The Distribution of Income: The Lorenz Curve

The Lorenz Curve A Lorenz curve is a plotting of data showing the percentage of income enjoyed by each percentage of households ranked according to their incomes. A Lorenz curve can be plotted directly from the data in Box 1. The vertical axis plots the percentage of national income, with the scale running from zero to 100. The horizontal axis plots the percentage of families ranked according to their amount of income. In the graph in Box 2, the curve is enclosed in a square. The first point on the curve is the origin, because zero percent of the families naturally earn zero percent of national income. The last point in the box corresponds to point Z with coordinates of 100 percent on both axes. At point Z, 100 percent of families naturally account for 100 percent of national income. The other points in the box correspond to the data in Box 1. For example, point A indicates that the lowest 20 percent of families had only 4.6 percent of the income in 1987. To see this, go from the point on the horizontal axis corresponding to 20 percent up to the Lorenz curve. Then draw a horizontal line to the vertical axis and note that it intersects that axis at 4.6 percent. The other points on the curve are a bit trickier to interpret. Go first to point B, corresponding to 40 percent on the horizontal axis and 15.4 percent on the vertical axis. The cumulative share of income going to the families in the lowest 40 percent of the population is 4.6 percent plus 10.8 percent, which equals 15.4 percent. Similarly, point C shows the cumulative share going to the lowest 60 percent of the population, which equals 32.3 percent. Finally, point D corresponds to the cumulative share of national income going to the lowest 80 percent of families. The graph shows that this corresponds to 56.3 percent of national income. It follows that the richest 20 percent of families earn (100 percent - 56.3 percent) of income, which is 43.7 percent. As you can see, this agrees with the data in Box 1. What would the Lorenz curve look like if there were no income inequality? If each 20 percent of the population earned exactly 20 percent of the income, 40 percent of the population would earn 40 percent of national income, 60 percent of the population would earn 60 percent of the income, and 80 percent of the population would earn 80 percent of the income. The Lorenz curve would therefore be a diagonal line through the square, called the line of income equality. The lower the position of the Lorenz curve with respect to the line of income equality, the less equal the income distribution in a nation. Economic policies can be used to reduce the degree of income inequality in a nation. Taxes that take proportionately more from the rich than the poor can result in an after-tax Lorenz curve that's closer to the line of income equality. Programs that provide cash assistance to the poor can increase the income shares going to the lowest fifth of the population and also move the Lorenz curve in the direction of income equality. Distribution within Income Ranges Another way we can gauge inequality of income is to look at the percentages of families that earn income within certain ranges. The table in Box 3 shows that 20.8 percent of families had annual incomes over $50,000 in 1988. On the other hand, only 6.2 percent of families had incomes less than $5,000 that year. To see where your family stood in terms of money income relative to other families in 1988, compare your family's 1988 income with the data in the table. For example, if your family had 1988 pretax income of $50,000, you enjoyed higher income than was received by 79.2 percent of the U.S. population!