Lorenz Curve
The goal of this curve is to measure the level of income inequality in a country, as compared with other countries.
Becoming familiar with the Lorenz Curve:
The following diagrams display five Lorenz curves, each relating to a different country. The more concave the curve, then the higher the degree of income inequality in the country. For example:
 Income inequality in Country B is greater than income inequality in Country A.
 Income inequality in Country C is greater than income inequality in Country B.
 There is total income equality in Country A.
 There is total income inequality in Country E, meaning that one household receives all the income of the country, and all other households receive nothing.
Lorenz curves for five countries
Sketching the Lorenz Curve
The Lorenz curve represents a concave curve starting at point 0 and ending at point A, as shown in the following diagram.
The symbol used to represent the curve is the letter L.
How to Sketch the Lorenz Curve
In this example, the country has 200 households.
Step 1 :
To divide the families into deciles:
a table is prepared, which lists all of the households according to the level of income in descending order.
The list is then divided into 10 groups of equal size (i.e., 20 families each). Each group contains 10% of the country’s households. The top group, which is called the upper decile, contains the wealthiest families in the country, and the bottom group, called the lowest decile, contains the poorest families in the country.
The higher a family’s position on the list, then the greater its income.
Step 2:
Dividing the country income into deciles:
We sum the total income of each decile and calculate its ratio in terms of the combined household income in the country.
Household incomes divided by deciles
Decile  Families  Income per household  Total income in the decile  The decile’s percentage of the total national income  Cumulative percentage of the total national income 
Column 1  Column 2  Column 3  Column 4  Column 5  Column 6 
Tenth decile (the upper)  1. The Smiths, 2. The Fields, 3. The Bakers, . . . ., 20. The McDonalds.  $400,00
$300,00 $390,000 
$1,750,000 
35% 
100% 
Ninth decile  21 – 40 
$1,500,000 
30% 
65% 

Eighth decile  41 60 
$750,000 
15% 
35% 

Seventh decile  61 – 80 
$500,000 
10% 
20% 

Sixth decile  81 – 100 
$200,000 
4% 
10% 

Fifth decile  101 – 120 
$150,000 
3% 
6% 

Fourth decile  121 – 140 
$75,000 
1.5% 
3% 

Third decile  141 – 160 
$45,000 
0.9% 
1.5% 

Second decile  161 – 180 
$25,000 
0.5% 
0.6% 

First decile (the lowest)  180 – 200 
$5,000 
0.1% 
0.1% 
How to read the table:
Start with the row of the fifth decile. The income of all families in the fifth decile totals $150,000, amounting to 3% of the country’s total income. If the income of the fifth decile is added to the income of the other deciles below it,
The axes
 The Xaxis represents the deciles in ascending order from left to right. The first decile is the poorest, and the tenth decile is the wealthiest.
 The Yaxis represents household income as a percentage of the country’s total income. Percentages rise from bottom to top, i.e., from 0% to 100%, with a space representing 10% between each line.
Every point on the curve corresponds to two numbers. The diagram displays the Lorenz curve drawn according to the information contained in the table.
Explanation of the curve
 Point D shows that the four lowest deciles in the country together earn 3% of the country’s total income (Column 6 of the fourth decile row in Table 6.1). All the other deciles jointly earn the remainder – in this case, 97% of the country’s total income.
 Similarly, point F shows that the six lowest deciles together earn 10% of the country’s entire income. All other deciles, (the top four) earn the remainder – in this case, 90% of the country’s income.
 Point G shows that the nine lowest deciles in the country jointly earn 65% of the total national income. The remaining (top) decile earns the remainder – in this case, 35% of the country’s income.
 Point K shows us that all ten deciles in the country (the entire population) together earn 100% of the country’s entire income.