1 markEconomics of Growth and DevelopmentPoverty, inequality and human developmentThe poverty gap and the FGT indicesModerateabout 2 min

IIT JAM 2022 Question 42: Poverty, inequality and human development

Monthly per capita consumption expenditure (MPCE, in Rs.) of 10 households is 2800, 3000, 1200, 3500, 1400, 2500, 4000, 1000, 900, 1300. With the poverty cutoff $Z = 2000$ , the squared poverty gap ratio is _______ (round off to 3 decimal places).

Answer and worked solution

Answer: 0.092 to 0.093

The squared poverty gap ratio is the FGT index $P_2 = \dfrac{1}{N}\sum_{\text{poor}}\left(\dfrac{Z - y_i}{Z}\right)^2$ , using all $N = 10$ households in the denominator.

The poor households (below $2000$ ) are $1200, 1400, 1000, 900, 1300$ , with normalised gaps $0.4, 0.3, 0.5, 0.55, 0.35$ . Their squares sum to $0.16 + 0.09 + 0.25 + 0.3025 + 0.1225 = 0.925$ . Dividing by $10$ gives $P_2 = 0.0925$ , accepted anywhere from $0.092$ to $0.093$ .

Plain-text version

Monthly per capita consumption expenditure (MPCE, in Rs.) of 10 households is 2800, 3000, 1200, 3500, 1400, 2500, 4000, 1000, 900, 1300. With the poverty cutoff Z = 2000, the squared poverty gap ratio is _ (round off to 3 decimal places).

Poverty, inequality and human development has come up 92 times in 7 exams since 2010.

What this question tests

This question is on The poverty gap and the FGT indices, part of Poverty, inequality and human development in Economics of Growth and Development.

Measures of how poor the poor are, not just how many.

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