Problem:

Suppose society consists of 5 households whose incomes are $8,000, $12,000, $20,000, $40,000, and $80,000.

1. What is the total income in this society?
2. What percentage of total income is earned by the poorest quintile?
3. What percentage of total income is earned by the richest quintile?
4. What percentages of total income are received by the second, third, and fourth quintiles?
5. Construct a Lorenz curve for this five-household economy.

Answer:

1. Total income in the society is $8,000 + $12,000, $20,000 + $40,000 + $80,000 = $160,000.
2. In this example with only one household, the poorest quintile consists only of the lowest-income household, that earning $8,000. As a percentage of total income, this is 5%: 8,000/160,000 = .05, or 5%.
3. The richest quintile consists only of the highest-income household, that earning $80,000. This is half, or 50%, of the total income of $160,000.
4. Second quintile: $12,000/$160,000 = 7.5%
   Third quintile: $20,000/$160,000 = 12.5%
   Fourth quintile: $40,000/$160,000 = 25%
5. The Lorenz curve plots the percentage of total income against the cumulative percentage of households. The values are below:

   Households	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 households are comprised of the bottom three households whose shares are 5%, 7.5%, and 12.5%, for a cumulative total of 25%.