Question

A group of 10 people have the following annual incomes: \(\$ 55,000, \$ 30,000, \$ 15,000, \$ 20,000, \$ 35,000\) \(\$ 80,000, \$ 40,000, \$ 45,000, \$ 30,000, \$ 50,000 .\) Calculate the share of total income each quintile of this income distribution received. 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 for \(2005 ?\)

Short answer

In the given example, the top quintile has a \(33.75\%\) share of total income, while the bottom quintile has a \(8.75\%\) share. Comparing these values to the U.S. income distribution for 2005, the top quintile in the given example has a smaller share of total income compared to the \(50.4\%\) share of the top quintile in 2005. However, the bottom quintile in the given example has a larger share of total income compared to the \(3.4\%\) share of the bottom quintile in 2005.

Step-by-step solution

Calculate the total income

First, we have to find the total income of this group of 10 people. To do this, simply add up each individual's income: Total Income = \(55,000 + \)30,000 + \(15,000 + \)20,000 + \(35,000 + \)80,000 + \(40,000 + \)45,000 + \(30,000 + \)50,000 = \$400,000$

Sort the incomes in ascending order and divide into quintiles

Arrange the incomes in ascending order: \(15,000, \)20,000, \(30,000, \)30,000, \(35,000, \)40,000, \(45,000, \)50,000, \(55,000, \)80,000$ Now divide the incomes into quintiles. Since there are 10 people, each quintile should represent 2 people: 1. Quintile 1 (Lowest 20%): \(15,000, \)20,000$ 2. Quintile 2: \(30,000, \)30,000$ 3. Quintile 3: \(35,000, \)40,000$ 4. Quintile 4: \(45,000, \)50,000$ 5. Quintile 5 (Highest 20%): \(55,000, \)80,000$

Calculate the share of total income each quintile received

Now, for each quintile, we will calculate the total income it represents and the share of total income received: Quintile 1: \(15,000 + \)20,000 = \$35,000$. Share of total income = \(\frac{35,000}{400,000}\) = \(0.0875\) or \(8.75\%\) Quintile 2: \(30,000 + \)30,000 = \$60,000$. Share of total income = \(\frac{60,000}{400,000}\) = \(0.15\) or \(15\%\) Quintile 3: \(35,000 + \)40,000 = \$75,000$. Share of total income = \(\frac{75,000}{400,000}\) = \(0.1875\) or \(18.75\%\) Quintile 4: \(45,000 + \)50,000 = \$95,000$. Share of total income = \(\frac{95,000}{400,000}\) = \(0.2375\) or \(23.75\%\) Quintile 5: \(55,000 + \)80,000 = \$135,000$. Share of total income = \(\frac{135,000}{400,000}\) = \(0.3375\) or \(33.75\%\)

Compare these values with the quintiles of the U.S. income distribution for 2005

Based on the data provided for the given example, the top quintile (Quintile 5) has a share of total income of \(33.75\%\), while the bottom quintile (Quintile 1) has a share of total income of \(8.75\%\). You need to compare these values to the official statistics of the U.S. income distribution for 2005. If the given information is not available, you may use the following estimates for 2005, as an example: Top quintile had \(50.4\%\) share, and the bottom quintile had \(3.4\%\) share. By comparing these values, we can see that in the exercise's example, the top quintile has a smaller share of total income (\(33.75\%\)) compared to the top quintile of the U.S. income distribution for 2005 (\(50.4\%\)). On the other hand, the bottom quintile in the given example has a larger share of total income (\(8.75\%\)) compared to the bottom quintile of the U.S. income distribution for 2005 (\(3.4\%\)).

Key concepts

Income Inequality

Income inequality is a measure of how unevenly income is distributed among individuals in a group, such as a country or community. It can be visualized by comparing the income of different fractions of the population, often divided into quintiles or percentiles. A higher level of income inequality indicates a larger income gap between the wealthiest and the poorest individuals.

Understanding income inequality involves looking at the distribution of wealth across these quintiles. For example, if the top quintile contains individuals who earn significantly more than those in the bottom quintile, the society may be considered highly unequal. This disparity has implications for social welfare, economic stability, and growth. To address income inequality, governments may implement policies such as progressive taxation, social welfare programs, and minimum wage laws to redistribute income and reduce the gap.

Quintile Income Share

The quintile income share is a common way to understand the distribution of income across a population. A quintile represents 20% of a population, and by dividing a population into five equal-sized groups, one can see what percentage of the total income each group receives. This method reveals concentrations of wealth and helps in comparing economic disparities.

To illustrate, in the textbook exercise, the quintile shares of the group's total income range from 8.75% for the lowest quintile to 33.75% for the highest quintile. These figures provide a clear picture of how income is spread across the different segments of the population. In educational contexts, ensuring that students grasp the calculation and implications of these shares is of utmost importance. Enhancing the learning experience can include using real-life examples, incorporating visual aids like pie charts, and discussing the social implications of the findings.

Economic Disparities

Economic disparities refer to the differences in income, wealth, and economic opportunities among individuals, groups, or regions. It's a broader concept that encompasses income inequality but also includes access to education, employment, healthcare, and other factors that contribute to a person's economic standing.

Analyzing economic disparities helps societies identify and address the root causes of inequity. In the context of the textbook exercise, comparing the quintile income share of the group with that of the U.S. income distribution for 2005 highlights the economic disparities within and between different populations. The exercise underscores the importance of using accurate statistical data to understand the magnitude of economic differences and the social policies that may be required to mitigate them.