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Chapter 18: Problem 9

Draw a Lorenz curve showing the distribution of income for the five people in the following table. $$ \begin{array}{l|c} \text { Name } & \text { Annual Earnings } \\ \hline \text { Lena } & \$ 70,000 \\ \hline \text { David } & 60,000 \\ \hline \text { Steve } & 50,000 \\ \hline \text { Jerome } & 40,000 \\ \hline \text { Lori } & 30,000 \\ \hline \end{array} $$

Short Answer

Expert verified
The Lorenz curve for the given table shows the distribution of income amongst the five individuals. It provides a visual representation of the economic inequality between these individuals. The closer the Lorenz curve is to the line of equality, the more evenly income is distributed; the further away, the greater the income inequality.

Step by step solution

01

Calculate Total Income

Add all the individual earnings together to find the total income: \(70,000 + 60,000 + 50,000 + 40,000 + 30,000 = \$250,000\)
02

Calculate Cumulative Percentage of Total Income

Arrange the individual incomes in increasing order and calculate the cumulative percentage of total income for each individual. For example, for Lori, who earns the least, her percentage of total income is \((30,000/250,000) * 100 = 12\%\). Consider these percentages to be Lorenz Y-values and the cumulative percentage of people as Lorenz X-values. Here, since there are 5 people, each individual represents 20% of the population.
03

Preparation for Plotting the Lorenz Curve

Combine the cumulative percentage of total income (Lorenz Y-values) for each individual with their corresponding Lorenz X-values, which represent the cumulative percentage of people. This will yield a set of coordinates. For example, Lori's coordinates are \((20, 12)\) as she makes up 20% of the people and 12% of the income.
04

Plot the Lorenz Curve

Starting from the origin (0,0), plot the coordinates on the graph: (20, 12), followed by the rest of the individual's coordinates. Connect these points to form the Lorenz curve. Also draw the line of equality which is the 45 degrees diagonal from the origin to the top right corner of the graph. This line represents a perfectly equal distribution of income. Comparing the Lorenz curve to the line of equality gives a visual representation of the income inequality among the individuals.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Income Distribution
Income distribution refers to how a nation鈥檚 total income is spread among its population. It's an indicator that helps us understand who gets what portion of the economic pie. When discussing income distribution, we're essentially talking about the frequency and amount of income individuals or households receive over a specific time period.
  • It can highlight disparities or equalities within different socioeconomic groups.
  • Income distribution is vital in shaping social and economic policies that aim to address wealth gaps.
Analyzing income distribution requires gathering data on people's earnings and understanding which portions of the population earn more or less. This understanding helps economists and policymakers work toward fairer economic systems.
Economic Inequality
Economic inequality is the unequal distribution of income and opportunities among a population. It's a broad concept that not only includes differences in income but also considers disparities in wealth, access to resources, and other opportunities. Greater inequality suggests a wider gap between the richest and the poorest in a society.
  • Economic inequality can impact a country's health, education, and social cohesion.
  • It often arises due to factors like education levels, globalization, technological changes, and government policies.
Understanding economic inequality is essential for developing measures to ensure more equitable growth and prosperity, reducing social tensions, and fostering a more inclusive economic environment.
Cumulative Income Shares
Cumulative income shares are a way to measure the share of total income held by cumulative segments of the population, typically arranged from the poorest to the richest. By looking at cumulative income shares, we can determine how income is distributed across different population segments.
  • It helps in understanding how much of the total income is earned by specific percentages of the population.
  • Cumulative income shares data form the basis for constructing a Lorenz curve.
To calculate cumulative income shares, arrange individual incomes in ascending order and calculate each segment's contribution to the total income cumulatively. This data represents the cumulative share of people compared to their cumulative share of income, forming foundations for further graphical analyses.
Graphical Analysis of Income
The graphical analysis of income, such as plotting a Lorenz curve, provides a visual representation of income distribution and inequality. The Lorenz curve is particularly useful in comparing actual income distribution to a perfectly equal distribution.
  • It involves plotting cumulative income shares against cumulative population shares.
  • The more the Lorenz curve sags below the line of equality (a 45-degree line representing equal distribution), the greater the level of inequality.
Creating a Lorenz curve begins by arranging all income earners from lowest to highest, calculating their cumulative income shares, and plotting these against their cumulative shares of the population. By analyzing these visual distinctions, observers can make informed assessments regarding the economic landscape.

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Most popular questions from this chapter

An article in the Economist on the work of the late Nobel Laureate James Buchanan made the following observation: "It was important...to understand the ways that government could fail systematically." a. What does government failure mean in this context? How does public choice theory help us understand how "government could fail systematically"? b. The same article noted that "rent-seeking is a very useful concept to have around when thinking about policy." What is rent seeking? Why is the concept useful when thinking about policy?

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Cecil Bohanon, an economist at Ball State University, and Brian Pizzola, an economist with the accounting firm Ernst \& Young, used a proposed tax on income earned by credit card lenders in Minnesota to explain how tax incidence is determined. The tax, which state lawmakers did not pass, would have been imposed on lenders who charged credit card customers more than 15 percent interest on their balances. Bohanon and Pizzola explained that many of those who paid high interest rates were consumers with fewer other sources of credit, and there was nothing to prevent lenders from further raising interest rates after the tax was imposed. John Spry, an economist at St. Thomas University, stated that the proposed tax was "highly regressive \(\ldots\) twenty percent of the new tax would be paid by Minnesota families with the lowest 10 percent of income. Thirty-seven percent of the tax would be paid by families with the lowest 20 percent of income." a. Explain why John Spry believed that the proposed tax would have been "highly regressive." b. Do Bohanon and Pizzola believe the elasticity of demand of those who would have been most affected by the tax was more or less elastic than the elasticity of supply of credit card lenders? Briefly explain.

(Related to the Chapter Opener on page 600 ) In 2017 , the Trump administration proposed changes to the federal tax code, including reducing the top corporate income tax rate from 35 percent to 15 percent. An article in the Wall Street Journal noted, "A tax overhaul could give companies more incentive to invest." a. What type of investments is the article referring to? Why would cutting the corporate income tax rate lead companies to engage in more investment? b. Some policymakers and economists are critical of cuts in the corporate income tax rate because they argue that such cuts increase income inequality. Does the incidence of the corporate income tax matter in evaluating this argument? Briefly explain.

Describe the main factors economists believe cause inequality of income.
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