A Unified Approach to Measuring Poverty and Inequality
When every general mean registers an increase over time, gGM(x,y; a) > 0. When a = 1, the curve’s height is the usual mean income growth rate. This rate is equal to the growth of the generalized Lorenz growth curve at p = 100 percent. At a = 0 the curve shows the growth rate for the geometric mean, and so forth. As we will see later, each of these growth curves can help in understanding the link between growth and change in inequality over time. Figure 2.12 shows the growth curves of general mean incomes. The vertical axis denotes the growth rate of general mean income, and the horizontal axis denotes the values of parameter a. Following the same notations as the previous two growth incidence curves, suppose that there are two societies, X and X'. 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 gGM(x, y) denotes the growth rates of general mean income of society X over time, whereas the dotted growth curve gGM(x', y') denotes the growth rates of general 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 a. What information do these two growth curves provide? Growth between x and y is pro-poor in the sense that general means for lower a, which focus more on the lower end of the distribution, have positive growth, whereas
Growth rate of general mean income
Figure 2.12: General Mean Growth Curves
gG ( M x,y)
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