The Lorenz Curve
The Coefficient of Inequality


Norman is an economist who works on the
distribution of income between households in a country. The cumulative
distribution he used is called a Lorenz curve. A Lorenz curve goes from
0 to 1 and includes the points (0, 0) and (1,
1). The points on this Lorenz curve are determined
by ranking all households by income and then computing
the percentage of households whose income is less than or equal to a
given percentage of the total income of the country. If a given percent
of the households receive the same percent of income, the Lorenz
curve is the line
y = x and is called absolute equality. The coefficient of inequality
is used to describe the difference between the Lorenz curve and the absolute
equality curve.
What is know:
 The income distribution for a given country is represented by a
Lorenz curve defined by the equation
L(x) = 5x^{3}/(x^{2} + x +3)
 The coefficient of inequality is given as
where L(x ) is the Lorenz curve.
