Question:
Monthly per capita consumption expenditure (MPCE) of 10 households in a region is given below.
Households H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 MPCE(in Rs.) 2800 3000 1200 3500 1400 2500 4000 1000 900 1300
Assuming the poverty cutoff (Z) of MPCE to be Rs. 2000, the squared poverty gap ratio is _______(round off to 3 decimal places)
Monthly per capita consumption expenditure (MPCE) of 10 households in a region is given below.
Assuming the poverty cutoff (Z) of MPCE to be Rs. 2000, the squared poverty gap ratio is _______(round off to 3 decimal places)
| Households | H1 | H2 | H3 | H4 | H5 | H6 | H7 | H8 | H9 | H10 |
| MPCE(in Rs.) | 2800 | 3000 | 1200 | 3500 | 1400 | 2500 | 4000 | 1000 | 900 | 1300 |
Assuming the poverty cutoff (Z) of MPCE to be Rs. 2000, the squared poverty gap ratio is _______(round off to 3 decimal places)
Updated On: Nov 26, 2025
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Correct Answer: 0.092
Solution and Explanation
To calculate the squared poverty gap ratio, we follow these steps:
Step 1: Identify the Poverty Gap (Gi)
The poverty gap for each household is calculated as the difference between the poverty cutoff (Z) and the household's MPCE, provided the MPCE is less than Z. If MPCE is greater than or equal to Z, the poverty gap is zero. For Z = 2000:
Households with MPCE less than 2000 are H3, H5, H8, H9, and H10. Their poverty gaps are:
G3 = 2000 - 1200 = 800
G5 = 2000 - 1400 = 600
G8 = 2000 - 1000 = 1000
G9 = 2000 - 900 = 1100
G10 = 2000 - 1300 = 700
Other households have a zero poverty gap.
Step 2: Calculate Squared Poverty Gap (Gi2)
For households with a non-zero poverty gap, square the gap:
G32 = 8002 = 640000
G52 = 6002 = 360000
G82 = 10002 = 1000000
G92 = 11002 = 1210000
G102 = 7002 = 490000
Step 3: Compute the Average Squared Poverty Gap
Sum the squared gaps for all households and divide by the total number of households (N = 10):
Average Squared Gap = (640000 + 360000 + 1000000 + 1210000 + 490000)/10 = 370000
Step 4: Calculate the Squared Poverty Gap Ratio (SPGR)
SPGR = Avg. Squared Gap / Z2 (Where Z = 2000):
SPGR = 370000 / 4000000 = 0.0925
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