Chapters 5 & 6 How does our understanding of integration and the Fundamental Theorem of Calculus allow us to compare income inequality? The Gini index is a statistical measure of income distribution. It ranges from 0 (or 0%) for perfect equality to 1 (or 100%) for perfect inequality. - A country where every resident has the same income would have a Gini index of 0. - A country in which one resident earned all the income, while everyone else earned nothing, would have a Gini index of 1. Source: htt s: data.worldbank.or indicator SI.POV.GINI?Vie A F'W=ma The Gini index is a statistical The Gini index is defined to be two measure of income distribution. times the area between the line of It ranges from 0 (or 0%) for perfect equality (y=x) and the Lorenz perfect equality to 1 (or 100%) curve, showing the percentage of for perfect inequality. income held by each percentile of the A country where every country's population: resident has the same income would have a Gini 1. Perfect Equality 2. Unequal index of 0. 100% . . . . . . . A country in which one resident earned all the G1=0 6Participation Cumulative income, while everyone else .G2>0 earned nothing, would have a Gini index of 1. 096 0% Cumulative 100% 0% Cumulative 100% %Population %Population 3. More Unequal 4. Total Inequality Source: https://data. worldbank.org/indicator/SI. POV.GINI?vi ew= map . . . .. G3>G2 G4=1 0% Cumulative 100% 0% Cumulative 100% % Population %PopulationThe Gini index is a statistical Talks are underway for Ukraine to join measure of income distribution. the European Union an alliance which It ranges from 0 (or 0%) for currently includes the countries of perfect equality to 1 (or 100%) Austria, Belgium, Bulgaria, Croatia, for perfect inequality. Cyprus, Czechia, Denmark, Estonia, A country where every Finland, France, Germany, Greece, resident has the same Hungary, Ireland, Italy, Latvia, income would have a Gini Lithuania, Luxembourg, Malta, index of 0. Netherlands, Poland, Portugal, A country in which one Romania, Slovakia, Slovenia, Spain resident earned all the and Sweden. income, while everyone else earned nothing, would have a We are going to compare the income Gini index of 1. distribution of Ukraine with that of Poland, a country in the EU which is geographically close to Ukraine. Source: https://ec.europa.eu/commission/presscorner/ detail/en/IP 21 5203Mth in Context 5: The Gini index is defined to be two times the area between the line of perfect equality (y=x) and the Lorenz curve, showing the percentage of income held by each percentile of the country's population. 1. Shade the area we need to find first so that we can calculate the Gini index. Then, write an expression for THIS AREA that includes a definite integral. 20 points Shade: Lorenz Curve- Ukraine 2020 Expression: +Line of Equality Po|y. {Ukraine} y = 1.5625)(5 - 2.5781x4 + 1.34-38x3 + 0.2406)? + 0.4313x 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Cumulative Percentage of the Population The Gini index is defined to be two times the area between the line of perfect equality (y=x) and the Lorenz curve, showing the percentage of income held by each percentile of the country's population. 3. Shade the area we need to find first so that we can calculate the Gini index. Then, write an expression for THIS AREA that includes a definite integral. 20 points Shade: Lorenz Curve Poland 2018 Expression; +Line of Equality Poly. (Poland) 0.9 - 0.8 . 0.7 - 0.5 - 0.5 - 0.4 - 0.3 - Cumulative Wealth 0.2 - 0.1 - y = 2.0833x5 - 3.75)(4 + 2.2708)(3 + 0.1125x2 + 0.2833x 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Cumulative Percentage of the Population The Gini index is defined to be two times the area between the line of perfect equality (y=x) and the Lorenz curve, showing the percentage of income held by each percentile of the country's population. 4. Using the Fundamental Theorem of Calculus as well as the definition to the left, find the Gini index for Poland in the year 2018, making sure to show all your work. 20 points