ordered from poorest to richest, and Y is the cumulative percentage of income, then equality of income distribution is given bị the line Y=X. Suppose the real distribution is given by the Lorenz curve defined by: =x² +* 21 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 Anua
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- 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 ItUsing 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.
- The income distribution for a certain country in 1996 was estimated by the function f(x) = 0.66x2 +0.34x. In 2000 the income distribution was estimated by the function f(x) = 0.3x 0.72x2 -0.02x3 a. Find the coefficient of inequality for each of the years 7. b. Which year had a more equitable income distribution? Why?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. Do the top and bottom quintiles in this distribution have a greater or larger share of total income than the top and bottom quintiles of the U.S. income distribution?Explain how the Gini coefficient is derived from the Lorenz curve by making use of the graph provided;
- 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).2.2 = X Suppose that the Lorenz Curve for country A is given by yA and for country B is yB mine which of the two countries has greater inequality in its income -0.3x2 + 0.7x. Use the Gini index to deter- distribution.A governmental agency determines that the Lorentz curves for the distribution of income for two occupations: dentist and teacher in a certain state are given by the following functions in the picture. For which profession is the distribution of income more fairly distributed.
- 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.Q8.4) Formula for Gini Coefficient from Lorenz CurveA / A + BWhat does the A and B represent?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).