What Is the Lorenz Curve? A Simple Guide to Understanding Wealth Distribution

Financial inequality is a pressing issue in many countries today. For instance, in the United States, the top 1% of earners have seen their share of pre-tax income double since 1980, now holding nearly 35% of the nation's wealth.

Economists rely on various tools to measure and analyse wealth distribution to understand and address these inequalities. One of the most widely used methods is the Lorenz Curve. It helps visualise the gap between rich and poor, revealing whether economic growth benefits everyone or just a select few.

The Lorenz Curve definition refers to a graph showing the income or wealth distribution within a population. It shows the proportion of total income earned by cumulative percentages of the population, from the poorest to the richest.

In an ideal world, where everyone has the same income, the Lorenz Curve would be a straight 45-degree line from the bottom left to the top right corner. This is known as the "Line of Equality." 

However, in reality, the Lorenz Curve usually bows below this line, indicating that income is not distributed equally. The more it curves away from the Line of Equality, the greater the level of inequality.

Imagine a small community of 10 people. If each person earns the same amount, say $10,000, the Lorenz Curve would follow the Line of Equality because the distribution is perfectly equal. But what if the distribution looks like this:

In this scenario, the Lorenz Curve would dip below the Line of Equality:

At its core, the Lorenz Curve is a graphical representation that shows the cumulative distribution of income or wealth within a population. Mathematically, the Lorenz Curve L(p) at a given population percentile p is defined as:

In simpler terms, this formula calculates the proportion of total income earned by the bottom p percent of the population.

Governments, economists, and researchers use the Lorenz Curve to study income distribution trends and develop economic policies to reduce inequality. By comparing Lorenz Curves across different time periods or countries, we can assess the effectiveness of taxation, minimum wage laws, and social welfare programs.

Now that we understand the Lorenz Curve, let's talk about another important tool used to measure inequality: the Gini Coefficient. This number helps us put inequality into perspective with a single value.

The Gini Coefficient is a number between 0 and 1 that tells us how equal or unequal the distribution of income or wealth is in a country:

The Gini Coefficient quantifies the degree of inequality depicted by the Lorenz Curve. Specifically, it measures the area between the Curve and the Line of Equality (the 45-degree line representing perfect equality). The Gini Index formula looks like this:

In simpler terms, the more the Lorenz Curve deviates from the Line of Equality, the larger the area between them and, consequently, the higher the Gini Coefficient, which indicates greater inequality.

In practice, most countries have Gini Coefficients between 0.25 and 0.60. For instance, Scandinavian countries like Sweden and Norway often report lower Gini Coefficients, reflecting more equal income distributions. Conversely, some nations in Latin America and Africa exhibit higher Gini Coefficients, indicating more pronounced income disparities.

Two countries might have the same Gini Coefficient but vastly different income distributions. Additionally, the Gini Coefficient doesn't account for differences in wealth distribution, which can provide a more comprehensive picture of economic inequality.

Creating and understanding a Lorenz Curve is a great way to visualise how income or wealth is distributed within a population. You can do this manually or use tools like Excel or a Lorenz Curve calculator online to simplify the process. Let's walk through the steps:

The Lorenz Curve is best known for showing how income is spread across a population, but it can also be used in other areas. Let’s explore some real-world examples of how it is applied outside of income distribution.

While income refers to what people earn, wealth refers to what they own, such as houses, cars, savings, and investments. The Lorenz Curve can illustrate how wealth is distributed across a population. Often, wealth is more unevenly distributed than income, with a small percentage of people owning a large portion of total wealth. Plotting a Lorenz graph clearly shows this disparity.

In many economies, the wealthiest 10% of the population owns a disproportionate share of total assets—sometimes exceeding 70%. A Lorenz Curve in such a scenario would deviate significantly from the Line of Equality, emphasising the concentration of wealth among a small segment of society.

Governments and financial institutions use this graph analysis to develop tax policies, inheritance laws, and economic reforms that aim to reduce wealth inequality.

The Lorenz Curve is not limited to financial metrics; it can also illuminate social factors like education and healthcare access.

We can see how education is distributed by plotting the cumulative percentage of the population against the cumulative percentage of educational attainment. In this context, a steep Lorenz Curve would indicate that a small segment of the population has a large share of educational opportunities while the majority have less access.

Similarly, the Lorenz Curve can depict disparities in healthcare services. If a small portion of the population utilises most healthcare resources, the curve will show a significant deviation from the line of equality.

Businesses can use the Lorenz Curve to analyse market dynamics and customer behaviour.

Companies can plot the cumulative percentage of firms against the cumulative percentage of market share to assess the concentration of a market. A Lorenz Curve that bows significantly below the line of equality indicates that a few firms dominate the market.

Retailers might use the Lorenz Curve to understand purchasing patterns, such as which customers contribute the majority of sales. This insight can inform targeted marketing strategies.

Environmentalists and economists can apply the Lorenz Curve to study the distribution of environmental impacts.

By plotting the cumulative percentage of countries against the cumulative percentage of global CO2 emissions, the Lorenz Curve can reveal which nations contribute most to pollution. A steep curve would indicate that a few countries are responsible for the majority of emissions.

The Lorenz Curve is a simple way to see and understand income inequality. It shows how wealth or income is shared among people in a society. Economists and governments use it to spot economic problems and find ways to make income distribution fairer.