The Lorenz curvey=L(x)y=L(x) of a country plots the proportion of the total income of the population (y axis) that is cumulatively earned by the bottom x of the population. For instance, if the point (0.2,0.1)(0.2,0.1) is on the Lorenz curve, it means that the bottom 20%20% of the population earns 10%10% of the total income. The curve of perfect equality is then the line y=x

The Gini index GG of a country is a number between 0 and 1 that measures income inequality within a country. The closer it is to 0, the more equal the income distribution is. The Gini index is defined as being twice the area between the line of equality y=x and the Lorenz curve y=L(x)of a country.

Suppose that the Lorenz curve of a country is modeled by the function L(x)=(11/16)*x^(2)+(5/16)*x