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 Gini index for the three income distributions used in parts (a) and (b). Discuss the values obtained.
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 Gini index for the three income distributions used in parts (a) and (b). Discuss the values obtained.
Step by step
Solved in 2 steps with 3 images
