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)

Answer 1

Correct Answer: 0.092

To calculate the squared poverty gap ratio, we follow these steps:
Step 1: Identify the Poverty Gap (G_i)
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 (G_i²)
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