Measuring Inequality - DARP

20 CHAPTER 2. CHARTING INEQUALITYFigure 2.2: Frequency Distribution of Income Source: as for Figure 2.1corresponds to the proportion of the population with $30 000 or less. And wecan repeat this operation for every point on either the empirical curve or on thesmooth theoretical curve.The visual relationship between Figures 2.1 and 2.3 is now obvious. As afurther point of reference, the position of mean income has been drawn in atthe point A in the two …gures. (If you still don’t see it, try turning the pageround!).The Lorenz curve was introduced in 1905 as a powerful method of illustratingthe inequality of the wealth distribution. A simpli…ed explanation of it runs asfollows.Once again line up everybody in ascending order of incomes and let themparade by. Measure F (y), the proportion of people who have passed by, alongthe horizontal axis of Figure 2.4. Once point C is reached everyone has goneby, so F (y) = 1. Now as each person passes, hand him his share of the “cake”–i.e. the proportion of total income that he receives. When the parade reachespeople with income y, let us suppose that a proportion (y) of the cake hasgone. So of course when F (y) = 0, (y) is also 0 (no cake gone); and whenF (y) = 1, (y) is also 1 (all the cake has been handed out). (y) is measuredon the vertical scale in Figure 2.4, and the graph of plotted against F is the