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Mathematical Applications for the ...

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

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BuyFindarrow_forward

Mathematical Applications for the ...

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

Gini coefficient If the Lorenz curve for the income distribution for a given year is L ( x ) =   x p use integration to find a simple formula for the corresponding Gini coefficient.

To determine

To calculate: The formula for Gini coefficient by using the integration where, the Lorenz curve for the income distribution for a year is L(x)=xp.

Explanation

Given information:

The Lorenz curve for the income distribution for a given year is L(x)=xp.

Formula used:

Gini Coefficient:

The Gini coefficient is used to calculate the inequality of income distribution as,

201[xL(x)]dx

Where, L(x) is the Lorenz curve.

Calculation:

Consider the Lorenz curve,

L(x)=xp

Apply the formula of Gini coefficient as,

201[xL(x)]dx

Substitute xp for L(x) in above integral to get:

201[xxp]dx

Now, integrate the above expression with respect to x,

201[xxp]dx=2[x22xp+1(p+

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Chapter 13 Solutions

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