12. For the last 30 years the Gini index of the United States has been about G = 0.4 (slightlyincreasing during that period). Find the value of p in the Lorenz functions L,(r) = xP thatgives this Gini index.%3D 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

We have Lorenz function, Lpx=xp Gini index= G = 0.4 We know, the Gini index is equal to double area…

12. For the last 30 years the Gini index of the United States has been about G = 0.4 (slightly increasing during that period). Find the value of p in the Lorenz functions L,(x) = xP that gives this Gini index. %3D

12. For the last 30 years the Gini index of the United States has been about G = 0.4 (slightly increasing during that period). Find the value of p in the Lorenz functions L,(x) = xP that gives this Gini index. %3D

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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
The graph shows a Lorenz curve for an economy with a total income of 30000; Share of Income a 40% 60% 80% 100% A B C D E 20% suppose that A=100%, b=48%, c=23%, D=9% and E=2% What is the income share of each quintile in percentage? (enter the numbers with % sign, such as 5%) Quintile 1 (poorest quintile) = type your answer... type your answer... type your answer... Percentile Quintile 2 = Quintile 3 = Quintile 4=
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Draw the Lorenz curve and compute the Gini index of a group whose annual incomes (in thousands of dollars) are given by the following frequency table. Value Frequency 30 2 50 4 60 5 90 4 100 3 120 2
a) With the following data draw a Lorenz Curve, putting labels on the graph and writing out data point values. Explain what the Lorenz Curve illustrates, and what the results mean. b) Now explain how one gets the Gini Coefficient from the Lorenz Curve, and what information the coefficient provides.
Using the above Lorenz Curve, answer the following questions. . . Approximately what percentage of the income does the richest 20% of Country A earn? Approximately what percentage of the income does the poorest 20% of Country B earn? If the government of Country B increased the progressivity of income taxes, would its Lorenz Curve move closer to the 45-degree reference line, closer to Country A's Lorenz Curve, or not move at all?
Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
Q2] Given is the data for Country A and B: Population Fraction Country A's Income Country B's Income bottom 25% 5 million 10 million 2nd 25% 10 million 15 million 3rd 25% 30 million 20 million top 25% 55 million 55 million a) Compute the cumulative income share and neatly plot (using Excel) the Lorenz curve for these two countries with labels. Feel free to use excel template that I have uploaded and copy paste the plot. b) Compute the Gini coefficient assuming the region beneath the two respective Lorenz curve is For country A = 0.2875 For country B = 0.3250