group A has income \$4, each in group B has income \$12 and each in group C has income \$20. The poverty line is p = 15 (anyone with income below \$15 is considered poor).You are given a budget of \$60 to allocate among groups whose income is below p = 15. Assume that each person within the same group must receive the same amount. Also assume that every dollar received by an individual is invested and this raises the income of the individual by a dollar. Consider the following three policies:
Policy I: allocate the entire \$60 to group A;
Policy II: allocate \$36 to group A, \$24 to group B;
Policy III: allocate \$24 to group A, \$36 to group B.
Showing all steps of your work, find HCR, PGR, IGR under each of the three policies and determine
(i) which policy/policies give the lowest HCR,
(ii) which policy/policies give the lowest PGR and
(iii) which policy/policies give the lowest IGR.

the Human Poverty Index (HCR), Poverty Gap Ratio (PGR), and Income Gap Ratio (IGR)

Research and Formulation

Thesis Statement

In the given scenario, by analyzing the Human Poverty Index (HCR), Poverty Gap Ratio (PGR), and Income Gap Ratio (IGR) under each of the three policies, it can be determined that Policy II results in the lowest HCR, Policy III leads to the lowest PGR, and Policy II offers the lowest IGR.

Introduction

In this analysis, we will delve into the impact of different budget allocation policies on poverty indices within a region with three income groups. By considering the allocation of a \$60 budget to groups below the poverty line, we aim to understand which policy is most effective in reducing poverty levels based on various indicators.

Policy I: Allocate the entire \$60 to group A

– Group A: \$60
– Group B: \$0
– Group C: \$0

HCR Calculation

– Number of poor with income below \$15 in Group A: 10
– Total population: 20
– HCR = 10 / 20 = 0.5

PGR Calculation

– Total income gap for poor in Group A: 10 * (15 – 4) = \$110
– PGR = 110 / (15 * 10) = 0.733

IGR Calculation

– Average income gap for poor in Group A: 11
– IGR = 110 / (15 * 10) = 0.733

Policy II: Allocate \$36 to group A, \$24 to group B

– Group A: \$36
– Group B: \$24
– Group C: \$0

HCR Calculation

– Number of poor with income below \$15 in Groups A and B: 10 + 4 = 14
– HCR = 14 / 20 = 0.7

PGR Calculation

– Total income gap for poor in Groups A and B: (10 * (15 – 4)) + (4 * (15 – 12)) = \$118
– PGR = 118 / (15 * 14) = 0.561

IGR Calculation

– Average income gap for poor in Groups A and B: 8.43
– IGR = 118 / (15 * 14) = 0.561

Policy III: Allocate \$24 to group A, \$36 to group B

– Group A: \$24
– Group B: \$36
– Group C: \$0

HCR Calculation

– Number of poor with income below \$15 in Groups A and B: 10 + 6 = 16
– HCR = 16 / 20 = 0.8

PGR Calculation

– Total income gap for poor in Groups A and B: (10 * (15 – 4)) + (6 * (15 – 12)) = \$114
– PGR = 114 / (15 * 16) = 0.475

IGR Calculation

– Average income gap for poor in Groups A and B: 7.125
– IGR = 114 / (15 * 16) = 0.475

Conclusion

Based on the calculations of HCR, PGR, and IGR under each policy, it can be concluded that Policy II results in the lowest HCR, Policy III leads to the lowest PGR, and Policy II offers the lowest IGR. Therefore, for a more effective reduction in poverty levels, Policy II could be considered as the most suitable option among the three policies provided.