Asked by anonymous
One type of function often used to model Lorenz curves is f(x) = ax+(1−a)xp. Suppose that and that the Gini index for the distribution of wealth in a country is known to be 4/9, and assume that a = 1/3.
Determine the correct value of p and use that to find how much of the wealth is owned by the wealthiest 5% of the population?
Determine the correct value of p and use that to find how much of the wealth is owned by the wealthiest 5% of the population?
Answers
Answered by
oobleck
we've already done two of these for you. Why don't you take a stab at this one?
Answered by
AJ L
I'm having trouble determining this one. Seems like p comes out negative, but I don't know what I might've done wrong.
Answered by
AJ L
I keep getting p=-7, but that might be wrong. @oobleck tell me what you get if you try the problem.
Answered by
oobleck
∫[0,1] (x - (x+2px)/3) dx = 1 - p/3
1 - p/3 = 4/9
p/3 = 13/9
p = 13/3
How did you get -7?
1 - p/3 = 4/9
p/3 = 13/9
p = 13/3
How did you get -7?
Answered by
AJ L
Ah, I figured out where I went wrong. I didn't distribute one of the negatives for f(x). Just redid it and got p=5. Not sure you did your integral right.
Answered by
AJ L
My integral was set up as 2∫[0,1] [x - x/3 - (2/3)x^p]dx since the Gini Index is G=2∫[0,1] (x - f(x))dx
Answered by
AJ L
Since our function is now f(x)=(1/3)x + (2/3)x^5, this means that the wealthiest 5% of the population own 16.6% of total income
Answered by
AJ L
Here's a graph of the Lorenz Curve I did: .desmos.com/calculator/zyrkdoo05p
Answered by
AJ L
And I meant 16.75% of total income my bad
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.