Problem: Suppose society consists of 5 families whose incomes are $8,000, $12,000, $20,000, $40,000, and $80,000. - What is the total income in this society?
- What percentage of total income is earned by the poorest quintile?
- What percentage of total income is earned by the richest quintile?
- What percentages of total income are received by the second, third, and fourth quintiles?
- Construct a Lorenz curve for this five-family economy.
| Answer: - Total income in the society is $8,000 + $12,000, $20,000 + $40,000 + $80,000 = $160,000.
- Since there are only 5 families, the poorest quintile consists only of the lowest-income family, that earning $8,000. As a percentage of total income, this is 5%: 8,000/160,000 = .05, or 5%.
- The richest quintile consists only of the highest-income family, that earning $80,000. This is half, or 50%, of the total income of $160,000.
- Second quintile: $12,000/$160,000 = 7.5%
Third quintile: $20,000/$160,000 = 12.5%
Fourth quintile: $40,000/$160,000 = 25% - The Lorenz curve plots the percentage of total income against the cumulative percentage of families. The values are below:
Households | Percentage of Income | 0% | 0% | 20% | 5% | 40% | 12.5% | 60% | 25% | 80% | 50% | 100% | 100% |
Each value in the Income column is constructed by accumulating the quintile shares. For example, the poorest 60% of families are comprised of the bottom three families whose shares are 5%, 7.5%, and 12.5%, for a cumulative total of 25%. The Lorenz curve is shown below:
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