Lorenz curves also can be used to provide a relative measure of the distribution of the total assets of a country. Using data in a report by the economic committee of a certain country, an economist produced the following Lorenz curves for the distribution of total assets in the country in 1963 and 1983, shown below. f(x) = x10 Lorenz curve for 1963 gx) = x3 Lorenz curve for 1983 Find the Gini index of income concentration for each Lorenz curve and interpret the results. What is the Gini index for 1963? (Round to three decimal places as needed.) What is the Gini index for 1983? O (Round to three decimal places needed.) Interpret your results. O A. Total assets were more equally distributed in 1963 O B. Total assets were more equally distributed in 1983 Oc. Total assets were distributed the same in 1963 as in 1983.

Lorenz curves also can be used to provide a relative measure of the distribution of the total assets of a country. Using data in a report by the economic committee of a certain country, an economist produced the following Lorenz curves for the distribution of total assets in the country in 1963 and 1983, shown below. f(x) = x10 Lorenz curve for 1963 gx) = x3 Lorenz curve for 1983 Find the Gini index of income concentration for each Lorenz curve and interpret the results. What is the Gini index for 1963? (Round to three decimal places as needed.) What is the Gini index for 1983? O (Round to three decimal places needed.) Interpret your results. O A. Total assets were more equally distributed in 1963 O B. Total assets were more equally distributed in 1983 Oc. Total assets were distributed the same in 1963 as in 1983.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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The Board of Directors convened a special meeting to discuss the implications of the quote above. You are required to produce a brief on the statement above, specifically referring to the implications it holds for the brand. You were able to locate the following graph denoting the Lorenz curve from which the Gini coefficient was derived The Board expects the following points to be addressed in your brief: Explain how the Gini coefficient is derived from the Lorenz curve by making use of the graph provided; Answer in detail
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.
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.
100% Cumulative percentage of income 90% -Jарan 80% --- Portugal 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Cumulative percentage of households Figure 5 Lorenz curves for Japan and Portugal Examine the Lorenz Curves for Japan and Portugal shown in Figure 5. Which of the following statements are correct? Select one or more answers. Select one or more: O The top quintile (top 20%) of households in Portugal have a higher share of total income than the top quintile (top 20%) of households in Japan. The bottom decile (bottom 10%) of households in Japan have a lower share of total income than the bottom decile (bottom 10%) of households in Portugal. Portugal will have a lower Gini coefficient than Japan. Japan has a lower level of income inequality than Portugal.
The Board of Directors convened a special meeting to discuss the implications of the quote above. You are required to produce a brief on the statement above, specifically referring to the implications it holds for the brand. You were able to locate the following graph denoting the Lorenz curve from which the Gini coefficient was derived The Board expects the following points to be addressed in your brief: Explain the implications of a Gini Coefficient of 0.643 relating to the South African economy, retail sector and brand of the organisation. Derive practical examples from the Lorenz curve to substantiate your explanation
Below is the Lorenz curve of the country Laurania. Lorenz Curve of Laurania 100 100 Cumulative percentage of total population (%) Assuming that variables X, Y and Z in the graph above are equal to 30, 82 and 30, respectively, what is the Gini coefficient for this country? Cumulative percentage of total Income (%)
A Lorenz curve is used to study income distributions (see graph). If x is the cumulative percentage of income recipients, ordered from poorest to richest, and Y is the cumulative percentage of income, then equality of income distribution is given by the line Y=X. Suppose the real distribution is given by the Lorenz curve defined by: 20 y =x? +x The Gini coefficient (G) measures the degree of deviation from equality Y=X for a specific Lorenz curve y is given by: G= A/(A+B). Determine G Areas produced by the Lorenz curve B Curve `Lorenz Population Entry
Explain how the Gini coefficient is derived from the Lorenz curve by making use of the graph provided;
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…
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
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
Q2] Compute the Gini coefficient assuming the region beneath the two respective Lorenz curve is 0.4 for country A and 0.2 for country B.