Log out Go to App
Go to App

Learning Materials

Features

Discover

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Which type of tax raises the most revenue for the federal government? What is the largest source of revenue for state and local governments?

(Related to Solved Problem 18.4 on page 621 ) Evaluate the following statement: "Policies to redistribute income are desperately needed in the United States. Without such policies, the roughly 13 percent of the population that is currently poor has no hope of ever climbing above the poverty line."

What is the relationship between market failure and government failure?

According to an article in the New York Times, some New Yorkers were deciding to buy existing condominiums (condos) rather than newly constructed condos. One reason given was that some buyers "seek to avoid the 1.825 percent transfer tax that buyers must pay on a brand-new condo. (In resales, the seller pays the tax.)" Analyze this reason for buying a resale rather than a new condo.

Suppose that a country has 20 million households. Ten million are poor households that each have labor market earnings of \(\$ 20,000\) per year, and 10 million are rich households that each have labor market earnings of \(\$ 80,000\) per year. If the government enacted a marginal \(\operatorname{tax}\) of 10 percent on all labor market earnings above \(\$ 20,000\) and transferred this money to households earning \(\$ 20,000\), would the incomes of the poor rise by \(\$ 6,000\) per year? Briefly explain.
See all solutions

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free