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draw the Lorenz curve and compute the Gini index of a group whose incomes are 25, 32, 60, 40, 38, 50

Microeconomics

13th Edition

ISBN:9781337617406

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter15: The Distribution Of Income And Poverty

Section: Chapter Questions

Problem 2WNG

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If a country had perfect income equality what would the Lorenz curve look like?
What is measured on the two axes of a Lorenz curve?
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
What are the Gini Coefficient and the Lorenz Curve? Be sure to explain how these terms are related and what they are used to measure.
Explain how the Gini coefficient is derived from the Lorenz curve by making use of the graph provided;
Consider the Lorenz curves for income for Deneb and Elnath as shown in this figure: Lorenz curves for Deneb and Elnath cumullative income share (%) 8 8 2 2 2 2 2 2 2 2 100 90 80 70 60 40 30 Lorenz curve for Elnath 0 0 10 20 30 40 50 60 70 80 90 100 income percentiles Lorenz curve for Deneb [If the image above doesn't appear click here to open it in a new tab.] Which of the following statements is true? [Hint: You do not need to calculate any areas to answer this question correctly!] The relative income inequalities of Deneb and Elnath cannot be determined from the information given. Income inequality is more extreme in Deneb than it is in Elnath. Deneb and Elnath have the same degree of income inequality. Income inequality is more extreme in Elnath than it is in Deneb.
What would happen to the Lorenz curve if it included wealth distribution?
1. Consider an illustrative economy with the following five incomes: {10, 15, 25, 45, 50}. Calculate the Gini coefficient. Construct a table with the values for the Lorenz curve (use 20%, 40%, 60%, 80%, 100% thresholds).
A group of 10 people have the following annual incomes: $24, 000, $18, 000, $50, 000, $100, 000, $12, 000, $36, 000, $80, 000, $10, 000, $24, 000, $16, 000. Calculate the share of total income that each quintile receives from this income distribution. What percent of the total income is represented by the highest quintile? Round your answer to the nearest tenth. Provide your answer below:
ITEM No.4 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 50 4 60 90 100 3 120
Figure 18-7 100 Income (cumulative percent) 80 72 60 48 40 882 20 12 0 20 40 60 80 Households (cumulative percent) 100 Figure 18-7 shows the Lorenz curve for a hypothetical country. Refer to Figure 18-7. The second highest 20 percent of households earn 42 percent of the society's total income. earn 28 percent of the society's total income. e earn 24 percent of the society's total income. earn 72 percent of the society's total income.
The term obtained by dividing the area of inequality shown by a Lorenz curve by the area of the right-triangle formed by the axes and the diagonal (the line of equality).