Application Exercise 10d: Constructing a Lorenz curve
The table below contains the share of household net worth (wealth) held by each quintile of households in Australia in 2019-20
Quintile | Household net worth (wealth) ($’000) 2019-20 (i) | % of total
(ii) | Cumulative % of total wealth (iii) |
Lowest quintile | 35.1 | 0.7 | 0.7 |
Second quintile | 252.6 | 4.8 | 5.5 |
Third quintile | 588.4 | 11.3 | 16.8 |
Fourth quintile | 1,067.2 | 20.5 | 37.3 |
Highest quintile | 3,267.1 | 62.8 | 100* |
Total | 5210.4 | 100 |
|
* Note: Cumulative % of total wealth (iii) sums to 100.1 due to rounding. Students should ensure final point on Lorenz curve is 100.
Tasks
- Complete the table above by inserting percentages in column (iii). Use Table 10.6 earlier to guide your calculations.
See table above
- Use the figures in the completed table to construct a Lorenz curve for household net worth in 2019-20. (Ensure that you use approximately half a page and draw the curve roughly to scale.)
- Explain what would happen to the Lorenz curve if the distribution of household net worth (wealth) changed such that the top quintile owned a lower proportion of total wealth and the lowest quintile owned a higher proportion of total wealth.
If the top quintile (Q%) owned a smaller proportion of total wealth and the lowest quintile (Q!) owned a larger proportion of total wealth, the Lorenz curve (LC) would shift inwards, closer to the Line of Absolute Equality. This would mean the extent to which the distribution of wealth diverges from absolute equality would have been reduced.
- Write three sentences comparing and contrasting the distribution of EDHI (as shown in Figure 10.6D earlier) and the distribution of wealth in Australia (as shown by your own Lorenz curve constructed in this task.) Explain how the Lorenz curve can indicate which is distributed more and less equally.
The Lorenz curve for EDHI (Equivalised Household Disposable Income) is much closer to the line of absolute equality compared to the Lorenz curve for wealth in Australia. This indicates that the gap between the line of absolute equality and the LC for EDHI is much smaller than the gap between the LC for wealth and the line of absolute equality. This indicates that income (as measured by EDHI), although not equally distributed, is much more evenly distributed than wealth in Australia. The distribution of wealth is much less equal.