   Chapter 13.6, Problem 35E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Income distribution Suppose the Lorenz curve for the distribution of income of a certain country is given by y = x e x − 1 Find the Gini coefficient of income.

To determine

To calculate: The Ginni coefficient of income if Lorenz distribution of income for a certain country is given by y=xex1.

Explanation

Given Information:

Lorenz distribution of income for a certain country is given by,

y=xex1

Formula used:

The Ginni coefficient of income for Lorenz distribution y is given by,

G=01(xy)dx1/2

The formula for integration by parts is given by:

udv=uvvdu

Calculation:

As it is provided that Lorenz distribution of income for a certain country is given by,

y=xex1

Now, the Ginni coefficient of income for Lorenz distribution y is given by,

G=01(xy)dx1/2

Thus, to obtain the Ginni coefficient for the provided Lorenz distribution, substitute xex1 for y in above equation to get,

G=01

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