A Lorenz curve is given by y L x where 0 x 1 represents the lowest fraction of the population of a society in terms of wealth and 0 sys1 represents the fraction of the total wealth that is owned by that fraction of the society Use this information to complete parts a through g Click the icon to view an example of a Lorenz curve Now show that 2A 1 2 L x dx First rewrite the expression 1 2 L x dx in terms of B 1 1 2 L x dx 1 2B Substitute the expression for B in terms of A found in a previous step for B and then simplify 1 2 0 D 1 2 24 1 1 A Therefore G 2A 1 2 L x dx by the O Substitute Simplify transitive property completing the proof e Compute the Gini index for the cases L x x and p 1 3 1 9 2 3 4 The Gini index for p 1 3 is 0 130 Type an integer or decimal rounded to three decimal places as needed The Gini index for p 19 Type an integer or decimal rounded