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 bythe line Y=X. Suppose the real distribution is given by the Lorenz curve defined by:20y =x? +xThe 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 GAreas produced by the LorenzcurveBCurve`LorenzPopulationEntry

Lorenz curve is used to depict the distribution of income amongst the recipients in the form of a…

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

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

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter12: Income Distribution, Poverty, And Discrimination

Section: Chapter Questions

Problem 17SQ

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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.
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.
a. Is the presence of an underground economy likely to result in a Gini coefficient that overstates or understates poverty? b. Consider a simple economy where 90 percent of citizens report an annual income of $10,000 while the remaining 10 percent report an annual income of $110,000. What is the Gini coefficient associated with this economy? c. Suppose the poorest 90 percent of citizens actually have an income of $15,000 because each receives $5,000 of unreported income from the underground economy. What is the Gini coefficient now?
By finding the ___________, Gini Coefficient is determined/calculated. a. difference between the richest and poorest of the population b. area between a Lorenz curve and the line of absolute equality c. percentage of the population living on more than $1 a day d. proportion of the population with more than a primary education e. percentage of the population living on less than $1 a day
When the Lorenz curve lies above thediagonal,a. the poorest 20 percent of the populationreceive more than 20 percent of income.b. the richest 20 percent of the populationreceive more than 20 percent ofincome.c. everyone receives the same income.d. the curve is wrong because it is impossible forthe graph to look like this.
In the figure above, which of the following is true? a. Distribution OYB is preferred to OZB, b. Line OYB represents a less equal distribution of income than line OZB. c. Line OXB represents the most equitable distribution of income. d. Line OXB is the line of perfect income equality. e. All of the above are true.
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.
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).
Consider a Maldives island with ten inhabitants. Answer the questions below. a) Plot the Lorenz curve for the income distribution: (2,2,4,6,8,20,30,40,60,100) (2,2,4,6,8,20,30,40,60,100) Consider an income redistribution that takes 20% of income from each of the three richest individuals and distribute equally to individuals that have an income below the poverty line (9). Plot the Lorenz curve again to demonstrate that inequality has decreased. What happened to the coefficient of variation between the two periods? What can you conclude about the change in inequality between periods from this? b) Show on the same diagram the Lorenz curve for the income distribution: (8,18,20,22,26,28,30,32,40,48)(8,18,20,22,26,28,30,32,40,48) Compare and comment this new Lorenz curve with the Lorenz curves in part (a). Then, show that the three social welfare functions, W=∑MhW=∑Mh, W={MinWh}W={MinWh}, and W={MaxWh}W={MaxWh} rank the income distributions in parts (a) and (b) differently. c) Calculate the…
Suppose a Lorenz curve for a particular country is f(x)=x^2for 0≤x≤1. What is the Gini index of income concentration for this country? Give your answer to the nearest integer
Find the Gini index for the given Lorenz curve. L(x) = 0.7x + 0.3x2
Questions Explain three methods of measuring the income inequality of a nation? Page 3 other 2 pages in the pic As in the case of income distribution, calculation of wealth distribution is done by different entities using different measurements, resulting in a disparity in outcomes. In fact, commonly, wealthis narrowly defined as financial wealth—namely, cash on handand the money value of tangible and nonliquid assets. Even justthe market valuation of financial portfolios is commonly used todefine financial wealth. However, some may extend the definitionto include the value of income streams and insurance rights that,for the most part, cannot be transacted or encumbered. Theseinclude Medicare, Medicaid, and Social Security. When suchtransfers and public assistance are included, the poor and manyelderly could benefit, reducing the wealth disparity (Galbraith2016). To obtain net wealth, the value of the debts are subtractedsubtracted from the value of the assets. Galbraith stated…