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Chapter 33: Problem 1

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

Expert verified
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

01

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.
02

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.
03

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.

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Most popular questions from this chapter

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