(a) Find the Gini index of f(x). (b) Find the values of a and b so that the income distributions between the two universes are the same. Show complete solutions. (c) What percent of total income does the poorest 25% of Universe 30.13 receive? What percent of total income does the richest 10% of Universe 30.13 receive?

(a) Find the Gini index of f(x). (b) Find the values of a and b so that the income distributions between the two universes are the same. Show complete solutions. (c) What percent of total income does the poorest 25% of Universe 30.13 receive? What percent of total income does the richest 10% of Universe 30.13 receive?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

1. Due to the creation of the multiverse, two parallel universes, Universe 30.13 and Universe 30.14,
were formed. Suppose that the equations of the Lorenz curves of Universe 30.13 and Universe
30.14, respectively, are given as follows:
g (x) = ax5 + b
1.5
f (x) = 0.1x + 0.9x²
(a) Find the Gini index of f(x).
(b) Find the values of a and b so that the income distributions between the two universes are
the same. Show complete solutions.
(c) What percent of total income does the poorest 25% of Universe 30.13 receive? What
percent of total income does the richest 10% of Universe 30.13 receive?
(d) Suppose that the Gini index of a third parallel universe, Universe 30.15, is lower than that
of Universe 30.13. If we will compare the graphs of the Lorenz curves of the two universes,
which Lorenz curve is closer to the line y = x? Explain.
(e) If the Gini index of Universe 30.15 is given to be 0.4441, is it correct to say that Universe
30.13 is wealthier than Universe 30.15? Justify your answer.

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