Homework #3 Key Problems 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 $500,000. Sketch the Lorenz curve for this income distribution. Describe the distribution by comparing the Lorenz curve to the line of perfect equality. Can you approximate the Gini coefficient? (Hint: Use graph paper and count blocks to approximate areas.) 5-1. Page 156 Take the highlighted columns and plot against each other with proportion of population on the x-axis and proportion of income on the y-axis. # of People Proportion of Pop. Income Cumulative Income Proportion of Income 00.00$ $30, $30,000$60, $30,000$90, $30,000$120, $30,000$150, $30,000$180, $30,000$210, $30,000$240, $100,000$340, $500,000$840,

Line of perfect equality 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. From a quintile perspective, the bottom quintile makes less than 10% of the income while the 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.

Line of perfect equality Lorenz curve 5-1. Gini Coefficient = 2A A = approx. 29 squares Total = 100 squares 29/100 = 0.29 A = x 2 = 0.58 Approx. Gini = 0.58 A

The following table provides information on the distribution of money income among families in the United States Page Year First Quintile Second Quintile Third Quintile Fourth Quintile Fifth Quintile %9.5%15.8%24.0%46.8% %8.9%14.9%23.2%49.4% %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 First quintile – 3.8% to 3.4%. Second quintile – 9.5% to 8.6% 5-5. Page

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 The middle class in the second, third, and fourth quintiles received less of the income distribution in 2009 than they did in 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 Page