Explanation Given Information: The income distribution for black household and Hispanic households are y = 2.292 x 4 − 3.127 x 3 + 2.006 x 2 − 0.1710 x + 0.0005556 and y = 1.830 x 4 − 2.564 x 3 + 1.806 x 2 − 0.1137 x + 0.0003512 respectively. Formula used: The power rule of integration is; The integration of function f ( x ) = x n is given by; ∫ x n d x = x n + 1 n + 1 + c n ≠ − 1 Here c is any arbitrary constant. The sum rule is; ∫ f ( x ) ± g ( x ) d x = ∫ f ( x ) d x ± ∫ g ( x ) d x Calculation: Consider the given income distribution for 2012 in United States for Black households and Hispanic households as below For Black households, y = 2.292 x 4 − 3.127 x 3 + 2.006 x 2 − 0.1710 x + 0.0005556 For Hispanic households, y = 1.830 x 4 − 2.564 x 3 + 1.806 x 2 − 0.1137 x + 0.0003512 The formula for Gini coefficient of income is; Gini coefficient = ∫ 0 1 x − y ( x ) 1 2 Thus, to find the Gini coefficient of income for Black households first solve the integration as; ∫ ( x − y ( x ) ) d x = ∫ x − ( 2.292 x 4 − 3.127 x 3 + 2.006 x 2 − 0.1710 x + 0.0005556 ) = x 2 2 − 2.292 x 5 5 + 3.127 x 4 4 − 2.006 x 3 3 + 0.1710 x 2 2 − 0.0005556 x Evaluate the limits as; ∫ 0 1 ( x − y ( x ) ) d x = ( 1 2 − 2

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 13.3, Problem 45E

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To calculate: The Gini coefficient of income for black household and Hispanic household if income distribution for black household and Hispanic households are y=2.292x4−3.127x3+2.006x2−0.1710x+0.0005556 and y=1.830x4−2.564x3+1.806x2−0.1137x+0.0003512 respectively.

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Chapter 13.3, Problem 44E

Chapter 13.3, Problem 46E

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Chapter 13 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 13.1 - CHECKPOINT 1. For the interval [0, 2]. determine...Ch. 13.1 - Prob. 2CP Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E

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The Gini coefficient of income for black household and Hispanic household if income distribution for black household and Hispanic households are y = 2.292 x 4 − 3.127 x 3 + 2.006 x 2 − 0.1710 x + 0.0005556 and y = 1.830 x 4 − 2.564 x 3 + 1.806 x 2 − 0.1137 x + 0.0003512 respectively.

Solution Summary: The author calculates the Gini coefficient of income for black households and Hispanic households based on the given income distribution for 2012 in United States.

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To calculate: The Gini coefficient of income for black household and Hispanic household if income distribution for black household and Hispanic households are y=2.292x4−3.127x3+2.006x2−0.1710x+0.0005556 and y=1.830x4−2.564x3+1.806x2−0.1137x+0.0003512 respectively.

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Chapter 13 Solutions