Chapter 2: Income Standards, Inequality, and Poverty
societies, X and X'. The income distributions of society X at two different points in time are x and y, whereas those of society X' are x' and y'. The dashed growth curve gLPM(x, y) denotes growth rates of lower partial mean income of society X over time, whereas the dotted growth curve gLPM(x', y') denotes growth rates of lower partial mean income of society X' over time. Suppose the growth rates of mean income across these two distributions are the same and are denoted by g– > 0. Thus, the solid horizontal line at g– denotes the growth rate if the growth rate had been the same for all percentiles or the cumulative population share. What information do these two growth curves provide? Growth between x and y is pro-poor in the sense that mean incomes of the population’s bottom percentiles have positive growth, whereas mean incomes of the population’s upper percentiles have negative growth. Growth between x' and y', in contrast, is not pro-poor because mean incomes of the population’s bottom percentiles have negative income growth, whereas mean incomes of the population’s upper percentiles have positive growth. In society X, the growth rates of the mean income of the bottom 20th percentile of the population and that of the bottom 40th percentile of the population are denoted by point C and point D, respectively. In society X', however, the growth rate of mean income of the bottom 20th percentile of the population and that of the bottom 40th percentile of the population are denoted by point C' and point D', respectively. Note that growth of mean income is the growth at the 100th percentile income where the two growth curves meet because they have been assumed to have the same growth rate of mean income. General Mean Growth Curve The final of the three growth curves is the general mean growth curve. Considering the income distributions x and y discussed previously, we denote the general mean of order a of distribution x and distribution y by WGM(x; a) and WGM(y; a), respectively. The growth of general mean of order a is denoted by g GM (x, y; a) =
WGM (y; a) − WGM (x; a) × 100%. WGM (x; a)
(2.15)
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