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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

Income distribution In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from y   = 0.99 x 2 . 1 for one year to y =   0.32 x 2   + 0.68 x for the next year. Find the Gini coefficient of income for both years and compare the distributions of income before and after the tax law was passed. Interpret the result.

To determine

To calculate: The Gini coefficient of income for both years and comparison of the distributions of income before and after the law was passed and the interpretation of the result where in an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from y=0.99x2.1 for one year to y=0.32x2+0.68 for the next year.

Explanation

Given information:

It is provided that the law was passed and the interpretation of the result where in an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from y=0.99x2.1 for one year to y=0.32x2+0.68 for the next year.

Formula used:

Gini Coefficient:

The Gini coefficient is used to calculate the inequality of income distribution and is given by:

201[xL(x)]dx

Where L(x) is the Lorenz curve.

Calculation:

The Lorenz curve before the change is:

y=0.99x2.1

Consider the formula so to calculate the Gini coefficient for this curve:

201[xL(x)]dx

Substitute 0.99x2.1 for L(x) in above integral to get:

201[x(0.99x2.1)]dx

Solve as:

=2[x220.99x3.13.1]01=2[(1)220.99(1)3.13.1]2[(0)220.99(0)3.13.1]=2[120

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Chapter 13 Solutions

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