# Graphing a Lorenz Curve and Calculating the Gini Coefficient

### EDUCATOR'S VERSION

This lesson printed from:

http://www.econedlink.org/e885

Posted April 5, 2010

Grades: 9-12

Author: Mike Fladlien

Posted: April 5, 2010

### DESCRIPTION

In this lesson, students receive raw data to construct a Lorenz Curve and calculate the Gini Coefficient. This lesson prepares AP Microeconomics students for the Advanced Placement exam. The teacher will briefly interpret the Gini Coefficient.

### KEY CONCEPTS

Distribution of Income, Economic Equity

### STUDENTS WILL

- Graph a Lorenz Curve from simple data.
- Calculate the Gini Coefficient.
- Interpret 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.

### 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.

### 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.

### 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.)