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Suppose that you have the following information from Nigeria. The lowest 20% of the income distribution receives 1.0% share of overall income. The next quintile gets 2.5%, the third one receives 8.5%, the fourth quintiles has 20% and finally, the highest quintile receives 68% of overall income. Graph the Lorenz curve from the Nigerian data given above, carefully labeling the axes. On the axes, label all values that correspond to the five points that make up the Lorenz curve.

User Napoleon
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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.

User MISJHA
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