3. Constructing a Lorenz curve from personal income data The Smith quintuplets and the Johnson quintuplets grew up across the street from each other. Now in their 40s, the siblings eam the incomes shown in the following table: Smith Al Smith Bob Smith Income (Dollars) 20,000 60.000 Johnson Karl Johnson Income (Dollars) 120,000 Chris Smith Larry Johnson Moe Johnson Nate Johnson Oliver Johnson 140,000 100,000 80,000 Dave Smith Ed Smith 40,000 60,000 80,000 100,000 Total for Smiths 400,000 Total for Johnsons 400,000 Let's think of the Smiths and the Johnsons as two economies and analyze income Inequality within each of the economies Chris Smith's share of the total Smith income is while Oliver Johnson's share of the total Johnson income is Rank the Smith brothers by income from lowest to highest, and calculate each brother's share of the total Smith economy's income. Because there are five brothers, each brother represents a quintile of the income distribution Draw a bar graph below showing each Smith brother's share of aggregate family income, from lowest Quintile to highest qumbile. Use the orange rectangle (square symbols) to show the lowest quintile; use the blue rectangle (orce symbols) to show the second ouintile use the grey rectangle (star symools) to show the third quinbille use the purple rectangle (diamond symbols) to show the fourth quintile and use the green rectangle (triangle symbols) to show the highest quintile Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically. 49 35 Lowest Quible 30 Second Quintile PERCENTAGE OF INCOME Third Quinte 5 Fourth Ouinte LOWEST SECOND THIRD QUINTILE FOURTH HIGHEST Highest Quinto Rank the Johnson brothers by income from lowest to highest and calculate each brother's share of the total Johnson economy's income. Because there are five brothers, each brother represents a Quintile of the income distribution Draw a bar graph below showing each Johnson brother's share of aggregate family income, from lowest quntle to highest quintiin. Use the orange rectangle square symbols) to show the lowest ouintile, use the blue rectangle (circle symbols) to show the second quinte; use the grey rectangle (star symbols) to show the third quite use the purple rectangle (diamond symbols) to show the fourth quintile; and use the green rectangle (tangle symbols) to show the highest quintile. 35 Lowest Quinte 35 Lowest Quintile Second Quinti PERCENTAGE OF INCOME 3 Third Quintile 10 Fourth Ouinte LOWEST SECOND THIRD QUINTILE FOURTH HIGHEST Highest Quinte On the following graph, plot the Lorenz curve for the Smith economy using the green points (triangle symbol). Then plot the Lorenz curve for the Johnson economy using the purple points (diamond symbol). You should think of each brother as representing 20% of the total households in his respective economy. (Hint: You may want to refer back to your previous answers.) 100 10 Smith Economy TIVE PERCENTAGE OF INCOME Johnson Economy On the following graph, plot the Lorenz curve for the Smith economy using the green points (triangle symbol). Then plot the Lorenz curve for the Johnson economy using the purple points (diamond symbol). You should think of each brother as representing 20% of the total households in his respective economy. (Hint: You may want to refer back to your previous answers.) 2 100 A Smith Economy 8 Johnson Economy CUMULATIVE PERCENTAGE OF INCOME 3 20 CUMULATIVE PERCENTAGE OF HOUSEHOLDS 100 The answers.) economy has more income inequality than the economy. (Hint: You may want to refer back to your previous Suppose that the Smiths decide that there is too much income inequality in their economy. They vote to make Chris pay Ala lump sum in order to be more like the Johnsons. For the two economies Locent carves to become identical, Chris must olve AIS