Grade 12 World Issues - Unit 3 Lesson 4
Challenge to Diversity – Economics
Lorenz Curve
The Lorenz curve was developed by Max O. Lorenz in 1905 as a graphical
representation of income distribution. The Lorenz curve portrays observed
income distributions and compares this to a state of perfect income equality. It
can also be used to measure distribution of assets. Some doctrines (e.g.
Socialism) consider it to be a graphical representation of social inequality as well
as income inequality.
The Lorenz curve is a graph that shows the percentage of households plotted on
the x-axis and income percentage on the y-axis.
In a perfectly equal income distribution, every person has the same
income. For the Lorenz curve, the bottom N% of society would always
have N% of the income, and a perfectly equal distribution would be a
straight line y = x.
In a perfectly unequal distribution, one person has all the income and
everyone else has none. The curve would y = 0 for all x < 100 and y =
100 when x = 100.
Lorenz Curve…2
The logic for a perfectly equal income (i.e., equal distribution) is 10% of the
population would have 10% of the income, 20% or the population would have
20% of the income, and so on. Thus, the Lorenz curve in perfectly equal income
is a straight line.
It is more common for incomes to be distributed unevenly through a population.
The more the line curves to the right (see Figure above), the more unequal
income distribution becomes.
Note: The Lorenz curve cannot rise above the line of perfect equality. Offer one
reason for this statement.
Graph the data in Table 1 and Table 2 to build a Lorenz curve for each dataset.
You should plot the data on one graph for comparative purposes.
Table 1. Distribution of Wealth in Canada (1998)
Percentage of
Percentage
Households
of Income
20
5.7
40
11.8
60
17.7
80
24.6
100
40.2
Table 2. Distribution of Wealth in the World (1994)
Percentage of
Percentage
Households
of Income
20
1.4
40
1.9
60
2.3
80
11.7
100
82.7
Lorenz Curve…3
The following steps can be used to plot a Lorenz curve for world income
distribution (Table 2).
1. Start at the lowest point by plotting the intersect of 1.4% of the income and
20% of the population.
2. Calculate the accumulated percentage of income gained by the lowestearning 40% of the population. 1.4% + 1.9% = 3.3%
3. Plot the intersect of 3.3% of the income and 40% of the population.
4. Calculate the accumulated percentage of income gained by the lowestearning 60% of the population. 1.4% + 1.9% + 2.3% = 5.6%
5. Plot the intersect of 5.6% of the income and 60% of the population.
6. Calculate the accumulated percentage of income gained by the lowestearning 80% of the population. 1.4% + 1.9% + 2.3% + 11.7%
7. Plot that intersect for 80% of the population.
8. Draw a smooth curve through the plotted points. You begin at (0,0) and
end at (100,100) since 0% of the population earns nothing and 100% of
the population earns 100% of the total income.
Contrast your two Lorenz curves. Provide two statements about the differences
you observe.
What do the different curves suggest about income distribution within Canada
versus income distribution throughout the world?
Lorenz Curve…4
We can learn more about world wealth. That is, how is income distribution
changing? Let us examine income distribution versus Gross Domestic Product
(GDP).
We will consider the world in the following groupings:
Africa
Asia (including China)
Eastern Europe
Latin America and the Caribbean
Western Europe, North America and Oceania.
We will also consider time.
Plot the datasets in Table 3 as a Lorenz curve. Note: The amounts are
cumulative percentages. In other words, graph the data as provided.
Table 3. Distribution of World Population by Income
Cumulative
Cumulative
Cumulative
Percentage of
Percentage of
Percentage of
World
World Income
World Income
Population
1988
1993
0
0
0
10
0.9
0.8
20
2.3
2.0
50
9.6
8.5
75
25.9
22.3
85
41.0
37.1
90
53.1
49.2
95
69.8
66.3
99
91.7
91.5
100
100.0
100.0
NOTE: The increases in the Cumulative Percentage of the World Population
data in Table 3 are NOT equal. This data column is your x-axis. Your
graph should have equal increases (e.g., 0..10..20..30..40..50..) since the
differences in the increases is the same. That is, an increase from 10 to
20 has the same impact as an increase from 50 to 60. When you plot the
data, you need to be careful and accurate. The data does NOT go
0..10..20..30..40 It goes 0..10..20..50..75…
Lorenz Curve…5
Table 4. Real per capita Income by Percentage Income Distribution for the
World in 1988 and 1993
Percentage
Income in
Income in
of Income
1988
1993
Distribution
5
277.4
238.1
10
348.3
318.1
15
417.5
372.9
20
486.1
432.1
25
558.3
495.8
30
633.2
586.0
35
714.5
657.7
40
802.7
741.9
45
908.3
883.2
50
1 047.5
1 044.1
55
1 314.4
1 164.9
60
1 522.7
1 505.0
65
1 898.9
1 856.8
70
2 698.5
2 326.8
75
3 597.0
3 005.6
80
4 370.0
4 508.1
85
5 998.9
6 563.3
90
8 044.0
9 109.8
95
11 518.4
13 240.7
99
20 773.2
24 447.1
Questions
1. From Table 4, describe the difference in Real Incomes of the World’s
richest and poorest people. What changes do you observe between 1988
and 1993?
2. Describe the distribution of world incomes using your Lorenz curve and
Table 3.
3. How has the distribution of world income changed between 1988 and
1993? Provide one observation.
Lorenz Curve…6
4. What do you think should be done about the distribution of incomes?
Provide three ideas.
5. In your opinion, should economists tell politicians what to do?
In summary…
A Lorenz curve is one way of illustrating with a graph the distribution of a
population’s income.
If income was distributed evenly, everyone earns the same income. Using a
hypothetical Country A where everyone earns $10 000 per year. Income is
evenly distributed.
On a Lorenz curve, we graph both income (y-axis) and population (x-axis) as
percentages. Thus, the upper limits on each axis must be 100. At these limits,
100% of the population earns 100% of the income. Likewise, zero percent earns
zero income. If income is equally distributed, 10% of the population must earn
10% of the income, 20% of the population earns 20% of the income, and so on.
This straight-line relationship does not exist for most countries. Typically, a small
group of rich earn a greater share of the total income.
On a Lorenz curve, the closer the actual income distribution approaches the
theoretical straight-line relationship, the more even or equal the distribution of
income among all members of the population.
I get it…
Draw and label a Lorenz curve using the following information. Income is
unequally distributed in Country B. Here, 80% of the people are very poor and
only earn 10% of the income. The remaining 20% of the population earn 90% of
the income.
Lorenz Curve…Answers for Page 2
The logic for a perfectly equal income (i.e., equal distribution) is 10% of the
population would have 10% of the income, 20% or the population would have
20% of the income, and so on. Thus, the Lorenz curve in perfectly equal income
is a straight line.
It is more common for incomes to be distributed unevenly through a population.
The more the line curves to the right (see Figure above), the more unequal
income distribution becomes.
Note: The Lorenz curve cannot rise above the line of perfect equality. Offer one
reason for this statement.
We are measuring percentages. Thus, the number cannot be
negative (e.g., 20% of the population cannot have -10% of the
income. There cannot be negative income. You can zero or some
income. You cannot have less than zero income; less than zero
income is impossible).
For practice, graph the data in Table A and Table B to build a Lorenz curve.
Table A. Distribution of Wealth in Canada (1998)
Percentage of
Percentage
Households
of Income
20
5.7
40
11.8
60
17.7
80
24.6
100
40.2
Table B. Distribution of Wealth in the World (1994)
Percentage of
Percentage
Households
of Income
20
1.4
40
1.9
60
2.3
80
11.7
100
82.7
Grade 12 Geography – Canada and World Issues
Unit 3 – Challenge to Diversity – Economics
Lorenz Curve
The Lorenz Curve is a graph showing the proportion of
the distribution assumed by the bottom percent of the
values.
It is most often used to represent income distribution.
In this case, it shows for the bottom x% of households,
the percentage (y%) those households possess of the
total income.
The percentage of households is plotted on the x-axis
and the percentage of income on the y-axis.
It can also be used to show distribution of assets.
Some political doctrines (e.g. socialism) consider it to
represent social inequality.
Every point on the Lorenz Curve represents a
statement like "the bottom 20% of all households
have 10% of the total income".
A perfectly equal income distribution would be one
in which every person has the same income. This
would be a straight line (y = x), and it would be
called the Line of Perfect Equality (or the 45° Line).
By contrast, a perfectly unequal distribution would
be one in which one person has all the income and
everyone else has none. In that case, the curve
would be at y = 0 for all x < 100, and y = 100 when x
Lorenz Curve…2
= 100. This curve is called the Line of Perfect
Inequality.
Since the curve uses percentages and must always
rise to 100% but not exceed 100%, it is impossible
for the Lorenz Curve to rise above the Line of
Perfect Equality or sink below the Line of Perfect
Inequality
NOTE: Economic inequality has always existed. A
country's economic structure (e.g., capitalism,
socialism), war, and individuals abilities to create
wealth all create economic inequality.
The Gini Coefficient is the measure of distribution
inequality. Roughly, it is the ratio of the area between
the Lorenz Curve and the Line of Perfect Equality.
The Gini Coefficient is a number between 0 and 1,
where 0 corresponds to perfect equality (i.e.,
everyone has the same income) and 1 corresponds to
perfect inequality (i.e., one person has all the income,
and everyone else has zero income).