Lp = x^p for p is greater than or equal to 1- Does a low Gini index correspond to an equitable or inequitable distribution of wealth? Explain.- for a general L(x), explain why G=2A Scientists studying the economics of a country, community, or group of people are often interestedin the distribution of wealth, where wealth is understood to mean the income or the personal assetsof individual households. A powerful tool for illustrating how wealth is distributed across a societyis the Lorenz curve (invented by the American economist Max Otto Lorenz in 1905).A typical Lorenz curve is given by y = L(x), where 0 < x < 1 and 0 < y < 1. The variableI represents the fraction of all households in the society and y = L(x) represents the fraction ofthe total wealth that is owned by the fraction x of the society. For example, for the Lorenz curveshown in Figure 1, we see that L(0.5) = 0.2, which means that 0.5 (50%) of the society owns 0.2(20%) of the wealth.bottombotomy A1-Line of perfectequality0.8 of householdscontrol 0.6 ofthe wealth.Lorenz curve0.5 of householdscontrol 0.2 ofthe wealth.0.2B0.50.8 a1 1Fraction of HouseholdsFigure IFraction of Total Wealth 7. The information in the Lorenz curve is often summarized in a single measure called the Giniindex (proposed in a 1912 paper by the Italian statistician Corrado Gini). The Gini index isdefined as follows. Let A be the area of the region between y = x and y = L(x) and let B bethe area of the region between y = L(x) and the x-axis (see Figure 1). Then the Gini indexAis G =A+BCompute the Gini index for L, when p = 1.1 and when p= 4.(A+B)A =(x - L(w) dx6= 2 L-S Llo)dxA =G = 2AS LIx) dx%3D|-2A =A- i-S Lx) dxA =(1-0)= (0.04762.1o.6%3D

Answered: Does a low Gini index correspond to an…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Related questions

Question

Lp = x^p for p is greater than or equal to 1

- Does a low Gini index correspond to an equitable or inequitable distribution of wealth? Explain.

- for a general L(x), explain why G=2A

Scientists studying the economics of a country, community, or group of people are often interested
in the distribution of wealth, where wealth is understood to mean the income or the personal assets
of individual households. A powerful tool for illustrating how wealth is distributed across a society
is the Lorenz curve (invented by the American economist Max Otto Lorenz in 1905).
A typical Lorenz curve is given by y = L(x), where 0 < x < 1 and 0 < y < 1. The variable
I represents the fraction of all households in the society and y = L(x) represents the fraction of
the total wealth that is owned by the fraction x of the society. For example, for the Lorenz curve
shown in Figure 1, we see that L(0.5) = 0.2, which means that 0.5 (50%) of the society owns 0.2
(20%) of the wealth.
bottom
botom
y A
1-
Line of perfect
equality
0.8 of households
control 0.6 of
the wealth.
Lorenz curve
0.5 of households
control 0.2 of
the wealth.
0.2
B
0.5
0.8 a1 1
Fraction of Households
Figure I
Fraction of Total Wealth

7. The information in the Lorenz curve is often summarized in a single measure called the Gini
index (proposed in a 1912 paper by the Italian statistician Corrado Gini). The Gini index is
defined as follows. Let A be the area of the region between y = x and y = L(x) and let B be
the area of the region between y = L(x) and the x-axis (see Figure 1). Then the Gini index
A
is G =
A+B
Compute the Gini index for L, when p = 1.1 and when p= 4.
(A+B)
A =
(x - L(w) dx
6= 2 L-S Llo)dx
A =
G = 2A
S LIx) dx
%3D
|-2
A =
A- i-S Lx) dx
A =
(1-0)= (0.0476
2.1
o.6
%3D

Expert Solution

Step 1

Gini coefficient is a way to measure income inequality. The Gini-coefficient is calculated by the ratio of the area between the Lorenz curve and the perfect equality line, and the area below the perfect equality line. Its value measures the extent of income inequality and its value lies always between 0 to 1.

The lower value of the Gini coefficient indicates the equitable distribution of wealth in comparison to a higher value which indicates the inequitable distribution of wealth. If the value of the coefficient is near 1, there is greater income inequality and if the value if close to 0, there is lower income inequality. G = 0.0476 indicated lower inequality.

Step by step

Solved in 2 steps

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.

Similar questions