The following income distribution data are for Brazil.
$$\begin{array} { l c }
\hline { \text { Quintile } } & \text { Percent Share } \
\hline \text { Lowest } 20 \% & 3.0 \% \
\text { Second quintile } & 6.9 \% \
\text { Third quintile } & 11.8 \% \
\text { Fourth quintile } & 19.6 \% \
\text { Highest } 20 \% & 58.7 \% \
\text { Highest } 10 \% & 43.0 \%
\end{array}$$
(a) Carefully graph the Lorenz curve, labeling the axes.

Question

The following income distribution data are for Brazil.
 $$\begin{array} { l c } 
\hline { \text { Quintile } } & \text { Percent Share } \
\hline \text { Lowest } 20 \% & 3.0 \% \
\text { Second quintile } & 6.9 \% \
\text { Third quintile } & 11.8 \% \
\text { Fourth quintile } & 19.6 \% \
\text { Highest } 20 \% & 58.7 \% \
\text { Highest } 10 \% & 43.0 \%
\end{array}$$ 
(a) Carefully graph the Lorenz curve, labeling the axes.

Quizplus · Accepted Answer

The Answer is To graph the Lorenz curve based on the given income distribution data for Brazil, follow these steps:

1. Label the axes: The horizontal axis (x-axis) represents the cumulative percentage of households, divided into quintiles (20% increments). The vertical axis (y-axis) represents the cumulative percentage of income earned by those households.

2. Plot the points: You will plot the cumulative percentage of households against the cumulative percentage of income. Start with the point (0,0), which represents 0% of households earning 0% of the income.

3. Calculate the cumulative income: Add up the income shares cumulatively for each quintile. For example, the cumulative income share for the second quintile is the sum of the income shares of the first and second quintiles (3.0% + 6.9% = 9.9%).

4. Plot the cumulative income shares against the cumulative household shares. Here are the points you would plot, based on the data provided:

- (0%, 0%)
- (20%, 3.0%)
- (40%, 3.0% + 6.9% = 9.9%)
- (60%, 9.9% + 11.8% = 21.7%)
- (80%, 21.7% + 19.6% = 41.3%)
- (100%, 41.3% + 58.7% = 100%)

5. Draw the Lorenz curve: Connect the points with a smooth curve. The curve will start at (0,0), bow towards the bottom right corner, and end at (100%, 100%).

6. Draw the line of equality: This is a straight line from (0,0) to (100%, 100%), representing perfect income equality (where each quintile earns exactly 20% of the income).

The Lorenz curve will lie below the line of equality, indicating the degree of income inequality. The further the Lorenz curve is from the line of equality, the greater the income inequality.

Please note that the actual drawing of the graph is not possible in this text-based format, but the instructions provided should allow you to create the Lorenz curve on graph paper or using graphing software.

The Following Income Distribution Data Are for Brazil (A) Carefully Graph the Lorenz Curve, Labeling the Axes