Mr. Maurer
AP Economics
Name: ______________________________
Income Inequality – Problem Set #1
1. Use the data on page 637 in your textbook to make Lorenz curves for the United States for the
years 1955, 1969, 1985, and 2001. Make a separate Lorenz curve for each year. Be sure to use
the same scale for each Lorenz curve and to label each Lorenz curve completely.
I’m not putting the actual Lorenz curves on here. It would take too long and I don’t think it would be
that helpful. If you had trouble drawing them, talk to me in class Monday.
Questions 2 – 8 refer to the
Lorenz curve at left. Countries
A and B are represented by the
two curves. Letters X, Y, and Z
represent enclosed areas.
2. What can you say about the
relative distribution of income in
Country A and Country B?
Country A’s income is distributed
more equally than Country B’s.
3. Which country has the higher
Gini coefficient? Country B.
4. What does the straight diagonal
line represent? Perfect income
equality.
5. Represent Country A’s Gini coefficient in terms of X, Y, and Z.
X ÷ (X+Y+Z)
6. Represent Country B’s Gini coefficient in terms of X, Y, and Z.
(X+Y) ÷ (X+Y+Z)
7. What is the Gini coefficient for the straight diagonal line?
0
8. Identify two tax policies that Country B could take to move its Lorenz curve more in line with
Country A’s. A progressive income tax or an estate tax.
Questions 9 - 11 refer to the income data below:
Quintile
Percentage of income
Percentage of income
before taxes and transfers income after taxes and transfers
Lowest 20%
1.1
5.1
Second 20%
7.9
11.1
Third 20%
15.5
16.5
Fourth 20%
24.7
23.8
Highest 20%
50.7
43.5
9. This government’s tax and transfer policies generally shifted income away from which quintile(s)
and to which quintile(s)?
Away from the fifth (highest) quintile and toward the first and second quintile.
10. What type of income tax system does this country probably have? Explain.
A progressive income tax system – income is distributed more equally after taxation.
11. Would the Gini Coefficient for the country above be greater with or without this system taxes and
transfers? It would be greater.
Questions 12 – 15 are based on the Lorenz curve
to the left, which represents the country of
Jakeland. The letters X and Y represent enclosed
areas.
12. If the area of X + Y is 100 square units and the
area of X is 28 square units, what is the Gini
coefficient for Jakeland?
.28
13. If the area of X + Y is 100, and the Gini
coefficient of Jakeland is .40, what is the area of X?
40
14. If Jakeland adopted a regressive income tax
system, which significantly increased income
inequality, what would happen to the area of Y?
The area of Y would decrease.
15. Instead, assume that Jakeland adopts a very progressive income tax system, indicate on the diagram
the likely change this would cause in the distribution of income in Jakeland (draw a new curve).
Your new curve should be closer to the straight red line than the original curve.
16. Plot the following income distribution data for both countries carefully on the same Lorenz curve
below.
Again, I’m not actually plotting the curve, let me know if you had trouble.
Country X
Country Y
Quintile
Percentage of income
Percentage of income
Lowest 20%
Second 20%
Third 20%
Fourth 20%
Highest 20%
5.0
11.8
17.0
23.1
43.0
4.1
9.2
14.1
20.9
51.7
Assume that the Gini coefficients for the two countries are
.35 and .4. What is the Gini coefficient for each country?
Country X’s Gini coefficient is .35 and Country Y’s Gini
coefficient is .4, because Country Y has greater income
inequality the Country X.