1. Quadratic Lorenz Curve. Suppose the cumulative income distribution is given by x^2 , where 0...

1. Quadratic Lorenz Curve. Suppose the cumulative income distribution is given by x^2 , where 0 ≤ x ≤ 1, that represents the Lorenz curve of an economy. What is the Gini coefficient? Graph your results. For your information, the area under the Lorenz curve x^2 from 0 to 1 is 1/3 .

Expert Solution

Gini coefficient would be the ratio of area between Lorenz curve and 45 degree equality line to the total area under the 45 degree equality line. We can calculate it as or or or or or or .

With the info you have provided, we can calculate it as , where A is the area between the Lorenz curve and equality line and B is the area below the Lorenz curve. But, A+B is the area below the equality line, which is 0.5. Hence, we have, A=0.5-B, and for B=1/3, we have A=0.5/3. Hence, the Gini coefficient would be .

The graph is as below.

Rahul Sunny answered 2 years ago

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