In order to study the effects of World War II on a certain country's economy, an economist used data from that country's census bureau to produce the following Lorenz curves for the distribution of income in 1935 and 1947. 2.2 f(x)=x Lorenz curve for 1935 1.5 g(x)=x Lorenz curve for 1947 Find the Gini index of income concentration for each Lorenz curve and interpret the results. What is the Gini index for 1935? (Round to three decimal places as needed.)

In order to study the effects of World War II on a certain country's economy, an economist used data from that country's census bureau to produce the following Lorenz curves for the distribution of income in 1935 and 1947. 2.2 f(x)=x Lorenz curve for 1935 1.5 g(x)=x Lorenz curve for 1947 Find the Gini index of income concentration for each Lorenz curve and interpret the results. What is the Gini index for 1935? (Round to three decimal places as needed.)

Economics For Today

10th Edition

ISBN:9781337613040

Author:Tucker

Publisher:Tucker

Chapter12: Income Distribution, Poverty, And Discrimination

Section: Chapter Questions

Problem 1SQP

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Using data from a nation's census, an economist produced the following Lorenz curves for the distribution of that nation's income in 1962 and 1972. f(x) = 3x +2 x2 5 5 Lorenz curve for 1962 g(x) = 2 x+ 3 x2 5 5 Lorenz curve for 1972 Find the Gini index of income concentration for each Lorenz curve and interpret the results. Identify the integrand for the computation of the Gini index for 1962 and 1972. The Gini index for 1962 is given by2 ∫ 0 1 ....... dxand the Gini index for 1972 is given by 2 ∫ 01 .......... dx.
Explain how the Gini coefficient is derived from the Lorenz curve by making use of the graph provided;
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.
Which of the following statements regarding the Gini coefficient are correct? A. It is the measure of the average difference in income between every pair of individuals in the population. B. It can be calculated exactly as g=A/(A+B), where A is the area between the Lorenz curve and the 45-degree line, and A + B is the area under the 45-degree line. C. The fraction A/(A+B) is an accurate approximation when the population is small. D. If 50% of a large population owned 2% of the wealth each, then the Gini coefficient equals 0.6.
2.1 In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from y = 0.97x for one year to y = 0.33x + 0.67x for the next year. Find the Gini coefficient of income for both years. (Round your answers to three decimal places.) before after Compare the distributions of income before and after the tax law was passed. Interpret the result. O The change increases the difference in incomes. The change makes no difference in incomes. O There is not enough information to compare the incomes. The change decreases the difference in incomes. O The change makes the incomes equal. Need Help? Read It
Describe what has happened to the value of the Gini Coefficient since 1980? What is the implication for income inequality over this period?
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…
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.
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The government of a small country is planning sweeping changes in the tax structure in order to provide a more equitable distribution of income. The Lorenz curves for the current income distribution and for the projected income distribution after enactment of the tax changes are as follows. f(x) = x2.1 Current Lorenz curve g(x) = 0.6x+0.4x2 Projected Lorenz curve after changes in tax laws Find the Gini index of income concentration for each Lorenz curve. Will the proposed changes provide a more equitable income distribution? Explain. Identify the integrand for the computation of the current and projected Gini indices. The current Gini index is given by 2 ∫ 0 1 ....... dx and the projected Gini index is given by 2 ∫ 0 1 ...... dx.
Canada had the following distribution of Income after taxes in 2006 Based on the information in the tables, which one is the correct Gini coefficient of income inequality? Deciles cumulative share of income Lorenz curve for after tax income in Canada 0% (2006) 1 0% 1 2 2%| 3 6% 0.8 4 11% 0.6 18% 0.4 26% 0.2 37% 50% 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 9 67% share of population 10 100% cumulative share of income equidistribution line O a. 0.47 O b. 0.43 O c. 0.42 O d. 0,44 O e. 0.23 O share of income
Which of these is true of the Lorenz curve? The further away it is from the 45 degree line the more unequal is distribution. The closer it is to the 45 degree line the more unequal is distribution.