# Graphing a Lorenz Curve and Calculating the Gini Coefficient

### INTRODUCTION

1. Suppose you have spent all day splitting wood with your four brothers. When you go home, your mother has made an apple pie. How do you split the pie?

2. In much the way you split the apple pie, nations distribute income. In this lesson, you will learn how to analyze the distribution of income and determine how equitable the income is distributed.

1. Using the Graphic Organizer follow along with your teacher's PowerPoint. In this PowerPoint, Income Inequality, you will construct a Lorenz Curve by following step-by-step directions. Your teacher will facilitate instruction by answering your questions and providing feedback.

2. You will also calculate the Gini Coefficient in the same way.

3. After you have learned how to calculate the Gini Coefficient, you will be shown Gini Coefficients from selected countries. You will briefly discuss the Gini Coefficients for these countries.

4. You will complete a simple problem for assessment.

[NOTE: Here is a Calculator to use.]

### PROCESS

1. You will interact with a PowerPoint presentation. Using a graphic organizer, perform the tasks on the PowerPoint and check your work against the slides. Your teacher will assist in making the calculations and graphing the data.

2. You will be receive a simple problem as homework or class work.

### CONCLUSION

Visit the site Income Distribution By Country . At this website, selected Gini Coefficients around the world are graphically displayed.

You will be able to see how Gini Coefficients show income inequality by looking at the geographical area and making inferences about the type of government. You also have the tools to analyze income distributions among nations. If the Gini Coefficient for Namibia is 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, graph the Lorenz Curve and calculate the Gini Coefficient.

### EXTENSION ACTIVITY

1. When you graduate from college, chances are that you will begin your career in an entry-level position. As you gain experience, your pay will increase. How will the position of a worker change among the quintiles as the worker gains experience? Will workers be "stuck" in a quintile?

2. When workers retire, their income usually drops as they rely on retirement benefits. For example, teachers often retire at 67 percent of their annual salary. What does retirement suggest about the mobility of workers between quintiles?

3. Since workers often move between quintiles, does the Lorenz Curve show something constant about income inequality or does it provide a snapshot?