Chapter 2: Income Standards, Inequality, and Poverty
poverty-value curves that lead to a unanimous relationship in terms of the poverty gap measure and the squared gap measure. These two curves are known as the poverty deficit curve and the poverty severity curve. When the poverty deficit curve of one distribution lies above the poverty deficit curve of another distribution, then the former distribution has higher poverty—in terms of the poverty gap measure for all poverty lines—than the latter distribution. Similarly, if the poverty severity curve of a distribution lies above the poverty severity curve of another distribution, then the former distribution has higher poverty in terms of the squared gap measure for all poverty lines. We now elaborate these two concepts. Figure 2.15 outlines the poverty deficit curve concept. We use the poverty incidence curve (panel a) to construct the poverty deficit curve (panel b). The poverty incidence curve of distribution x is denoted by Fx. The height of a poverty deficit curve at a poverty line is the area underneath the poverty incidence curve to the left of the poverty line. In figure 2.15, the height of the poverty incidence curve at poverty line z is denoted by height B, which is the shaded area below the poverty incidence curve Fx to the left of z. For instance, for the poverty line z, if q people are identified as poor, then Fx(z) = q/N percent, which is the percentage of the poor population. What does the area underneath the incidence curve denoted by B mean? To understand, first note that the lightly shaded area denoted by A is the average income of the q poor people times the share of the poor. Figure 2.15: Poverty Deficit Curve and the Poverty Gap Measure b. Poverty deficit curve
C Deficit
Cumulative distribution
a. Poverty incidence curve
Fx
Dx
Fx(z) A
Dx ′
B B
z Income
xN
z Income
xN
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