Final answer:
If everyone in a population earned the same amount, the Lorenz curve would be a straight line at a 45-degree angle, representing perfect equality of income distribution. Comparisons of past income distributions, like those in the U.S. for 1980 and 2011, show how income inequality has increased as the curve deviates from this line.
Step-by-step explanation:
If every person in a population earned the same amount, the Lorenz curve would be a straight line at a 45-degree angle, often referred to as the line of perfect equality. The Lorenz curve is a graphical representation of the distribution of income or wealth within a society, where the x-axis represents the cumulative percentage of households, and the y-axis represents the cumulative percentage of income.
The 45-degree line shows that each portion of the population earns a percentage of income exactly equal to the percentage of the population. In this scenario, for example, the bottom 20% of the income distribution would receive 20% of the total income; the bottom 40% would receive 40% of the total income, and so on until the top 100% receives 100% of the income. This line is a theoretical benchmark that reflects a society with absolute income equality.
Comparing actual data, such as the U.S. income distributions over various years, can illustrate changes in income inequality. For instance, the income distribution in 1980 was closer to the line of perfect equality compared to the more unequal distribution in 2011. Shifts away from the 45-degree line on a Lorenz curve indicate a rise in income inequality within the population.