Graphing a Lorenz Curve and Calculating the Gini Coefficient

INTRODUCTION

1. Begin with an attention getting question about a fictitious story. Pretend that you have four brothers. You have all been splitting wood all day. At the end of the day, you find that your mom has made an apple pie that she wants you to share with your brothers. How would you share the pie? [Some possible answer include: each brother gets 20 percent; one brother isn't hungry and wants only a sliver and will share his piece of the pie with an older, hungrier brother; some might propose a competition to see who gets the most pie; the pie might be split by who produced the most for the family.]

2. In much the same way, income is divided among citizens of a country. In this lesson, you will show how to construct a Lorenz Curve and calculate the Gini Coefficient for the Advanced Placement Microeconomics exam.

[NOTE: The Lorenz Curve is a macroeconomics concept, but the Acorn book outlines that the concepts are taught in microeconomics.]

PROCESS

1. Give each student a Graphic Organizer to follow the progression of the Income Inequality PowerPoint.

2. Show each step and assist students as they calculate percentages and graph the data.

3. Distribute a problem for students to work on in class or as homework.

CONCLUSION

Have the students visit the site Income Distribution by Country . At this website, selected Gini Coefficients around the world are graphically displayed.

The students should be able to see how Gini Coefficients show income inequality by looking at the geographical area and making inferences about the type of government. They also have the tools to analyze income distributions among nations. Ask them, if the Gini Coefficient for Namibia was 70.7, what does that tell you about the income distribution in that African country? Sweden has a Gini Coefficient of 23. What does that Gini Coefficient indicate about income distribution?

Calculate the Gini Coefficient by taking the ratio of the area inside the Lorenz Curve and dividing the area by the area under the line of perfect equality. Since the area under the line of perfect equality is 0.5, one actually multiplies. This fact explains why countries might have a large Gini Coefficient.

ASSESSMENT ACTIVITY

The small country of Alpha has 10 citizens. The citizens and their earned incomes are listed below:

Citizen       Earned Income

Zak              $ 2,000

Erika           $10,000

Bill               $ 1,500

Juan            $ 15,000

Harry           $ 16, 000

Jose            $ 9,000

Emily           $ 30,000

Kai               $ 12,000

Robert         $ 8,000

Kathleen      $ 20,000

From the data, have the students graph the Lorenz Curve and calculate the Gini Coefficient.

The answer key for the teacher: Gini Coefficient Answer Key.

EXTENSION ACTIVITY

1. Discuss how earners are seldom stuck in a quintile. (Often, college graduates begin in the lowest 20 percent of income earners and move up to higher quintiles as their skills and education increase. Also, as wage earners retire, they move to lower quintiles. These observations suggest that the Lorenz Curve is a snapshot in time.)

2. Discuss the question, "What is a household?" Does a household have to have four family members or can the composition of households be varied? When economists plot the Lorenz data, they place cumulative percent of households on the x-axis. What implications does using a vague tag like households have for interpreting the distribution of income? (Students tend to interpret a household as one like their own. Many households have varied compositions. This makes the interpretation of the Lorenz Curve difficult.)