Edited by Mark Blaug and Peter Lloyd
Chapter 57: The Lorenz Curve
Nanak Kakwani INTRODUCTION The Lorenz curve is widely used to represent and analyze the size distribution of income and wealth. Lorenz proposed this curve in 1905 in order to compare and analyze inequalities of income and wealth in a country during different epochs, or in different countries during the same epoch. When all income recipients are ranked in ascending order of income, the Lorenz curve is described by a function L(p), which is interpreted as the fraction of total income received by the lowest pth fraction of population. It satisfies the following conditions (Kakwani 1980): (a) If p = 0, L(p) = 0 (b) If p = 1, L(p) = 1 (c) Lr (p) 5 1 x $ 0 and Ls (p) 5 .0 m mf (x) (d) L (p) # p where income x of a person is a random variable with probability density function f(x) with mean income m and Lr (p) and Ls (p) are the first and second derivatives of L (p) with respect to p. These conditions imply that the Lorenz curve is represented in a unit square. In Figure 57.1, the diagonal OB through the unit square is called the egalitarian line. The Lorenz curve lies below this line. If the curve coincides with the egalitarian line, it means that each person receives the same income, which is the case of perfect equality. In the case of perfect inequality of incomes, the Lorenz curve coincides with OA and AB, which implies that all the income...
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