Question

What is a Lorenz curve? What would the curve look like if income were equally distributed? Could the curve ever bow upward above the line of income equality?

Short answer

Answer: The Lorenz curve is a graphical representation of income inequality within a population, plotting the cumulative percentage of total income received by a given percentage of the population. The curve cannot bow upward above the line of income equality because this would indicate that a certain percentage of the population receives more than its proportional share of income, contradicting the definition of income inequality and the basic principles of the Lorenz curve.

Step-by-step solution

Understand the Lorenz Curve

A Lorenz curve is a graph that shows the degree of income inequality in a population. It plots the cumulative percentage of total income received by a given percentage of the population, with the population ordered from the poorest to the richest. The horizontal axis shows the cumulative percentage of the population, and the vertical axis shows the cumulative percentage of total income.

Lorenz Curve for Equally Distributed Income

If income were equally distributed among the population, then the Lorenz curve would be a straight line with a 45-degree angle, which is also known as the line of income equality. This is because, in a perfectly equal distribution, the percentage of income received by any given percentage of the population would be equal. For example, the poorest 20% of the population would receive 20% of total income, the poorest 50% would receive 50% of total income, and so on.

Lorenz Curve Bowing Upward

The Lorenz curve cannot bow upward above the line of income equality because this would indicate that a certain percentage of the population receives more than its proportional share of income. Any Lorenz curve above the line of equality suggests that the poorer part of the population has a higher share of income than the richer part, which contradicts the definition of income inequality and the basic principles of the Lorenz curve. Therefore, a Lorenz curve cannot bow upward above the line of income equality.

Key concepts

Income Inequality

Income inequality refers to the unequal distribution of income within a population. It highlights the economic disparities between different groups, often leading to social and economic challenges. Income inequality can arise from a variety of factors, including different levels of education, access to resources, and economic opportunities.

Observing income inequality closely helps policymakers understand the scale and nature of inequality in a society. One common way to visualize income inequality is by using the Lorenz curve. This curve helps in identifying how income is distributed across the population, specifically showing how much of the total income is received by any given portion of the population. By examining the graph, we can see how far the actual income distribution deviates from a perfectly equal distribution, which provides insight into the level of inequality present.

In practice, higher deviation from the line of equality suggests more pronounced income inequality. Economists and governments often use this information to design policies aimed at reducing these disparities and promoting a more balanced economic environment.

Cumulative Percentage of Income

The cumulative percentage of income is an essential aspect of understanding income distribution within a population. It represents the total income accumulated by a certain percentage of the population, starting from the poorest individuals. The concept can be illustrated by explaining that if we were to arrange everyone's income from lowest to highest, the cumulative percentage of income at any point tells us how much of the total income the lowest-earning individuals have received up to that point.

When this data is plotted on a graph, with the population percentage on the horizontal axis and the cumulative percentage of income on the vertical axis, it forms the Lorenz curve. Points on the line represent the sum of income earned by a specific percentage of the population. For example:

• The point corresponding to 20% of the population might indicate the cumulative percentage of income received by the lowest-earning 20%.
• Similarly, a point corresponding to 50% would show the income received by the lowest-earning half of the population.

This visualization allows viewers to quickly grasp which portions of the population receive more or less income relative to others. When the curve bows significantly from the 45-degree line (line of equal income distribution), it indicates greater inequality.

Line of Income Equality

The line of income equality, also known as the line of perfect equality, serves as a benchmark on a Lorenz curve graph. It is depicted as a 45-degree line that stretches from the origin (0,0) to the point (100,100). This line represents a scenario where every percentage of the population receives an equivalent percentage of the total income.

In such an ideal situation, the distribution is perfectly uniform; for example, the poorest 10% of the population would earn exactly 10% of the income, the poorest 50% would earn 50%, and so on. The line of income equality, therefore, acts as a reference point to understand how income is distributed compared to an equitable distribution.

The Lorenz curve generally bows downwards from this line, illustrating the reality of income inequality. If the Lorenz curve lies along the line of equality, it indicates a perfectly equal income distribution, which is exceptionally rare in real-world scenarios. However, it is an important theoretical tool for assessing and comparing income distributions across different societies or over time, guiding efforts toward more equitable distribution policies.