Central State University Gini Index of Income Concentration Problems

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cfzvgu38

Mathematics

Central State University

Question Description

I’m stuck on a Calculus question and need an explanation.

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Find the Gini index of income concentration for the Lorenz curve with the following equation. 1 y=-xV4 + 12x Click the icon to view the table of integrals. The Gini index of income concentration is (Type an integer or decimal rounded to four decimal places as needed.) Х Table of Integrals 3 Integrals involving Va+bu, a #0 and b=0 21a + bu) Va + bu du = 3b 2(3bu – 2a) + bu du = V(a + bu)3 1562 Jurva+ budu = 2 (155°u? – 12abu + Ba?) Vla+ bu)3 105b3 1 27a+ bu du = Va+bu b 2(bu – 2a) du = u Va + bu a + bu 362 u? 2 (36%u2 - 4abu +8a) du = a + bu a + bu 15b So wat bu 1 1 Va + bu - va du = In a>0 uva + bu va a TVa+bu + va Va + bu b Va+bu - Va du = In 2avā a + bu + va a>0 u? Va + bu au Textbook Ask My Instructor Print Print Dono
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Explanation & Answer

View attached explanation and answer. Let me know if you have any questions.

Lorenz curve : L ( x ) = y =

1
x 4 + 12 x
4

Gini index = 2  L ( x ) dx
1

0

1
x 4 + 12 xdx
0 4
1 11
= 
(12 x + 4 − 4 ) 4 + 12 xdx
2 0 12
1 1
=
(12 x + 4 ) 4 + 12 x − 4 4 + 12 x  dx
24 0 

= 2

=

1
...

ZqMnsne (494)
UC Berkeley

Anonymous
Excellent resource! Really helped me get the gist of things.

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