In a sample economy comprising 5 individuals, the daily per capita consumption expenditure… — State PSC Exam

In a sample economy comprising $5$ individuals, the daily per capita consumption expenditures are recorded as $₹20$ , $₹30$ , $₹40$ , $₹50$ , and $₹110$ . The official poverty line for this economy is established at $₹50$ per day. What is the Poverty Gap Index ( $PGI$ ) of this economy, expressed as a percentage?

Answer: 24 %

Answer

The Poverty Gap Index of the economy is 24%

The Poverty Gap Index (

PGI

) is calculated as the average of normalized poverty gaps across the entire population:

PGI = \frac{1}{N} \sum_{i=1}^{N} \left(\frac{Z - y_i}{Z}\right)

for all

y_i < Z

. For this population (

N=5

Z=50

), the normalized gaps are

0.60

0.40

0.20

0

, and

0

. Taking the mean gives

1.20 / 5 = 0.24

, which equals

24\%

Step-by-Step Solution

Identify poor individuals and determine consumption shortfalls relative to the poverty line

Three individuals have expenditures below

₹50

, with shortfalls of

₹30

₹20

, and

₹10

Poverty gap measures depth of poverty, considering only individuals below or at the poverty line (

y_i \le Z

Calculate the normalized poverty gap for each individual

Normalized gaps are

0.60

0.40

0.20

0.00

, and

0.00

Normalizing by the poverty line (

Z

) expresses individual shortfalls as proportions of

Z

Sum normalized gaps and average over total population N

PGI = \frac{1}{5} (0.60 + 0.40 + 0.20 + 0 + 0) = 0.24

24\%

The Poverty Gap Index formula is

PGI = \frac{1}{N} \sum_{i=1}^{N} \frac{\max(0, Z - y_i)}{Z}

Key Concept

Poverty Gap Index (PGI) calculation and intensity of poverty measurement

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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