If the Lorenz curves for years a and b are given by La(x) and Lb(x), respectively, then from year a to year b, the change in the Gini coefficient (Gb─ Ga) is given by 2 f10 [la(x) - Lb (x)] dx In below Problems, complete the following.

(a) Use the data in the table and make a new table for x and the corresponding values of [La(x) ─Lb(x)] for the given years, where year b is 2012.

(b) Use the table from part (a) in the Trapezoidal Rule to approximate 2 f10 [la(x) - Lb (x)] dx which gives Gb─ Ga, the difference of the Gini coefficients for the two years.

(c) Is the value of the integral positive or negative? In which year was the income more Equally distributed?

Complete parts (a)-(c) above for Blacks in 1990 and 2012.

Transcribed Image Text:

0.0 0.8 1.0 х 0.2 0.4 0.6 L(x) for Blacks 1.0 1.0 2012 0.0 0.028 0.106 0.247 0.482 0.031 0.111 0.260 0.511 0.0 1990 х 0.0 0.8 1.0 0.2 0.4 0.6 L(x) for Asians 2012 2009 0.0 0.030 0.119 0.269 0.506 1.0 1.0 0.027 0.109 0.253 0.483 0.0