Explanation Given information: The distribution of income becomes more nearly equal when the Lorentz curve changes from y = 0.998 x 2.6 for 1 year to y = 0.57 x 2 + 0.43 x for the next year. Formula used: The Gini coefficient of income is provided by 2 ∫ 0 1 [ x − L ( x ) ] d x . Calculation: Consider the functions, y = 0.998 x 2.6 and y = 0.57 x 2 + 0.43 x The Lorentz curve changes from y = 0.998 x 2.6 for 1 year to y = 0.57 x 2 + 0.43 x for the next year. The Gini coefficient for one year is, 2 ∫ 0 1 [ x − L ( x ) ] d x Put L ( x ) = 0.998 x 2.6 , So, the Gini coefficient becomes, 2 ∫ 0 1 [ x − 0.998 x 2.6 ] d x = 2 [ x 2 2 − ( 0.998 ) x 3.6 3.6 ] 0 1 = 2 [ 1 2 2 − ( 0

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Chapter 13, Problem 13T

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To calculate: The Gini coefficient of income for each year. Also determine whether the distribution of income is more or less equitable after the law is passed. Give the interpretation from the result. The Lorentz curve changes from y=0.998x2.6 for 1 year to y=0.57x2+0.43x for the next year.

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Chapter 13, Problem 12T

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The Gini coefficient of income for each year. Also determine whether the distribution of income is more or less equitable after the law is passed. Give the interpretation from the result. The Lorentz curve changes from y = 0.998 x 2.6 for 1 year to y = 0.57 x 2 + 0.43 x for the next year.

Solution Summary: The author calculates the Gini coefficient of income for each year and determines whether the distribution is more or less equitable after the law is passed.

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To calculate: The Gini coefficient of income for each year. Also determine whether the distribution of income is more or less equitable after the law is passed. Give the interpretation from the result. The Lorentz curve changes from y=0.998x2.6 for 1 year to y=0.57x2+0.43x for the next year.

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Chapter 13 Solutions