The Gini Index, named after Corrado Gini (1912), is used to measure the distribution of income among a country's citizens. It is based on the Lorenz...

I need help starting up the first question as I do not understand how I am supposed to show proof. For question 1, I understand that I must show the area between y=x and y=L(x).

For question 2, I also need help on how to start the question. Am I supposed to plug something into the equation shown?

The Gini Index, named after Corrado Gini (1912), is used to measure the distribution of incomeamong a country’s citizens. It is based on the Lorenz curve L(a:), named after Max Lorenz (1905). The Lorenz curve is a representation of the proportion of total income of a population cumulatively.In the function L(a:), 1: represents the percentage of the population, and L(a:) represents the percent oftotal income held by 58% of the population. That is, if 25% of the population holds 12% of the total income,then L(0.25) = 0.12. The Lorenz curve is always below the line y = a: between 0 and 1. As well, L(0) = 0 and L(1) = 1. 1. (5 marks) Mathematically, the Gini index G is defined as the area between y = a: and y = L(a:)divided by the total area under the line 3; = :12. That is, G = MAB, where A and B are the areas indicated in the diagram. Show that G = 2 fol a: — L(a:)da:. 2. (10 marks) The Lorenz curve of a population is provided as L(a:) = 24:?332 1|! 1 — £132. Determine theGini index of the population. 3. (1 mark) Would a larger or smaller Gini index be preferable? Explain.