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
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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
...
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UC Berkeley
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