Question

A group of 10 people have the following annual incomes: \(24,000, \)18,000, \(50,000, \)100,000, \(12,000, \)36,000, \(80,000, \)10,000, \(24,000, \)16,000. Calculate the share of total income that each quintile receives from this income distribution. Do the top and bottom quintiles in this distribution have a greater or larger share of total income than the top and bottom quintiles of the U.S. income distribution?

Short answer

In this income distribution, the top quintile receives 48.6% of the total income, slightly less than the 52% share in the U.S. income distribution. The bottom quintile receives 5.9% of the total income, significantly larger than the 3% share in the U.S. income distribution.

Step-by-step solution

Calculate the total income of the group

Add all individual annual incomes together to find the total income of the group: \(Total\,Income = \$24,000 + \$18,000 + \$50,000 + \$100,000 + \$12,000 + \$36,000 + \$80,000 + \$10,000 + \$24,000 + \$16,000 \) \(Total\,Income = \$370,000 \)

Sort the individual incomes in ascending order

Arrange the individual annual incomes in ascending order to divide them into quintiles later: \( \$10,000, \$12,000, \$16,000, \$18,000, \$24,000, \$24,000, \$36,000, \$50,000, \$80,000, \$100,000 \)

Define the quintiles and find the sum of each quintile

There are 10 people in the group, so each quintile will have two people. Divide the sorted incomes into quintiles: - Quintile 1 (Bottom): \( \$10,000 + \$12,000 = \$22,000 \) - Quintile 2: \( \$16,000 + \$18,000 = \$34,000 \) - Quintile 3: \( \$24,000 + \$24,000 = \$48,000 \) - Quintile 4: \( \$36,000 + \$50,000 = \$86,000 \) - Quintile 5 (Top): \( \$80,000 + \$100,000 = \$180,000 \)

Calculate the share of total income for each quintile

To find the share of total income for each quintile, divide the sum of each quintile by the total income: - Quintile 1 (Bottom): \( \$22,000/ \$370,000 = 0.059 = 5.9\% \) - Quintile 2: \( \$34,000/ \$370,000 = 0.0919 = 9.19\% \) - Quintile 3: \( \$48,000/ \$370,000 = 0.130 = 13\% \) - Quintile 4: \( \$86,000/ \$370,000 = 0.232 = 23.2\% \) - Quintile 5 (Top): \( \$180,000/ \$370,000 = 0.486 = 48.6\% \)

Compare the top and bottom quintiles with the U.S. income distribution

According to the U.S. Census Bureau, the income distribution for the top and bottom quintiles in the U.S. are as follows: - Top Quintile: Approximately 52% - Bottom Quintile: Approximately 3% Comparing these values with our calculated shares: - Top Quintile: 48.6% （ours） vs. 52% （U.S.） - Bottom Quintile: 5.9% （ours） vs. 3% （U.S.） In conclusion, the top quintile in our distribution has a slightly smaller share of total income than the top quintile of the U.S. income distribution, while the bottom quintile in our distribution has a significantly larger share of total income than the bottom quintile of the U.S. income distribution.

Key concepts

Quintiles

Quintiles are a way to divide a group into five equal parts to better analyze data, particularly in income distribution. To understand how quintiles work, imagine standing in a line of 10 people ranked by their income. You would divide this line into five equal parts, each containing two people. Each segment represents 20% of the population. These segments are known as quintiles.

In this exercise, using incomes such as $10,000, $12,000, and so on, sorting these values, and splitting them into quintiles allows us to assess how income is distributed across this group. It helps identify which income levels fall into each quintile and thus, analyze how evenly or unevenly wealth is spread. This approach provides a window into the available resources or differences within a particular economy or population.

In practical use, quintiles offer an immediate vision of disparity or equity. They can pinpoint how wealth aggregates either within lower, middle or higher brackets, helping policymakers or analysts propose solutions to balance economic inequalities.

Income Inequality

Income inequality refers to the degree to which income is distributed unevenly among a population. It's a critical issue as it highlights disparities in economic wealth and resources. The exercise vividly shows this by providing calculated shares of total income apportioned to each quintile.

For instance, in our case:

• The bottom quintile earns 5.9% of total income.
• The top quintile earns 48.6% of total income.

This stark disparity illustrates income inequality. In a perfectly equal world, each quintile would receive exactly 20% of the total income. However, that's rarely the case. Larger shares going to the top quintiles suggest concentration of wealth at the top, while the less wealth trickle to the lower quintiles.

Income inequality matters because it can affect various aspects of life, including health, education, and political influence. Reducing this inequality can lead to a more just and equitable society, potentially enhancing the quality of life for everyone involved.

U.S. Income Distribution

U.S. income distribution reflects the way income is spread across different segments of the American population. It's a topic often discussed when assessing the United States' economic health and social structure. As shown in this exercise, the top quintile of U.S. income earners generally controls around 52% of the nation's total income, while the bottom quintile controls merely 3%.

These figures demonstrate a significant concentration of wealth at the upper end of the income spectrum. Such patterns in U.S. income distribution suggest that there may be fewer opportunities for income growth for the lower quintiles compared to those at the top. The comparison made in the exercise reveals that in our hypothetical group, the bottom quintile fares better than the typical U.S. bottom quintile at 5.9%, providing an example of how they might otherwise be impacted.

Understanding U.S. income distribution helps policymakers, economists, and citizens grasp the challenges and opportunities within the economy. It can drive discussions about taxation, wages, and social services, aiming to create a fair society with opportunities for everyone.