Homework #3 KeyProblems taken from the Chapter 5 problems

Consider a hypothetical economy with 10 people, 8 of whom have income of $30,000, 1 of whom has income of $100,000, and 1 of whom has income of $500,000. Sketch the Lorenz curve for this income distribution. Describe the distribution by comparing the Lorenz curve to the line of perfect equality. Can you approximate the Gini coefficient? (Hint: Use graph paper and count blocks to approximate areas.)

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Take the highlighted columns and plot against each other with proportion of population on the x-axis and proportion of income on the y-axis.

# of People

Proportion of Pop. Income Cumulative

IncomeProportion of Income

0 0.00 $0 $0 0.001 0.10 $30,000 $30,000 0.042 0.20 $30,000 $60,000 0.073 0.30 $30,000 $90,000 0.114 0.40 $30,000 $120,000 0.145 0.50 $30,000 $150,000 0.186 0.60 $30,000 $180,000 0.217 0.70 $30,000 $210,000 0.258 0.80 $30,000 $240,000 0.299 0.90 $100,000 $340,000 0.40

10 1.00 $500,000 $840,000 1.00

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Cumulative proportion of population

Cum

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Line of perfectequality

Lorenz curve

5-1.According to the Lorenz curve in this economy, 80% of the people make roughly 30%of the income, while the top 10% of the people make almost 60% of the income. Froma quintile perspective, the bottom quintile makes less than 10% of the income whilethe top quintile makes roughly 70% of the income. Simply put, 8 people account for roughly 30% of the income while 2 people account for 70% of it.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Cumulative proportion of population

Cum

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Line of perfectequality

Lorenz curve

5-1.Gini Coefficient = 2AA = approx. 29 squaresTotal = 100 squares29/100 = 0.29A = 0.290.29 x 2 = 0.58Approx. Gini = 0.58

A

The following table provides information on the distribution of money income among families in the United States.

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YearFirst

QuintileSecond Quintile

Third Quintile

Fourth Quintile

Fifth Quintile

1989 3.8% 9.5% 15.8% 24.0% 46.8%

1999 3.6% 8.9% 14.9% 23.2% 49.4%

2009 3.4% 8.6% 14.6% 23.2% 50.3%

Source: DeNavas-Walt et al. (2010), Table A-2.

• 5-5a: Explain the concept of a quintile in the distribution of income.• A quintile denotes 20% of the distribution. Thus, there are 5 quintiles in a

distribution.

• 5-5b: Suppose that we define as poor those in the bottom two quintiles of the income distribution. Explain what happened to the share of money income earned by the poor from 1989 to 2009• The poor in the bottom two quintiles received less of the income distribution

in 2009 than they did in 1989. First quintile – 3.8% to 3.4%. Second quintile – 9.5% to 8.6%

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• 5-5c: Suppose that we define the middle class very broadly as those in the second, third, and fourth quintiles of the income distribution. Explain what happened to the share of money income earned by the middle class from 1989 to 2009.• The middle class in the second, third, and fourth quintiles received less of the income

distribution in 2009 than they did in 1989. Second quintile – 9.5% to 8.6%. Third quintile – 15.8% to 14.6%. Fourth quintile – 24.0% to 23.2%

• 5-5d: Explain two significant factors that a table of information such as this ignores.• First, the table does not tell us if incomes are rising or declining. It only gives the

percentage of the whole. Second, the table doesn’t designate whether the figures are before or after taxes. If they are before taxes, the income distribution will change after taxes are factored in.

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