Inequality is measured by comparing the income of different individuals or groups within a society. Here, we're given the income for five different groups with the same number of people (quintiles) in years 1998-2016. The poorest quintile received 5% of the total income generated in 1998, while the richest quintile received 44% of the total income. The poorest quintile income share decreased to 3.2% in 2016, while the richest quintile share rose to 53.1%. This suggests that there was an increase in income inequality from 1998 to 2016.

A more comprehensive measurement of inequality is the Gini coefficient that compares two different distributions of income. The horizontal axis shows the cumulative percentage of households (from poor to rich) and the vertical axis shows the cumulative percentage of income. A perfectly equal distribution would look like a diagonal line from the lower-left corner to the upper-right corner of the graph. When poor people have lower incomes than rich people, the line showing the distribution of income is always below the ideal diagonal line and the Gini coefficient measures the distance of the line from the diagonal on the scale from 0 (perfect equality) to 1 (complete inequality).

(a) To complete the table, we need to distribute the total annual income in the economy, $500,000,000, to the five income groups in 2004:

• The poorest received 3.8% of the total annual income, or $19,000,000.
• The second quintile received 9.9% of the total annual income, or $49,500,000.
• The third quintile received 15.2% of the total annual income, or $76,000,000.
• The fourth quintile received 22.5% of the total annual income, or $112,500,000.
• The richest quintile received 48.6% of the total annual income, or $243,000,000.

Each group consists of 2,000 individuals with the same income, so we can easily calculate the individual income in each group by dividing the total annual income in that group by 2,000, see the fourth column of the table below.The group will be below the poverty line if the average income will be lower than the official poverty line of $27,400. The table shows that 40% of the Perkopia citizens were below the poverty line in 2004.

(b) If the government introduced a welfare program in which any individual with an income of less than $27,400 per year received a lump-sum transfer payment of $10,000 in 2004 and there was no change in labor-supply, the poverty rate after the introduction of the welfare program declined to 20% as the second group's income increased from $24,750 to $34,750.

(c) Carolina, a resident of Perkopia who earned $26,942 in 2004, so she qualified for the transfer of $10,000. Her income would then increase to $36,942 and she would be comfortably above the poverty line. Alternatively, she could accept the overtime work and increase her income by $1,100 to $28,042. That would give her an income just above the poverty line and she would no longer qualify for the welfare transfer. By comparing these two alternatives (no additional work, or additional work), the following statements would, or would not, apply.

• The $10,000 in aid presents a disincentive for Caroline to make more than $27,400 per year. (Yes)
• Caroline would gain more income by turning down the overtime than she would if she accepted the overtime.. (Yes)
• Caroline may accept the overtime if she feels that taking it will increase the chances of her receiving a significant promotion (Yes)