Learning Materials
Features
Discover
How do we calculate inequality in society? How do we know if inequality is improving or worsening in a specific country? This article helps answer those questions by explaining the Lorenz curve.
Millions of flashcards designed to help you ace your studies
Sign up for free
Achieve better grades quicker with Premium
Geld-zurück-Garantie, wenn du durch die Prüfung fällst
Did you know that StudySmarter supports you beyond learning?
Review generated flashcards
Start learning or create your own AI flashcards
Team Lorenz Curve Teachers
The Lorenz curve graphically shows the degree of income or wealth inequality in an economy. It was developed by economist Max O. Lorenz in 1905.
To interpret the Lorenz curve, we need to first understand how it is represented on the diagram. There are two curves in Figure 1 below.
We first have the 45° straight line, known as the line of equality. It has a slope of 1 which illustrates perfect equality in income or wealth.
The Lorenz curve lies beneath the 45° line of equality. The further away the curve is from the 45° line, the greater the income or wealth inequality in an economy. We can see that in the diagram below.
The x axis shows the percentage of the total population. The y axis shows the percentage of total income or wealth. The word ‘cumulative’ in both axes means up and including.
Fig. 1 - The Lorenz Curve
Interpreting the data from the Lorenz curve is quite simple. Pick a point from the x axis and read off the y axis. For example, reading off the diagram, 50% of the population has access up to and including 5% of the country's national income. In this example, income is distributed very unequally as half of the population has a very small share of the country’s national income.
The Lorenz curve can shift closer or further away from the 45° line of equality. In the diagram below, the Lorenz curve has moved closer to the line of equality. This means that inequality in this economy has decreased.
Fig. 2 - Lorenz curve shifts
According to the diagram above, initially, only 90% of the population had access to 45% of the country’s national income. After the curve shifted, 90% of the population has access to 50% of the country’s national income.
The Lorenz curve is linked to the Gini coefficient. You can calculate the Gini coefficient using this curve.
The Gini coefficient is the measure of the distribution of income.
Graphically, the Gini coefficient measures how far the Lorenz curve is from the line of equality. It quantifies the level of economic inequality in an economy.
Fig. 3 - Gini coefficient calculated from Lorenz Curve
In the diagram above, the shaded area is Area A. The remaining white space is Area B. Plugging the values for each area into the formula gives us the Gini Coefficient.
The Gini coefficient is calculated with the following formula:
A coefficient of 0 means that there is perfect equality. This means that every 1% of a population has access to 1% of national income, which is unrealistic.
A coefficient of 1 means that there is perfect inequality. This means that 1 individual has access to the entire country’s national income.
A lower coefficient indicates that income or wealth is distributed more equally across the population. A higher coefficient indicates that there is severe income or wealth inequality and is mainly due to political and/or social disruption.
The Lorenz curve is important because it helps economists measure and understand income or wealth inequality.
Economists are interested in how income and wealth inequality changes over time in an economy. It also allows them to compare the level of economic inequality between different countries.
Both the US and Norway are high-income countries. However, they have very different Lorenz curves and Gini coefficients. Norway's Lorenz curve is much closer to the line of equality than the United States’. By comparison, income is distributed more equally in Norway than in the US.
While the Lorenz curve is helpful for economists to make comparisons on the level of income and wealth distribution, it does have some limitations. Most of these limitations lie with the data.
For example, the Lorenz curve doesn't take into account:
The Lorenz curve below has been plotted to fit the data describing England’s income distribution.
Fig. 4 - England's Lorenz Curve
Thanks to the curve, we can see that wealth is unequally distributed across England. The top 10% hold 42.6% of the country’s total net wealth. Those in the bottom 10% hold 0.1% of England’s total net wealth.
To find the Gini coefficient, divide the area between the line of equality by the sum of the total area under the line of equality. In 2020, England’s Gini coefficient reached 0.34 (34%), a slight decrease from the previous year.
Now you have seen how economists show graphically how income and wealth are distributed in an economy with the Lorenz Curve. Go to 'Equitable Distributions of Income' to learn how income can be distributed equitably.
The Gini coefficient can be calculated from the Lorenz Curve using the formula A/(A+B).
The Lorenz curve is important as it allows economists to measure income and wealth inequality in a country and compare it to different countries.
Sign up for free to gain access to all our flashcards.
What is the Lorenz curve?
The Lorenz Curve is a graph that shows income or wealth inequality in an economy.
What shifts the Lorenz curve?
Any factor that improves income or wealth distribution, such as high levels of education, will shift the Lorenz curve closer to the line of equality. Any factor that worsens income or wealth distribution shifts the curve further from the line of equality.
What is the importance of the Lorenz curve?
It is important because it helps economists measure and understand income and wealth inequality, which they can use to make comparisons between different economies.
How do I calculate the Gini Coefficient from the Lorenz curve?
The area between the line of equality and the Lorenz curve is Area A. The remaining space between the Lorenz curve and x axis is Area B. Using the formula Area A/(Area A + Area B), you can calculate the Gini coefficient.
At StudySmarter, we have created a learning platform that serves millions of students. Meet the people who work hard to deliver fact based content as well as making sure it is verified.
Lily Hulatt is a Digital Content Specialist with over three years of experience in content strategy and curriculum design. She gained her PhD in English Literature from Durham University in 2022, taught in Durham University’s English Studies Department, and has contributed to a number of publications. Lily specialises in English Literature, English Language, History, and Philosophy.
Get to know Lily
Gabriel Freitas is an AI Engineer with a solid experience in software development, machine learning algorithms, and generative AI, including large language models’ (LLMs) applications. Graduated in Electrical Engineering at the University of São Paulo, he is currently pursuing an MSc in Computer Engineering at the University of Campinas, specializing in machine learning topics. Gabriel has a strong background in software engineering and has worked on projects involving computer vision, embedded AI, and LLM applications.
Get to know Gabriel
Vaia is a globally recognized educational technology company, offering a holistic learning platform designed for students of all ages and educational levels. Our platform provides learning support for a wide range of subjects, including STEM, Social Sciences, and Languages and also helps students to successfully master various tests and exams worldwide, such as GCSE, A Level, SAT, ACT, Abitur, and more. We offer an extensive library of learning materials, including interactive flashcards, comprehensive textbook solutions, and detailed explanations. The cutting-edge technology and tools we provide help students create their own learning materials. StudySmarter’s content is not only expert-verified but also regularly updated to ensure accuracy and relevance.
Learn moreSave explanations to your personalised space and access them anytime, anywhere!
Sign up with Email Sign up with AppleBy signing up, you agree to the Terms and Conditions and the Privacy Policy of Vaia.
Already have an account? Log in
Sign up to highlight and take notes. It’s 100% free.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App 
