Suppose, the poverty line as measured by Monthly Per Capita Expenditure is Rs. 1,000. Data for 10 Households:
- State A MPCE (in Rs.): 800, 850, 900, 950, 1200, 1150, 1050, 1100, 1250, 1300
- State B MPCE (in Rs.): 400, 450, 550, 650, 1100, 1350, 1300, 1200, 1250, 1400
- Head Count Ratio of State A is less than Head Count Ratio of State B.
- Poverty Gap Ratio of State A is less than Poverty Gap Ratio of State B.
In the light of the above statements, choose the most appropriate answer from the options given below:
Show Answer & Explanation
Correct Answer: (D)
Explanation:
Let’s analyze both statements with the Poverty Line (PL) = ₹1,000.
- Statement I (Incorrect): The Head Count Ratio (HCR) is the percentage of households below the poverty line.
- State A (Poor): 800, 850, 900, 950. (Count = 4)
- State B (Poor): 400, 450, 550, 650. (Count = 4)
- Both states have an HCR of 4/10 or 40%. Therefore, Statement I (which claims A is less than B) is incorrect.
- Statement II (Correct): The Poverty Gap Ratio (PGR) measures the *depth* of poverty (how far, on average, the poor are from the PL).
- State A Gaps: (1000-800) + (1000-850) + (1000-900) + (1000-950) = 200 + 150 + 100 + 50 = Total Gap 500
- State B Gaps: (1000-400) + (1000-450) + (1000-550) + (1000-650) = 600 + 550 + 450 + 350 = Total Gap 1950
- The total (and average) poverty gap in State A is significantly less than in State B. This means poverty in State B is much deeper and more severe. Thus, PGR of A is less than PGR of B.
📚 Additional Info: Measuring Poverty
This question highlights the difference between the *incidence* of poverty and the *depth* of poverty. These are key concepts from the Foster-Greer-Thorbecke (FGT) class of poverty measures.
1. Head Count Ratio (HCR)
- What it is: The proportion of the population that is below the poverty line.
- Formula:
HCR = q / N(whereqis the number of poor people, andNis the total population). - In this question:
HCR (A) = 4/10 = 0.4andHCR (B) = 4/10 = 0.4. - Limitation: HCR tells you *how many* are poor, but not *how poor* they are. It also doesn’t change if the poorest person becomes even poorer.
2. Poverty Gap Ratio (PGR)
- What it is: Measures the average shortfall of income/expenditure of the poor from the poverty line. It tells you the *depth* of poverty.
- Formula:
PGR = (1 / (N * PL)) * Σ(PL - y_i)(Sum of all poverty gaps, divided by the total population and the poverty line). - In this question:
- PGR (A) = (1 / (10 * 1000)) * 500 = 0.05
- PGR (B) = (1 / (10 * 1000)) * 1950 = 0.195
- Interpretation: The PGR (0.05) for State A is much smaller than for State B (0.195), proving Statement II is correct.
3. Squared Poverty Gap (SPG)
- What it is: This is the PGR, but with the gaps squared.
- Purpose: It measures the *severity* of poverty. By squaring the gaps, it gives much more weight to the poorest of the poor (e.g., the 600 gap in State B) than to those just below the line (e.g., the 50 gap in State A). This metric is highly sensitive to inequality *among* the poor.