Use the following table to work Problems 11 to 13 The table...

Use the following table to work Problems 11 to 13 The table shows shares of income in Australia. $$\begin{array}{lc} \begin{array}{l} \text { Households } \\ \text { (quintile) } \end{array} & \begin{array}{c} \text { Income share } \\ \text { (percentage of total) } \end{array} \\ \hline \text { Lowest } & 7 \\ \text { Second } & 13 \\ \text { Third } & 18 \\ \text { Foourth } & 24 \\ \text { Highest } & 38 \end{array}$$ Draw the Lorenz curves for the income distribution in Australia and in Brazil and South Africa (use the data in Fig. 19.6 on $\mathrm{p} .491$ ). Is income distributed more equally or less equally in Brazil and South Africa than in Australia?

Use the following table to work Problems 11 to 13 The table shows shares of income in Australia.
$$\begin{array}{lc}
\begin{array}{l}
\text { Households } \\
\text { (quintile) }
\end{array} & \begin{array}{c}
\text { Income share } \\
\text { (percentage of total) }
\end{array} \\
\hline \text { Lowest } & 7 \\
\text { Second } & 13 \\
\text { Third } & 18 \\
\text { Foourth } & 24 \\
\text { Highest } & 38
\end{array}$$
Draw the Lorenz curves for the income distribution in Australia and in Brazil and South Africa (use the data in Fig. 19.6 on $\mathrm{p} .491$ ). Is income distributed more equally or less equally in Brazil and South Africa than in Australia?

Key Concepts

Comparative Analysis of Distributions

Comparing income distributions across different regions or countries involves analyzing their respective Lorenz curves. By examining how each curve deviates from the line of perfect equality, one can determine whether one distribution is more or less equal than another, providing a visual comparison of economic equity.

Lorenz Curve

A Lorenz curve is a graphical representation of income or wealth distribution where the cumulative percentage of total income is plotted against the cumulative percentage of recipients. It provides insight into how evenly or unevenly income is distributed and is a key tool for visualizing inequality.

Cumulative Distribution

The concept of cumulative distributions involves adding up individual or group shares (such as quintiles) to show what proportion of the total income is controlled by the bottom x% of the population. It is essential for constructing the Lorenz curve by accumulating income shares across ordered groups.

Income Inequality

Income inequality refers to the extent to which income is distributed unevenly among a population. In the context of Lorenz curves, a more bowed curve away from the line of perfect equality indicates a higher degree of inequality, while a curve closer to the line suggests a more equal distribution.

Transcript

00:01 So here we have our household screen tile from the lowest which is the first one to the second the third the fourth and the highest for australia and brazil and south africa so in order to draw our lawrence curve first we need to calculate our cumulative percentages so for each country we have the percentage of total income.

00:28 That's why we need to calculate the cumulative for the lowest screen tile is going to be the same one which is 7 % and 2%.

00:40 Then we're going to add up.

00:42 The one for australia is going to be 20%.

00:46 The one for brazil and south africa is going to be 7%.

00:51 The next one, our third one, is going to be 38%.

00:55 The previous 20 % plus the 18 % of the third queensland in australia and is going to be 17 % in brazil and south africa.

01:08 The next one is going to be 66 % for australia, the 38 % plus 24%.

01:18 And for brazil and south africa is going to be 35%.

01:24 And the highest quintile, the last one, i'm sorry, i did a mistake right here.

01:31 This one wasn't 66, is going to be 62.

01:36 I'm sorry, it's 38 plus 24, 62.

01:41 And the highest one is going to be 100 for australia and 100 for brazil and south africa.

01:51 And these are the points we're going to plot to get our lawrence curves.

02:02 So in order to plot our lawrence curve in the x axis we have our households, the cumulative percentage.

02:09 And on the y axis we got the income also as cumulative percentage.

02:15 So as a community percentage, first we're going to draw...

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