The Lorenz Curve and the Gini
Coefficient are Misleading
visitors
Paradoxically, economies with the most income inequality, such as the Saudi Arabian feudal model, have the most apparent income equality, as indicated by the flatness of the Lorenz Curve and measured by the Gini coefficient. Consider a population described in the table below.
The Lorenz curves with the lowest Gini Coefficient describe populations with the biggest middle class. The feudal model yields a Gini coefficient of .81 and the industrial model a coefficient of .74.
Here is the data:
| Heirarchy Ratio | 10 | 50 | |||||||
| Cohort | Class | Annual Income | Population | Cohort Income | Cumulative Population | Cumulative Income | Area under curve | Area if Triangle | Gini Coefficient |
| 0 | 0 | ||||||||
| 1 | Serfs | $ 100 | 10,000,000 | $ 1,000,000,000 | $ 10,000,000 | $ 1,000,000,000 | 5,000,000,000,000,000 | ||
| 2 | Vassals | $ 1,000 | 200,000 | $ 200,000,000 | $ 10,200,000 | $ 1,200,000,000 | $ 220,000,000,000,000 | ||
| 3 | Shieks | $ 10,000 | 4,000 | $ 40,000,000 | $ 10,204,000 | $ 1,240,000,000 | $ 4,880,000,000,000 | ||
| 4 | Elders | $ 100,000 | 80 | $ 8,000,000 | $ 10,204,080 | $ 1,248,000,000 | $ 99,520,000,000 | ||
| 5 | Princes | $ 1,000,000 | 2 | $ 1,600,000 | $ 10,204,082 | $ 1,249,600,000 | $ 1,998,080,000 | ||
| King | $ 10,000,000 | 1 | $ 320,000 | $ 10,204,082 | $ 1,249,920,000 | $ 39,992,320 | |||
| $ 5,224,981,558,072,320 | 6,377,142,856,734,720 | 0.81 |
And here is the Lorenz curve:
Now consider a more American Model:
Here is the data:
| Heirarchy Ratio | 3 | 8 | |||||||
| Cohort | Class | Annual Income | Population | Cohort Income | Cumulative Population | Cumulative Income | Area under curve | Area of Triangle | Gini Coefficient |
| 0 | 0 | ||||||||
| 1 | Unskilled | $ 100 | 5,000,000 | $ 500,000,000 | $ 5,000,000 | $ 500,000,000 | 1,250,000,000,000,000 | ||
| 2 | Skilled | $ 300 | 625,000 | $ 187,500,000 | $ 5,625,000 | $ 687,500,000 | $ 371,093,750,000,000 | ||
| 3 | Managers | $ 900 | 78,125 | $ 70,312,500 | $ 5,703,125 | $ 757,812,500 | $ 56,457,519,531,250 | ||
| 4 | Group Managers | $ 2,700 | 9,766 | $ 26,367,188 | $ 5,712,891 | $ 784,179,688 | $ 7,529,258,728,027 | ||
| 5 | Vice Presidents | $ 8,100 | 1,221 | $ 9,887,695 | $ 5,714,111 | $ 794,067,383 | $ 963,285,565,376 | ||
| Senior Vice Presidents | $ 24,300 | 153 | $ 3,707,886 | $ 5,714,264 | $ 797,775,269 | $ 121,447,956,190 | |||
| Executives | $ 72,900 | 19 | $ 1,390,457 | $ 5,714,283 | $ 799,165,726 | $ 15,229,616,110 | |||
| CEO | $ 218,700 | 2 | $ 521,421 | $ 5,714,285 | $ 799,687,147 | $ 1,905,981,151 | |||
| $ 1,686,165,261,780,840 | 2,279,349,215,095,860 | 0.74 |
Here is the Lorenz Curve:
Clearly the Saudi Arabian type feudal distribution is flatter than the American Middle class distribution.
Clifford W. Lazar email a Comment
Los Angeles, CA USA
10/11/04
Income Distribution Economics Lorenz Curve Gini Coefficient
Income Distribution Economics Lorenz Curve Gini Coefficient