Final answer:
The Lorenz curve can be graphed by calculating the cumulative income for each quintile of the population and then plotting these points on a graph with the cumulative share of population on the x-axis and cumulative share of income on the y-axis. The points are then connected to display the income inequality in a graphical form.
Step-by-step explanation:
To graph the Lorenz curve using the income distribution data from Nigeria, you begin by plotting cumulative shares of population on the x-axis against cumulative shares of income on the y-axis. The first step is converting the given income shares for each quintile into cumulative percentages:
- The bottom 20% of the population has 1.0% of total income.
- The bottom 40% (20% + next 20%) has 1.0% + 2.5% = 3.5% of total income.
- The bottom 60% adds the third quintile, so 3.5% + 8.5% = 12.0% of total income.
- The bottom 80% includes the fourth quintile, so 12.0% + 20.0% = 32.0% of total income.
- Finally, the bottom 100% receives 100% of the income by definition.
On a graph, the cumulative share of the population will be labeled on the x-axis at 20%, 40%, 60%, 80%, and 100%, while the corresponding cumulative income will be labeled on the y-axis at 1.0%, 3.5%, 12.0%, 32.0%, and 100%, respectively.
Each pair of these values (20%, 1.0%), (40%, 3.5%), (60%, 12.0%), (80%, 32.0%), and (100%, 100%) represent points on the Lorenz curve, which you then connect smoothly. Typically, a Lorenz curve starts at the origin (0%,0%) and ends at the point (100%,100%). You will also draw a 45-degree dashed line (line of equality) from the origin to the point (100%,100%) to represent perfect income equality. The Lorenz curve will typically lie below this dashed line.